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Archive for June, 2006

Ahman Green and Deuce McAllister

Posted by Doug on June 30, 2006

The topic of Ahman Green and Deuce McAllister came up in the comments to this post on running back deterioration. I am going to set aside the particulars of their team situations (e.g. the Reggie Bush factor) and just take a quick look at what the historical data says about running backs coming back from significant injuries. Specifically, I found all running backs since 1970 who:


  • Finished in the fantasy top 20 for two straight years, and then. . .

  • Missed at least half the games in the following season. . .

  • at age 26 through 29 (Green was 28 last year and McAllister was 27)

Then I checked to see what the rest of their careers looked like. YR is the year of the injury-plagued season, age is the player's age for the next season, and the numbers shown are the player's fantasy rank among all running backs during the given year. To get your bearings, check out the Terrell Davis line. He was the #2 ranked running back, then he was the #1 running back, then he got hurt and ranked #77. The following two years he ranked 58th and 46th.


Player YR age N-2 N-1 N N+1 N+2 N+3 N+4 N+5 N+6
===============================+=====================================
Ahman Green 2005 29 | 2 13 69
Deuce McAllister 2005 28 | 7 17 54
Terrell Davis 1999 28 | 2 1 77 58 46
Jamal Anderson 1999 28 | 10 2 119 22 65
Raymont Harris 1998 29 | 20 15 71 121
Dorsey Levens 1998 29 | 19 3 51 6 49 71 50 70 42
Greg Bell 1990 29 | 4 7 96
Dalton Hilliard 1990 27 | 16 1 68 48 18 55
Marcus Allen 1989 30 | 10 15 60 13 59 46 5 19 24
Billy Sims 1984 30 | 10 15 25
Wilbert Montgomery 1983 30 | 6 6 102 19 83
Sherman Smith 1980 27 | 17 7 118 43 51 107
Greg Pruitt 1979 29 | 8 20 88 51 38 97 94 135
Lawrence McCutcheon 1978 29 | 5 4 72 101 75 119
Marv Hubbard 1975 30 | 16 17 73 108
Essex Johnson 1974 29 | 16 8 108 74 75
Mercury Morris 1974 28 | 7 10 80 25 83

On one hand, there is very little historical precedent for someone in a situation like the one Green and McAllister find themselves in to return all the way to their peak production. But that's probably true of anyone in that age group who was once a top-10 back and then had a large dropoff for any reason.

On the other hand, they don't have to return to their peak production, or even anywhere close to it, in order to be worth the price you'll pay for them in a fantasy league. Footballguys.com currently has McAllister and Green ranked 24th and 32nd, respectively, for redraft leagues and 22nd and 33rd for keeper leagues. Of the players on the list above who actually played the next year, nearly half of them were able to turn in seasons at or above that level.

I'm guessing that the fantasy football market, as usual, is pricing these guys pretty accurately right now.

8 Comments | Posted in Fantasy, General

Ten thousand seasons with no standards

Posted by Doug on June 29, 2006

In case you just stumbled in today, this post is the latest in a long string. Read these first: I, II, III, IV, V.

I got into a conversation yesterday with one of the two readers of this blog who I actually see in person on a regular basis. I conjectured, based on yesterday's results, that, assuming we keep the eight four-team divisions and demand that the winners of those divisions get seeds one through four in the playoffs, the current system (two wildcards) is the one that maximizes the chances of the best team in football ending up with the Lombardi Trophy. My reasoning: if you eliminate the wildcard, you will too often shut the best team out of the playoffs altogether (we saw this in yesterday's post). And if you have more than two wildcards, you will too often make the best team navigate an extra round of playoffs.

My friend then made this bold claim:

I'll bet that if you let all 16 teams from each conference into the tournament, then the best team's chances of winning it all would be greater than they are with the current system.

At first I thought this was ridiculous, but it didn't take too much thought to realize that he might be right. For one thing, letting everyone in would guarantee that the best team actually makes the playoffs. And in the usual case, where they win their division and post a good record, all it really does is add a game against the 16th seed and a game against the 8th or 9th seed. Not too much different from a couple of byes. Sure, there is a slim chance of an upset. But there is also a chance of an upset that knocks off the best team's toughest competition.

Only one way to find out.

I'm going to apologize in advance for the lack of decent formatting. I just don't have time to get it done the way it ought to be done. So it's going to be long and unwieldy. I will look at four different playoff formats, two of which will be review. For each one, I'll show the number of times (out of 10,000) that the true #1 team in the NFL won the Super Bowl, the number of times the true #2 won it, and so on. Then, I'll show how often the Super Bowl winner had each given number of regular season wins. I'll add some brief thoughts at the end.

The current system: two wildcards


Tm# SBwins Cumulative
=====================
1 2399 2399
2 1441 3840
3 1064 4904
4 826 5730
5 652 6382
6 559 6941
7 492 7433
8 386 7819
9 312 8131
10 293 8424
11 231 8655
12 210 8865
13 176 9041
14 162 9203
15 138 9341
16 120 9461
17 100 9561
18 73 9634
19 83 9717
20 58 9775
21 44 9819
22 50 9869
23 38 9907
24 24 9931
25 21 9952
26 14 9966
27 9 9975
28 12 9987
29 4 9991
30 8 9999
31 1 10000
32 0 10000


Wins Times Cumulative
======================
6 2 2
7 7 9
8 150 159
9 651 810
10 1528 2338
11 2413 4751
12 2502 7253
13 1674 8927
14 822 9749
15 214 9963
16 37 10000

If you can see that the 4th-best team in football won the Super Bowl 8.26% of the time, that a 9-7 team won the Super Bowl 6.51% of the time, and that one of the top four teams in football won it 57.3% of the time, then you're reading the tables right. You'll note that I've added a cumulative column to make things a bit easier to summarize. You'll also note that the numbers don't match those shown in the original posts. That's due to random variation, of course. Although, amazingly, the top team won exactly 2399 out of each run of 10,000.

No wildcards - four division winners play a standard tournament


Tm# SBwins Cumulative
=====================
1 2315 2315
2 1448 3763
3 1039 4802
4 853 5655
5 625 6280
6 533 6813
7 499 7312
8 406 7718
9 308 8026
10 288 8314
11 249 8563
12 228 8791
13 191 8982
14 162 9144
15 167 9311
16 96 9407
17 104 9511
18 88 9599
19 80 9679
20 55 9734
21 54 9788
22 53 9841
23 32 9873
24 32 9905
25 27 9932
26 15 9947
27 18 9965
28 15 9980
29 9 9989
30 7 9996
31 4 10000
32 0 10000


Wins Times Cumulative
======================
6 1 1
7 17 18
8 158 176
9 711 887
10 1600 2487
11 2368 4855
12 2462 7317
13 1607 8924
14 797 9721
15 242 9963
16 37 10000

Four wildcards - division winners get seeds 1 through 4, four next-best teams regardless of division get seeds 5--8. Straight 8-team tournament with no re-seeding between rounds.


Tm# SBwins Cumulative
=====================
1 2285 2285
2 1411 3696
3 1006 4702
4 795 5497
5 689 6186
6 572 6758
7 488 7246
8 400 7646
9 362 8008
10 311 8319
11 260 8579
12 217 8796
13 194 8990
14 156 9146
15 130 9276
16 136 9412
17 100 9512
18 74 9586
19 84 9670
20 72 9742
21 55 9797
22 52 9849
23 31 9880
24 34 9914
25 18 9932
26 26 9958
27 19 9977
28 9 9986
29 7 9993
30 5 9998
31 1 9999
32 1 10000


Wins Times Cumulative
======================
7 37 37
8 507 544
9 1239 1783
10 1874 3657
11 2099 5756
12 2032 7788
13 1335 9123
14 623 9746
15 223 9969
16 31 10000

Twelve wildcards (i.e. all teams make playoffs) - division winners get seeds 1 through 4. Straight 16-team tournament with no re-seeding between rounds.


Tm# SBwins Cumulative
=====================
1 2111 2111
2 1318 3429
3 999 4428
4 804 5232
5 635 5867
6 559 6426
7 489 6915
8 372 7287
9 344 7631
10 322 7953
11 268 8221
12 249 8470
13 189 8659
14 200 8859
15 159 9018
16 150 9168
17 147 9315
18 132 9447
19 106 9553
20 74 9627
21 79 9706
22 64 9770
23 56 9826
24 36 9862
25 41 9903
26 22 9925
27 27 9952
28 17 9969
29 13 9982
30 8 9990
31 5 9995
32 5 10000


Wins Times Cumulative
======================
2 2 2
3 4 6
4 23 29
5 83 112
6 151 263
7 358 621
8 728 1349
9 1296 2645
10 1686 4331
11 1889 6220
12 1807 8027
13 1209 9236
14 552 9788
15 176 9964
16 36 10000

Thoughts:


  • I am floored by how little the playoff format seems to matter.

  • While it doesn't matter much "morally," the 16-team free-for-all would lead to some embarrassment, as a .500-or-worse team would be a near-lock to win the Super Bowl every fifteen years or so. You probably noticed some 2-14 and 3-13 teams winning Super Bowls in that format. Those were really strange seasons, but a 6-10 Super Bowl winner would be a real possibility.

  • If we re-seeded between rounds of the 16-team free-for-all, I bet the best team would win more than 24% of the time.

8 Comments | Posted in Statgeekery

Ten thousand seasons with no wildcards

Posted by Doug on June 28, 2006

A few weeks ago, I did several posts (I, II, III, IV) on the idea of simulating a bunch of NFL seasons and seeing what kind of crazy stuff happens.

I had intended to play Tagliabue and implement various alternative playoff systems, then observe how things played out. Programming new playoff formats turned out to be tougher than I expected, so I tabled it.

But now I have finally gotten around to implementing at least one: in this post I'm going to eliminate the wildcard. Byes are no more and the eight division winners will play a standard tournament.

My first reaction would be to suspect that the more teams you let in the playoffs, the more you decrease the chance of the best team winning it. Therefore I'd guess that the wildcard reduces the chance of the best team winning it all. But it's not clear. In baseball, the wildcard adds an extra playoff round for every team, but that's not necessarily so in football. If the best team is a #1 or #2 seed, then the existence of wildcard teams doesn't affect their chances much. They still just have to win three games. If the best team is a #5 or #6 seed, then the existence of the wildcard obviously increases their chances, from zero to nonzero. So the only scenario in which the wildcard system decreases the best team's chances is if they are the #3 or #4 seed.

Let's recall how often the best team wins in the current format. If you believe the model, it's about 24% of the time. The second-best team wins about 14.5% of the time. In ten thousand runs, this is how often each of the top ten teams won the Super Bowl:


Tm# SBwins
==========
1 2399
2 1448
3 1060
4 846
5 670
6 584
7 464
8 388
9 327
10 285

Here's how it goes with no wildcards:


Tm# SBwins
==========
1 2246
2 1431
3 1074
4 827
5 625
6 562
7 488
8 386
9 334
10 294

Almost no change at all. That's remarkable. Whether you think 23% is too high or too low, everyone ought to favor the current wildcard system. It gives us four extra postseason games every year without meaningfully altering the chances of the best team winning. Well done, NFL.

I'll bet if we added two more wildcard teams and turned the postseason into a 16-team tourney, the best team's chances would plummet. I'll put that on the to-do list.

16 Comments | Posted in Statgeekery

This post is untitled

Posted by Doug on June 27, 2006

It's a shame I have standards, because "Splits Happen" would be a perfect title for it.

This post is just a quick reminder that random variation is capable of making splits appear for no reason at all. Therefore, when you see that a player or team shows a striking split, you don't have to find an explanation for it. There may not be one. Let me prove it.

Steve Smith 2005 vs. teams whose name ends with a consonant


WK Opponent Fant Pts
=================================
1 New Orleans 19.8
2 New England 3.4
4 Green Bay 1.2
6 Detroit 18.3
9 Tampa Bay 16.6
10 New York 3.4
14 Tampa Bay 10.3
15 New Orleans 22.5
16 Dallas 1.8
=================================
AVERAGE 10.8

Steve Smith 2005 vs. vowel-ending teams


WK Opponent Fant Pts
=================================
3 Miami 34.8
5 Arizona 23.9
8 Minnesota 26.1
11 Chicago 16.9
12 Buffalo 5.5
13 Atlanta 12.5
17 Atlanta 19.8
=================================
AVERAGE 19.9

Smith was about 10 points per game better against the vowel-ending squads. You could argue that the vowel-enders just happened to be bad defenses last year, but they really weren't. And anyway, there were plenty of receivers who did better last season against the consonant teams.

Here's another one.

Cadillac Williams 2005 vs. teams whose names have 9 or fewer letters


WK Opponent Fant Pts
=================================
1 Minnesota 20.8
2 Buffalo 18.8
3 Green Bay 15.8
4 Detroit 1.9
9 Carolina 5.4
11 Atlanta 18.9
12 Chicago 9.1
14 Carolina 23.6
16 Atlanta 22.0
=================================
AVERAGE 15.1

Cadillac Williams 2005 vs. long-name teams


WK Opponent Fant Pts
=================================
8 San Francisco 2.5
10 Washington 2.0
13 New Orleans 10.3
15 New England 2.7
17 New Orleans 8.1
=================================
AVERAGE 5.1

I'm sure you've got the point by now, but this is kind of fun. One more.

LaDainian Tomlinson 2005 vs. teams A--M


WK Opponent Fant Pts
=================================
1 Dallas 13.2
2 Denver 17.2
8 Kansas City 14.0
11 Buffalo 14.9
14 Miami 7.5
15 Indianapolis 8.5
16 Kansas City 6.5
17 Denver 15.6
=================================
AVERAGE 15.3

LaDainian Tomlinson 2005 vs. teams N--Z


WK Opponent Fant Pts
=================================
3 New York 45.3
4 New England 28.8
5 Pittsburgh 19.0
6 Oakland 34.1
7 Philadelphia 3.3
9 New York 39.3
12 Washington 39.3
13 Oakland 11.0
=================================
AVERAGE 27.5

LaMont Jordan was almost 10 points per game better at home than on the road last year. Peyton Manning was a lot better on the road. Rudi Johnson dominated in the second half of the year while Willis McGahee was much stronger early in the year. Hines Ward was essentially owned by his division foes in 2004, but he had huge numbers against them in 2005.

Do these facts mean anything? Maybe. But the point is: maybe not. I am not trying to convince you to ignore splits altogether --- in some situations they may be meaningful. I am just reminding you that you needn't force-fit some theory to explain the splits you see. There may simply be no explanation.

12 Comments | Posted in Statgeekery

Running back deterioration III

Posted by Doug on June 26, 2006

For reference, Running back deterioration I and Running back deterioration II.

The general question we want to answer here is: assuming age and talent are equal, does previous workload help us predict future career length?

There is a mathematical technique called regression whose exact purpose is to answer questions like this. Suppose Factors A, B, and C play a role in determining Quantity D. Assuming you've got enough past data and assuming certain technical conditions are met, regression will give you a formula that tells you how to take a known A, B, and C and use them to predict the value of Quantity D.

And that's exactly what we want to do. We want a formula that will predict the future career length of a back given his his level of quality and his previous workload. The formula we get will tell us how important previous workload is (if at all).

The big problem here is that we can't just input each running back's "level of quality" into the formula. We have to decide on how to measure this. I'm going to use career-to-date VBD value as my measure of quality. While not perfect, I believe it does a pretty decent job of giving us a rough estimate of a running back's quality.

So I took all running back seasons since 1978 by running backs age 27 or older, and I recorded the following data:


  1. His VBD value for that year
  2. His career VBD prior to that year
  3. His career workload prior to that year
  4. His age
  5. The number of career rushes he had after that season

I plugged all that data into the computer and it spit out the following formula:

Future rushes =~ 3203 - 104*age + 2.3*VBDLastYr + .813*PreviousVBD - .13*PreviousRsh

For the purposes of this discussion, the key number is the -.13. It says: all else equal, every rushing attempt you had before last year will cost you .13 predicted future rushes. So if two backs are completely equal in every way, but one of them had an extra 500 rushes when he was young, you would expect the player with the higher workload to have 500*.13 = 65 fewer rushes during the rest of his career. The 104 next to "age" indicates that, all else equal, a player who is one year older will expect to have 104 fewer carries left in the tank. Combining these two numbers, we could infer that it would take about 800 previous rushes to age a back as much as one chronological year does.

Just for grins, let's see what this formula predicts for some of today's backs. The formula was created using data from backs who had completed their age 27 season, had at least 100 rushes the previous season, and at least 400 rushes prior to that, so we should only apply it to players meeting those conditions. Here they are:


Proj Fut.
Player Age rushes
=================================
Shaun Alexander 29 973
Edgerrin James 28 946
Tiki Barber 31 636
Thomas Jones 28 624
Ricky Williams 29 564
Fred Taylor 30 486
Michael Bennett 28 467
Marcel Shipp 28 466
Warrick Dunn 31 350
Priest Holmes 33 318
Curtis Martin 33 291
Corey Dillon 32 217
Stephen Davis 32 140
Mike Anderson 33 105

You might think that Alexander's projection of 973 future rushing attempts seems a little low, and you might think Edgerrin James' 946 seems even lower. But remember that this isn't supposed to be interpreted as the most likely outcome. Rather, it's an expected value, or a weighted average. The formula is not saying, "I project Shaun Alexander to have 973 more rushes in his career." It's saying something closer to, "there is some chance that Alexander will suffer a catastrophic injury early next year and never play again, there is some chance that he will lose effectiveness and only play for two more unimpressive seasons, there is some chance that he will play five more seasons, and there is some chance that he will play eight more seasons and shatter Emmitt Smith's rushing record. When I average these possible outcomes together, taking into account my best guess at the probabilities of each, I get 973 future rushes."

In some ways, the formula seems smart. Even though Thomas Jones is three years younger than Tiki Barber, the formula "recongizes" that Barber has a much longer history of excellence than Jones does, and so it projects him to get more future carries. Of course, the formula doesn't really recognize anything; it doesn't know Thomas Jones from a hole in the ground (or even from a binary string of 1s and 0s that represents a hole in the ground). All it's doing is attempting to predict the future in the way that best mimics the past. The past data we fed into the computer said that, in general, players who didn't accumulate much value earlier in their career --- like Thomas Jones --- don't have careers as long as those who did (like Barber).

The formula estimates that Tiki Barber has 636 carries left in him right now. It's instructive to look at what Tiki's projection will look like at the beginning of next year. If he gets hurt, let's say after 130 carries and zero VBD, then this time next year the formula will project that he is essentially finished: about 70 carries left. If, on the other hand, he has a year just like 2005, then the formula will project him to have about 500 more carries remaining.

No matter how old you are (within reason), as long as you were productive in your most recent season, the formula thinks you've got something left. But if you're on the north side of 30 and have a bad season, it will turn on you in a hurry. Since the formula was generated in such a way as to best fit the past data, the lesson is clear: age isn't much of a problem --- and neither is workload --- if you're productive. But once you start sliding, it's hard to put the brakes on.

Unfortunately, what I just said amounts to: old-but-productive running backs will continue to be productive right up until the point that they cease being productive. Genius.

But we've gotten off track. This post was supposed to be about age vs. workload and for the first time we can actually put a number on it. The number is .13. That's how many future rushes each past rush costs you.

Let's talk a bit about that number and the uncertainty associated with it. Regression answers two basic questions:


  1. What is our best guess at the number?
  2. given the sample size and the amount of variation we saw in our input data, how sure are we that the number isn't zero?

We answered #1 above. It's .13. I didn't tell you, though, that the answer to #2 is "not very." [For regression buffs, the p-value is about .22.] The point is: even though we have an estimate of .13, we do not have statistically significant evidence, in the generally agreed-upon sense, that workload has any effect on future career length.

Postscript: applied regression is *##$!!*!***##! pretty tricky stuff. I had run this regression earlier and gotten different results. Quite a bit different. But then I realized that my data might be afflicted with a dread disease known as serial correlation, which is but one of many illnesses that can mess with your regression results. Most of these diseases have cures which can be administered simply by typing a few keystrokes into your regression software, but first you've got to recognize the illness.

As a mathematician, I understand these things on some theoretical level, but I sometimes have a hard time seeing them in practice and I have very little experience correcting them. Fortunately, I have a friend who is an economist, and economists are experts at diagnosing these sorts of problems.

The moral of the story: unless you know what you're doing --- or have a friend who does --- be very careful with regression.

15 Comments | Posted in Fantasy, Statgeekery

Super Bowls and quarterbacks picked #1 overall

Posted by Doug on June 23, 2006

Random trivia: a surprisingly high percentage of quarterbacks picked #1 overall in the draft have Super Bowl rings.

In the Super Bowl era, here is the list of #1 overall pick quarterbacks:


2005 Alex Smith
2004 Eli Manning
2003 Carson Palmer
2002 David Carr
2001 Michael Vick
1999 Tim Couch
1998 Peyton Manning
1993 Drew Bledsoe
1990 Jeff George
1989 Troy Aikman
1987 Vinny Testaverde
1984 [should we count Steve Young? I guess not.]
1983 John Elway
1975 Steve Bartkowski
1971 Jim Plunkett
1970 Terry Bradshaw

Eight of these guys' careers are over (that's counting Couch and Testaverde) and four of them won Super Bowls. Of the active seven, Drew Bledsoe has a Super Bowl ring, although it's debateable whether that's within the spirit of the question.

Of Smith, Manning, Manning, Palmer, Carr, and Vick, how many will win Super Bowls? If the over/under was 0.5, I'd take the over. If it was 1.5, I'd probably take the under, but I'd have to think about it a little more.

[NOTE: this investigation was inspired by comments made by message board poster "SSOG" in a thread titled "How likely is Brady Quinn to win a SB?" started by longtime Friend Of P-F-R Chase at the footballguys message board. Here is the whole thread.]

32 Comments | Posted in History, NFL Draft

Shutdown defenses II

Posted by Doug on June 22, 2006

Yesterday's post was about how teams did against their opponents' best and second-best wide receivers.

From a fantasy football standpoint, this could be worthwhile information to have. If you can't decide between, say, Steve Smith and Chad Johnson, you might first look at their 2006 slate of opponents and see if one is expected to be playing against tougher pass defenses than the other. If you wanted to dig deeper, you could check to see if one of them is expected to play against defenses that were tougher against wide receivers specifically. Those ideas have been around for a long time. But as far as I know it's not common practice to take it a step further and examine whether Smith or Johnson figures to be playing against a slate of defenses that will be tougher against #1 receivers specifically.

The table at the end of yesterday's post shows enormous variation in how teams fared last year against WR1s and WR2s. Some teams, like the Bears, shut down WR2s while being eaten alive by WR1s. The Redskins, on the other hand, actually allowed more production (in terms of raw numbers) against opposing WR2s than the corresponding WR1s. If these tendencies are caused by personel --- like the mythical shutdown corner --- or by defensive scheme, then we would expect them to persist from year to year. If that's the case, then we've got ourselves a valuable bit of fantasy football information.

But it's not and we don't.

I gathered six years of this data and checked the year-to-year correlation. The correlation coefficient is .10 and is not significantly different from zero. If you don't know what that means, it means roughly this: there is not sufficient evidence to conclude that a team's 2005 "DIFF" will be related in any way to it's 2006 "DIFF." (Yeah, yeah, I know, it merely means it's not related in any linear way.) I guess it's possible that there is some year-to-year carryover among teams that maintain the same coaching staff and mostly the same group of players in the secondary, but that that carryover is being diluted by less stable teams to the point where we can't see it in the data. More likely, in my mind, is that random variation accounts for the differences we saw among teams' relative performances against WR1s and WR2s and random variation will also account for the differences we see in 2006.

11 Comments | Posted in Fantasy

Shutdown defenses

Posted by Doug on June 21, 2006

Last week I posted a quick entry about Champ Bailey in which I noted that Denver's opponents' top wide receivers did very well against the Broncos last year. I wondered aloud whether Bailey was as good as his reputation suggests.

That led to a lot of interesting comments, which prompted me to write a quick program to check how WR1s did against every team. If you want to see a team that really got eaten alive by top wide receivers, take a look at the Kansas City Chiefs:


WK Opposing WR1 REC YD TD
===========================================
kan 2005 1 Laveranues Coles 6 66 0
kan 2005 2 Randy Moss 5 127 1
kan 2005 3 Rod Smith 7 80 1
kan 2005 4 Terrell Owens 11 171 1
kan 2005 6 Santana Moss 10 173 2
kan 2005 7 Chris Chambers 2 88 1
kan 2005 8 Keenan McCardell 5 73 0
kan 2005 9 Randy Moss 1 7 1
kan 2005 10 Lee Evans 3 66 2
kan 2005 11 Andre Johnson 6 50 0
kan 2005 12 Deion Branch 5 49 0
kan 2005 13 Rod Smith 6 79 0
kan 2005 14 Terry Glenn 6 138 2
kan 2005 15 Plaxico Burress 2 34 0
kan 2005 16 Keenan McCardell 6 58 0
kan 2005 17 Chad Johnson 4 55 0
TOTAL 85 1314 11

A reader pointed out that top wide receivers did not do well against the Packers and indeed they did not:


WK Opposing WR1 REC YD TD
===========================================
gnb 2005 1 Roy Williams 2 13 0
gnb 2005 2 Antonio Bryant 3 32 0
gnb 2005 3 Joey Galloway 5 53 2
gnb 2005 4 Steve Smith 2 12 0
gnb 2005 5 Donte Stallworth 1 6 0
gnb 2005 7 Travis Taylor 3 36 0
gnb 2005 8 Chad Johnson 5 62 0
gnb 2005 9 Hines Ward 1 12 0
gnb 2005 10 Brian Finneran 4 50 0
gnb 2005 11 Travis Taylor 2 33 0
gnb 2005 13 Muhsin Muhammad 0 0 0
gnb 2005 14 Roy Williams 4 53 1
gnb 2005 15 Derrick Mason 5 97 0
gnb 2005 16 Muhsin Muhammad 5 58 1
gnb 2005 17 Joe Jurevicius 2 11 1
TOTAL 44 528 5

I am defining each team's top wide receiver as the guy who scored the most total fantasy points during the season. So, for example, Terrell Owens was Philadelphia's top wide receiver last year. Since he was not playing when the Eagles met the Packers in week 12, you see no entry for week 12 in the Packers' table above.

Here is a table showing every team's performance against top wide receivers last season, ordered from worst to best (fantasy points per game).


TM YR G REC YD TD
===========================
nyg 2005 | 14 73 1104 12
kan 2005 | 16 85 1314 11
nwe 2005 | 16 72 1165 13
sea 2005 | 13 75 1077 8
mia 2005 | 16 82 1144 13
sfo 2005 | 16 86 1387 7
hou 2005 | 16 80 1108 11
dal 2005 | 15 67 1141 8
stl 2005 | 15 74 1109 8
chi 2005 | 15 75 1140 8
ari 2005 | 14 79 968 9
buf 2005 | 16 86 1270 6
ten 2005 | 16 73 1003 10
nor 2005 | 15 58 846 10
phi 2005 | 16 66 998 9
den 2005 | 16 85 1250 4
min 2005 | 15 74 1023 6
car 2005 | 15 75 957 7
cin 2005 | 16 78 1079 6
cle 2005 | 13 67 869 5
ind 2005 | 15 71 968 6
sdg 2005 | 16 79 992 7
oak 2005 | 15 69 993 5
det 2005 | 16 69 982 6
atl 2005 | 16 87 1058 5
jax 2005 | 14 60 786 6
bal 2005 | 16 70 965 4
pit 2005 | 16 69 969 3
was 2005 | 14 51 720 2
gnb 2005 | 15 44 528 5
nyj 2005 | 16 54 647 3
tam 2005 | 16 53 788 1

As you can see from the lists above, some teams (like the Chiefs) faced a tougher collection of WR1s than others (like the Packers). We're going to want to adjust for that. The aggregate 2005 average points per game posted by the collection of WR1s faced by the Chiefs was 9.7. The Chiefs allowed an average of 12.5. The aggregate 2005 average points per game posted by the top recievers the Packers faced was only 8.6. The Packers allowed 5.6. Instead of comparing the raw numbers (12.5 vs. 5.6), it makes sense to compare the differences. So we'll say the Chiefs were a +2.8, meaning they were 2.8 points per game worse than expected against WR1s. The Packers were a -3.0.

This started as a discussion of Champ Bailey, but you'll notice that I have carefully avoided mentioning Champ Bailey, Al Harris, and whoever the top corner in Kansas City is. That's because I now have it on good authority from several independent and reliable sources, including footballoutsiders, who track these things carefully, that no team has its top corner covering the other team's top wide receiver all of the time or even close to all of the time. So this isn't about measuring "shutdown corners" anymore. Still, it's interesting to see if certain teams, either through scheme or personel, tend to take the top receiver away relative to the other receivers.

Which brings up another point that was mentioned in the comments of the Champ Bailey post: some teams gave up a lot of yards to WR1s, and in general, simply because their opponents passed the ball a ton. Denver, for example, performed quite well in terms of passing yards allowed per attempt, but their opponents attempted 613 passes --- the most in the league --- so of course the Broncos are going to give up some yards. The Packers, on the other hand, were the second-least-passed-upon team in the league last year, which is part of why they did not give up many yards to top wide receivers.

I've chosen to focus on the difference between the production allowed to the top wide receiver and the production allowed to the second wide receiver. This should be independent (errr, or close enough) of how many passing attempts the team allowed. A glut or a lack of passing attempts ought to affect the WR1 and WR2 equally, so the difference between the two shouldn't be polluted by that bias.

So here's the plan:


  1. Compute the production (fantasy points per game) allowed to WR1s
  2. Adjust that to take into account the quality of the WR1s faced by the team
  3. Compute the production (fantasy points per game) allowed to WR2s
  4. Adjust that to take into account the quality of the WR2s faced by the team
  5. Look at the difference between the adjusted production allowed to WR1s and the adjusted production allowed to WR2s. That should give us a ranking of the "shutdown defenses." For reasons discussed above, it will not give us a ranking of the shutdown corners.

Here are the Denver and Green Bay lines:


+====== WR1 ======+====== WR2 ======+
TM YR DIFF | G R YD TD | G R YD TD |
==========+=======+=================+=================+
den 2005 | -1.7 | 16 85 1250 4 | 16 82 928 6 |
gnb 2005 | -3.1 | 15 44 528 5 | 13 24 378 4 |

DIFF is what we're sorting by. A negative number indicates a team that did a better job (relatively) against WR1s than against WR2s. Then you see the raw numbers allowed to WR1s and WR2s. What this means: Denver's opponents' WR1s racked up a lot of yards, but so did the WR2s. Relatively speaking, their performance was 1.7 points per game better against WR1s. If Champ Bailey were in fact always covering the other team's best wide receiver this would be evidence that he's pretty good, or at least that he's good relative to Denver's other corner. But he's not, so it's evidence of, well, I don't know what it's evidence of, but it's kind of interesting. Here is the full list:


+====== WR1 ======+====== WR2 ======+
TM YR DIFF | G R YD TD | G R YD TD |
==========+=======+=================+=================+
mia 2005 | +4.0 | 16 82 1144 13 | 12 40 567 1 |
chi 2005 | +3.9 | 15 75 1140 8 | 12 30 305 0 |
kan 2005 | +3.8 | 16 85 1314 11 | 15 49 577 3 |
sea 2005 | +3.4 | 13 75 1077 8 | 13 46 473 4 |
nyg 2005 | +3.0 | 14 73 1104 12 | 15 66 886 2 |
ind 2005 | +2.7 | 15 71 968 6 | 15 41 503 1 |
ari 2005 | +2.3 | 14 79 968 9 | 13 41 449 3 |
phi 2005 | +1.7 | 16 66 998 9 | 15 51 580 3 |
dal 2005 | +1.7 | 15 67 1141 8 | 14 35 504 3 |
nor 2005 | +1.5 | 15 58 846 10 | 14 24 390 3 |
cin 2005 | +1.4 | 16 78 1079 6 | 15 46 574 2 |
det 2005 | +1.1 | 16 69 982 6 | 15 39 416 2 |
oak 2005 | +0.6 | 15 69 993 5 | 12 28 441 2 |
nwe 2005 | +0.3 | 16 72 1165 13 | 15 66 1028 3 |
atl 2005 | +0.3 | 16 87 1058 5 | 16 39 468 1 |
cle 2005 | +0.3 | 13 67 869 5 | 16 46 496 4 |
buf 2005 | +0.3 | 16 86 1270 6 | 13 47 693 2 |
car 2005 | -0.2 | 15 75 957 7 | 16 64 832 3 |
sfo 2005 | -0.3 | 16 86 1387 7 | 16 69 912 6 |
bal 2005 | -0.3 | 16 70 965 4 | 13 41 556 1 |
hou 2005 | -0.5 | 16 80 1108 11 | 14 66 992 5 |
stl 2005 | -0.8 | 15 74 1109 8 | 13 62 840 7 |
sdg 2005 | -1.4 | 16 79 992 7 | 14 61 752 3 |
den 2005 | -1.7 | 16 85 1250 4 | 16 82 928 6 |
min 2005 | -1.7 | 15 74 1023 6 | 16 55 638 6 |
pit 2005 | -1.8 | 16 69 969 3 | 14 54 764 2 |
ten 2005 | -1.9 | 16 73 1003 10 | 15 51 747 10 |
jax 2005 | -2.2 | 14 60 786 6 | 13 50 737 5 |
nyj 2005 | -3.1 | 16 54 647 3 | 16 43 527 5 |
gnb 2005 | -3.1 | 15 44 528 5 | 13 24 378 4 |
tam 2005 | -4.4 | 16 53 788 1 | 14 36 544 5 |
was 2005 | -5.7 | 14 51 720 2 | 14 61 851 6 |

7 Comments | Posted in General

The inevitable

Posted by Doug on June 20, 2006

I'm surprised it took as long as it did.

I had planned to use today's entry to attack the age-vs-workload question using regression, but I ran into some technical problems with that. Maybe I'll get them fixed at some point. But they are not fixed right now and so today will be the first weekday since March 23rd that I have not posted some actual content.

Unfortunately, it won't be the last.

I teach in an intensive three-week summer school program for high school students. That started yesterday, so it'll have me pretty busy for the next few weeks. I will probably post two or three times per week until mid-July, and then we'll see what happens after that.

When I first started this, it felt like a struggle to come up with enough ideas to keep it going every day. Now I've got plenty of ideas but I'm struggling to find the time to write them up. That I find myself in the latter situation, which is far preferable, is largely attributable to the contributions made by you, the readers, in the comments and via email.

Thanks.

17 Comments | Posted in General

Running back deterioration II

Posted by Doug on June 19, 2006

For reference, here is Running back deterioration I.

Tip of the cap to my good buddy monkeytime for suggesting the following study.

Before diving in, though, I want to say something about the point of this study and the previous one. Many of you pointed out in the comments that determining a running back's real mileage is a whole lot more complex than just looking at his career-to-date NFL carries. That is certainly true.

After giving it some thought, I rationalized realized that quantifying workload is not what I want to do here. It's just way too big a job. Rather, my goal for these studies is to see if one simple factor (career-to-date rushes) gives us any clues. If so, great. If not, then maybe that means workload doesn't matter, or maybe it means that we're measuring it improperly, or maybe that means that it's simply too subtle to have been picked up in these studies. Regardless, it means we've got more work to do. But it's hard work and it's for another time. Remember, I started the last entry by asking: Should a 27-year-old running back with 1700 previous career rushes, for instance, be considered “older” than a 28-year-old running back with only 1000? I'm going to continue to focus on just that simple idea.

The idea for this second study is to find all backs who met a certain performance benchmark during their career. For example, we might look for all runners who finished in the Top 12 (by fantasy points) at least four times. Now that's a pretty exclusive group. Lamar Smith isn't in it.

After throwing out the still-active players, we are left with 28 runners. Now we'll count up each of their career-to-date rushes through (and including) their age 27 season. We'll order them from least to most and then divide them into three groups: low mileage, medium mileage, and high mileage. Here they are:

Player Rsh Thru Age 27
================================
James Brooks 426
Wendell Tyler 583
Terry Allen 641
Earnest Byner 672
Herschel Walker 721 LOW MILEAGE
Chuck Muncie 748
Roger Craig 749
William Andrews 793
Lydell Mitchell 801

Wilbert Montgomery 835
John Riggins 928
Chuck Foreman 939
Neal Anderson 947
Lawrence McCutcheon 950
Ricky Watters 990 MEDIUM MILEAGE
Tony Dorsett 1026
Franco Harris 1135
Curt Warner 1189
Marcus Allen 1289

Terrell Davis 1343
Eddie George 1360
Thurman Thomas 1376
Ottis Anderson 1401
Earl Campbell 1404 HIGH MILEAGE
Eric Dickerson 1465
Barry Sanders 1763
Walter Payton 1865
Emmitt Smith 2007

Now we look at their careers from age 28 on:


Mileage N RshAfter27
=======================
Low 9 1070.9
Medium 10 1204.7
High 9 1385.2

The backs who had more mileage before age 28 also logged more miles from age 28 on. So again we see no evidence that high mileage backs are having their careers shortened by the early workload.

Obviously, the benchmark had two arbitrary paramters in it: top 12, and four times. If we change it to something else, we'll get similar results. Here are a couple of examples:

Benchmark: top 20 at least five times


Mileage N RshAfter27
=======================
Low 9 1070.1
Medium 11 1192.2
High 9 1381.3

Benchmark: top 5 at least once


Mileage N RshAfter27
=======================
Low 19 544.4
Medium 20 708.5
High 19 1169.7

I have tried several sets of cutoffs but have not found one where the high mileage group does not come out on top. But I'm still left with the same feeling I had in the first study. Namely, the premise of this study is that we are identifying groups of comparably skilled players. But if you look at those lists you still don't get that feel. Wendell Tyler wasn't a one-year wonder, but he wasn't Eric Dickerson either. Despite meeting the same benchmark, the groups are not truly comparable.

So let's try to stack the deck in favor of the low-mileage group. Let's look at all running backs who finished in the top 24 at least once, and then classify them as either low-, medium-, or high-mileage as above. But then let's throw out any low- or medium-mileage back who was in the top 24 only once. So we're comparing low-mileage backs who finished in the top 24 at least twice to high-mileage backs who finished in the top 24
at least once
.


Mileage N RshAfter
=====================
Low 29 497.9
Medium 40 470.5
High 70 656.3

Still the high-pre-age-28-mileage backs had the longest post-age-28 careers.

This design helps to minimize some of the concerns with the earlier studies, but it has problems of its own. In particular, the group of backs who made the top 24 at least once is pretty large and contains a lot of fringe types. This lets in a lot of guys with low mileage, which drives the "high-mileage" cutoff down to a point where it's not really high-mileage in an absolute sense. In other words, the categories might more properly be called super low, low, and other instead of low, medium, and high.

9 Comments | Posted in Fantasy, General

Champ Bailey

Posted by Doug on June 16, 2006

I'm going to postpone further discussion of running back workloads until next week so I can have a bit more time to ponder all your comments.

While perusing the footballguys news blogger, I came across this article on Champ Bailey. This quote caught my eye:

Broncos cornerback Champ Bailey continues to stand out from his peers. Bailey is what every team is looking for, the rare defender who can take an opponents' best player out of a game.

I got curious and checked it out. The #1 wide receivers for Denver's opponents combined for 86 catches, 1253 yards, and 5 TDs last season. Not bad for someone who had been taken out of the game, and that doesn't count Deion Branch's 8-153-0 and Hines Ward's 5-59-1 in the playoffs.


Wk Receiver Rec Yd TD
=============================
1 Chambers 5 40 0
2 McCardell 4 54 0
3 Kennison 8 112 0
4 J. Smith 5 109 1
5 S. Moss 8 116 0
6 Branch 7 87 0
7 Burress 6 84 1
8 Owens 3 154 1
10 R. Moss 6 87 1
11 Coles 6 62 0
12 K. Johnson* 6 54 1
13 Kennison 4 108 0
14 Mason 6 53 0
15 Evans** 2 5 0
16 R. Moss 5 72 0
17 McCardell 6 51 0

* - Glenn had 4-56-0
** - Moulds had 9-110-0

I realize that Bailey isn't always covering the #1 guy and that lots of other factors are in play. And a quick glance at some play-by-play logs (like Owens in week 8 and Kennison in week 3) shows that some of these numbers were in garbage time.

I don't really have a point. But now I'm curious. Fill me in, AFC West fans: is Bailey still the man, or is he coasting on reputation?

22 Comments | Posted in General

Running back deterioration: age or mileage?

Posted by Doug on June 15, 2006

Question: do NFL running backs wear down because of age, or do they wear down because of mileage? Should a 27-year-old running back with 1700 previous career rushes, for instance, be considered "older" than a 28-year-old running back with only 1000?

This seems like a simple question, but I have had a tough time designing a study that sheds any light on it. Today, tomorrow, and Monday I'll describe a couple of studies that I think have a bit of promise. I'm not completely happy with either of them, though, and suggestions are welcome.

The first idea is simple. I find all pairs of running back seasons where the two backs had very similar production at the same age, but where the previous mileage of the two backs was significantly different. Then I see whether the low mileage back had the longer career after that season. Here is an example:


Name YR age Prev RSH YD After
===================================================
Thurman Thomas 1993 27 1376 | 355 1315 | 1146
James Wilder 1985 27 758 | 365 1300 | 463

I am trying to keep things very simple here by considering only rushes and yards. Once I have an experimental design I'm happy with, I can think about adding other things like receptions, possibly era adjustments, height, weight, and so forth. The RSH and YD columns demonstrate that Thomas' 1993 and Wilder's 1985 were in fact quite similar. There are, of course, some differences not captured in the rushing totals, but I'm not too concerned about that. I'm just trying to identify pairs of seasons that were pretty close in terms of rushing workload and quality. The Prev column shows how many career rushes each of them had before that season. So you can see that Thomas had substantially more mileage on him at that point. The After column shows that Thomas had 1146 rushes after his age 27 season while Wilder had only 463. If the low mileage backs had significantly longer careers, that would be evidence that wear and tear do play a role in the decline of running backs.

In principle, I like this study quite a bit. In practice, there are some complications.

First of all, "similar" is not a binary concept. How similar do two seasons need to be for me to include them as a pair in this study? And how to measure similarity? The usual tradeoff presents itself: you can require that the seasons be extremely similar and get a small sample size, or you can include pairs of seasons that aren't quite as similar and expand the sample. There is no correct answer. If this were baseball, with 100 years of history to fall back on, you can get a big enough sample without letting in any pairs of seasons that don't feel similar enough. With NFL data, I'm reluctant to include anything before 1978. And since we can only look at backs whose careers are over (or very close to it), we're left with a pretty small window.

Second of all, I said I wanted to match pairs of seasons that were similar, but where the previous workloads of the two backs were significantly different. What does "significantly different" mean? 500 previous career rushes? 300? 800?

Here is another complication I wasn't expecting. Emmitt Smith, for example, has lots of seasons that are similar to lots of other guys.


Name YR age Prev RSH YD After
===================================================
Charlie Garner 2000 28 736 | 258 1142 | 543
Emmitt Smith 1997 28 2334 | 261 1074 | 1814

Emmitt Smith 1997 28 2334 | 261 1074 | 1814
Harvey Williams 1995 28 499 | 255 1114 | 267

Terry Allen 1995 27 641 | 338 1309 | 1173
Emmitt Smith 1996 27 2007 | 327 1204 | 2075

Dorsey Levens 1997 27 162 | 329 1435 | 752
Emmitt Smith 1996 27 2007 | 327 1204 | 2075

And so on. If I included all these, the pairs would not be independent. Would that necessarily bias the results one way or the other? I'm not sure, but I think it might. Guys that had long careers (like Emmitt) might tend to be over-represented because their long careers mean more years to potentially match up with other backs.

So I decided to only include each back once, with his best match. So only the Emmitt-Garner match would be included. This leads to some arbitrariness. Suppose Back X's best match is to Back Y. Then we'd include the X-Y comparison in the study. Now along comes Back Z, whose best match is also to Back Y, but that match isn't as close as the X-Y match. So Back Z doesn't get included in the study or he gets paired with someone who is not quite as comparable as Back Y.

In general, there are a lot of parameters to tweak. And tweaking them just a little changes who gets included and who gets paired with whom. That's unfortunate.

All that said, though, I have yet to find a collection of settings that shows any evidence for the low mileage backs having longer careers. Here is the collection of pairs that I'm currently happiest with, listed in order of the strength of the match.


Name YR age Prev RSH YD After
===================================================
Jerome Bettis 1999 27 1807 | 299 1091 | 1373
Adrian Murrell 1997 27 560 | 300 1086 | 515

Eddie George 2002 29 2078 | 343 1165 | 444
James Stewart 2000 29 765 | 339 1184 | 374

Terry Allen 1995 27 641 | 338 1309 | 1173
Walter Payton 1981 27 1865 | 339 1222 | 1634

Earl Campbell 1981 26 1043 | 361 1376 | 783
Herschel Walker 1988 26 360 | 361 1514 | 1233

Rodney Hampton 1995 26 1241 | 306 1182 | 277
Antowain Smith 1998 26 194 | 300 1124 | 1290

Charlie Garner 2000 28 736 | 258 1142 | 543
Emmitt Smith 1997 28 2334 | 261 1074 | 1814

Ottis Anderson 1983 26 1105 | 296 1270 | 1161
Greg Bell 1988 26 597 | 288 1212 | 319

Priest Holmes 2001 28 459 | 327 1555 | 948
Curtis Martin 2001 28 2010 | 333 1513 | 1175

Gary Anderson 1988 27 323 | 225 1119 | 321
George Rogers 1985 27 995 | 231 1093 | 466

Raymont Harris 1997 27 317 | 275 1033 | 92
Curt Warner 1988 27 1189 | 266 1025 | 243

Roger Craig 1989 29 1274 | 271 1054 | 446
Dorsey Levens 1999 29 606 | 279 1034 | 358

Tony Dorsett 1984 30 1834 | 302 1189 | 800
Lamar Smith 2000 30 480 | 309 1139 | 534

Thurman Thomas 1993 27 1376 | 355 1315 | 1146
James Wilder 1985 27 758 | 365 1300 | 463

Mike Anderson 2000 27 0 | 297 1487 | 568
Wilbert Montgomery 1981 27 835 | 286 1402 | 419

Anthony Johnson 1996 29 330 | 300 1120 | 186
Mike Pruitt 1983 29 1137 | 293 1184 | 414

Jamal Anderson 2000 28 992 | 282 1024 | 55
Lewis Tillman 1994 28 355 | 275 899 | 29

Pete Johnson 1981 27 762 | 274 1077 | 453
Harvey Williams 1994 27 217 | 282 983 | 522

Marshall Faulk 1999 26 1389 | 253 1381 | 1194
Robert Smith 1998 26 646 | 249 1187 | 516

Craig Heyward 1995 29 683 | 236 1083 | 112
Freeman McNeil 1988 29 1306 | 219 944 | 273

Barry Sanders 1994 26 1432 | 331 1883 | 1299
Chris Warren 1994 26 513 | 333 1545 | 945

Eric Dickerson 1988 28 1748 | 388 1659 | 860
Christian Okoye 1989 28 262 | 370 1480 | 614

Chuck Muncie 1981 28 923 | 251 1144 | 387
Bernie Parmalee 1995 28 226 | 236 878 | 105

Edgar Bennett 1995 26 398 | 316 1067 | 401
Gerald Riggs 1986 26 928 | 343 1327 | 718

The high mileage backs averaged 775 carries during the rest of their careers. The low mileage backs averaged 529. This certainly fails to provide evidence that low mileage is a good thing. But it doesn't prove that high mileage is a good thing either, for reasons I'll explain shortly.

First, I need to mention some fine print.


  1. As you can see, the matches are pretty weak near the bottom of the list. That's why I sorted them that way, so you can draw the line wherever you like.
  2. I included players who were born in 1973 or earlier, so a few active guys are on the list. Antowain Smith, Priest Holmes, and Mike Anderson appear as low mileage guys. Curtis Martin and Marshall Faulk appear on the high mileage side.

As you browse through the list, you'll notice that the pairs of comparable players often don't feel all that comparable. I mean, Tony Dorsett comparable to Lamar Smith? C'mon. Walter Payton and Terry Allen? Emmitt Smith and Charlie Garner? It just doesn't seem right to call some of those matches matches.

It could be hindsight playing tricks on us. Now that we know how Walter Payton's career turned out, it's easy to say he wasn't comparable to Terry Allen. But he had more than 1800 carries prior to his age 27 season. That's a bigger workload than LaDainian Tomlinson, who some people are worried about. Would it really have been that surprising if Payton had started to decline around that point?

Even accounting for the hindsight effect, though, I think the problem is real. Even though the guys had similar seasons in that particular year, that doesn't mean they were similar. Lamar Smith was a journeyman who put together a good season at age 30. Tony Dorsett was Tony Dorsett. Despite the fact that their numbers were similar at age 30, Dorsett was just plain better. And it's no coincidence that the better player had the bigger previous workload.

In short, it's very difficult to find truly comparable pairs where the previous workloads were significantly different. That's why this study isn't enough for me to rule out that workload plays a role in aging running backs.

More tomorrow.

27 Comments | Posted in Fantasy, General

More on backup quarterbacks

Posted by Doug on June 14, 2006

Last week, I took a quick look at how top wide receivers do when a backup quarterback is playing. I decided to expand that look to second receivers, running backs, and tight ends. Then I wrote it up for my other site: footballguys.com. Here's the link.

While we're on the subject, I hope you'll forgive me a brief commercial message, because this seems like an appropriate time for me to point out that if you play fantasy football, a $25 subscription to footballguys is the best value out there. But everything is free until July 15th, so go check it out.

1 Comment | Posted in Fantasy, General

Roethlisberger’s decision

Posted by Doug on June 13, 2006

I'd better post something about Ben Roethlisberger's motorcylce accident.

First of all, I have yet to hear anyone criticize Roethlisberger for riding a cycle. No, everyone is on him for riding a cycle without a helmet. Why is riding the cycle OK, but riding it without a helmet is not? Because riding with the helmet is safer, I guess. But driving in a car is safer than either. I don't have data, but I'd guess that the marginal difference in severe injury probability between a car trip and a helmeted cycle trip is greater than that between a helmeted cycle trip and an unhelmeted one. (Feel free to chime in with data if you've got it.) It seems arbitrary to focus on the helmet. But that's not what this rant is about.

And while I do agree with the sentiment for the most part, this is not a libertarian-style "it's his life and he can do whatever he likes as long as he doesn't infringe on others' rights to do the same" rant. No, I am actually going to argue that Big Ben's decision to continue to ride his cycle sans helmet was, in fact, not a stupid one at all.

As everyone knows, getting out of bed in the morning is a risk. You probably got in your car and drove to work this morning, knowing full well that there was a small probability that that decision would be the direct cause of your grisly death. That is exactly what Roethlisberger did when he hopped on the bike with no helmet yesterday. Yes, you're saying, but I have to drive to work. Ben doesn't have to ride without a helmet. He could simply take the same ride with a helmet, and be 42% safer.

I'll grant that Roethlisberger would not literally shrivel up and die if he were forced to wear a helmet. But everyone has certain psychological needs, and it's just plain as day to me that one of Ben Roethlisberger's is satisfied by riding a motorcycle without a helmet.

Whatever you think about his decision, he is one of the best in the world at a job that requires a lot of decision making, so it is at least clear that he is not a stupid person. When Kellen Winslow was hurt in a bike wreck last May, Bill Cowher lectured Roethlisberger about the need to wear a helmet, but Ben refused to start wearing one.

When a smart person consciously makes a decision like that --- especially after so recently seeing a colleague demonstrate the potential consequences --- there is a reason for it. Having a very cautious personality myself, I can't begin to fathom what that reason is, but there is one and I think we ought to respect it. To use the usual words --- risk-taking, thrillseeking --- is to vastly oversimplify an incredibly complicated issue, but Ben Roethlisberger needs that thrill. You may not need it, but he does.

I believe that, in almost all cases, the good aspects of our personalities are inextricably tied to the bad ones. I don't understand the exact connection, but there is no doubt in my mind that whatever it is that compels Big Ben to bike without a helmet also plays a crucial role in his being such a great football player. Is it really surprising that a successful football player would be wired in such a way that he has an inner drive to do things that might not be in the best interests of his physical health?

Steeler fans, the choice is not between a helmetless Big Ben and a helmeted one. It's between a helmetless Big Ben and no Big Ben at all. The Big Ben that wins Super Bowls at age 23 is the very same Big Ben as the one who consciously chooses not to wear a helmet when he rides. You could try to separate the two with contractual obligations, but I guarantee that aspect of his personality would manifest itself some other way. It's part of the package.

35 Comments | Posted in Rant

Coaching changes and lurking variables

Posted by Doug on June 12, 2006

Lots of teams changed head coaches this year.

I have a crazy theory that changing coaches just for the sake of changing coaches is usually a good thing. Maybe not every year, but unless my team's record is good and getting better, I'd be inclined to fire the coach and start afresh every two or three years. I realize this is contrary to the coaching-continuity-is-everything line of thinking that the Steelers' Super Bowl title has wrought, so I probabaly should take a full blog post to explain it more clearly sometime. But for today, let's just do a quick investigation of how teams do after changing coaches.

Since 1990, we have seen 80 teams change head coaches between seasons. On 53 of those occasions, the team improved its record, and another four times the team's record stayed the same. If we count those four as half improve and half decline, then we get that 55 of the 80 teams improved. That's 68.8%. During the same span, teams that did not change coaches improved their record only 45.7% of the time. [Technical note: I have thrown out teams that changed coaches in mid-season in either year N or year N+1. My intent was to focus on situations where a conscious between-seasons choice was made between continuity and a new direction.]

Despite the fact that it appears to support my point, that is an extremely misleading statistic. While there is unquestionably an association between changing coaches and improving your record, there may or may not be a causal relationship. There is a lurking variable here, and its name is team quality. In the NFL, bad teams tend, as a group, to improve their records more often than good teams do. Bad teams also tend to change coaches more than good teams do. These two facts might lead to the statistic we saw above even if there is no causal relationship at all between changing coaches and improving your record.

One simple way to remove this bias would be to group the teams into groups of roughly equal quality. So let's do that.


YrN === changed coaches ===+=== did not change ======
Wins Imp Same Dec Imp% | Imp Same Dec Imp%
=====+========================+=========================
0-3 | 14 1 0 96.7 | 9 1 1 86.4
4-5 | 15 0 1 93.8 | 27 5 9 72.0
6-7 | 14 0 8 63.6 | 42 6 23 63.4
8-9 | 8 1 9 47.2 | 34 10 38 47.6
10+ | 2 2 5 33.3 | 23 17 93 23.7
=====+========================+=========================
53 4 23 68.8 | 135 39 164 45.7

From 6 wins on up, there is no difference between the improvement rate of the teams that changed coaches and those that didn't. For the 10+ win group, the percentages appear to be different, but a switch of just one team from the improved to the declined column would make them almost identical.

For the really bad teams, though, the story might be different. I'm too lazy to run the appropriate statistical tests, but it is notable that bad teams that change coaches improve "almost always" while bad teams that don't change coaches only improve "usually." Obviously, what's needed now is to see if that improvement sticks. Perhaps all the gains from the first year are given back in the next year. I'll put an investigation of that on the to-do list.

18 Comments | Posted in General

Asterisk

Posted by Doug on June 9, 2006

I've gotten a couple of emails in the last few weeks alerting me to a situation that I'm sure many others were already aware of. But this is the first I'd heard of it. Friday is rant day, and I think this deserves a rant. Here is one of the emails:

Why are the New York Giants of 1930 listed in first place, while the Green Bay Packers won the title that year, and have a better record?

First let me say that this is a completely appropriate email, and that nothing I write in this post should be interpreted to mean that the emailer was in any way out of line.

I get emails like this every so often. Normally they alert me to a legitimate error in my data or in my programs. I fix it, thank the emailer, and move on. But this time is a little different. The page in question is the 1930 standings page, which does indeed show the following:


W L T PF PA
New York Giants 13 4 0 308 98
Green Bay Packers 10 3 1 234 111

So I went to Total Football to verify. Those are indeed the correct W-L-T numbers for each team, but Total Football lists them in the opposite order. The problem boils down to this:


  • 10/13 = .769

  • 13/17 = .765

  • 10.5/14 = .750

Instead of being counted as half a win and half a loss, ties were simply discarded before computing winning percentage back in those days, which is Just Plain Wrong, and that's the nicest way I know how to put it. If you disagree, then consider that your system would rank a 1-0-15 team ahead of a 15-1-0 team. That's a contrived example, but it is illustrative. Discarding ties would be appropriate if tie games conveyed no information about which team was stronger. But that's not what tie games do. They convey information that the teams were equally strong on that day, which is a very different thing.

Someone please tell me if there is something that I'm missing here. Did forfeits used to count as ties or something like that?

The NFL eventually figured out the error of its ways, because ties are now apparently counted as half a win and half a loss in computing the winning percentages. As best as I can figure it, the change occurred between the 1971 and 1972 seasons. Total Football lists Washington's 9-4-1 record as .692 in 1971, which indicates that the erroneous system was still in place at the time. But it lists the Eagles' 2-11-1 mark in 1972 as .179, which is in compliance with the new (correct) way of counting ties.

Correct me if I'm wrong, but my understanding is that they didn't have a postseason back in 1930. The team with the best record was simply declared the champion. It should have been the Giants, but it was the Packers. Sports fans and pundits really love their asterisks, generally too much, but this is a rare case where an asterisk is completely appropriate.

As I said, I am quite sure I am not the first person to notice this. But it was something of a shock to me. I haven't yet decided whether I should "fix" the standings at the site.

17 Comments | Posted in History, Rant

When bad QBs happen to good receivers

Posted by Doug on June 8, 2006

So I've got Chad Johnson in a keeper league and I'm wondering how much this Carson Palmer situation ought to concern me. On one hand, Johnson's best year was when Jon Kitna was quarterbacking the Bengals. On the other, I don't think Anthony Wright, Doug Johnson, and Dave Ragone are even as good as Kitna. How big a dropoff --- if any --- should we expect from Johnson in the first four games of the season? (It's pure speculation on my part, obviously, but I'd bet money that Palmer doesn't return until after the week five bye.)

My first instinct in this situation is look for comparable situations and see if there are any obvious answers. So that's what I did. I looked for all teams since 1996 that had a quarterback who ranked in the top 10 in fantasy points per game while playing between 8 and 14 games. I then identified the team's top wide receiver, in terms of fantasy points per game, and examined how that receiver did with and without his main quarterback.

I threw out a number of teams because it just didn't feel right to include them. I threw out the 2000 Rams, who split the year between Warner and Green. I threw out all the Viking seasons that were split between some pair of Brad Johnson, Jeff George, and Randall Cunningham. I threw out a few others, trying to keep only the teams that had a typical Backup Quarterback [TM] step in.

Since there are obviously a lot of factors to consider, I won't try to summarize the data. I'll just present it and let you sift through it. Some fine print is at the bottom. Enjoy.


2005 Arizona Cardinals
Main QB: Kurt Warner
Top WR: Anquan Boldin

WK QB R Y T
================================
3 Josh McCown 6 88 0
4 Josh McCown 8 116 1
5 Josh McCown 10 162 1
7 Josh McCown 0 0 0
8 Josh McCown 3 69 1
15 John Navarre 8 134 1
16 Josh McCown 9 81 1
17 Josh McCown 8 81 0
Points per game in 8 games with Warner: 9.9
Points per game in 8 games with other QBs: 12.9

2005 St. Louis Rams
Main QB: Marc Bulger
Top WR: Torry Holt

WK QB R Y T
================================
6 Jamie Martin 6 70 0
12 Ryan Fitzpatrick 10 130 1
13 Ryan Fitzpatrick 6 75 0
14 Ryan Fitzpatrick 10 95 0
15 Ryan Fitzpatrick 3 16 1
16 Jamie Martin 10 163 1
17 Jamie Martin 4 40 0
Points per game in 7 games with Bulger: 15.7
Points per game in 7 games with other QBs: 11.0

2004 St. Louis Rams
Main QB: Marc Bulger
Top WR: Torry Holt

WK QB R Y T
================================
13 Chris Chandler 10 160 1
14 Chris Chandler 6 151 1
15 Jamie Martin 6 95 0
Points per game in 13 games with Bulger: 11.1
Points per game in 3 games with other QBs: 17.5

2003 Denver Broncos
Main QB: Jake Plummer
Top WR: Rod Smith

WK QB R Y T
================================
2 Steve Beuerlein 5 71 0
6 Steve Beuerlein 4 70 1
7 Steve Beuerlein 3 24 0
8 Danny Kanell 4 23 0
9 Danny Kanell 4 58 0
Points per game in 10 games with Plummer: 7.2
Points per game in 5 games with other QBs: 6.1

2003 Minnesota Vikings
Main QB: Daunte Culpepper
Top WR: Randy Moss

WK QB R Y T
================================
3 Gus Frerotte 3 85 0
4 Gus Frerotte 8 172 3
5 Gus Frerotte 5 81 2
Points per game in 13 games with Culpepper: 15.5
Points per game in 3 games with other QBs: 21.3

2003 San Francisco 49ers
Main QB: Jeff Garcia
Top WR: Terrell Owens

WK QB R Y T
================================
9 Tim Rattay 2 17 1
11 Tim Rattay 8 155 1
12 Tim Rattay 5 49 1
Points per game in 13 games with Garcia: 9.5
Points per game in 3 games with other QBs: 13.4

2003 Tennessee Titans
Main QB: Steve McNair
Top WR: Derrick Mason

WK QB R Y T
================================
12 Billy Volek 4 47 0
15 Billy Volek 9 137 0
17 6 90 2
Points per game in 13 games with McNair: 10.7
Points per game in 3 games with other QBs: 13.1

2002 Philadelphia Eagles
Main QB: Donovan McNabb
Top WR: James Thrash

WK QB R Y T
================================
12 Koy Detmer 2 45 0
13 A.J. Feeley 2 16 0
14 A.J. Feeley 5 23 1
16 A.J. Feeley 1 34 0
17 A.J. Feeley 1 8 1
Points per game in 10 games with McNabb: 8.7
Points per game in 5 games with other QBs: 4.9

2001 Minnesota Vikings
Main QB: Daunte Culpepper
Top WR: Randy Moss

WK QB R Y T
================================
13 Todd Bouman 7 158 1
14 Todd Bouman 7 144 2
15 Spergon Wynn 3 34 0
16 Spergon Wynn 2 10 0
17 Spergon Wynn 2 9 0
Points per game in 11 games with Culpepper: 11.8
Points per game in 5 games with other QBs: 10.7

2000 Denver Broncos
Main QB: Brian Griese
Top WR: Rod Smith

WK QB R Y T
================================
4 Gus Frerotte 8 134 0
12 Gus Frerotte 11 187 1
13 Gus Frerotte 4 82 1
14 Gus Frerotte 2 25 0
15 Gus Frerotte 5 82 0
16 Gus Frerotte 6 101 0
17 Gus Frerotte 8 80 0
Points per game in 9 games with Griese: 14.8
Points per game in 7 games with other QBs: 11.6

1997 Arizona Cardinals
Main QB: Jake Plummer
Top WR: Rob Moore

WK QB R Y T
================================
1 Kent Graham 7 96 0
2 Kent Graham 6 108 0
3 Kent Graham 3 27 0
5 Kent Graham 8 147 1
6 Kent Graham 8 108 0
7 Stoney Case 4 87 0
8 Stoney Case 6 101 0
Points per game in 9 games with Plummer: 14.8
Points per game in 7 games with other QBs: 10.5

1997 Jacksonville Jaguars
Main QB: Mark Brunell
Top WR: Jimmy Smith

WK QB R Y T
================================
1 Rob Johnson 6 106 2
2 Steve Matthews 8 117 0
Points per game in 14 games with Brunell: 8.7
Points per game in 2 games with other QBs: 17.1

1996 Oakland Raiders
Main QB: Jeff Hostetler
Top WR: Tim Brown

WK QB R Y T
================================
1 Billy Joe Hobert 4 31 2
2 Billy Joe Hobert 8 96 0
17 David Klingler 5 65 0
Points per game in 13 games with Hostetler: 10.2
Points per game in 3 games with other QBs: 10.4

1996 San Francisco 49ers
Main QB: Steve Young
Top WR: Jerry Rice

WK QB R Y T
================================
5 Elvis Grbac 7 72 1
6 Elvis Grbac 7 108 1
7 Elvis Grbac 7 84 2
9 Jeff Brohm 5 36 0
11 Elvis Grbac 5 49 0
12 Elvis Grbac 6 58 1
Points per game in 10 games with Young: 10.9
Points per game in 6 games with other QBs: 11.8

Fine print: this was done only by looking at game logs, so every game was defined as either a "starter" game or a "backup" game. For example, even though Marc Bulger started the Rams' week 6 game in 2005 and played part of it, the game counts as a Jamie Martin game because Martin threw more passes than Bulger in the game. This pollutes the data a bit, but it's the best I can do with just game logs.

8 Comments | Posted in Fantasy

Who is throwing to whom?

Posted by Doug on June 7, 2006

I had intended to continue the ten thousand seasons experiment for another day or so, by investigating different playoff formats. The programming for that has proved more challenging than I thought it would. It's not so challenging that I can't get it done at some point, just challenging enough that I can't get it done right now. I'll get back to it soon.

In the mean time, my thoughts are starting to turn more and more toward fantasy football, so much so that I am considering the idea of possibly starting to think about doing some projections. Maybe. Anyway, for me, the first step on that road is to collate some team data. In particular, one thing I always like to look at is what percentage of each team's passing yards went to wide receivers, tight ends, and running backs. And then break that down further into primary wide receiver, next wide receiver, and so on.

Another thing I like to do is try to squeeze as much data as I can into preformatted text tables, so here is my latest effort. The top line tells you that in 2003, the Cardinals leading wide receiver (by yardage) accounted for 42% of the team's receiving yardage. Their next wide receiver accounted for 13%. Under the T (for total) you'll see that the wide receiver group as a whole accounted for 70% of the team's yards. Likewise, tight ends contributed 18% and running backs 12%.

At the bottom are the league averages for the past three years.


==== WR =====|=== TE ===|=== RB ==
TM YR 1 2 3 T | 1 2 T | 1 2 T
============================================
ari 2003 | 42 13 6 70 | 16 2 18 | 6 3 12
2004 | 25 20 17 69 | 13 2 15 | 6 5 16
2005 | 30 30 9 77 | 6 3 9 | 5 5 14

atl 2003 | 32 14 5 55 | 21 3 24 | 13 5 21
2004 | 21 14 10 49 | 29 1 30 | 11 8 21
2005 | 21 17 15 55 | 30 1 31 | 8 4 14

bal 2003 | 25 18 7 50 | 28 6 34 | 8 5 16
2004 | 16 15 13 55 | 12 9 30 | 7 5 15
2005 | 32 14 4 52 | 25 5 31 | 9 6 16

buf 2003 | 25 24 19 72 | 11 3 15 | 5 3 13
2004 | 35 29 5 75 | 7 3 13 | 6 4 12
2005 | 29 26 16 80 | 5 1 6 | 6 4 15

car 2003 | 34 26 12 73 | 6 2 10 | 6 5 17
2004 | 36 19 13 70 | 8 3 12 | 10 4 17
2005 | 45 13 8 71 | 6 4 10 | 11 4 19

chi 2003 | 25 20 12 75 | 15 3 18 | 3 2 7
2004 | 26 18 9 59 | 11 3 14 | 16 5 27
2005 | 34 16 11 75 | 10 1 11 | 6 3 13

cin 2003 | 38 23 8 69 | 9 6 17 | 5 4 13
2004 | 36 28 11 81 | 6 2 9 | 5 2 10
2005 | 36 24 11 80 | 5 2 8 | 8 2 12

cle 2003 | 27 21 19 71 | 5 3 12 | 11 4 17
2004 | 26 18 14 69 | 9 8 19 | 6 3 11
2005 | 30 15 13 68 | 12 5 17 | 11 2 15

dal 2003 | 23 20 16 60 | 10 6 16 | 15 4 23
2004 | 27 11 7 60 | 27 0 27 | 6 3 13
2005 | 31 23 9 66 | 21 1 22 | 6 3 12

den 2003 | 27 20 6 55 | 25 2 28 | 10 3 17
2004 | 28 27 9 67 | 14 5 20 | 6 3 13
2005 | 33 23 6 65 | 14 5 20 | 6 5 15

det 2003 | 15 13 11 54 | 15 5 20 | 11 8 26
2004 | 26 17 8 62 | 12 3 15 | 10 6 22
2005 | 23 14 12 60 | 17 1 19 | 9 6 22

gnb 2003 | 21 18 15 59 | 7 7 16 | 11 6 25
2004 | 30 27 8 71 | 8 2 11 | 6 6 19
2005 | 31 14 9 59 | 7 6 18 | 9 7 22

hou 2003 | 34 16 14 67 | 13 3 15 | 12 2 17
2004 | 32 18 12 73 | 5 1 6 | 17 2 21
2005 | 26 18 16 69 | 6 1 8 | 13 7 23

ind 2003 | 30 20 11 67 | 13 8 21 | 7 4 12
2004 | 26 24 23 72 | 9 7 16 | 10 1 11
2005 | 27 25 13 71 | 12 5 18 | 8 2 11

jax 2003 | 22 17 13 67 | 8 4 13 | 10 6 21
2004 | 35 16 8 70 | 5 3 13 | 10 5 17
2005 | 31 20 13 77 | 5 4 10 | 7 2 13

kan 2003 | 21 18 10 53 | 22 1 24 | 17 4 24
2004 | 23 17 5 52 | 27 3 30 | 6 5 18
2005 | 27 13 11 59 | 23 1 25 | 9 5 16

mia 2003 | 32 12 9 57 | 20 4 24 | 12 6 19
2004 | 27 19 11 62 | 23 3 27 | 4 2 11
2005 | 32 20 13 70 | 17 2 18 | 7 3 11

min 2003 | 39 13 11 63 | 10 1 10 | 15 3 23
2004 | 21 16 14 59 | 15 2 18 | 8 5 23
2005 | 18 15 11 63 | 16 5 22 | 10 4 15

nor 2003 | 27 16 13 63 | 12 8 21 | 14 1 15
2004 | 37 20 15 76 | 10 3 12 | 6 5 12
2005 | 26 18 14 69 | 11 5 17 | 8 3 14

nwe 2003 | 21 14 13 64 | 11 8 18 | 12 3 18
2004 | 23 21 12 67 | 10 5 18 | 7 6 15
2005 | 23 17 11 65 | 10 5 17 | 6 5 18

nyg 2003 | 29 17 9 61 | 15 4 21 | 13 3 18
2004 | 24 14 6 49 | 22 1 23 | 19 4 23
2005 | 33 19 5 58 | 24 2 27 | 14 0 15

nyj 2003 | 31 18 8 63 | 10 4 14 | 12 7 23
2004 | 26 24 12 69 | 6 3 9 | 11 8 22
2005 | 28 24 8 67 | 11 9 21 | 5 4 12

oak 2003 | 29 19 12 65 | 8 4 15 | 13 4 20
2004 | 25 17 14 65 | 8 4 15 | 7 6 19
2005 | 26 24 14 74 | 8 1 9 | 14 3 18

phi 2003 | 18 17 15 53 | 10 9 19 | 12 10 29
2004 | 29 16 9 58 | 9 6 16 | 17 3 25
2005 | 20 15 14 58 | 17 2 20 | 16 2 22

pit 2003 | 34 25 10 76 | 4 3 8 | 9 3 16
2004 | 34 24 20 82 | 3 3 6 | 5 3 11
2005 | 31 18 15 69 | 15 2 17 | 7 4 14

ram 2003 | 40 23 12 80 | 6 3 9 | 7 2 11
2004 | 30 28 11 82 | 4 1 5 | 7 4 13
2005 | 31 18 12 79 | 3 2 6 | 7 7 15

sdg 2003 | 27 9 8 55 | 12 4 18 | 22 2 26
2004 | 19 11 9 52 | 27 2 32 | 12 2 16
2005 | 25 19 9 55 | 29 1 30 | 10 4 14

sea 2003 | 29 23 16 71 | 13 2 15 | 8 6 15
2004 | 32 13 13 72 | 9 6 19 | 5 3 9
2005 | 21 19 13 74 | 15 2 18 | 5 2 8

sfo 2003 | 31 17 11 65 | 12 3 16 | 9 6 20
2004 | 19 16 12 55 | 24 3 28 | 6 4 17
2005 | 33 17 13 69 | 3 2 7 | 11 6 24

tam 2003 | 30 15 11 64 | 6 2 9 | 15 5 26
2004 | 33 12 9 65 | 10 3 15 | 11 6 20
2005 | 39 11 9 63 | 11 3 18 | 9 7 20

ten 2003 | 32 20 13 74 | 9 4 18 | 4 3 9
2004 | 32 30 7 70 | 8 5 17 | 4 4 14
2005 | 20 8 8 49 | 14 14 36 | 9 3 15

was 2003 | 37 18 11 73 | 3 1 6 | 6 5 22
2004 | 33 23 7 71 | 11 2 17 | 8 4 12
2005 | 44 6 6 60 | 23 4 30 | 6 2 9

NFL 2003 | 29 18 12 65 | 12 4 17 | 10 4 18
2004 | 28 20 11 66 | 12 3 17 | 8 4 16
2005 | 29 18 11 66 | 14 3 18 | 9 4 15

In some cases, injuries and other circumstances cause these numbers to be a bit misleading. The Eagles' #1 wide receiver last year was Terrell Owens, of course, and the number listed is 20% of their receiving yards. But it was more like 35 or 40 when he was actually playing.

Off the top of my head, here are a few situations worth watching:


  • Will the addition of Javon Walker and apparent lack of a tight end in Denver turn the Broncos into a Cardinal/Bengal type team, where more than 75% of the yardage goes to wide receivers?
  • New Rams coach Scott Linehan has some history of utilizing tight ends, but the Rams top three tight ends --- rookies Dominique Byrd and Joel Klopfenstein and second year man Jerome Collins --- have zero career catches.
  • The Ravens lost most of their RB receiving yards when Chester Taylor left for Minnesota. Taylor was replaced by Mike Anderson, who has never caught a ton of balls. Will they essentially abandon the passes to running backs, as Seattle and Washington have done?
  • Will Keyshawn Johnson catch any passes in Carolina? If so, will that eat into Steve Smith's numbers?
  • Will Brandon Loyd's and Antwaan Randle El's numbers (if any) come at the expense of Chris Cooley? Or will they come at the expense of Santana Moss, whose percentage of team yards was almost as high last year as Steve Smith's?

14 Comments | Posted in Fantasy, General

Ten thousand 2005s

Posted by Doug on June 6, 2006

Prerequisite reading material:

How often does the best team win?

Ten thousand seasons

Ten thousand seasons again

In the previous posts, I simulated ten thousand generic NFL seasons. In some of those seasons the "Seattle Seahawks" were great. In some they were terrible. In some they played a tough schedule, in others an easy one. In this post, I'll simulate ten thousand 2005 NFL seasons. The Seattle Seahawks will be a very good team in each of them, and they will play an easy schedule in each of them.

Mechanically, the procedures are similar, but philosophically there is a world of difference. The generic seasons had teams whose strengths I knew, so I could say things like "the best team" and "Chicago was not very good." I knew who the best team was and I knew how good Chicago was or wasn't. Exactly. Only because I knew those team strengths could I assign the proper probabilities to each game.

But if I want to simulate the 2005 season, I've got a problem: I don't know the team strengths. Neither do you. We have to guess. The guess I'm going to use is the team's rating from the simple rating system. I'm not going to spend time here making a case that that's the best guess or even necessarily a good guess. If you don't think the simple rating system is an adequate representation of team strength, that's fine. No hard feelings. But you'd better stop reading now, because that's the foundation this post rests on.

For those still with me, I'll make one more disclaimer. If I happen to say something like:

Seattle was the 4th-best team in football.

What I actually mean is:

According to the measurement of team strength that we have agreed upon --- which we acknowledge is imperfect in some obvious and some non-obvious ways --- Seattle appears to be the 4th-best team in football.

I am not trying to quash discussion of the merits of the various ways of estimating team strength and I am well aware of the weaknesses of the one I have chosen. But we've got to pick something and go with it, and the prose just seems to flow a bit better if you allow me to use the above shorthand notation. As you know, I can use all the help I can get with making the prose flow.

Now let's get to it. I'll just throw this summary out and then we'll discuss it.

Rating is the team's rating, which is my guess as to its true strength. Avg Wins is the average number of wins each team had over the course of the 10,000 seasons. Div is the number of division titles each team won. WC is the number of times each team got into the playoffs as a wildcard. PO = Div + WC. It is the number of times each team made the playoffs. SB is the number times each team made it to the Super Bowl and Champ is the number of times they won it.


TM Rating AvgWins Div WC PO SB Champ
=====+=========+========+================+===========
ind | 10.8 | 11.2 | 7128 1572 8700 | 2688 1640
sea | 9.1 | 11.1 | 8936 395 9331 | 3461 1780
car | 5.1 | 10.4 | 6304 1818 8122 | 1681 741
den | 10.8 | 10.4 | 4342 2797 7139 | 1825 1092
pit | 7.8 | 10.3 | 5741 1543 7284 | 1469 778
nyg | 7.5 | 10.1 | 5083 2534 7617 | 1785 817
sdg | 9.9 | 9.9 | 3190 2907 6097 | 1343 797
jax | 4.8 | 9.6 | 2727 2951 5678 | 674 321
kan | 7.0 | 9.4 | 2298 2842 5140 | 737 371
cin | 3.8 | 9.3 | 3015 1974 4989 | 516 242
was | 6.0 | 9.2 | 2986 2765 5751 | 989 416
chi | 1.4 | 9.1 | 5653 793 6446 | 721 256
nwe | 3.1 | 8.7 | 5001 476 5477 | 425 194
tam | -1.0 | 8.5 | 1969 2333 4302 | 315 103
dal | 3.2 | 8.3 | 1552 2249 3801 | 409 166
atl | -1.2 | 8.2 | 1652 2122 3774 | 236 73
mia | -0.8 | 8.0 | 3385 481 3866 | 165 52
rav | -1.8 | 7.4 | 773 829 1602 | 61 22
min | -3.5 | 7.3 | 1864 774 2638 | 113 36
gnb | -3.7 | 7.1 | 1616 755 2371 | 93 29
ram | -5.1 | 6.9 | 528 1013 1541 | 59 10
cle | -4.2 | 6.8 | 471 518 989 | 32 9
crd | -5.0 | 6.7 | 481 884 1365 | 46 9
phi | -2.3 | 6.6 | 379 878 1257 | 61 16
rai | -2.8 | 6.3 | 170 427 597 | 22 9
det | -6.7 | 6.3 | 867 417 1284 | 27 6
buf | -5.8 | 6.2 | 889 179 1068 | 20 7
nyj | -6.4 | 6.0 | 725 136 861 | 18 6
oti | -7.6 | 5.8 | 108 256 364 | 4 2
htx | -10.0 | 5.1 | 37 112 149 | 1 0
nor | -11.1 | 4.9 | 75 139 214 | 4 0
sfo | -11.1 | 4.7 | 55 131 186 | 0 0

Indianapolis averaged 11.2 wins per season in the simulation. They won the AFC South 71.2 percent of the time, they made the playoffs 87% of the time, they made it to the Super Bowl about 27% of the time and won it 16.4% of the time.

If you were to translate this into an English sentence, it would not be: at the beginning of the season, we should have estimated that the Colts had a 16.4% chance of winning the Super Bowl. It would be something more like: knowing what we now know in hindsight about how good these teams were in 2005, if we were to play the season again with those strengths remaining the same, the Colts would have a 16.4% chance of winning the Super Bowl. Alright, that's pretty bad English but I hope you get the point.

The probability of winning the Super Bowl depends two things: the team's strength and their schedule (including the playoff schedule). You can see the effect of both in the table. Denver and Indianapolis were essentially equally strong, but the Colts' chances of winning the Super Bowl were significantly higher. And Seattle's were even higher, despite being a weaker team. Carolina had a title chance that was disproportionately high (compared to their true strength) and San Diego's was disproportionally low. We'll revisist them in a moment.

Also note that the spread on average wins --- from Indy's 10.8 to Houston's 4.7 --- is much smaller than the spread on actual wins in the 2005 season. This makes sense. I think it's safe to say that there is almost never an NFL team that is morally a 14-2 team or a 2-14 team. There are, though, probably three or four teams each year --- maybe more --- that are capable of going 14-2 if things break right for them, and there are another few that might slip to 2-14 if things don't. And the result is that we see 14-2 teams and 2-14 with some regularity. This idea might strike some people as controversial, but it's really no different from pointing out that no basketball player truly is a 50-point-per-game player even though certain players do score 50 from time to time.

OK, time to play god. Let's move the Chargers to the NFC South and the Panthers to the AFC West and see what happens.


TM Rating AvgWins Div WC PO SB Champ
=====+=========+========+================+===========
sdg | 9.9 | 11.7 | 8209 1158 9367 | 3344 1790
clt | 10.8 | 11.3 | 7255 1615 8870 | 2881 1610
sea | 9.1 | 11.1 | 8921 398 9319 | 2879 1520
den | 10.8 | 10.6 | 5370 2328 7698 | 2134 1196
pit | 7.8 | 10.4 | 5795 1684 7479 | 1563 787
nyg | 7.5 | 10.1 | 5063 2508 7571 | 1478 727
jax | 4.8 | 9.7 | 2592 3360 5952 | 731 317
kan | 7.0 | 9.6 | 2980 2784 5764 | 902 441
was | 6.0 | 9.3 | 3015 2879 5894 | 827 366
cin | 3.8 | 9.3 | 2979 2222 5201 | 570 256
chi | 1.4 | 9.0 | 5504 754 6258 | 522 184
nwe | 3.1 | 8.7 | 4984 487 5471 | 476 195
car | 5.1 | 8.5 | 1385 2076 3461 | 388 179
tam | -1.0 | 8.3 | 979 2862 3841 | 173 63
dal | 3.2 | 8.3 | 1530 2287 3817 | 306 138
atl | -1.2 | 8.0 | 782 2516 3298 | 147 38
mia | -0.8 | 8.0 | 3298 551 3849 | 180 56
rav | -1.8 | 7.4 | 778 960 1738 | 62 23
min | -3.5 | 7.3 | 1933 661 2594 | 88 19
gnb | -3.7 | 7.0 | 1681 634 2315 | 86 22
ram | -5.1 | 6.9 | 559 1011 1570 | 36 6
cle | -4.2 | 6.8 | 448 593 1041 | 25 6
phi | -2.3 | 6.7 | 392 924 1316 | 49 19
crd | -5.0 | 6.6 | 458 793 1251 | 37 12
rai | -2.8 | 6.5 | 265 524 789 | 33 10
det | -6.7 | 6.3 | 882 369 1251 | 28 6
buf | -5.8 | 6.2 | 935 222 1157 | 32 10
nyj | -6.4 | 6.0 | 783 152 935 | 18 2
oti | -7.6 | 5.9 | 113 315 428 | 4 1
htx | -10.0 | 5.1 | 40 127 167 | 1 1
nor | -11.1 | 4.8 | 30 133 163 | 0 0
sfo | -11.1 | 4.7 | 62 113 175 | 0 0

Interesting.

21 Comments | Posted in Statgeekery

Ten thousand seasons again

Posted by Doug on June 5, 2006

You'd better read Thursday's post and Wednesday's if you haven't yet. Thanks to the many who posted thoughtful comments during the weekend, and apologies for not giving them the thought they deserve. I had a a busy weekend. But I will do my best to address some of them when and if I get a chance.

Today will just be a few more observations from the same experiment, but note that there will be a subtle shift in focus. Last week, I was asking questions about how often the actual best team won the Super Bowl. Today, I'll be investigating how often a team with a given record wins its division or a Super Bowl.

How often will a team with a sub-.500 record win its division?

In 10,000 seasons, a division winner had a sub-.500 record 870 times. If the league structure remains as it is now, we can expect this to happen about once every 11 or 12 years on average. I find this tolerable, I guess. We'll see shortly how often these teams go on to win the Super Bowl.

Amazingly, on two occasions teams won their division with a 5-11 record. This is pretty hard to arrange. Both times, the four teams in the division won a total of 17 games. Since there are 12 intradivision games, this means that those divisions must have been 5-35 in interdivision games.

Again, 10,000 years is a long time.

Because the teams' true strengths were rigged to be symmetric about zero --- which is a very reasonable assumption in general but might possibly break down at the extremes --- there is no point in computing how often a division produces four teams with winning records. It will be (theoretically) the same as the above.

How often will we see a four-way tie in a division?

I think a four-way tie would be cool. It happened 109 times in 10,000 simulated seasons, or once every 92 years on average. In one of the simulated seasons (#2702, if you must know), there was a four-way tie at 11-5 in the AFC West. The Broncos were left out of the playoffs despite having the best true strength in the division and having the best record in the AFC. The Bills won the AFC East at 8-8 and went on to beat the 9-7 Cardinals in the Super Bowl, which makes up for that time they went 15-1 but were bounced from the playoffs early. Strange year.

How often will a team with a sub-.500 record win the Super Bowl?

Fourteen times in 10,000 years. There is about an 13% chance of this happening at some point in the next 100 years. I find this to be tolerable also.

When this format was announced five years ago, I thought the small divisions created too much opportunity for a losing team to get into the playoffs, and hence win the title. But I'm finding that there is something aesthetically pleasing about the small divisions, and a 0.14% chance of a team with a losing record winning the Super Bowl is a price I'm willing to pay.

Here is the full list of the how often the Super Bowl champ had a given number of wins:


Wins Times
===========
7 14
8 135
9 665
10 1541
11 2344
12 2499
13 1728
14 779
15 255
16 40

How often will we see an undefeated team?

We saw 115 undefeated regular seasons, which means roughly one every 87 seasons. As you can see from the table above, 40 of those 114 undefeated teams won the Super Bowl. That might seem low, but it's about 35%. In the comments of the last post maurile computed that, when they make the playoffs, the best team in football wins the Super Bowl about 27% of the time. An average 16-0 team was probably a bit better than an average best-team-in-the-league. So 35% is in the ballpark of what we'd expect.

The moral of the story: going 19-0 is hard. It's probably even harder than the media folks who write and blab every November about how hard it is even realize. I am 34 years old right now. If I live to be 100, and if the NFL remains just as it is now, there is about a 23% chance that I will see a 19-0 team.

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