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Coaching records in close games

Posted by Doug on March 16, 2007

Several months ago a reader emailed and asked me if I could post coach's records in games decided by 3 points or less. Well, I lost that email and I'm sure the emailer has lost hope of my ever getting around to it. But here I am, against all odds, finally getting around to it.

The following is a list consisting of all coaches who (a) coached at any point after 1950, and (b) coached in at least 64 total games. N represents the number of non-close games he coached in his career, C is the number of close games, and CWin% is his winning percentage in the close ones.

Winning percentage in games decided by 3 points or less

N C CWin%
Vince Tobin 58 22 0.727
John Madden 112 30 0.717
Charley Winner 83 15 0.700
Nick Skorich 80 18 0.694
Joe Gibbs 138 46 0.674
Bobby Ross 117 27 0.667
John Rauch 61 9 0.667
Jim Lee Howell 69 15 0.667
Tony Dungy 135 41 0.659
Mike Holovak 92 16 0.656
Ray Rhodes 56 24 0.646
Jim Hanifan 75 18 0.639
Art Shell 78 30 0.633
Lawrence Shaw 81 15 0.633
Pete Carroll 45 19 0.632
Steve Mariucci 120 24 0.625
Mike Holmgren 185 55 0.618
George Halas 376 99 0.616
Marv Levy 191 64 0.609
Mike Sherman 73 23 0.609
Bill Parcells 226 77 0.604
Jack Patera 81 20 0.600
Ray Malavasi 65 20 0.600
George Allen 133 35 0.586
Bum Phillips 122 41 0.585
Joe Walton 93 18 0.583
Forrest Gregg 125 37 0.581
Sam Rutigliano 74 31 0.581
Jim Fassel 87 25 0.580
Steve Owen 211 50 0.580
Ron Meyer 104 19 0.579
Jerry Glanville 103 26 0.577
Don Shula 392 98 0.571
Mike Ditka 167 49 0.571
Bill Cowher 190 50 0.570
Jimmy Johnson 114 30 0.567
Jim Haslett 73 23 0.565
Allie Sherman 89 23 0.565
Dick Jauron 69 32 0.562
Wally Lemm 118 17 0.559
Dick Nolan 132 28 0.554
Mike McCormack 62 19 0.553
Don Coryell 164 39 0.551
Sam Wyche 152 39 0.538
Marvin Lewis 51 13 0.538
Bud Grant 193 66 0.538
John Robinson 115 28 0.536
Jack Christiansen 53 14 0.536
Tom Flores 141 43 0.535
Dave Wannstedt 131 45 0.533
Mike Tice 51 15 0.533
Neill Armstrong 49 15 0.533
Marty Schottenheimer 251 76 0.533
Jack Del Rio 47 17 0.529
Lou Saban 178 46 0.522
Ted Marchibroda 135 51 0.520
Tom Landry 344 74 0.514
Dan Reeves 266 94 0.511
Mike Shanahan 173 51 0.510
Jack Pardee 126 44 0.500
Vince Lombardi 108 28 0.500
Wayne Fontes 107 26 0.500
Alex Webster 55 15 0.500
Herman Edwards 72 24 0.500
Raymond Parker 149 39 0.500
John Fox 54 26 0.500
Mike Martz 78 18 0.500
Raymond Berry 67 20 0.500
Jeff Fisher 144 55 0.491
Jon Gruden 97 47 0.489
Dennis Green 163 45 0.489
Brian Billick 97 31 0.484
Joe Kuharich 114 28 0.482
Weeb Ewbank 217 49 0.480
Jim Mora 174 65 0.477
Bill Belichick 150 42 0.476
Curly Lambeau 299 75 0.473
Norm VanBrocklin 142 37 0.473
Ray Perkins 88 32 0.469
Paul Brown 227 45 0.467
Chuck Knox 264 70 0.464
Barry Switzer 51 13 0.462
Walt Michaels 62 25 0.460
Bill McPeak 58 12 0.458
Buddy Ryan 75 36 0.458
Greasy Neale 99 12 0.458
Rich Kotite 74 22 0.455
Andy Reid 95 33 0.455
Bruce Coslet 107 31 0.452
Sid Gillman 200 37 0.446
Pop Ivy 69 9 0.444
Blanton Collier 103 9 0.444
Bart Starr 105 26 0.442
George Wilson 126 34 0.441
Harland Svare 63 17 0.441
John Ralston 53 17 0.441
Wade Phillips 59 25 0.440
Tommy Prothro 84 16 0.438
Jerry Burns 72 23 0.435
Lindy Infante 68 28 0.429
Bill Walsh 115 37 0.419
John McKay 96 37 0.419
Hank Stram 195 43 0.419
Dick Vermeil 178 51 0.412
Leeman Bennett 87 32 0.406
Tom Coughlin 133 43 0.395
Chuck Noll 285 57 0.395
Howard Hickey 57 9 0.389
Joe Schmidt 67 17 0.382
Dan Henning 84 28 0.375
Butch Davis 48 16 0.375
George Seifert 133 43 0.372
Dom Capers 101 27 0.370
Dennis Erickson 74 22 0.364
David Shula 58 22 0.364
Walt Kiesling 78 21 0.357
Norv Turner 106 38 0.355
John Mackovic 46 18 0.333
Marion Campbell 100 29 0.328
Chuck Fairbanks 70 16 0.312
Monte Clark 88 31 0.306
Joe Bugel 61 19 0.263

I'm not sure what to make of these numbers, but they're kind of fun I guess.

Given the sample sizes, only a few of these close winning percentages appear to be clearly different from chance. And in a group this big, you expect for a few people to appear different from chance even if there is no real effect. Furthermore, the correlation between close-game winning percentage and non-close-game winning percentage is only .14 (and not significantly different from zero). So my five-minute assessment of the situation is that close-game winning percentage probably says more about the good or bad luck the coach experienced rather than about the coach himself.

Posted in General | 12 Comments »

Bracketology update

Posted by Doug on March 15, 2007

On Monday I offered a few thoughts about how to fill in your tournament brackets.

My interest in the issue is mainly theoretical (I am a mathematician, after all). If the entries in your pool satisfy a certain assumption, then it's reasonable to conclude something about your optimal strategy. It's an interesting mathematical problem with what I think is an elegant solution. But I have to admit that, other than just making sure it passed the sniff test, I didn't give a whole lot of thought to the reasonableness of the assumption.

Blog reader Patrick L. sent me some data from his office pool which indicates that people tend to overbet high seeds in these pools. This is the percentage of people whose entry includes a national champion of the given seed. OP is Patrick's office pool, TS is the implied probabilities from, and Hist is the historical frequencies:

                  OP      TS    Hist
#1 seeds 59% 53% 55%
#2 seeds 38% 23% 18%
everyone else 3% 24% 27%

Also, Yahoo's contest entry distributions are now posted, and they are even heavier on #1 seeds: 64/23/13.

In light of this, Patrick suggests that picking a #3 or #4 seed to win it all may be the optimal strategy. That seems believable to me.

Yahoo's distributions show further evidence of overbetting on favorites. Texas was picked in the first round by 97% of yahoo's entrants, whereas the Vegas odds imply that they have only about a 79% chance of beating New Mexico State. Virginia Tech (a #5 seed) was picked by 71% of the entrants over Illinois (#12) despite only having a 57% chance of winning according to the Vegas odds. The former is probably due to Kevin Durant's likeness being plastered all over everything for the last few weeks. The latter is probably due to an over-reliance on seedings instead of other objective measures like computer rankings or Vegas lines, as was mentioned in the comments to Monday's post.

Posted in Non-football | 2 Comments »

2006 QB in Review

Posted by Chase Stuart on March 14, 2007

Over the summer, we looked at the worst and best passers since the NFL merger. With 2006 in the books, a supplement to those blogs became necessary.

As a group, NFL QBs averaged 5.825 adjusted yards per attempt in 2006, which is in line with prior data. For those needing a quick refresher, here's how we score each QB. Adjusted yards per attempt is calculated by taking a QB's passing yards, subtracting 45 yards for every INT, adding 10 yards for every passing TD, and dividing by total pass attempts. Then we take the difference between the individual's adjusted yards per attempt and the league average, and multiply by total attempts (this is because a great QB that throws 500 times is more valuable than a great QB that throws 400 times.)

Here's a list of how many points each QB scored last year (only those with 100 attempts shown here):

1058 Peyton Manning 7.72
956 Drew Brees 7.55
756 Marc Bulger 7.11
716 Donovan McNabb 8.09
701 Carson Palmer 7.17
545 Tony Romo 7.44
524 Philip Rivers 6.96
522 Damon Huard 7.96
233 Kurt Warner 7.21
224 Jeff Garcia 7.02
223 Tom Brady 6.26
175 Mark Brunell 6.50
112 J.P. Losman 6.09
110 Tim Rattay 6.91
68 Jay Cutler 6.32
33 Daunte Culpepper 6.07
26 David Garrard 5.93
-23 Chad Pennington 5.78
-31 Jake Delhomme 5.75
-44 Jon Kitna 5.75
-56 Steve McNair 5.71
-62 Byron Leftwich 5.49
-74 Ben Roethlisberger 5.67
-79 Jason Campbell 5.44
-79 Matt Leinart 5.62
-110 Drew Bledsoe 5.17
-129 Seneca Wallace 4.91
-146 Trent Green 5.09
-171 Michael Vick 5.38
-199 Derek Anderson 4.13
-214 Matt Hasselbeck 5.25
-238 David Carr 5.29
-245 Alex Smith 5.27
-273 Rex Grossman 5.26
-316 Brett Favre 5.31
-328 Jake Plummer 4.79
-337 Chris Simms 2.64
-343 Aaron Brooks 4.04
-346 Vince Young 4.86
-367 Eli Manning 5.12
-392 Brad Johnson 4.93
-486 Andrew Walter 4.07
-494 Charlie Frye 4.56
-565 Bruce Gradkowski 4.10
-579 Joey Harrington 4.33

Jay Cutler played better than Jake Plummer, yet some people still pin the Broncos lost post-season hopes on the mid-season switch. I maintain that the real error was not making the switch soon enough.

Damon Huard had an incredible year, while Trent Green was below average. Tony Romo played better than I remembered. The Eagles three QBs (1091) actually topped Manning, who was the only Colts QB to throw a pass in 2006. Jason Campbell wasn't half bad, but Mark Brunell was better. Matt Leinart wasn't as good as Kurt Warner, and Alex Smith was only good compared to his 2005 version. Rex Grossman, Brett Favre and Eli Manning are polarizing figures, but all of them were below average passers in 2006. And Joey Harrington is still terrible (more on this later).

Changes to the All Time list
Peyton Manning now has 5,985 career points of value, vaulting him from 7th to 4th all time. Kurt Warner and Trent Green flip-flopped, and Warner is now 8th and Green 9th on the career list. Brett Favre continued his free-fall, from 15th to now 20th on the list; conversely, Marc Bulger jumped up from 31st to 21st. Donovan McNabb leaped from 52nd to 29th. Matt Hasselbeck was 28th and Drew Brees 81st before the season began; now they're 42nd and 43rd, respectively. And Carson Palmer snuck into the top fifty.

On to the negative side: Mike Vick dropped to below average for his career with a bad 2006. Drew Bledsoe continues to slide, and is at -574 for his career. Charlie Frye (-671), Alex Smith (-809), Eli Manning (-850) and David Carr (-988) have some work to do to resurrect their careers.

Jake Plummer (-1425), Kerry Collins (-1461) and Jon Kitna (-1495) continue to produce below average work but are always given another chance. At least Kitna was just about average last year.

And then there was Joey. After another miserable season, Harrington now stands as The Worst QB Of All Time (-2,953). This was Harrington's third season of negative 500 points or greater (fewer?). Rick Mirer, you have been surpassed.

2006 Notables, under 100 pass attempts: Charlie Batch (+233), A.J. Feeley (+151), Kyle Boller (+125), Chris Weinke (-94), Tarvaris Jackson (-157) and Kerry Collins (-235) all had significant impacts despite limited playing time. And Brodie Croyle (-108) got into the triple digits on only seven pass attempts; he was 3/7 for 23 yards with two interceptions.

Posted in Statgeekery | 18 Comments »

How to fill out your brackets

Posted by Doug on March 12, 2007

So you're not much of a college basketball fan. You follow your alma mater, and possibly keep loose tabs on the rest of their conference, but that's about as far as it goes. But the tourney is good entertainment and, as is customary, you enter a bracket pool so you can have a rooting interest where none would otherwise exist. How do you maximize your chances winning the thing?

If you're like me, the first thing you do is you head someplace like this smorgasboard of computer ranking algorithms and check out a few of them to get a quick feel for which teams appear to be over- or under-seeded. Some of them even do the work for you by putting a specific probability estimate on each team's chances of advancing to each round.

Whatever the rules of your bracket pool, you probably get some sort of score associated with your entry. And the highest score wins. In most pools, you can use estimates like those above to compute (at least approximately) the expected score of each possible entry. Now simply find the entry with the highest expected score and turn it in.

That's what I used to do. Only recently did I realize that that's wrong. Maximizing your expected score is not the same as maximizing your chance of having the highest score. Your goal is the latter, not the former.

To see why they're not the same, imagine a simple pool where you are simply trying to pick the winner of the tournament. Let's say that in the very likely event of a tie, the winner will be selected randomly from among those who correctly picked the champion. You believe these are the probabilities of each team winning the tourney:

Ohio State: 25%
UCLA: 20%
Kansas: 15%
UNC: 15%
Florida: 10%
Texas A&M: 10%
Washington State: 5%

The "score" of your entry in this simple pool is either one or zero, depending on whether you pick the champ correctly or not. So the entry with the highest expected score is Ohio State. But Ohio State might or might not be the entry that maximizes your chance of winning the pool. It depends on who everyone else picked. If you were the only Buckeye-picker, then great. But if 90% of the other pool participants picked Ohio State, then you'd be better off picking Washington State.

So, while Ohio State is the "best" pick in some sense, it's also likely to be a "crowded" pick, and that's the problem. You may be better off going with a "worse" pick, if it's a pick that's less popular. That's a simple example, but the same issues are present in a real pool. Even if there aren't necessarily ties, the best picks are also going to be the most popular picks, and that's going to cause the same kind of crowding. If you pick the entry that you believe is most likely to occur, then there will be lots of other entries that look very similar to yours. This is problematic because you know you're going to miss on a lot of games. And if your entry is too centrist, it's likely that there will be an entry that looks just like it except that it got a few of the games you missed.

The other extreme is to pick an entry with Cinderellas and longshots aplenty. This avoids the crowding problem. With a wacky entry, even if you miss a lot of games, there are not likely to be many entries close to yours to capitalize on your mistakes. The problem here is that, if you turn in a wacky entry, you probably won't end up being even close. That's what makes it a wacky entry.

To make this a little more concrete, imagine two extreme strategies:

Strategy #1: pick a final four with two #1 seeds, a #2 seed and a #3 seed.
Strategy #2: pick a final four with two #9 seeds and two #7 seeds.

The upside of Strategy #1 you're very likely to hit at least a couple of the final four teams. The downside is that, if your final four hits, you're probably not the only one who has it.

The upside of Strategy #2 is that, even if you just get one or two of the final four teams correct, you're probably still doing better than everyone else. The downside is that you're not likely to hit even one.

And of course you don't have to be at one extreme or the other. There is a continuum of possibilities in between. So where do you want to position yourself? You can't answer that question unless you know what the other entries in your pool look like, and you're probably not going to know that. So you have to make some assumptions.

If it's a big contest with a mixture of hardcore and casual fans, I think it's reasonable to expect that the entries will generally cluster around the most likely outcomes, but that there will be some longshot entries mixed in. With that in mind, I'm going to make the following assumption:

Assume the entries in your pool are distributed the same as the distribution of actual outcomes of the tournament.

Roughly speaking, what this means is that, if you think Ohio State as a 25% chance of winning the tourney, then about 25% of the pool's participants will pick Ohio State to win it. If you think there is a 1% chance of a final four consisting of Florida, UCLA, Texas A&M, and Georgetown, then about 1% of the pool's entries will have that for a Final Four. If you think Virginia Tech has a 59% chance of beating Illinois in the first round, then around 59% of the entries will have Virginia Tech beating Illinois. And so on.

Is this a reasonable assumption? I think it's at least in the ballpark. publishes the entries in its Tournament pick 'em contest and they match up reasonably well with objectively-generated probabilities (e.g. from Sagarin ratings and the like). Not perfectly, but reasonably. This shouldn't be too surprising. Sports gambling markets are often cited as an example of the wisdom of crowds and are generally believed to be pretty efficient.

So let's go back and apply this assumption to our drastically simplified pool, where we are only picking the champion. If these are the probabilities of each of these teams winning the title:

Ohio State: 25%
UCLA: 20%
Kansas: 15%
UNC: 15%
Florida: 10%
Texas A&M: 10%
Washington State: 5%

Then our assumption would imply that the above is also the distribution of entries. Twenty-five percent of the people would take Ohio State, 20% UCLA, and so on. If that's the case, then what is the best pick?

There is no best pick! Your chances of winning are the same no matter who you pick.

If there are 100 entries for example, then 25 of them took Ohio State. So if you are one of those 25 riding the Buckeyes, your chances of winning are 1%: a 25% chance they'll win, and then a 1-in-25 chance that you'll win the tiebreaker. If you take Washington State, you've also got a 1% chance of winning: 5% chance of the Cougars winning, then a 1-in-5 chance of winning the tiebreaker. Regardless of which team you look at, the analysis will turn out the same: you have a 1% chance of winning. One percent, of course, is one of a hundred, because you are one of a hundred people in the pool.

But that's an oversimplified situation. What happens in more complicated settings?

As many of you know, I teach math for a living. Last summer, I got a student and a colleague interested in investigating this question with me. Some very interesting (to us, anyway) mathematics arose from the investigation.

As an abstract model of the tournament prediction problem, we imagined the following game. Suppose that a random number, called the target, is to be chosen. Millions of participants will guess what the number will be, and whoever guesses closest is the winner. Let's say, just for example, that it is to come from the standard normal distribution. So there is about a 2/3 probability that the target will be between -1 and 1, a 95% chance that it will be between -2 and 2, a 99% chance that it will be between -3 and 3, and so on. Your job is to guess closer to the target than any other competitor, and let's assume that their guesses are distributed as independent standard normals as well. In other words, two-thirds of the guesses will be between -1 and 1, 95% between -2 and 2, and so on.

If you guess near zero, then you are likely to be close to the target. But you are also likely to be crowded out by the multitudes of other guesses that are in the same vicinity. If you make a guess far out in the tail, like say 3.4, then there aren't many guesses near yours, but the target isn't likely to be near your guess either. If you picture a standard bell curve, you can picture the choice as being between a tall skinny piece of the distribution (a guess near zero) or a short fat piece (a guess far from zero). Which gives you the better chance of winning?

As it turns out, it doesn't matter. Either is as good as the other. And anywhere in between is also just as good.

Even more interesting is that it does not matter that the distribution is standard normal. No matter what the distribution is (well, there are a few technical caveats, but I don't feel like I'm betraying the spirit of the results to say that it doesn't matter), as long as the distribution of entries is the same as the distribution of possible outcomes, and as long as the pool has a lot of entries, it doesn't matter what you guess.

So, at least to the extent that you believe our abstract game models your pool reasonably well, any guess is as good as any other. Fill out your bracket based on geography, uniform color, fierceness of mascot, or whatever other criteria you want. Your chances are as good as anyone else's.

If you're a casual follower of college hoops, you might find this liberating. While I haven't given you any actual advice on how to fill out your brackets, at least I've absolved you of any guilt you may have had about entering a contest where you have no idea what you're doing.

Posted in Non-football, Statgeekery | 17 Comments »

NFL Draft Contest

Posted by Doug on March 9, 2007

UPDATE: "live" scoring will take place here

There is very little in this world that I enjoy more than cooking up contests with funky rules. So here I am announcing the

First Annual NFL Draft Contest

Prize: 20 virtual dollars with which to sponsor a page at p-f-r. Also honor and glory.

How it works:

1. Select, in order, the players you think will be selected in the first round of the 2007 NFL draft. Post them in the comments to this post, like this:

1 - JaMarcus Russell - QB - LSU
2 - Calvin Johnson - WR - Ga Tech
32 - Greg Olsen - TE - Miami

The NFL teams that these players get drafted by are irrelevant. And don't worry about the exact format; just make sure every player is identified unambiguously.

2. Every player who gets picked in the first round is worth one (1) point. That point will be split among all participants who correctly predicted that player to be picked in that slot. EXAMPLE: suppose Adrian Peterson is picked third. If 14 participants had Peterson being picked third, they each get 1/14 of a point. If only four participants had Peterson going third, they each get 1/4 of a point.

3. Every participant's score will be computed via the following formula:

SCORE = (total points from #2 above) * (1 + N/25)

Where N is the number of days before the draft you posted your entry.

This isn't as complicated as it looks. If you post on the morning of the draft, your score is the number of points you got in step 2. If you post 25 days before the draft, you get double points for each correct pick. If you post 15 days before the draft, you get to multiply your points by 1.6. And so on.

We're about 50 days out right now, so you can get triple points if you're willing to take a stab at it today. That's a pretty steep multiplier. Note, however, that waiting gives you two advantages. Not only do you have more information about how the players are grading and what the teams are thinking, but you also have, because you can see the earlier entries, more information about the payoffs for picking certain players.

Obviously, you're not allowed to change your entry in any way once posted.

4. Participant with the highest SCORE wins.

I think you'll find that there is some nontrivial strategy here. Or maybe not. I made up the rules in about 20 seconds. But I do think these rules should result in an entry pool that is fairly nonhomogeneous. In my opinion, that's the first prerequisite for an interesting contest.


a. If you don't care about winning yourself, but want to keep your friend from winning, you could simply wait for him to post his entry and then flood the contest with entries identical to his. For that reason, everyone is limited to one entry per person. This will be enforced by the honor system. If caught breaking this rule, you, your children, and your children's children will be banned from all future p-f-r contests. For three months *.

b. Just to make it interesting, I'll stipulate that you are allowed to name the same player in more than one slot. For instance, if you want to put Calvin Johnson in the #1 slot and the #2 slot, that's legal. You'd then get credit if he is drafted either first or second. Of course, by doing that, you forfeit the chance of getting points from both the first and the second picks (or maybe not --- I wouldn't put anything past Matt Millen).

c. I won't enter the contest myself, which will allow me to arbitrate any dispute impartially. Any ambiguities in the rules will be clarified by me in whatever way causes me the least amount of hassle.

Posted in NFL Draft | 26 Comments »

Chad Pennington and Thomas Jones

Posted by Chase Stuart on March 7, 2007

There are lots of things to write about the Thomas Jones trade, but most of them aren't that interesting to your average sports fan. I heard one comment, though, that piqued my interest. Roughly speaking, the claim was this:

Chad Pennington is going to be helped out a ton by Thomas Jones. Last year, it wasn't fair how the Jets asked him -- while recovering from consecutive arm surgeries -- to carry the entire offense. It was all on him and his arm, and he played through it all. Now, with Jones there, Pennington should be much better this year.

As usual, "much better" can be interpreted lots of ways. I'll look at two, adjusted yards per attempt, and team wins. As I started thinking about how to test this theory empirically, I realized there are quite a few assumptions we'll have to make to really examine this. There are thousands of QB seasons to look at, so here is how we'll narrow down the list.

  • We'll only look at quarterbacks that played on the same team in consecutive years, played in at least ten games in each season, and threw for at least 2,000 yards in each year. Those last two numbers are pretty arbitrary, but they seem to establish a decent floor.
  • The 2006 Jets RBs, as a group, rushed 426 times for 1,449 yards, a 3.40 YPC average. You may remember, this was after a historically bad start, too. Jets RBs, as a group, ranked 26th in rushing yards and 30th in YPC. We'll have to be arbitrary again, but the assumption we're using is that Thomas Jones is good, and this helps Pennington. If the Jets RBs, as a group, stink again next year, this analysis would be meaningless. So I'll only look at QBs that played on teams that moved up at least 10 rankings in rushing yards and 10 ranking spots in rushing YPC average the following year.
  • Only 37 QBs since the merger have met those requirements, but we'll have to narrow the list a bit more. Why? Our system now will spot someone like the 1990 version of Troy Aikman, who played in 15 games and threw for 2,579 yards for Dallas. The next year, the Cowboys RBs improved from ranking 24th and 23rd to 9th and 8th, in rushing yards and rushing YPC, respectively. And Aikman played in 12 games in 1991, throwing for 2,754 yards. But in 1990, his leading receiver was Kelvin Martin (732 yards), while in 1991 Michael Irvin (1523) more than doubled Martin's output. That surely helped Aikman more than anything else, and the key factor here is that we all expect Coles and Cotchery to lead the Jets in receiving in 2007. So I'm going to stipulate that another requirement is that the same two receivers lead the team in receiving yards the same year. I italicized receivers, because I don't mean wide receivers. If a RB or TE ranks first or second, that's fine too. Additionally, the order doesn't matter, because the Jets won't change much if it's Cotchery that leads the Jets in receiving yards next year, or if Coles does it again.

That whittles the list down to twelve. I think that's a pretty good number. There's too much information for one table, so here is how those QBs all did in the first year, Year N. The categories should be self-explanatory, except note that YdRk is how that team's running backs ranked in rushing yards, and YpcRk is how that team's running backs ranked in rushing yards per carry. I also threw Pennington on the top of the list, but did not include his numbers in the averages.

Name Nyr Tm YdRk YpcRk Receiver1 Receiver2 AY/A W-L
Chad Pennington 2006 nyj 26 30 ColeLa00 CotcJe00 5.78 10-6
Matt Hasselbeck 2002 sea 21 22 RobiKo00 JackDa00 6.62 7 -9
Jay Fiedler 2001 mia 24 30 ChamCh00 McKnJa00 5.86 11-5
Kerry Collins 1999 nyg 25 28 ToomAm00 HillIk00 5.73 7 -9
Mark Brunell 1997 jax 22 23 SmitJi00 McCaKe00 7.23 11-5
Brad Johnson 1996 min 18 18 ReedJa00 CartCr00 6.36 9 -7
John Elway 1994 den 28 27 MillAn00 SharSh00 6.48 7 -9
Wade Wilson 1988 min 20 23 CartAn00 JoneHa00 7.50 11-5
Ken O'Brien 1987 nyj 19 17 ToonAl00 ShulMi00 6.27 6 -9
Warren Moon 1986 oti 26 27 HillDr00 GiviEr00 5.02 5-11
Ron Jaworski 1980 phi 16 21 SmitCh00 CarmHa00 7.23 12-4
Jim Hart 1978 crd 23 25 TillPa00 GrayMe01 5.18 6-10
Ron Jaworski 1977 phi 24 24 CarmHa00 KrepKe00 4.10 5 -9
Average 22 24 6.13 8 -8

To be clear, the above table should be read as follows: Chad Pennington played for the 2006 Jets, whose RBs ranked 26th in rushing yards and 30th in rushing yards per carry, and his top receivers were Laveranues Coles and Jerricho Cotchery. He averaged 5.78 adjusted yards per attempt, and his team went 10-6.

The rest of the above table list is filled with QBs on bad rushing teams, who played a lot in Year N and Year N+1, and whose top receivers remain unchanged. Here's how those QBs did in Year N+1:

Name N+1yr Tm YdRk YpcRk Receiver1 Receiver2 AY/A W-L
Matt Hasselbeck 2003 sea 7 9 JackDa00 RobiKo00 6.68 10-6
Jay Fiedler 2002 mia 1 3 ChamCh00 McKnJa00 6.02 9 -7
Kerry Collins 2000 nyg 5 15 ToomAm00 HillIk00 6.13 12-4
Mark Brunell 1998 jax 6 4 SmitJi00 McCaKe00 6.77 11-5
Brad Johnson 1997 min 7 5 ReedJa00 CartCr00 5.96 9 -7
John Elway 1995 den 15 3 MillAn00 SharSh00 6.64 8 -8
Wade Wilson 1989 min 6 11 CartAn00 JoneHa00 5.78 10-6
Ken O'Brien 1988 nyj 4 6 ToonAl00 ShulMi00 5.67 8 -7
Warren Moon 1987 oti 13 5 HillDr00 GiviEr00 5.99 9 -6
Ron Jaworski 1981 phi 4 2 CarmHa00 SmitCh00 5.26 10-6
Jim Hart 1979 crd 3 2 TillPa00 GrayMe01 3.72 5-11
Ron Jaworski 1978 phi 8 10 CarmHa00 KrepKe00 4.84 9 -7
Average 7 6 5.79 9 -7

I wasn't sure what before running the numbers what the results would tell us, but the results are clear: don't bump up Chad Pennington's 2007 projections just yet. Not surprisingly, team winning percentage went up with improved running games. But while half of the dozen QBs technically saw an increase in their adjusted yards per attempt ratio, only two of them, and none in the last 19 years, saw significant increases. So the next time you hear someone tell you how Chad Pennington's efficiency numbers should increase this year with an improved rushing attack, ask them why, because it didn't help Wade Wilson or Jim Hart.

Because like Pennington, Wilson and Hart were the starting QBs on the same team for two straight years. And like Pennington, Wilson and Hart had the same top two receivers (Coles/Cotchery, Tilley/Gray, and Carter/Jones) both years. Pennington, Wilson and Hart all had really bad running games the first year, and then added a marquee RB in the off-season (Thomas Jones, Ottis Anderson and Herschel Walker). And they have it even better than Pennington's projections, because we know that the receivers stayed healthy and the RBs did very well, and the rushing game became very good. Yet both quarterbacks saw significant decreases in their passing efficiencies.

I'm not saying that will happen to Pennington, but it's clear that it's incorrect to assume that the addition of Thomas Jones will help Pennington's statistics. By weighing the deck as much as possible -- assuming Pennington plays at least 10 games and throws for 2,000 yards next year, assuming that the Jets running game improves significantly, and assuming that Coles and Cotchery are healthy enough to lead the Jets in receiving -- there's still no evidence to expect Pennington to play better. He might play better because he's finally not recovering from off-season surgery, the offensive line has improved with experience, and he's got a year in this new system under his belt, but I'm not sure his numbers will improve because of Thomas Jones the runner. (I say the runner, because if someone like Reggie Bush came over and the Jets running game improved, Pennington's numbers would likely go up because of Reggie Bush the receiver. But Jones isn't in that class as a receiving back, so it's a moot point in this example.)

I'm filing this post under "Fantasy", so I should include some fantasy football information as well.

|==============Year N==============| |=============Year N+1=============|
QBID Rk Att Yards TD/INT FP Rk Att Yards TD/INT FP
HassMa00 19 419 3075 15/10 230 4 513 3844 26/15 306
FiedJa00 10 450 3290 20/19 282 26 292 2024 14/ 9 176
CollKe00 25 332 2316 8/11 152 8 529 3610 22/13 268
BrunMa00 8 435 3281 18/ 7 267 15 354 2601 20/ 9 220
JohnBr00 19 311 2258 17/10 186 13 452 3036 20/12 234
ElwaJo00 5 494 3490 16/10 276 5 542 3970 26/14 312
WilsWa00 14 332 2746 15/ 9 214 20 362 2543 9/12 170
OBriKe00 12 393 2696 13/ 8 185 18 424 2567 15/ 7 184
MoonWa00 12 488 3489 13/26 228 7 368 2806 21/18 236
JawoRo00 5 451 3529 27/12 288 13 461 3095 23/20 240
HartJi00 9 477 3121 16/18 215 26 378 2218 9/20 128
JawoRo00 5 346 2183 18/21 203 13 398 2487 16/16 180
Average 12 411 2956 16/13 227 14 423 2900 18/14 221

The numbers are pretty similar, with quarterback efficiencies going slightly down, TD/INT ratios going slightly up, and fantasy rankings going slightly down, after significantly improving their running games. (While not shown here, rushing yardage is included in fantasy points and fantasy ranking. E.g., Jay Fiedler rushed for 322 more yards the year before Miami added Ricky Williams than the year after. Once again, don't rush to bump Chad Pennington up your fantasy draft board just because the Jets added Thomas Jones.

Posted in Fantasy, History, Statgeekery | 19 Comments »

Ranking the receivers yet again

Posted by Doug on March 5, 2007

Here are four posts (I, II, III, IV) where I have made some attempt to rank the post-merger wide receivers. This will be another.

Let me start with this basic metric:

Adjusted receiving yards = (rec. yards) + 20*(rec. TDs) + 6*(receptions)

and the rationale behind it:

in The Hidden Game of Football, Carroll, Palmer, and Thorn argue that a touchdown is worth about one point more than having the ball at the one yard line. They also argue that 12 yards (or so) is worth one point. On that basis, they claim that it makes sense to give a 12ish-yard bonus for each touchdown scored. Ten is pretty close to 12, but a bit rounder, so they used that instead. I'm using 20 for no good reason except that it matches most people's intuitions better. You could also argue that the presence of a prolific touchdown-scorer at receiver opens up other red zone possibilities.

Why the six-yard bonus for each reception? The theory is that, given two players with the same number of yards, the one with more catches probably had more third-down catches. And third-down catches are more valuable than other catches because they keep drives alive. Someday I'll do some research with the aim of estimating the number of first-down catches snagged by old-time receivers for whom we don't have play-by-play data, but here is a quickie that gives me at least a little confidence that six yards is in the right ballpark.

I took all wide receiver seasons during the last three years during which the receiver in question had 40 or more first downs (there were 92 of them), and I ran a regression to predict the number of first downs a receiver would have based on his totals in catches and yardage. The result:

Estimated First Downs = 6 + .023*RecYd + .30*Rec

R^2 = .77, so it's a decent fit. Both coefficients are highly significant so there is no question that receptions are worth something, at least in terms of first downs, above and beyond the yardage they generate. The coefficient on receptions is about 13 times that on yards. So if first downs were the only thing that mattered, we'd give a 13-yard bonus per reception. But they're not the only thing that matter. Receivers do more than just actually catch passes that result in first downs. The receiver with fewer catches (and the same yards) presumably had bigger catches. In general, the first downs he did get must have been further down the field than the first downs achieved by the lower yards-per-catch guy. Gaining seven yards on third-and-six is great. But gaining eight yards on third-and-six is better. Gaining twenty is better still.

And what is the value of a first down anyway? Again using the estimates from The Hidden Game, we see that in general possession of the ball is worth about four points, which is equivalent to 50ish yards. So a typical punt that nets say, 30 yards, represents a net loss of 20 yards --- or somewhere between one and two points --- to the punting team. The regression says a catch is worth .3 first downs, so a catch must be worth .3*20, or 6 yards.

These are, of course, broad generalities. Some catches are worth much, much more than others. But we can't, at this point, track down all of Harold Carmichael's third down catches and try to assess the value of each one. So we have to estimate.

OK, so we've got a way to roll a receiver's stat line up into a single number. I think it feels about right, but whether or not that's the best way to do it doesn't concern me too much at the moment. If at some point I decide that 5 or 7 yards per reception makes more sense than 6, or if I want to start using 25 yards per touchdown instead of 20, I can make that change.

The next step is to adjust for the context in which the stats were generated. For all sorts of reasons, the game Cliff Branch was playing differed dramatically from the one Keyshawn Johnson played and is playing. In this post I ruminated on some ideas for accounting for that.

In 2006, 50% of the league's adjusted receiving yards (by WRs) were accounted for by 36 guys. The 36th guy was Deion Branch, who had 1158 adjusted yards. Branch will serve as the baseline for 2006. Anyone who did better than Branch gets credit for the difference. Anyone who did worse than gets a zero (not a negative score).

In 1973, 50% of the league's adjusted receiving yards were accounted for by 22 players, so the 22nd guy (Jerry LeVias, 817 adj. yards) is the baseline. So the top receivers in 1973 get compared to a lower baseline, which is appropriate because receiving yardage was tougher to come by in 1973. But at the same time, the top receivers of 2006 aren't getting unduly penalized for the fact that receiving yards are less concentrated at the top than they were in the 70s.

Finally, I give a receiver this much credit (same as in this post)

1100 * (PlayerAdjYards - BaselineAdjYards) / BaselineAdjYards

for every season in which he was above the baseline.

Here, according to this method, are the top 20 single seasons since 1970:

1. Wes Chandler 1982 1670
2. Jerry Rice 1995 1511
3. Cliff Branch 1974 1451
4. Torry Holt 2003 1443
5. Randy Moss 2003 1443
6. Dwight Clark 1982 1425
7. Isaac Bruce 1995 1398
8. Mike Quick 1983 1369
9. Herman Moore 1995 1352
10. Marvin Harrison 2002 1342
11. Sterling Sharpe 1992 1337
12. Jerry Rice 1986 1253
13. Roy Green 1983 1241
14. Carlos Carson 1983 1236
15. Jerry Rice 1993 1215
16. Jerry Rice 1987 1201
17. Roy Green 1984 1198
18. Harold Carmichael 1973 1186
19. Steve Smith 2005 1185
20. Jerry Rice 1994 1168

It's somewhat encouraging to see the top four seasons include one from each decade, but I can't deny that the 70s seem underrepresented in general. I'm not quite sure what to do about that, or if anything should be done about that. As you'll see, the top receivers of the 70s do rank much higher on this list than on any career stat list (e.g. Cliff Branch ranks #24 here but isn't in the top 50 in terms of total career receiving yards). Do they rank high enough? Who knows?

One final observation before I post the list: while this ranking does make an effort to account for the differing league environments each receiver played in, it makes no effort to account for the differing team environments. Marvin Harrison and Joey Galloway entered the league at essentially the same time, but Harrison has played most of his career with Peyton Manning, while Galloway has played most of his with Rick Mirer, Quincy Carter, Bruce Gradkowsi, et al. It's safe to say the environments they played in were very, very different. So this system is probably best thought of as a ranking of the receivers' statistics, not receivers themselves.

I won't be diminishing the suspense too much if I tell you that Jerry Rice ranks first, so I'll show his numbers to explain what everything means.

1. Jerry Rice 13629
1985 20 30 142
1986 1 29 1253
1987 1 32 1201
1988 3 31 801
1989 1 32 1116
1990 1 34 1159
1991 2 33 720
1992 3 34 860
1993 1 32 1215
1994 1 31 1168
1995 1 32 1511
1996 2 34 670
1998 6 34 492
2000 24 32 164
2001 13 33 450
2002 11 36 560
2003 26 36 140

Rice amassed 13629 Adjusted Yards Above Baseline (AYAB) in his career. Shown below are all the seasons in which he finished above the baseline. The first number after the year is Rice's rank in AY for that season, the second number is the rank of the baseline player, and the final number is his AYAB for the year.

Here are the top 51 among all receivers debuting in 1970 or later, or you can examine the full list of all receivers debuting since 1970 who finished above the baseline at least once:

1. Jerry Rice 13629
1985 20 30 142
1986 1 29 1253
1987 1 32 1201
1988 3 31 801
1989 1 32 1116
1990 1 34 1159
1991 2 33 720
1992 3 34 860
1993 1 32 1215
1994 1 31 1168
1995 1 32 1511
1996 2 34 670
1998 6 34 492
2000 24 32 164
2001 13 33 450
2002 11 36 560
2003 26 36 140

2. Marvin Harrison 7750
1996 28 34 85
1997 22 32 151
1998 33 34 6
1999 1 34 1012
2000 2 32 988
2001 1 33 1014
2002 1 36 1342
2003 5 36 862
2004 9 35 646
2005 8 36 673
2006 1 36 967

3. Steve Largent 6996
1976 13 24 323
1977 13 24 294
1978 1 26 850
1979 2 24 559
1980 6 28 461
1981 4 27 606
1982 14 29 292
1983 7 31 945
1984 7 30 777
1985 2 30 724
1986 8 29 547
1987 6 32 612

4. Torry Holt 6045
2000 4 32 935
2001 6 33 597
2002 10 36 581
2003 2 36 1443
2004 4 35 833
2005 6 36 904
2006 6 36 748

5. Cris Carter 5901
1988 29 31 33
1991 17 33 283
1992 28 34 51
1993 7 32 611
1994 3 31 885
1995 5 32 1115
1996 7 34 565
1997 8 32 536
1998 12 34 397
1999 5 34 563
2000 10 32 739
2001 26 33 119

6. James Lofton 5774
1978 12 26 250
1979 19 24 155
1980 2 28 611
1981 2 27 630
1982 5 29 713
1983 5 31 1043
1984 6 30 802
1985 8 30 497
1986 21 29 186
1987 12 32 378
1991 13 33 357
1992 19 34 147

7. Tim Brown 5625
1988 30 31 1
1992 26 34 59
1993 6 32 642
1994 5 31 787
1995 9 32 782
1996 11 34 466
1997 2 32 773
1998 15 34 361
1999 6 34 532
2000 15 32 534
2001 11 33 513
2002 24 36 170

8. Randy Moss 5388
1998 2 34 700
1999 3 34 621
2000 5 32 892
2001 8 33 542
2002 4 36 751
2003 1 36 1443
2004 29 35 95
2005 21 36 339

9. Isaac Bruce 5362
1995 2 32 1398
1996 4 34 601
1999 9 34 421
2000 6 32 868
2001 23 33 273
2002 15 36 373
2003 17 36 341
2004 7 35 661
2006 17 36 421

10. Michael Irvin 5327
1991 1 33 975
1992 2 34 962
1993 4 32 834
1994 9 31 612
1995 4 32 1138
1996 26 34 90
1997 10 32 490
1998 21 34 224

11. Terrell Owens 5253
1997 21 32 179
1998 8 34 449
2000 3 32 977
2001 3 33 854
2002 3 36 784
2003 11 36 598
2004 8 35 658
2005 36 36 0
2006 5 36 752

12. Jimmy Smith 5126
1996 10 34 516
1997 7 32 565
1998 7 34 476
1999 2 34 897
2000 12 32 638
2001 5 33 781
2002 19 36 336
2003 30 36 65
2004 17 35 471
2005 20 36 375

13. Sterling Sharpe 4913
1988 27 31 59
1989 2 32 1009
1990 6 34 456
1991 21 33 247
1992 1 34 1337
1993 2 32 997
1994 4 31 806

14. Rod Smith 4649
1997 9 32 516
1998 4 34 518
1999 23 34 182
2000 1 32 1040
2001 4 33 812
2002 18 36 348
2003 23 36 200
2004 15 35 491
2005 12 36 538

15. Gary Clark 4544
1985 13 30 314
1986 4 29 724
1987 3 32 759
1988 20 31 309
1989 7 32 702
1990 4 34 547
1991 3 33 714
1992 10 34 336
1993 24 32 135

16. Art Monk 4441
1980 23 28 90
1981 19 27 142
1982 21 29 145
1983 24 31 237
1984 3 30 1081
1985 3 30 657
1986 12 29 464
1988 15 31 402
1989 8 32 682
1990 21 34 122
1991 10 33 413

17. Henry Ellard 4400
1985 23 30 97
1987 18 32 305
1988 1 31 1065
1989 5 32 778
1990 3 34 650
1991 16 33 285
1992 34 34 0
1993 19 32 208
1994 7 31 729
1995 24 32 206
1996 30 34 72

18. Herman Moore 4232
1992 14 34 291
1993 12 32 275
1994 10 31 602
1995 3 32 1352
1996 1 34 713
1997 3 32 724
1998 20 34 271

19. Andre Reed 4159
1986 26 29 80
1987 14 32 340
1988 13 31 439
1989 4 32 833
1990 10 34 364
1991 5 33 565
1992 13 34 302
1993 22 32 145
1994 6 31 768
1996 17 34 232
1997 27 32 77
1998 31 34 8

20. Mark Clayton 4148
1984 2 30 1121
1985 10 30 351
1986 6 29 586
1987 15 32 337
1988 2 31 857
1989 18 32 407
1991 7 33 486

21. Wes Chandler 4135
1979 7 24 345
1980 10 28 367
1981 9 27 442
1982 1 29 1670
1983 17 31 432
1984 28 30 57
1985 4 30 647
1986 22 29 172

22. Harold Carmichael 3982
1973 1 22 1186
1974 4 25 606
1975 18 23 130
1977 11 24 348
1978 4 26 637
1979 15 24 184
1980 18 28 168
1981 12 27 293
1982 9 29 426

23. Andre Rison 3878
1989 27 32 60
1990 2 34 717
1991 8 33 475
1992 4 34 852
1993 3 32 892
1994 13 31 517
1997 14 32 361

24. Cliff Branch 3819
1974 1 25 1451
1975 3 23 481
1976 1 24 988
1977 22 24 49
1978 25 26 37
1979 20 24 106
1980 20 28 147
1982 8 29 435
1983 28 31 120

25. Chad Johnson 3818
2002 16 36 365
2003 4 36 919
2004 5 35 732
2005 3 36 971
2006 2 36 829

26. Drew Hill 3582
1985 5 30 581
1986 10 29 480
1987 7 32 592
1988 6 31 702
1989 21 32 330
1990 9 34 395
1991 6 33 500

27. Mike Quick 3450
1983 1 31 1369
1984 11 30 523
1985 1 30 747
1986 15 29 359
1987 10 32 451

28. Roy Green 3441
1982 18 29 196
1983 2 31 1241
1984 1 30 1198
1987 21 32 189
1988 10 31 572
1990 30 34 43

29. Dwight Clark 3401
1980 3 28 523
1981 7 27 460
1982 2 29 1425
1983 12 31 583
1984 18 30 232
1985 24 30 92
1986 25 29 83

30. Joe Horn 3313
2000 8 32 770
2001 7 33 558
2002 8 36 627
2003 14 36 482
2004 2 35 876

31. Cris Collinsworth 3296
1981 11 27 346
1982 4 29 765
1983 9 31 827
1984 14 30 416
1985 9 30 466
1986 11 29 474

32. John Stallworth 3254
1977 5 24 491
1978 10 26 261
1979 3 24 513
1981 10 27 350
1982 16 29 266
1984 4 30 1027
1985 11 30 342

33. Anthony Miller 3052
1989 6 32 720
1990 13 34 287
1992 6 34 579
1993 5 32 648
1994 17 31 362
1995 16 32 453

34. Keenan McCardell 3047
1996 13 34 358
1997 11 32 458
1998 26 34 115
1999 31 34 88
2000 14 32 595
2001 14 33 425
2003 8 36 671
2005 22 36 332

35. Hines Ward 3021
2001 20 33 305
2002 2 36 854
2003 7 36 763
2004 22 35 315
2005 17 36 419
2006 22 36 361

36. Keyshawn Johnson 2932
1996 27 34 86
1997 20 32 202
1998 5 34 492
1999 10 34 418
2000 23 32 222
2001 9 33 540
2002 20 36 334
2004 25 35 277
2005 26 36 207
2006 28 36 149

37. Mark Duper 2926
1983 11 31 688
1984 5 30 821
1986 3 29 808
1987 28 32 51
1990 26 34 68
1991 11 33 386
1992 23 34 99

38. Eric Moulds 2922
1998 3 34 598
1999 28 34 141
2000 11 32 703
2001 28 33 99
2002 5 36 720
2003 32 36 41
2004 19 35 412
2005 28 36 204

39. Irving Fryar 2875
1986 29 29 0
1990 22 34 105
1991 18 33 272
1992 20 34 135
1993 9 32 346
1994 8 31 624
1995 23 32 207
1996 6 34 568
1997 6 32 615

40. Drew Pearson 2859
1974 2 25 1134
1975 6 23 342
1976 7 24 535
1977 4 24 505
1978 23 26 54
1979 9 24 287
1982 29 29 0

41. Stanley Morgan 2808
1978 17 26 150
1979 10 24 278
1980 12 28 264
1981 17 27 200
1982 10 29 393
1983 18 31 382
1986 2 29 1065
1987 26 32 72

42. Derrick Mason 2778
2000 26 32 144
2001 16 33 389
2002 22 36 283
2003 6 36 859
2004 12 35 605
2005 14 36 456
2006 34 36 37

43. Steve Watson 2679
1981 3 27 615
1982 11 29 391
1983 10 31 781
1984 8 30 651
1985 17 30 239

44. Tony Hill 2643
1978 11 26 255
1979 5 24 384
1980 7 28 456
1981 21 27 104
1982 15 29 290
1983 20 31 363
1984 17 30 232
1985 7 30 546
1986 28 29 8

45. Wesley Walker 2635
1977 15 24 253
1978 2 26 698
1981 26 27 34
1982 6 29 691
1983 14 31 528
1986 13 29 429

46. Carlos Carson 2635
1982 20 29 180
1983 3 31 1236
1984 13 30 423
1985 25 30 68
1987 4 32 726

47. Ernest Givins 2601
1986 14 29 367
1987 8 32 553
1988 16 31 359
1989 29 32 33
1990 7 34 421
1991 14 33 303
1992 11 34 329
1993 17 32 231

48. Muhsin Muhammad 2582
1998 25 34 179
1999 7 34 520
2000 13 32 635
2002 36 36 0
2003 29 36 77
2004 1 35 966
2005 32 36 46
2006 27 36 156

49. Eric Martin 2543
1987 16 32 325
1988 8 31 661
1989 14 32 487
1990 14 34 229
1991 28 33 84
1992 8 34 493
1993 14 32 261

50. John Jefferson 2543
1978 3 26 676
1979 4 24 415
1980 1 28 967
1982 28 29 29
1983 16 31 455

51. Joey Galloway 2513
1995 20 32 333
1996 21 34 161
1997 12 32 412
1998 17 34 325
2002 26 36 116
2005 7 36 774
2006 20 36 390

Posted in General, History | 17 Comments »

The anatomy of a run

Posted by Doug on March 2, 2007

If you're in the market for a football podcast, you should check out the podcast: The Audible. During the season their coverage focused on fantasy football. Since then, they've been on-site at the Senior Bowl, the East-West Shrine game, and the combine covering draft prospects.

If you're a draftophile, all their stuff is worth listening to. But one that you'll definitely find interesting is their recent interview with Florida State running back Lorenzo Booker. The whole interview is interesting, as Booker appears to be an extremely impressive young man. In particular, though, there is a segment near the end where Booker describes what was going through his head during a particular run in a game against Notre Dame.

Here is the full interview if you want to listen to it (the Booker interview starts at about the 17-minute mark; the first part is an interview with financial advisor Robert Burks, who has as clients some NFL players and soon-to-be NFL players). Here is a transcript of Booker's description of the run. Read it and then watch the run.

As I'm running, I'm reading five different guys, and I'm reading their angles all at the same time. So, once you figure out a guy's angle, it's all about making him believe he's right.

And so from that standpoint I had made about three or four guys miss, and so I backed up out of the hole to kind of regain myself. I felt like I was in the hole and if I kept moving around someone was going to tackle me, so I backed up to kind of observe the whole situation again.

But as I backed up I felt like I was slipping. I knew the guy coming at me knew that I was slipping, but at the same time I knew that I could regain my balance at any time. So as I was backing up, I wanted to get him to the point to where he committed to the point to where he couldn't pull himself back.

And so once I stuck my foot in the ground it was over and the guy slid like he was a baseball player. The play was over after that.

Posted in General, NFL Draft | 5 Comments »


Posted by Doug on March 1, 2007

My colleague Sean Forman from baseball-reference is puzzled by the media's coverage of the latest steroid scandal. He asked me to solicit the opinions of football fans about the story itself or about his thoughts on the matter.

Posted in General | 17 Comments »

League Leaders

Posted by Chase Stuart on February 28, 2007

Anytime I hear a stat like "Eli Manning was 5th in the NFL in passing yards in 2005", the first question that comes to my mind is "Well, where did he rank in pass attempts?" If you rank higher in pass attempts than passing yards, it's going to be difficult to impress me by throwing for lots of yards; it means at least one person threw for more yards on fewer passes.

I was wondering what percentage of league leaders in a particular statistic (say, passing yards) also ranked first in opportunities (in this case, pass attempts). I was also curious which players had led the league while ranking the lowest in opportunities.

Here's the full list of the 37 QBs to lead the post-merger NFL in passing yards in a single season. The first column shows where each QB ranked in pass attempts that season.

7 2001 Kurt Warner
7 1983 Lynn Dickey
7 1974 Ken Anderson
7 1972 Joe Namath
6 1976 Bert Jones
5 2006 Drew Brees
4 2005 Tom Brady
4 1997 Jeff George
4 1995 Brett Favre
4 1979 Dan Fouts
4 1970 John Brodie
3 2000 Peyton Manning
2 2004 Daunte Culpepper
2 2003 Peyton Manning
2 1999 Steve Beuerlein
2 1998 Brett Favre
2 1996 Mark Brunell
2 1985 Dan Marino
2 1982 Dan Fouts
2 1975 Ken Anderson
1 2002 Rich Gannon
1 1994 Drew Bledsoe
1 1993 John Elway
1 1992 Dan Marino
1 1991 Warren Moon
1 1990 Warren Moon
1 1989 Don Majkowski
1 1988 Dan Marino
1 1987 Neil Lomax
1 1986 Dan Marino
1 1984 Dan Marino
1 1981 Dan Fouts
1 1980 Dan Fouts
1 1978 Fran Tarkenton
1 1977 Joe Ferguson
1 1973 Roman Gabriel
1 1971 John Hadl

To me, the accomplishments of Warner, Dickey, Anderson and Namath did is much more impressive than when Fouts or Moon led the league in passing attempts. I'm not saying you should throw for the most yards in the NFL when you pass more often than anyone else, just that it's less impressive when you do. Slightly fewer than half (17 of 37) of the league leaders in passing yards also led the league in atempts that season.

We can look at the same numbers for running backs, just using rushing yards and rush attempts.

9 1982 Freeman McNeil
8t 1996 Barry Sanders
6 1993 Emmitt Smith
6 1990 Barry Sanders
5 2001 Priest Holmes
4 1997 Barry Sanders
4 1994 Barry Sanders
3 1984 Eric Dickerson
3 1978 Earl Campbell
3 1976 O.J. Simpson
3 1974 Otis Armstrong
2 2006 LaDainian Tomlinson
2 2003 Jamal Lewis
2 2000 Edgerrin James
2 1998 Terrell Davis
2 1992 Emmitt Smith
2 1985 Marcus Allen
2 1979 Earl Campbell
2 1972 O.J. Simpson
2 1970 Larry Brown
1 2005 Shaun Alexander
1 2004 Curtis Martin
1 2002 Ricky Williams
1 1999 Edgerrin James
1 1995 Emmitt Smith
1 1991 Emmitt Smith
1 1989 Christian Okoye
1 1988 Eric Dickerson
1 1987 Charles White
1 1986 Eric Dickerson
1 1983 Eric Dickerson
1 1981 George Rogers
1 1980 Earl Campbell
1 1977 Walter Payton
1 1975 O.J. Simpson
1 1973 O.J. Simpson
1 1971 Floyd Little

Once again, the league leader in yards was the league leader in attempts 17 of 37 times. I think it's a little more difficult to draw conclusions from this list than the QB list, because a high number of rush attempts is probably a good sign that the RB is pretty darn good. Freeman McNeil led the league in rushing in 1982 despite eight other players rushing more often than he did, because he averaged 5.2 YPC. But that's not more impressive than when Barry Sanders in 1997 averaged 6.1 YPC, even if "only" three other RBs had more carries than Sanders that year. Presumably, if McNeil was a better RB, he would have ranked higher than 9th in carries that year. (Not that I think McNeil's 1982 performance was a fluke; in the playoffs, McNeil rushed for 362 yards on 62 carries, averaging 5.83 YPC.)

While comparing RBs to QBs might be just a small difference in degree, using the same tools to compare WRs is a difference in kind. The analog to pass attempts and rush attempts would be targets, but we don't have target data stretching back many years. So we'll have to use receptions, which may be a little misleading. Here's the list, anyway:

13t 1976 Roger Carr
13 2000 Torry Holt
11t 1996 Isaac Bruce
11t 1978 Wesley Walker
8 2006 Chad Johnson
8 1983 Mike Quick
7 2001 David Boston
6t 1977 Drew Pearson
5 2004 Muhsin Muhammad
5 1989 Jerry Rice
5 1979 Steve Largent
4 1998 Antonio Freeman
4 1981 Alfred Jenkins
4 1975 Ken Burrough
4 1970 Gene Washington
3 1997 Rob Moore
3 1984 Roy Green
2t 1988 Henry Ellard
2t 1995 Jerry Rice
2 1999 Marvin Harrison
2 1994 Jerry Rice
2 1993 Jerry Rice
2 1991 Michael Irvin
2 1985 Steve Largent
2 1982 Wes Chandler
2 1974 Cliff Branch
2 1971 Otis Taylor
1t 2005 Steve Smith
1t 1980 John Jefferson
1 2003 Torry Holt
1 2002 Marvin Harrison
1 1992 Sterling Sharpe
1 1990 Jerry Rice
1 1987 JT Smith
1 1986 Jerry Rice
1 1973 Harold Carmichael
1 1972 Harold Jackson


Here is the flip side: the league leaders in attempts who ranked lowest in yards.


Att. Leader YR Yd rank
Jon Kitna 2001 16
Drew Bledsoe 1995 11
Jim Hart 1974 7
Jim Zorn 1976 7
Vinny Testaverde 2000 6
Brett Favre 2006 6
Brad Johnson 2003 5
Steve Deberg 1979 5
Brett Favre 1999 4
Roman Gabriel 1970 4
Brett Favre 2005 3
Peyton Manning 1998 3
Dan Marino 1997 3
Drew Bledsoe 1996 3
Joe Montana 1982 2
Archie Manning 1972 2
John Elway 1985 2
Bill Kenney 1983 2
Fran Tarkenton 1975 2
Trent Green 2004 2


Att. Leader YR Yd rank
Ricky Williams 2003 10
Earnest Byner 1990 4
Ricky Watters 1996 4
Stephen Davis 2001 3
O.J. Simpson 1974 3
Emmitt Smith 1994 3
James Wilder 1984 3
Eddie George 2000 3
Jerome Bettis 1997 3
Thurman Thomas 1993 3
Ron Johnson 1972 3
Ron Johnson 1970 2
Jamal Anderson 1998 2
Walter Payton 1979 2
Barry Foster 1992 2
Tony Dorsett 1982 2
Walter Payton 1976 2
Larry Johnson 2006 2
Walter Payton 1978 2
Gerald Riggs 1985 2

Posted in General | 7 Comments »

Workout warriors

Posted by Doug on February 26, 2007

I teach for a living. If you're ever in a room full of teachers and you sense too much discord in the air, simply mention that students don't take their work seriously enough. That will bring the group into harmony. Knowing nods will be exchanged as stories of underachieving kids get bandied about, and unanimity will reign. I suspect there is a similar topic in every profession and for almost every group of people who share a particular interest.

With the NFL scouting combine now upon us, I am reminded what that subject is for football fans.

Scouts and organizations put way too much emphasis on players' measurables: height, weight, 40 time, and bench press.

Rarely do you find an NFL football fan who disagrees with that. And NFL fans are known for their disagreement. But not on this topic. Mike Mamula's name will be brought up, people will shake their heads in mock dismay, and we'll all feel good about ourselves as we wonder when will they ever get it?

Tight ends Zach Miller of Arizona State and Greg Olsen of Miami entered the draft as the top two players at the position. My impression is that they were about even, or that Miller had a slim edge going into the combine. But now Olsen has apparently moved ahead of Miller because Miller ran a slow 40 (4.8) and Olsen ran a fast one (4.5).

Ridiculous, right? Scouts have been poring over dozens of games worth of film on both Olson and Miller. Based on that, they came to the consensus that Miller was a slightly better prospect. And now because of a drill that has little to do with football --- they weren't even wearing pads --- that's switched. When will they ever get it?

So the question is: at what point, if any, do you have to start paying attention to the measurables? Is 4.5 vs. 4.8 a big enough difference to switch the two? If not, what if Miller had run a 4.9? A 5.1? I certainly do generally agree with the sentiment that organizations place too much emphasis on the combine. If 4.8 speed was good enough for Miller to amass a body of work in college that was sufficient to be ranked ahead of Olsen, then the combine shouldn't change that. But at the same time, the difference between a 4.5 and a 4.8 seems pretty significant.

So I'll just throw this out as a discussion question: is .3 seconds in the enough flip flop these two guys in your rankings? If so, then would .2 be? What about .1? Why? If not, would .4 be? .5? I'm not necessarily looking for a precise figure. I'm more interested in your thought process.

Posted in NFL Draft | 32 Comments »

Coaching and Choking in the Playoffs (Part 2)

Posted by Chase Stuart on February 22, 2007

Yesterday, we looked at lots of combinations of playoff games featuring a mix of regular season records and prior post-season coaching records. Today we're going to get a bit more precise as we conclude the study, and take a quick look at what happened in 2006.

I think its important to be especially clear on what our goal is. This blog has noted the distinction between retrodictive and predictive systems a few times, and in this comment, PFR reader Jim A provided a very useful link. The basic difference is that retrodictive systems answer the question "which team or coach has accomplished the most in the past" while predictive systems answer the question "which team or coach is most likely to win in the future?" What we're trying to create is a predictive system. There's no denying that Bill Belichick (13-3 playoff record) and Joe Gibbs (17-6 career playoff record) have been much more successful than Marty Schottenheimer (5-13) or Jim Mora Sr. (0-6). But that's as obvious as it is uninteresting. Any retrodictive system would have to place Gibbs and Belichick at the top, and Marty and Mora at the bottom.

But when we're talking about whether Schottenheimer should have been fired, we want to know whether he'll win in the future. We want to know the predictive ability of our system. If we find out that a coach's past post-season record is a useless indicator of his future post-season success, it doesn't mean that Schottenheimer is as accomplished as Belichick; it just means that going forward, we have no reason to expect Belichick to be better than Schottenheimer. Those two statements are very different, and that difference is essential to understanding where we're going with this.

Yesterday, I gave a preview of what we're going to look at today -- multiple regression analysis. For each of the 346 playoff games from 1970-2005, I recorded three input variables and one output variables. The output variable is win/loss; the input variables are: 1) each team's head coach's prior playoff record, 2) the difference in winning percentage of the two teams in the regular season, and 3) where the game was played (home, away or neutral (the Super Bowl)).

Before looking at the variables together, let's look at them individually. Home field advantage is strongly correlated with winning -- the Pearson correlation was 0.362 and the correlation was significant. The difference in regular season winning percentage was even more correlated, 0.442, and significant. As for our third variable, past playoff record? The correlation was just 0.03, and was not significant (0.386 on a 2-tailed test). In other words, there is no historical relationship between a coach's prior post-season record and his future post-season performance in a playoff game.

When you run a least squares multiple regression analysis, the following formula is created:

0.436 + 0.13*HFA + 1.32*RegSeaWin%Diff + 0.01 * PastPlayoffWinDiff

So we might say that a team at home (HFA = 1) that won 2 more games than its opponent (RegSeaWin%Diff = 0.125) and with even head coaches, should be expected to get 0.73 wins (or if the game is played 100 times, should win it 73 times). Notice how small the coefficient for past playoff record is -- the differential among the coaches is going to have minimal predictive power. Further, the P-value for past playoff win differential was 0.15, making it not statistically significant.

So what do you say to your friends who won't believe you when you say a coach's past post-season record is irrelevant to predicting his future post-season success? For starters, they'll probably cite some examples. Maybe the Patriots over the Chargers (2006), the Patriots over the Colts (2003, 2004) or Joe Gibbs' Redskins over lots of teams. But if they try and name several examples, remind them that over 350 playoff games have been played since 1970, so individual examples aren't going to prove much. Then throw out these five examples going the other way:

1) In 1982, Chuck Noll had a 14-4 career post-season record and 4 Super Bowl titles to his resume, while Don Coryell was a choke artist that had gone 2-5 in the playoffs. Coryell's team won in Pittsburgh, 31-28.

2) Tom Flores was coaching the defending SB Champions, had won 2 Super Bowls, and owned a sparkling 8-1 career playoff record. His 11-5 team lost in Seattle (12-4) to Chuck Knox, who had been 6-8 in the playoffs prior to that game.

3) The Great Tom Landry, owner of two SB rings and a 20-14 career post-season record, was coaching another great Cowboys team that went 12-4 in 1983. Hosting the 9-7 Rams, John Robinson in his playoff debut went into Dallas and won, 24-17.

4) Bill Walsh was 7-1 in the playoffs and had won two Super Bowls. His defending champion 49ers team played a Giants team with the same 10-6 record, and a coach in Bill Parcells that had a 1-1 career playoff record. But Parcells' Giants won in 1985, 17-3. (And before you start thinking Parcells shouldn't count as a choke coach because "he's Bill Parcells", note that Parcells lost all three times he had a five game advantage over his opponent. In 1994 (8-3 career playoff record at the time) he lost to Bill Belichick in his first post-season game, in 2003, Parcells (11-6) lost to John Fox in his first playoff game, and in 1989 Parcells (5-2) lost at home to John Robinson, who had an ugly 3-5 playoff record before that game.

5) Don Shula, who had coached in four Super Bowls and won two of them at the time, hosted a New England team in 1985 that was coached by Raymond Berry. Raymond Berry's first full season as a head coach was that year. But Berry's team went into Miami and won, 31-14.

The results are clear: the correlation between past playoff success and future playoff success is extremely small and not statistically significant. But let's take it one step further, as I think you should with almost any study that looks at the post-merger NFL: what's going on lately?

I eliminated all playoff games from before 1993, and ran the same numbers. Now we have a look at the modern, post-free agency era. The Pearson Correlation of past playoff records and winning the next game was 0.000, and of course, not significant. Home field was slightly more correlated than before (0.381) and significant, and regular season record was slightly less correlated (0.417) and significant. Running the least squares multiple regression, we get:

0.500 + 0.00*HFA + 1.32*RegSeaWin%Diff + 0.01 * PastPlayoffWinDiff

Once again, past playoff performance is practically irrelevant, and any effect is not significant statistically (0.21 p-value). What's most curious is how home field advantage has been zeroed out. Perhaps one of our readers can help me out, but the big problem I see is that home field advantage is very closely tied to regular season records: there have been only five games out of 130 where the home team had a worse record than the road team. So I believe what the regression is telling us is that once we know the regular season win differential between the two teams, knowing which team is home isn't very useful. Running the regression with only two variables (removing the HFA variable) does not make past playoff record any more useful.

All the statistical tests I've performed make it clear that in terms of a predictive system, knowing a coach's past post-season record is useless to predicting how he will do in a future playoff game. But for fun I thought I'd look at the 2006 playoff results now.

Here's how the first row in the table can be read. When Bill Belichick played Marty Schottenheimer, Belichick (coach 1) had a +17 playoff win differential (Belichick was 10 games over .500 at 12-2, while Schottenheimer was 7 games under .500 at 5-12), a -2 regular season win differential (New England went 12-4 this year, San Diego went 14-2), was on the road (0 = road, 1 = home) and won (0 = loss, 1 = win).

Coach1 Coach2 PWD RWD HFA W/L
BeliBi0 SchoMa0 17 -2 0 1
BeliBi0 DungTo0 12 0 0 0
BeliBi0 MangEr0 9 2 1 1
BillBr0 DungTo0 5 1 1 0
HolmMi0 SmitLo0 4 -4 0 0
ReidAn0 CougTo0 3 2 1 1
ReidAn0 PaytSe0 3 0 0 0
ParcBi0 HolmMi0 2 0 0 0
EdwaHe0 DungTo0 2 -3 0 0
SmitLo0 DungTo0 1 1 0.5 0
PaytSe0 SmitLo0 1 -3 0 0

Of the 11 games this year, only three times did the coach with the better playoff record win the game: Belichick over Schottenheimer and Mangini, and Reid over Coughlin. It's not much of a stretch to say those latter two games weren't surprising; the Eagles and Patriots were more than a notch above the Giants and Jets this year. The Schottenheimer/Belichick game will forever give ammunition to those who believe that past playoff performance is a strong predictor of future playoff performance -- after all, the most clutch coach ever took a worse team on the road and beat the least clutch coach ever. But let's remember that it was still just one game, and one game that could have very easily gone the other way. Belichick lost to Dungy, Billick lost to Dungy at home, and youngsters Sean Payton and Lovie Smith beat successful playoff coaches Andy Reid and Mike Holmgren.

I thought I'd close things today with just a little bit of anecdotal evidence. For all the Marty-bashing that goes on, his 5-13 record could easily be a lot better. The first five games I think of that he's lost in the playoffs all turned on a single play. If John Elway doesn't have The Drive (thanks to a 3rd and 18 completion), if Byner doesn't commit The Fumble, if Lin Elliot doesn't miss 3 field goals (KC loses 10-7), if Nate Kaeding hits a 40-yard FG in overtime, or if Marlon McCree falls down, Schottenheimer would have been 10-8 instead of 5-13. In terms of retrodictive analysis, that stuff's pretty irrelevant: it happened, and Schottenheimer lost. In terms of predictive analysis, I don't know if Marty would have had to have been any better a coach to have a career winning record in the playoffs.

Schottenheimer also lost a 14-10 game, a 17-16 game, a 24-23 game, and a 24-21 game. He's been in lots of close playoff games, but hasn't come out victorious in many. But considering he's got 200 career wins, and an extensive empirical study shows no correlation between past playoff success and the predictability of future playoff success, I have no doubt that Schottenheimer would have had an excellent chance to win a Super Bowl with the Chargers this year.

Posted in History, Statgeekery | 36 Comments »

Coaching and Choking in the Playoffs

Posted by Chase Stuart on February 21, 2007

Over a week ago, the San Diego Chargers became the first team to fire a head coach following a a fourteen-win season. Marty Schottenheimer's team lost its first playoff game, which seems less punishable when you remember what happened the previous two years. In 2004, a 15-1 Steelers team was a Doug Brien field goal away from losing its first playoff game, and got blown out the next week at home; the following year, Bill Cowher brought the city of Pittsburgh its fifth Super Bowl Championship. In 2005, a 14-2 Colts team lost its first playoff game; the following year, Tony Dungy brought the city of Indianapolis its first professional sports title ever (discounting the three ABA titles won in the early 1970s).

Marty Schottenheimer won't get a chance to bring the city of San Diego its first professional sports title (discounting the AFL title in 1963), and you'll hear lots of reasons why. If Schottenheimer was Bill Belichick, we know he wouldn't have been fired. But Belichick has a past history of post-season success, and Schottenheimer has a horrible history of playoff failure. Almost assuredly, if Schottenheimer did not have a poor career record in the playoffs, he would have been retained. While the loss of both assistant coaches was significant, it is my opinion that the overriding factor was the thought that "Marty won't win in the playoffs." This can only make sense if past post-season success is indicative of future post-season success. To make my bias clear, before I conducted this study I believed that statement to be false. Let's see what happens. (Note: I don't care to turn this into a debate on the reasons Schottenheimer was fired. There's currently an 847 post thread on that at our other site.)

From 1970-2005, there were 346 playoff games played in the NFL. To figure out if past playoff prowess is correlated with future post-season success, we need to isolate two factors: regular season record and home field advantage. Because regular season record is highly correlated with home field advantage (the team with the better record has usually been the home team), we're going to leave HFA out for now to make this a bit more palatable.

I hate having to write keys for charts, because that usually means the data isn't presented in its simplest format. But this was the best I could do. Every playoff game has a "clutch" coach and a "choke" coach. The clutch coach is simply the coach with the better career post-season record prior to that game ("better" will be explained in a bit).

RWD = Regular Season Win Differential
N = Number of times two teams met in the playoffs with that differential
Cl Win% = Winning percentage of the "clutch" coaches when they were X games better in the regular season than the opponent.
Ch Win% = Winning percentage of the "choke" coaches when they were X games better in the regular season than the opponent.
Cl Gm = Number of times the "clutch" coach had the better record
Ch Gm = Number of times the "choke" coach had the better record
Ev Gm = The number of times teams with that RWD met and the two coaches had "equivalent" prior post-season records. Equivalent here means both coaches were the same number of games above, at, or below .500. This is only to be complete, since we won't care about these games.

RWD N Cl Win% Ch Win% Cl Gm Ch Gm Ev Gm
6 2 1.000 1.000 1 1 0
5 9 0.667 1.000 3 5 1
4 20 1.000 0.625 9 8 3
3.5 3 1.000 1.000 1 1 1
3 35 0.900 0.833 20 12 3
2.5 4 1.000 0.500 1 2 1
2 74 0.857 0.657 28 35 11
1.5 12 0.600 1.000 5 3 4
1 112 0.682 0.623 44 53 15
0.5 15 0.429 0.500 7 2 6
0 120 0.538 0.462 52 52 16

First, a quick example. When the 1998 (15-1) Vikings played the 1998 (9-7) Cardinals in the playoffs, Dennis Green had a career 1-4 post-season record and Vince Tobin was 1-0 in the playoffs. Green's Vikings won, so that game is filed under RWD as 6, under Ch Gm as 1 (this was the only time the "choke" coach ever had six more regular season wins than his opponent) and under Ch Wins (not presented above) as 1. Then I divided Ch Wins by Ch Gm to get the Ch Win%, which is presented above. Whew.

Let's summarize the table. When two teams face off in the post-season where one team has won five or six more games than the other, the team with the better record (regardless of coaching history) is 11-1. The one loss was when Jerry Burns (1-0) beat mighty Bill Walsh (7-3) in the playoffs, so that's a "clutch" loss.

At four wins better than the opponent, "clutch" coaches are 9-0 but "choke" coaches are only 5-3. Tom Coughlin's upset of Mike Shanahan (1996), Ted Marchibroda's upset of Marty Schottenheimer (1995) and Chuck Noll's upset of Dan Reeves (1984) were the three surprises. All three were by seven points or less. Note that Shanahan (0-0) was considered the "choke" coach and Coughlin (1-0) the "clutch" coach by only the thinnest of margins. We'll address this later today and more thoroughly tomorrow.

At 3/3.5 games better, clutch coaches are 19-2 (John Robinson over Tom Landry in 1984, Chuck Knox over Don Shula in 1983), while choke coaches are 11-2 (Bill Cowher over Tony Dungy, 2005, and Bill Belichick over Mike Martz in SBXXXVI). This illustrates one of the drawbacks of such an approach. Robinson and Knox were both six games behind Landry and Shula (in terms of career post-season records) when they faced, and were clearly big underdogs with respect to playoff success. Martz and Dungy were only one and two games behind Belichick and Cowher at the time, so they had nearly identical playoff records when they faced. So the two clutch losses were much more extreme than the two choke losses.

A wide gap emerges, however, at 2/2.5 games better. Clutch coaches are 25-4, a very respectable winning percentage. Choke coaches are 24-13, which is decidedly more average. Interestingly, in the most extreme discrepancies in games where the choke coach was on a team with two more regular season wins, the choke coach followed history and lost. Dennis Green lost his post-season debut to Joe Gibbs, whose 15-4 record in the playoffs may have mattered more than his team's 9-7 regular season record in 1992. Additionally, Bill Belichick (10-1) beat Jack Del Rio in his post-season debut, but then again, that game was in Foxboro.

The two sets of data converge again when the two regular season teams were within 1.5 games of each other. Both the clutch coach (36-20) and the choke coach (37-21) won 64% of their games when they coached a team with a slightly better regular season record.

When two teams have the same regular season record, clutch coaches have a slight edge, winning 28 of the 52 games. If we had no other data to analyze, this would be what I'd be most curious to see. When the teams are even, who wins? There could be several factors affecting this, so 28/52 isn't conclusive of much.

When coaching a much stronger team, measured by regular season record, both clutch and choke coaches dominate in the post-season. When coaching teams that are a significant but not large amount better, clutch coaches have been noticeably more successful. When coaching teams that are slightly better, clutch and choke coaches appear identical.

As hinted at earlier, we may not be comparing apples to apples. If Coach A has a 1-0 post-season record, and he faces Coach B who owns a 0-1 post-season record, Coach A will be labeled clutch and Coach B will be labeled choke. If Coach A is 10-0 and Coach B is 0-10, the same labels -- clutch and choke -- will apply. But presumably we'd want to focus more heavily on games where there is a large difference in the post-season records. Otherwise, it would be like writing the difference between a 15-1 team and 9-7 team is the same as the difference between a 10-6 team and 9-7 team. Labeling them "good" and "bad" isn't very precise.

We just looked at how the "good" team in every post-season game did (good meaning has X many more regular season wins than the opponent) depending on whether the coach was previously clutch or a choker. Now we're going to look at "clutch" coaches in every post-season game, and see how they fare depending on whether they're coaching a "good" team or a "bad" team. This is susceptible to the same problems, of course, but gives us another way to look at the data. The only reason we talk about clutch coaches in the sense of prior post-season success is because we assume that a clutch coach can beat a choke coach with a bad team. When a good team beats a bad team, we aren't surprised. But how often do "clutch" coaches lead inferior teams to post-season success, and vice versa, how often do "choke" coaches hamper superior teams?

In this chart, we'll need a third column -- even games. Before we dismissed even games because we were analyzing clutch coaching, and if neither coach is clutch, we don't care about the game. Now we might care most about the even games, because that features two teams with the same records.

CF = Clutchness Factor. How many more career post-season wins above .500 the clutch coach had.
N = Number of games where the CF differential was X.
G Win % = Winning percentage by the clutch coach when he had the "good" team (better regular season record)
E Win% = Winning percentage by the clutch coach when the two teams were "even" (same regular season record)
L Win % = Winning percentage by the clutch coach when he had the "bad" team (worse regular season record)
G Gm = Number of games where the clutch coach was on the good team
E Gm = Number of games where the two teams were even
B Gm = Number of games where the clutch coach was on the bad team

CF N G Win% E Win% B Win% G Gm Ev Gm B Gm
10+ 4 --- 0.500 0.500 0 2 2
9 5 --- --- 0.400 0 0 5
8 6 1.000 1.000 0.500 3 1 2
7 4 1.000 --- 0.500 2 0 2
6 22 0.857 0.333 0.083 7 3 12
5 39 0.588 0.600 0.176 17 5 17
4 24 0.615 0.500 0.400 13 6 5
3 50 0.788 0.600 0.250 33 5 12
2 61 0.900 0.786 0.370 20 14 27
1 79 0.792 0.313 0.385 24 16 39

Once again, let's go through a quick explanation and a summary. I'm measuring a coach's record by how many games over .500 he is. If you're 10-5, you're at 5 games over. If you're at 6-13, you're at 8 games under. If those two coaches met, I'd record the difference as +12. This formula works well enough, and the most important thing is that we all know what the formula is, rather than finding the perfect formula.

When Mike Holmgren (9-8) met Joe Gibbs (17-5) in the second round of the 2005 NFC playoffs, Gibbs would be the clutch coach and filed under 10+ wins (since he's actually at +11). Gibbs lost, and he was on the "bad" team since Seattle had won three more games than Washington that year. But when Joe Gibbs (15-4) beat Dennis Green (0-0) thirteen years earlier, he also coached the worse team. Those are the only two times a coach with a 10+ advantage over his opponent coached the team with the worse record in the playoffs (and such a coach has never coached the better team).

On to the summary. When a playoff game features a clutch coach with a large advantage (7 games or more), the clutch coach is 5-0 when coaching the better team and 2-1 when the teams are even. When coaching the worse team, the clutch coach is 5-6. These numbers are more significant than you might initially realize; this means the choke coach is 0-5 when coaching the worse team (compared to 5-6 when the clutch coach has the worse team) and just 6-5 (vs. 5-0) when coaching the better team. Curiously, though, in the most extreme example, the choke coach won. Don Coryell (2-5) met Chuck Noll (14-4) in the playoffs in Pittsburgh, and both teams had gone 6-3 in the regular season. But Coryell's Chargers edged Noll's Steelers, 31-28.

The evidence goes the other way, however, when we look at times when the clutch coach had a 5 or 6 game edge on his opponent. When coaching good teams, he was 16-8; when coaching the worse team he was just 4-25. The converse means while coaching bad teams the choke coach still won 33% of his games, and the "choke" coach won nearly all of the games when he had the better team. The four losses? Chuck Noll (7-2) over Ted Marchibroda (0-1), in 1976; Dan Reeves (9-7) over Dennis Green (2-5) in the 1998 NFC Championship Game, Mike Shanahan (1-1) over Marty Schottenheimer (5-10) in 1997, and Herm Edwards (1-2) over Schottenheimer (5-11) in 2004. Outside of those games, the evidence strongly points to clutch coaches doing worse than choke coaches for this stretch. There are many more games like Bill Parcells losing to John Fox than Herm Edwards beating Schottenheimer.

When we look at coaches with 3 or 4 game advantages, we see a very small edge going to the "clutch" coaches. In those games clutch coaches are 6-5 against choke coaches when both teams have the same regular season record. When the clutch coach is on the good team, his record is 34-12 (74%), and when the clutch coach is on the bad team, his record is 5-12 (29%). Conversely, choke coaches win 71% of the time and 26% of the time when on the good, and bad teams, respectively.

This effect is magnified even more when we look at coaches with just slight advantages, a one or two game lead. I'm not sure this is conclusive of anything, because if there is something to this clutch ability, it shouldn't increase as we get to the least clutch coaches. Anyway, clutch coaches are 37-7 when they coach the good team, while choke coaches are just 41-25 when they're on the good team. Clutch coaches are also 16-14 against the chokers when the teams are even.

So where does that leave us? None of the above methods are perfect, since there are some drawbacks to those tools. In both examples, we made team strength (good/bad) and coaching history (clutch/choke) into binary categories, when of course they are not. As a result, some effects could be hidden. The best way to solve this is to use a regression analysis. I didn't do that today because regression analysis is useless to people who don't understand regression. The tables presented at least bring the numbers to life. Tomorrow, though, we'll sacrifice simplicity for precision, and the results are pretty interesting.

Posted in History, Statgeekery | 18 Comments »

Michael Irvin

Posted by Doug on February 20, 2007

Last week I wrote a couple of posts about methods for ranking the great wide receivers. Based on some good discussion in the comments following those posts, I've modified the method somewhat and am close to being comfortable calling it a Definitive Ranking System (as definitive as such things can ever be, anyway). But that's a post for later in the week if all goes well.

For now I want to talk about the one guy who always appears near the top of these kinds of lists but who isn't usually thought of as one of the all-time greats: Michael Irvin. Among all receivers whose careers started since the merger, Irvin ranked #2 in the receiving yardage category of the Gray Ink rating system I posted last week. He ranked #1 among all receivers debuting in 1978 or later according to this system that I posted back in May, and he ranked #7 among all receivers debuting since 1970 in my favorite WR ranking system EVER (though I admit it's one that probably doesn't produce the "best" rankings, it's the one I like best in theory).

Irvin's prime was something to behold:

Receivng yards: 1991--1995

Jerry Rice 1991-1995 1451
Michael Irvin 1991-1995 1419
Cris Carter 1991-1995 1068
Andre Rison 1991-1995 1025
Henry Ellard 1991-1995 1025
Tim Brown 1991-1995 1016
Anthony Miller 1991-1995 1011
Irving Fryar 1991-1995 999
Herman Moore 1991-1995 979
Sterling Sharpe 1991-1995 963
Andre Reed 1991-1995 899

He's barely behind the best receiver of all time, and a mile ahead of everyone else. Even if you consider all five-year stretches that started within five years of 1991, Irvin's is still second best, it's still close to Rice's best, and it's more than a hundred yards better than anyone else.

But that understates it. Irvin was playing on a conservative offense. During Rice's best stretch, the 49ers were throwing 536 passes per season, compared to 482 passes per year for the Cowboys during Irvin's peak. From 1991--1995, Irvin averaged more yards per team passing attempt than any player in post-merger NFL history.

Player Years AvYd AvTmAtt Yd/TmAtt
Michael Irvin 1991-1995 1419 482 2.95
Jerry Rice 1991-1995 1451 536 2.71
Marvin Harrison 1999-2003 1519 567 2.68
Randy Moss 1999-2003 1412 532 2.66
Jimmy Smith 1997-2001 1346 516 2.61
James Lofton 1980-1984 1175 465 2.53
Torry Holt 2000-2004 1474 591 2.49
Herman Moore 1992-1996 1211 489 2.48
Tim Brown 1993-1997 1269 518 2.45
Chad Johnson 2002-2006 1319 542 2.44
Harold Jackson 1972-1976 795 327 2.43
Rod Smith 1997-2001 1273 528 2.41
Cliff Branch 1974-1978 869 361 2.41
Hines Ward 2001-2005 1095 455 2.41
Terrell Owens 2000-2004 1293 543 2.38
Joe Horn 2000-2004 1258 535 2.35
Henry Ellard 1987-1991 1188 509 2.34
Steve Largent 1983-1987 1101 476 2.31
Sterling Sharpe 1989-1993 1245 542 2.30
Stanley Morgan 1978-1982 885 389 2.27
Ken Burrough 1975-1979 837 375 2.23
Andre Reed 1988-1992 1050 476 2.20
Eric Moulds 1998-2002 1176 538 2.19
Cris Collinsworth 1982-1986 994 455 2.18
Drew Pearson 1974-1978 860 394 2.18
Drew Hill 1985-1989 1070 494 2.17
Cris Carter 1996-2000 1152 532 2.17
Laveranues Coles 2002-2006 1072 497 2.16
Art Monk 1982-1986 972 451 2.15

Is this a contrived stat? Somewhat. But it's tough to argue with the logic behind it:

1. Gaining yards is good.

2. WRs can't gain yards unless their team is passing the ball.

As with any attempt to rate receivers, there are a lot of relevant factors that are not included in this stat. In other words, yes, I am aware that the presence of Emmit Smith probably helped open things up for Irvin, and that that Aikman guy was a fairly accurate passer. But the rest of the list is filled with receivers from some of the best offenses of all time. It's not like Jerry Rice, Marvin Harrison, Torry Holt, et al were playing with crummy running backs and offensive lines.

Michael Irvin's prime years were among the best five-year stretches that any wide receiver ever had.

Posted in General | 27 Comments »

Some much-needed culture

Posted by Doug on February 19, 2007

Joe Fischer is a frequent commenter on this blog who goes by the name "Pacifist Viking." He has a a blog of the same name that I recommend highly. The Minnesota Vikings are the primary subject of his musings, but he writes about a variety of other topics, including basketball, social issues in sport, and --- believe it or not --- literature. Real, honest-to-goodness literature. Recently, he has started comparing great NBA players to famous poets, like this:

Tim Duncan is akin to Alexander Pope: fundamentally sound, technically skilled, but ultimately dull. He inspires nobody; we remember him because we have to remember him, not because we want to.

And this:

Rodman is akin to Edgar Allan Poe. Like Poe, Rodman's brilliance never hid his tormented and haunted soul; in fact, his brilliance seemed a direct result of his soul, as if it exuded directly from it, and put the eccentric individual all the more on display. Both are remembered in large part for their weirdness and creepiness, but that weirdness and creepiness led to a greatness that should be remembered on its own.

For some reason I can't quite put my finger on, I think this is top-notch schtick. I honestly haven't read a poem in nearly twenty years, so maybe I just see it as an easy way to for me to learn something about poets. As many of you know, I'm a professor at a small liberal arts college and a graduate of a similar institution. So I am constantly telling my students about the value of a well-rounded education.

And now I'm telling you. Numerical data and cold logical analysis are what this blog is usually about, but that doesn't mean we can't benefit from an occasional dose of culture from our friends in the humanities. With that in mind, I asked Fischer to cook up some player/poet comps from the NFL.

Poets and players, by Joe Fischer of Pacifist Viking

Terrell Owens: Ted Hughes
Hughes is a brilliant poet, but he’s is probably better known for his personal life, particularly as the husband of poetry legend Sylvia Plath. Hughes seemed to have a devastating effect in his relationships: both Plath and lover Assia Wevill committed suicide while in a stormy relationship with Hughes. Likewise, Owens is by any measure a terrific football player, but he is best known for his flamboyant personality, selfishness, and mean-spirited treatment of coaches and teammates. He also has a devastating effect in relationships: he helped bottom out the 49ers, he ruined the 2005 Eagles, and he may be in the process of destroying the Cowboys.

Randy Moss: William Wordsworth
Wordsworth revolutionized British poetry with Lyrical Ballads (co-written with Samuel Taylor Coleridge). Romantic poetry is considered to have begun with Wordsworth, and his early poetry inspired and influenced many future poets, changing what seemed possible to do in poetry. While he remained respectable throughout his career, something changed at some point: he grew more socially conservative (he was an early admirer of the French Revolution, which influenced his poetry), and along the way his poetry lost the flair of his early years. Likewise, Randy Moss burst onto the scene with bravado, but he seems to have lost some of the spirit of his earlier career. When future football historians look back at Moss, they’re going to look at the first part of his career, as his later career has featured little worth noting. The later Moss lacks passion and inspires nobody.

Brett Favre: William Shakespeare
Here’s something you might not know: Shakespeare wrote some lousy plays. Have you read King John? It’s not fun. Most of his comedies are formulaic. While he is brilliant and rightfully legendary, he’s also human. He’s a writer of masterpieces and a writer of mediocrity. Likewise, Favre deserves the role of gridiron legend and statesman. But he’s human. Only injury will prevent him from breaking Dan Marino’s touchdown record next season, and only injury will prevent him from breaking George Blanda’s interception record. But it’s likely we’ll remember Favre for his masterpieces, not his mistakes.

Peyton Manning: T.S. Eliot
Isn’t there something about Manning that makes you think he’s operating on a whole other level, and that he knows it? He may seem pleasant enough, but there’s something about him (and his game) that seems to be constantly aware that he’s better than everybody else. He’s a perfect match for the pretentious Eliot. In The Wasteland, Eliot was so full of himself that he included an appendix to explain all the literary allusions he tried to use. The problem is, many people had trouble understanding the appendix, too.

Rex Grossman: Emily Dickinson
This is an insult to Dickinson, but the way Grossman plays football reminds me of Dickinson’s style of poetry. She writes with hyphens, she’s elliptical, she jumps and starts and halts. Even though it’s lyrical poetry based in the form of the ballad, it’s hard to read smoothly. Sharp sounds, sharp halts, a sort of helter skelter movement that is often jarring. Isn’t that Rex? The fumbling, the interceptions, the craziness, with a few beautiful throws mixed in. Rex Grossman plays football like a Dickinson poem.

Edgerrin James: John Donne
John Donne really has two poetic careers. When he was young, he wrote clever metaphysical poetry that played with form and was often about sex. When he grew older, he wrote in a more conventional style and usually about religion. Edgerrin James looks like he’s having two NFL careers: one as a highly successful running back on a great offense, and one as an overpaid running back behind a bad offensive line.

Clinton Portis: Robert Browning
Robert Browning sort of invented a new type of poetry: the dramatic monologue. He wrote poems not from an authorial perspective, but as if he were a particular character (sometimes an historical or literary character). He played roles in his poetry. And will any of us forget Clinton Portis’s characters? Instead of speaking as a poet, Browning wrote behind a mask as another character; instead of speaking as an athlete, Clinton Portis put on masks, called himself names like “Dr. I Don’t Know” and “Sheriff Gonna Getcha” and pretended to be somebody else. Outstanding.

Tom Brady: Alfred Tennyson
As British Poet Laureate, Tennyson is one of the lucky (and fairly rare) poets to be a legend in his own time (Queen Victoria was his biggest fan). Brady, too, is treated like a legend in his own time: the winning quarterback of Super Bowls 36, 38, and 39, he was actually the official coin flipper of Super Bowl 40, an honor usually designated for legends of the past (Dan Marino flipped it for Super Bowl 41). Tom Brady: getting legend treatment mid-career.

Michael Vick: e. e. cummings
e. e. cumming’s poetry is unique and instantly recognizable: he ignores capitalization and plays wild and loose with spacing and stanzas (there’s a deliberate lack of discipline, it seems). Yet one wonders if his poetry is gimmicky and inferior. So too with Vick: unique and recognizable, but is he productive? We’re not sure.

Larry Johnson: Robert Herrick
“Gather ye rosebuds, while ye may,/ Old Time is still a-flying;” Herrick famously wrote. After being so overused by Herm Edwards (NFL record carries in 2006), we can wonder whether Larry Johnson will have many more rosebuds to gather.

Posted in General | 10 Comments »

Gray ink reflections

Posted by Doug on February 16, 2007

Two days ago I presented a gray ink test for football players. The name is borrowed from Bill James' analogous test for baseball players and the purpose of the thing is to put a single number on the quality and quantity of a particular player's league-leading or near-league-leading seasons. Having had a couple of days to wade through the lists and reflect upon them, I have a couple of thoughts.

First, I decided the system was potentially a little too sensitive to the particular stats of the #10 (or #5) player. If there is a huge gap between #9 and #10, or between #10 and #11, then the stats of the #10 guy don't really reflect what I think they're supposed to reflect, which is the approximate production of a guy in roughly that position. So I decided to smooth things out a little by averaging the stats of the 9, 10, and 11 guys to get the baseline #10 production. Likewise, I averaged the 4, 5, and 6 players when using a #5 baseline.

But that's pretty minor.

The major thing I noticed is that the really great seasons get a lot of credit. The point of this metric, of course, was to give credit to just those seasons, but I think it might go too far.

For example (working with receiving yards and a baseline of #10), Harold Carmichael's 1973 earns him 799 points while Chad Johnson's 2006 nets him 175. Both led the league in receiving, but one gets 624 points more than the other. I specifically said last time that its ability to distinguish between a truly great league-leading season (like Carmichael's) and a fairly weak league-leading season (Johnson in 2006 just happened to be at the top of a group of 6 guys separated by fewer than 100 yards) was one of the selling points of this method. But I'm wondering if I haven't overdone it.

And in 1978, Carmichael got 306 points for finishing third in the league in receiving. Isaac Bruce got roughly half that (158) for leading the league in receiving in 1996. Is that right? One could certainly argue that it is. Even though he led the league, Bruce was just a handful of catches from finishing out of the top 10, the fact that he was at the top of a homogeneous pack instead of in the middle or at the bottom is not very important. But still, he did lead the league.

While the lists produce a pretty nice mixture of receivers from all eras, I look at some of those 70s seasons --- like the Carmichael seasons mentioned above, Cliff Branch's 692 points in 1974, and Drew Pearson's 684 points for finishing second in the same season --- and wonder if they aren't being over-credited. In 1974, there were 26 teams, most of which only really utilized two receivers at the most. In 2006, there are 32 teams, many of which use several wide receivers extensively. The #10 receiver in 1974 was #10 of around 50 or 60 "meaningful" receivers, while the #10 receiver in 2006 is #10 of about 80. Am I wrong about this?

Posted in General | 16 Comments »

Gray ink

Posted by Doug on February 14, 2007

For the purpose of assessing baseball players' Hall of Fame chances, Bill James devised something he called the "Black Ink Test." It essentially counts how many times a player led the league in any important stat, with extra credit given for the most important stats, e.g. home runs. The name derives from the fact that league leading stats are printed in bold type in most baseball encyclopedias. James also developed the "Gray Ink Test," which is similar, but counts top ten performances instead of only league leading ones.

These tests are a bit simplistic and fail to adjust for certain things. Leading an 8-team league (in 1952) counts the same as leading a 16-team league (in 2006), to name just one. But it wasn't intended to be anything more than what it is: a quick way to summarize some important information in a single number.

Despite not generally being a fan of Hall of Fame-type debates, I've gotten sucked into a few of them recently. And it certainly would be handy to have a quick way to summarize the number and quality of a given player's outstanding seasons more easily than saying, "he never led the league in receiving yards, but he finished in the top five three times and in the top 10 seven times." And then how do you compare that to the guy who led the league twice, but only had two other top ten finishes?

So I decided to develop a quick gray ink test for football players. Here's how it goes. (Fantasy football players will recognize it as being very similar to VBD.)

Step 1: pick a stat and pick a baseline. I'll use receiving yards as the stat and #10 as the baseline throughout this post, but you could do the same thing with 5 or 12 or 20 and with whatever stat you like.

Step 2: for each season of the player's career, compare his stat to the baseline stat. If it's above the baseline, he gets credit for the difference, normalized so that all years' baseline stats are treated the same. Specifically, the player gets credit for

1000 * (PlayerYards - BaselineYards) / BaselineYards

points worth of gray ink. The 1000 there is arbitrary, but is intended to be a typical number for the 10th-ranked receiver (if we were doing TDs instead of yards, I'd choose something more like 10 instead of 1000). Essentially, what this calculation does is attempt to ensure that players from offense-happy eras are not not unduly rewarded by inflation of the raw numbers. My assumption is that a player who had 1200 yards when the baseline was 800 has accomplished as much as a player who had 1500 yards when the baseline was 1000. The above calculation gives both players the same number of points: 500.

Step 3: add up the gray ink points for each season of each player's career.

Again, this is by no means intended to be The One Stat Which Ends All Discussions. It's just a quick way of capturing the number and quality of a player's outstanding seasons. One thing I like about it is that it distinguishes between different levels of leading the league. Brett Favre led the league in passing TDs in 1995 and Dan Marino led the league in 1984, but Favre had only 16 more TD passes than the #10 guy, while Marino had 16 more TD tosses than the #2 guy and 29 more than the #10 guy. If you count them as being the same thing, you're losing information. Likewise, Terrell Davis finished 2nd in rushing yards in 1996, but only 15 yards behind the leader. Had he gotten another 16 yards during the season, it really would not have changed anything about how impressive or how valuable his performance was, but in many debates during the coming decades, it would have changed that performance from a "top five performance" to a "league leading performance."

Here are some wide receiver lists. They include all receivers who debuted in 1970 or later (I'm still not sure how to properly account for the much smaller leagues that were the norm before the merger).

Receiving yards, baseline #10, typical baseline receiver = 1000 yards

Jerry Rice 3501
Michael Irvin 1679
Marvin Harrison 1402
Cliff Branch 1301
James Lofton 1285
Sterling Sharpe 1237
Torry Holt 1223
Steve Largent 1204
Wes Chandler 1178
Harold Carmichael 1148
Randy Moss 975
Henry Ellard 965
Drew Pearson 945
Gary Clark 807
Jimmy Smith 780
Tim Brown 735
Andre Rison 731
Isaac Bruce 713
Dwight Clark 685
Chad Johnson 677
John Jefferson 671
Ken Burrough 656
Isaac Curtis 594
Herman Moore 579
Mike Quick 563
Wesley Walker 554
Roy Green 537
Mel Gray 491
Stanley Morgan 476
Drew Hill 472
Anquan Boldin 466
Cris Collinsworth 456
John Stallworth 446
Carlos Carson 444
Anthony Miller 439
Art Monk 436
Rod Smith 430

Receiving yards, baseline #5, typical baseline receiver = 1200 yards

Jerry Rice 2283
Michael Irvin 1013
Cliff Branch 897
Marvin Harrison 851
Harold Carmichael 701
Steve Largent 650
Drew Pearson 645
Henry Ellard 633
Wes Chandler 625
Sterling Sharpe 615
Torry Holt 601
Randy Moss 517
John Jefferson 454
Ken Burrough 435
Gary Clark 425
Dwight Clark 387
Wesley Walker 358
Isaac Bruce 346
James Lofton 335
Stanley Morgan 321
Jimmy Smith 276
Roger Carr 272
Mike Quick 260
Antonio Freeman 245
Rob Moore 244
Isaac Curtis 226
Andre Rison 214
David Boston 206
Herman Moore 201
Carlos Carson 190
Eric Moulds 188
Rod Smith 178
Roy Green 173
Mel Gray 166
JT Smith 155
Chad Johnson 142
John Stallworth 141

Receptions, baseline #10, typical baseline receiver = 70 receptions

Jerry Rice 197
Marvin Harrison 108
Steve Largent 100
Dwight Clark 99
Cris Carter 99
Sterling Sharpe 98
Art Monk 85
Harold Carmichael 84
JT Smith 78
Ahmad Rashad 75
Herman Moore 68
Al Toon 65
Drew Pearson 59
Michael Irvin 58
Andre Rison 58
Torry Holt 58
Haywood Jeffires 57
Bob Chandler 55
Jimmy Smith 47
Tim Brown 46
Wes Chandler 43
Cliff Branch 39
Andre Reed 38
Randy Moss 36
Reggie Rucker 35
John Jefferson 35
John Stallworth 35
Anquan Boldin 32
Gary Clark 32
Rod Smith 30
Cris Collinsworth 30
Lynn Swann 29
Pat Tilley 28
Hines Ward 28
Chad Johnson 26
Muhsin Muhammad 26

Receptions, baseline #5, typical baseline receiver = 80 receptions

Jerry Rice 103
Dwight Clark 75
Marvin Harrison 69
Sterling Sharpe 60
Art Monk 58
JT Smith 52
Harold Carmichael 42
Cris Carter 40
Steve Largent 36
Herman Moore 35
Al Toon 35
Ahmad Rashad 34
Bob Chandler 32
Jimmy Smith 31
Haywood Jeffires 26
Reggie Rucker 24
Torry Holt 24
Drew Pearson 21
Wes Chandler 20
Cris Collinsworth 20
Andre Rison 19
Terance Mathis 18
Randy Moss 18
Tim Brown 16
John Jefferson 15
Rod Smith 14
Michael Irvin 13
John Stallworth 13
Stanley Morgan 10
Rob Moore 10
Wally Francis 9
Hines Ward 9
Andre Johnson 9
Muhsin Muhammad 9
Anquan Boldin 9

Receiving TDs, baseline #10, typical baseline receiver = 8 TDs

Jerry Rice 67
Marvin Harrison 29
Terrell Owens 28
Randy Moss 27
Sterling Sharpe 26
Mark Clayton 26
Cris Carter 24
Cliff Branch 23
Andre Rison 20
Steve Largent 19
Mike Quick 17
John Jefferson 13
Roy Green 13
Harold Carmichael 13
John Stallworth 12
Carl Pickens 12
Sammy White 12
Wes Chandler 12
Isaac Curtis 10
Nat Moore 10
Antonio Freeman 9
Charlie Brown 9
Wesley Walker 9
Lynn Swann 8
Bob Chandler 8
Mark Duper 8
Rich Caster 8
Daryl Turner 8
Herman Moore 7
Isaac Bruce 7

Receiving TDs, baseline #5, typical baseline receiver = 10 TDs

Jerry Rice 47
Terrell Owens 22
Marvin Harrison 20
Randy Moss 19
Mark Clayton 15
Cliff Branch 14
Sterling Sharpe 13
Mike Quick 11
Andre Rison 10
Steve Largent 10
John Jefferson 10
Roy Green 9
Nat Moore 8
Wes Chandler 8
Cris Carter 6
Charlie Brown 6
Lynn Swann 5
Sammy White 5
John Stallworth 5
Alfred Jenkins 4
Steve Watson 4
Hines Ward 4
Isaac Curtis 4
Rich Caster 4
Carl Pickens 4
Michael Jackson 4
Tony Martin 4
Wesley Walker 4

Posted in General | 14 Comments »

Worst receiver ever to have a 1000-yard season

Posted by Doug on February 13, 2007

This story from a few weeks ago indicates that Ashley Lelie has voided his contract and is now a free agent. I took a look at his numbers and was surprised to (re-)discover that Lelie had 1084 yards and seven touchdowns just two short years ago.

Immediately the title of this post popped into my head. I knew the answer probably wasn't Lelie, but I figured it would be a fun query to run, so I ran it. After Lelie, the next name that came to mind was Charles Johnson.

I took all receivers who had a 1000-yard season and played for at least four seasons. Then I found the ones who had the lowest average of their second-, third-, and fourth-best seasons. Lelie's best four seasons, for instance have been 1084, 770, 628, and 525. So his three-next-best average is 641. I found 20 receivers with lower three-next-best averages that that. Some of these guys probably shouldn't be on any kind of "worst wide receivers" list, but they ended up here anyway for one reason or another.

So don't think this is the definitive list. But here it is anyway, for you to use as a guide in your search for the animal described in the post's title. Personally, I think Nate Burleson is making a strong bid for the crown. Albert Connell might have a case too.

Patrick Jeffers 1082 330 127 24
Nate Burleson 1006 455 328 192
Pat Studstill 1266 479 389 252
Germane Crowell 1338 464 430 289
Brandon Stokley 1077 543 357 344
Charley Frazier 1129 717 381 306
Albert Connell 1132 762 451 191
R.C. Owens 1032 620 532 395
Marlin Briscoe 1036 603 532 447
Willie Jackson 1046 589 523 486
Dick Gordon 1026 610 534 477
Bob Boyd 1212 586 548 534
Stacey Bailey 1138 881 437 364
Bruce Hill 1040 673 641 403
Bob Mann 1014 696 560 517
Eric Metcalf 1189 614 599 576
Bake Turner 1009 974 428 402
Earnest Gray 1139 777 537 529
Tim Smith 1176 1141 660 72
Marcus Robinson 1400 738 657 515
Ashley Lelie 1084 770 628 525
Koren Robinson 1240 896 536 495
Bill Groman 1473 1175 437 328
Michael Westbrook 1191 736 664 559
Drew Bennett 1247 738 737 504
Rod Gardner 1006 741 650 600
Jim Benton 1067 981 511 505
Wally Francis 1013 862 695 441
Charlie Brown 1225 918 690 412
Lionel Manuel 1029 859 619 545
Charles Johnson 1008 815 642 577

Posted in General | 19 Comments »

Favre vs. Marino

Posted by Doug on February 12, 2007

There is currently a thread, and accompanying poll, on that topic at the footballguys message board. If you were starting a team from scratch right now and you could have either of those two as your quarterback, knowing you'd get 240 games out of him in his career, which one would you take? The poll is extremely close (98-96 in favor of Favre last I checked), and I must admit to not having had any idea which way to lean without doing some research.

But research I did, so off we go....

The Raw Numbers

Since the shapes of Marino's and Favre's careers are so similar, the short-brilliant-career vs. long-steady-career debate isn't really an issue. Their numbers of top five and top ten finishes in passing yards and passing touchdowns are very close. So let's hop straight to the totals.

Favre 8024 57500 414 273 61.1 7.0 6.0 85.0
Marino 8358 61361 420 252 59.4 7.3 6.5 86.4

Rate is the NFL's passer rating, and Marino has the slightest of edges there. AdjYPA is adjusted yards per attempt, which was developed by Pete Palmer et al in The Hidden Game of Football. The formula is (yards + 10*TDs - 45*INTs)/attempts, and the motivation is that their (copious) research indicated that an interception was worth about the same as 45 yards, and that a TD --- or more precisely, the difference between a TD and having the ball at the one --- is worth about 10 yards. If I could only have one stat, I'd want adjusted yards per pass, and Marino has a not inconsequential advantage in that stat. Fortunately, though, we don't have to limit ourselves to just one stat.

The Context

It's not as though wholesale changes have occurred, but passing numbers have, in some categories, crept up slowly since Marino came into the league. Here are the league averages in adjusted yards per attempt, passer rating, touchdown percentage, and interception percentage, since Marino's rookie year:

Year AYPA Rate TD% INT%
1983 5.64 75.8 4.37 4.37
1984 5.73 76.1 4.24 4.05
1985 5.58 73.5 4.11 4.17
1986 5.59 74.1 3.99 3.99
1987 5.73 76.5 4.57 3.90
1988 5.54 73.0 3.93 3.91
1989 5.81 75.8 4.04 3.86
1990 5.83 77.3 4.21 3.53
1991 5.69 76.4 3.66 3.49
1992 5.51 75.4 3.84 3.85
1993 5.59 76.7 3.57 3.23
1994 5.74 78.5 3.85 3.13
1995 5.79 79.3 3.96 3.05
1996 5.54 76.8 3.90 3.39
1997 5.71 77.1 3.89 3.03
1998 5.79 78.2 4.21 3.28
1999 5.63 77.0 3.95 3.36
2000 5.68 78.2 3.88 3.23
2001 5.65 78.5 3.88 3.34
2002 5.75 80.4 3.97 3.04
2003 5.57 78.4 3.95 3.24
2004 6.07 82.9 4.44 3.18
2005 5.79 80.0 3.89 3.09
2006 5.82 80.4 3.93 3.15

If you take a weighted average --- weighted by Marino's number of passing attempts during each season --- of the league passer rating numbers, you can conclude that a completely average quarterback would have compiled a passer rating of 76.2 given the attempts that Marino had. So Marino's rating of 86.4 is about 10.2 points better than average. A similar exercise with Favre pegs him at about 6.5 points better than average. Here is the summary:

Brett Favre 78.58 85.04 +6.47
Dan Marino 76.23 86.38 +10.15

Here is a similar table for touchdown percentage:

Brett Favre 3.94 5.03 +1.09
Dan Marino 4.02 5.03 +1.00

and interception percentage:

Brett Favre 3.23 3.32 +0.09
Dan Marino 3.63 3.02 -0.62

That right there is the biggest issue that Favre-backers have to explain. That amounts to about 3 or 4 interceptions per year, which is nontrivial. The AYPA table, which summarizes all this data, looks like this:

Brett Favre 5.71 6.00 +0.29
Dan Marino 5.68 6.49 +0.81

Half a yard per attempt is a significant difference. Several months back, Chase used this methodology to rank the best and worst quarterbacks of all time. In this post, he essentially translated the above data into a total yardage figure, and the results are shown here.

Player Name Value Career Attempts
Steve Young 7103 4149
Dan Marino 6752 8358
Joe Montana 6634 5391
Roger Staubach 5286 2911
Ken Anderson 5135 4475
Dan Fouts 5017 5604
Peyton Manning 4927 4333
Trent Green 3788 3329
Kurt Warner 3487 2340
Fran Tarkenton 3401 3445
John Elway 3155 7250
Bob Griese 3116 2491
Warren Moon 2908 6823
Jim Kelly 2885 4779
Brett Favre 2672 7612

The units on the Value column are yards. Marino was 6752 yards above average during his career and Favre was 2672 yards above average. That 4000-yard difference translates to about 320 points, roughly 20 points per year. This was before the 2006 season, but Favre's numbers were near average, so it wouldn't change his ranking much.

Frankly, most of what I wrote above could be replaced with a link to Chase's old post. But I decided to look at a variety of stats for the benefit of those people who don't happen to appreciate AYPA.

To summarize: while the raw numbers look extremely similar, the context is just different enough, and the fairly small edge Marino has in almost every category turns out to add up to a sizable difference. Twenty points per year is significant.

That's what the numbers say. Anyone arguing for Favre, then, must argue that the numbers aren't telling the whole story, and there are a few arguments there that seem to have some merit. Let's examine them.

[Prediction inserted here for my amusement: I predict that someone will find this post via a google search, read the first few lines, and then post a comment along these lines. "There's more to it than numbers!!!!11 Marino played with two great receivers and Favre played with a bunch of nobodies!!111 Also Favre won a ring!!!"]

Possible arguments for Favre

1. Marino had a better supporting cast (on offense)

Popular perception has it that Marino's wide receivers --- in particular, Mark Clayton and Mark Duper --- were better than Favre's. You'll often hear it said that Favre turned nobodies like Robert Brooks, Antonio Freeman, and even Bill Schroeder into great receivers. And I think there is something to that.

My reaction to that, though, is to point out that the same might be true of Duper and Clayton. They never did anything without Marino. Of course they never had the chance, but the point is that their numbers are entirely consistent with them being merely good receivers who happened to have one of the greatest quarterbacks of all time throwing to them. Do we really know that Duper and Clayton are better than Robert Brooks and Antonio Freeman?

It's impossible to say, but I think there is some evidence that Duper and Clayton really were very good. First, they decisively took their jobs, each in their second year, from Nat Moore and Duriel Harris, who were good and decent, respectively, though they were getting a bit old. Second, even into their thirties they kept Tony Martin on the bench for the first four years of his career, and Martin went on to have 1000-yard seasons in three different locations (including Miam at age 34). Now, lots of receivers are kept on the bench for all sorts of reasons --- Derrick Alexander kept Joe Horn on the bench in Kansas City, for instance, but no one would argue that Alexander was better than Horn --- so I'm not claiming this is any sort of decisive evidence. But we just don't have much to go on here, so I'm trying to examine every clue I can find.

Favre also worked with receivers who had success without Favre, namely Sterling Sharpe and Javon Walker. But he only got three years with Sharpe and three years with Walker, and none of those years were in Favre's prime. Marino got almost twenty combined years --- and all of his prime --- with Duper and Clayton. Others we haven't yet mentioned? Donald Driver seems to be pretty good, but not better than Irving Fryar, who had a couple of 1000-yard seasons in his mid-thirties with Ty Detmer throwing to him in Philadelphia.

Favre's tight ends perhaps rate a slight edge over Marino's, but I don't think that's clear. Both had good pass-catching backs at their disposal.

What about offensive lines? Favre played with three Pro Bowl offensive linemen: Mike Flanagan, Marco Rivera, and Frank Winters. Marino played with at least one Pro Bowler on the line almost every season of his career. Early on it was Bob Kuechenberg and Dwight Stephenson. Later it was Keith Sims and Richmond Webb. Because of this research that I did on Pro Bowl retention rates, I really don't have a lot of faith in number of Pro Bowl selections as a proxy for quality. I frankly have no idea how to compare the quality of Favre's offensive lines to those of Marino, and I'm suspicious of anyone that claims he can, unless that someone happens to have a lot of game films and a well-trained eye. But really, our only two choices are (1) throw up our hands and say that offensive line comparisons are off limits, or (2) go by reputation. If you want to go with (2), then Marino's supporting cast rates the edge here.

So I do think that this argument has merit. The evidence we have is highly ambiguous as usual, but I do think it helps Favre's case.

2. Favre was less one-dimensional / more mobile / better at improvising

This one I don't buy. If you're talking about Steve Young or Randall Cunningham or Michael Vick --- guys who can pick up 500+ yards rushing in a season --- then OK. Mobility has to enter the discussion. But Favre's career high was 216 rushing yards.

Now, anyone who watched Favre in his prime knows that he was indeed a master at keeping plays alive with his feet. I don't dispute that at all. But here's the thing: after he kept those plays alive with his feet, he passed the ball to a receiver, and that appears in his stat line. He's already been given credit for the pass. To give him additional credit for the mobility is double-counting.

Favre's mobility helped Favre produce better passing numbers than he would have if he wasn't mobile. Of that there is no doubt. But Favre's mobility did not allow him to produce better passing numbers than Marino. If you want to give credit to Favre for mobility, then you have to give credit to Marino for being taller. In each case, it's just one of the many attributes that helped these guys to be the great passers they were.

Another thing that needs mentioning here is Marino's own mobility, which was admittedly more subtle, but no less important. In about the same number of pass attempts, Favre was sacked 174 more times than Marino was. You can debate how much of that is due to the quarterback and how much is due to the line, but the quarterback has to be given some credit for it. Consider this: Troy Aikman, a great quarterback playing behind what is widely regarded as one of the best offensive lines in history, had a sack rate of 4.4% from 1992--1995. Marino's career sack rate was 3.1%.

If there is any edge in this category, it goes to Marino.

3. Favre won a ring and Marino didn't

As we all know, this begins and ends the discussion for many people.

Chase has a theory for why people are so blinded by the rings. I'm sure he'll chime in to correct me if I misstate it, but it goes something like this. The reason rings are overvalued in discussions like this is because people confuse the question "would you rather have been a fan of Favre's actual team during Favre's actual career or Marino's actual team during Marino's actual career?" with the question "which guy played better during his career?"

To put it another way, people interpret the question "which guy was better?" to mean "which guy would you rather have been?"

To suggest that Marino did not have the ability to lead a team to a Super Bowl championship seems as absurd as suggesting that Favre lost that same ability between the 1996 and 1997 seasons, never to regain it again. We have seen time and time again that players who have that alleged ability seem to have it right up until the point when they lose it, and that players who don't have it often seem quite capable of acquiring it with no advance warning. We saw that just last week.

Is there anyone who honestly believes that Marino, with the help of the NFL's best defense and with Desmond Howard chipping in over 200 return yards, couldn't have beaten the 1996 Patriots if given the chance?

My vote


Marino has slightly, but clearly, better numbers. Marino's ability to avoid sacks adds to that edge a little bit. Marino's failure to win a ring shouldn't enter into it at all. The only reasonable argument for Favre, in my view, is that he would have posted better numbers than Marino had he had Marino's supporting cast. It's going to be subjective, as always, but the objective parts of the argument are so close that I really can't fault anyone for voting for Favre on that basis.

Posted in General | 35 Comments »

Declining a touchdown

Posted by Doug on February 8, 2007

A few days after Boise State's Fiesta Bowl win over Oklahoma, I got an email from a reader named Dan who had a question about endgame strategy.

Here is the situation:

Tie game. Boise State ball on their own 25. 1:16 to play. Boise has two time outs remaining. On the first play, Bronco quarterback Jared Zabransky threw an interception which Sooner defensive back Marcus Walker returned for a touchdown.

As we all know, Boise came back to win the game, but that's neither here nor there. Dan's thoughts:

It has long been my contention that in situations like these, instead of scoring on that interception TD, Oklahoma should have gone out at the 1 (or the 1-inch line or whatever). Then, run the time down (or at least force Boise to use its timeouts - they had 2 left) and punch it in. Everyone I talk to says that this is lunacy - that you have to "TAKE THE POINTS!" (caps added since usually they are yelling it at me). But I think it is far from an obvious decision. Especially in a case like this when even if you just kneel it down a few times, a FG still wins the game.

From a strict win-probability-maximization standpoint, my intuition tells me that Dan is right. Let's walk through it. What if Walker had stepped out at the one inch line?

Since Boise had two timeouts remaining, the Sooners could have run three kneel-downs and then tried a chip-shot field goal on the last play of the game. Using that strategy, their probability of winning has to be about 98% (I'm estimating a 96% chance of making the field goal, and a 50% chance of winning in overtime after missing the field goal.) Using the strategy they actually used --- i.e. scoring the TD --- they were giving the Broncos the ball with two timeouts and 1:00 to play, down 7. If Boise's touchdown probability on such a drive is 4%, then the Sooners would have the same 98% chance of winning the game. If it's less than 4%, they'd be better off scoring the TD. If it's greater than 4%, they'd be better off not scoring it.

To generalize, here is the rule:

If your chance of making a 20-yard field goal is better than your chance of stopping your opponent from scoring a TD with 1:00 minute left and two timeouts, then step out. Otherwise, score the TD.

Frankly, both of those are such gimmes that it's tough for me to estimate which is greater. Unless your defense or your kicker is really, really terrible, you're never going to be able to estimate either of these probabilities with sufficient accuracy to be confident that one is greater than the other.

But the strategy I outlined above (three kneel-downs and a field goal) isn't OU's only option. They could have run two kneel-downs, forcing Boise to use its last two timeouts, then tried to score a touchdown on third down, and kick on fourth if that failed. With that strategy, the possibilities are as follows:

Score the TD on 3rd down. Give the ball back to Boise with about :45 remaining, no timeouts, and a seven-point deficit.

Fail to score, try the field goal on 4th down. Assuming your third-down play was a run, you're trying the field goal on the last play of the game. If your third-down play was an incomplete pass, you're trying the kick with about :40 remaining.

Turn the ball over on third down. Give the ball back to Boise with :40 remaining, no timeouts, and a tie game.

In the first case, you're not that much better off than you would be if you had scored the TD in the first place. In the second case, you're not better off than you would be if you just took a knee on third down, which I opined above isn't better than scoring the TD in the first place. And the turnover, of course, is disastrous.

So based on this admittedly thin analysis, I don't see much advantage in stepping out.

But this all changes if Boise has more --- or fewer --- than two timeouts remaining.

If they have three timeouts, then the only advantage of not scoring the TD is that you can force them to use all three of their timeouts and use about 10 seconds of their clock. That's not nothing, but I don't think it's worth the risk.

If they have no timeouts remaining (and you do), then you take a knee on first down. This runs the clock down to about :15. Now you take two shots at the end zone, and then kick a field goal on fourth if necessary. This probably gives you a better win probability than if you had simply scored the touchdown in the first place.

Now, if the time remaining when you made the interception was more like 2:00 instead of 1:00, then this could all start to look very different.

But what does seem clear to me that a loss caused by a purposeful decision not to score a free touchdown is unquestionably much, much worse than a regular loss. That's the kind of thing that could ruin a season, or a coach's or player's career. Further, the line is so fine between situations where this might make sense and situations where it doesn't that it would be mighty tough to give your defensive players clear instructions in August when you're reviewing fundamentals.

The bottom line is that, while I agree with Dan that it's not lunacy to consider the possibility, if you score the TD your win probability is in the 90s, probably the high 90s. There just isn't a lot of upside to getting cute.

But there is a situation where I think there is upside to declining a touchdown in this way, and that's the same situation but up one instead of tied. Had OU been up by one point at the time of the interception, then scoring the touchdown makes the lead eight --- still a one-score game --- and gives Boise the ball back, whereas stepping out of bounds at the one-inch line would have literally ended the game. Well, OK, not literally literally, but you know what I mean.

Posted in General | 19 Comments »