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Home Field Advantage II

Posted by Chase Stuart on July 13, 2006

Is there such a thing as a "dome field advantage?" Whenever a dome team has a strong season and happens to be very good at home, sportswriters get to write about the special dome field advantage. Supposedly, it's tougher to win in a dome because of the loud crowd noise, and maybe the artificial turf and the absence of natural elements. So do the facts bear this our? Do dome teams do better than regular teams at home?

According to the data, the answer is no. That's an important caveat, though. The numbers just show one thing: home wins minus road wins, for all teams that played in a dome. It's certainly possible that some special advantage exists for dome teams that wasn't examined in this study. But at the end of this post I'll throw out a theory on why there might actually be a "dome team disadvantage."

Since 1983, eight teams have played in a dome. The Atlanta Falcons (1992-2005), Detroit Lions (1983-2005), Houston Oilers (1983-1996), Indianapolis Colts (1984-2005), Minnesota Vikings (1983-2005), New Orleans Saints (1983-2004), Seattle Seahawks (1983-1999) and the St. Louis Rams (1996-2005).

There was a bit of noise in the data, so I eliminated the '95 Rams and last year's Saints teams. When the Rams relocated to St. Louis in 1995, the Edward Jones Dome wasn't complete. So the Rams first four home games were played at Busch Stadium, and the remainder in the Dome. The Rams went 3-1 at Busch and 1-3 indoors. Due to Hurricane Katrina, the Saints played three games indoors at the Alamodome in San Antonio (1-2), and four home games outdoors at Tiger Stadium in Baton Rouge (0-4) last year. The remaining "home" game was played at Giants Stadium, the star of yesterday's post.

The eight dome teams won 188 games more at home than on the road during the relevant time period, spanning 139 seasons. That comes out to an average of 1.35 more home wins per season.

The Houston Texans (2002-2005) play in Reliant Stadium, which has a retractable roof. I'm not sure which games were played with the roof open and which with the roof closed. The Dallas Cowboys (1983-2005) play at Texas Stadium, which is an open-air stadium -- basically a dome with a hole in the center. I didn't know whether to count either Texas team as a "dome" team or "regular" team, so I just put them in a separate category. Interestingly enough, my classification shouldn't matter: over 26 seasons the two teams won 35 more home games than road games, an average of 1.35 more wins per season.

So how does that compare to the rest of the NFL? The league has increased from 28 to 32 teams since the first year in the study. Over the 22 seasons (remember, the 1987 strike season data were excluded), that amounts to 649 seasons. NFL franchises have won 881 more games at home than on the road, for...an average of 1.36 more wins per season. If you eliminate all the dome teams, the Cowboys and Texans, and the 2005 Saints and 1995 Rams, NFL teams average 1.37 more wins per season at home than on the road.

We have 482 non-dome seasons, and 188 dome seasons. I'm not sure what a "significant" sample size would be, but considering how close the two averages were (1.35 and 1.37), at the least the burden of proof should shift to those who think dome teams have an advantage.

I promised you some theory in addition to the numbers. We've seen that dome teams appear to have the exact same home field advantage as regular teams. I say appear, because all the data show is that dome teams win the same additional number of games (compared to regular teams) at home than on the road. But is it possible that dome teams are actually worse at home but the numbers don't show it?

Isn't the general feeling that dome teams aren't as good on the road because they're not used to the conditions? This would artificially inflate a dome team's rating under my current system, because a team grades better at home the worse it does on the road. If dome teams actually perform poorly on the road -- as we might expect -- then the HFA of dome teams should should be greater than the league average, if dome teams are equally strong at home. This leads us to one of three conclusions:

  • Dome teams are actually weaker at home; they just look equal because they have trouble winning on the road.
  • Dome teams actually aren't weaker at all on the road; it just seems that way because we hear it all the time. The flipside of all the above numbers is that dome teams only lose 1.35 less games on the road than at home each year.
  • Something else. Maybe it's a small sample size. Maybe dome teams are below average at home when they're bad, but above average at home when they're good. Maybe schedule somehow factors in here. Maybe there's some other force driving the numbers that I haven't isolated. Who knows.

There's also the argument that dome teams are still actually better at home, but the numbers don't show it. Let's take a quick look at a few case studies. We'll use HFA rating as a shorthand for home wins minus road wins.

Atlanta's HFA rating was 9.5 during the 8 years the Falcons played at Fulton County Stadium; playing indoors the last 14 seasons, Atlanta's won 22.5 more games at home. The Houston Oilers' HFA was 21 in thirteen seasons at the Astrodome; the Titan's HFA rating was 9 in 9 years. But on the other hand, the Seahawks won just 23 more home games than road games in sixteen seasons in the Kingdome. Since moving to Qwest Field, Seattle's HFA is 12 in six years.

Here's an interesting one. From 1983-1994, the Raiders and Rams both won 9 more games when playing in Los Angeles than when on the road. The Raiders moved to Oakland and despite the notoriety of Raider Nation and the Black Hole, have an HFA of only 11 in 11 years. The Rams, in ten season indoors, won 15 more at home.

If there's such a thing as a Dome Field Advantage, it's certainly hard to quantify it. My guess is that when teams like the '98 Vikings, '99 Rams or the '05 Colts have a dominant offense and look unstoppable at home, it's a nice story to think it's the dome that helps. But in general, great teams almost always look pretty good, and usually look unbeatable at home no matter where they play. The same people that talk up how hard it is to play against a dome team because of the noise, probably mention how difficult it is to win in the cold against the Packers, Broncos and Chiefs. Even teams with no special weather advantage -- warm weather teams like Arizona, Tampa Bay and Dallas -- have above average HFA factors.

We know that over the last 22 years, home teams have won 58.5% of all games. I'll end with a breakdown of HFA separated out by total team wins.

Wins	HFA	Teams	HFA/Teams
1 -4 6 -0.67
2 12 14 0.86
3 29 25 1.16
4 48 44 1.09
5 76 54 1.41
6 94 60 1.57
7 79 69 1.14
8 112 70 1.60
9 121 77 1.57
10 94 73 1.29
11 79 55 1.44
12 66 43 1.53
13 46 22 2.09
14 4 15 0.27
15 2 4 0.50

3.5 -1.5 1 -1.50
4.5 5.5 3 1.83
5.5 -0.5 1 -0.50
6.5 9.5 3 3.17
7.5 -2.5 1 -2.50
8.5 7 4 1.75
9.5 2 2 1.00
10.5 3.5 3 1.17
Totals 881 649 1.36

7 Comments | Posted in Home Field Advantage

Home Field Advantage

Posted by Chase Stuart on July 12, 2006

In 2009, the Jets and Giants will move into a new joint stadium. It probably will be named after some corporation (JetBlue?), which is a big change from where both teams currently play: Giants Stadium. Jets fans don't like that their team plays in a stadium named after another team, and have claimed for years that it's negatively impacted the team's success. Giants fans, of course, think their stadium gives the team a great home field advantage.

While we don't know whether the name of where the Giants play home games will negatively affect New York's success, we have all the data we need to examine how Giants Stadium has been to the Jets and the Giants. That wouldn't make for much of a blog post though, so let's take a look at home field advantage throughout the entire NFL.

The Jets moved into Giants Stadium in 1983. So have the Jets really been harmed by being "homeless"? Measuring home field advantage may not be easy, but I think a team's home wins minus a team's road wins is a pretty accurate metric. Last year, Denver went 8-0 at home and 5-3 on the road, for example. Cincinnati went 5-3 at home, and 6-2 on the road. Ignoring the small sample size, that's strong evidence that the Broncos are a better home team than the Bengals.

If you just look at a franchise's winning percentage at home, you're going to overvalue the good teams. By subtracting a team's road wins from its home wins, you should get a strong idea of how good that team is at home (more on this and the NFC North at the end of this post).

So how do the Jets fair? Over the past six years, the Jets and Giants have the same number of home wins (27), while the Giants (23) have two more road wins than the Jets. This doesn't prove anything of course, but it's safe to say that the Jets and Giants were pretty equivalent in terms of football ability from 2000-2005. And while both teams won 27 games at home, it's arguable that the Jets actually enjoyed the better home field advantage since Gang Green was the worse team (based on the overall records).

Of course, I soon realized that six years wasn't enough. But this gives us a glimpse of two key ideas: home field advantage isn't consistent from year to year, and you should always be careful with your sample sizes. As Doug showed here we should always be careful with splits.

If you look at the last four seasons, the Jets have won nine more home games than road games; the Giants just three. If we go back ten years, the Jets have won 8 more at home than away, Big Blue won 8.5 more. So whatever cutoff you use may seem arbitrary and a different cutoff could very well get you a different result.

But let's use 1983, when the Jets left Shea Stadium. Because so many NFL teams have changed cities, this list of full of caveats, most of which are in the footnotes. I didn't put footnotes next to Jacksonville (1995-2005), Carolina (1995-2005) and Cleveland (1983-1995; 1999-2005), but you should note that those data are not from a full 22 seasons. One other note: I didn't include any data from the strike season of 1987.

HFA is the Home Field Advantage factor, which is simply total home wins minus total road wins. Ties were counted as half a win.


Team HFA

Kansas City 56
Denver 52
Detroit 41.5
Green Bay 40
Minnesota 39
Cincinnati 37
Tampa Bay 37
Buffalo 37
Chicago 35
Seattle 35
Pittsburgh 33.5
Dallas 33
Atlanta 32
Miami 31
Arizona1 28
New England 26
Washington 25.5
San Diego 24
Baltimore2 22.5
New York (N) 22
Houston3 21
San Francisco 20.5
Philadelphia 20.5
Indianapolis4 19
St. Louis5 16
Jacksonville 16
Cleveland 12.5
Oakland6 11
New York (A) 10.5
Tennessee7 9
LA Raiders8 9
LA Rams9 8
Carolina 8
New Orleans 6
St. Louis10 6
Houston11 2
Baltimore12 -1

1 Arizona (1994-2005) and Phoenix (1988-1993) Cardinals. For the St. Louis Cardinals, see footnote 10.
2 Baltimore Ravens (1996-2005). For the Baltimore Colts, see footnote 12.
3 Houston Oilers (1983-1996). For the Tennessee Titans see footnote 7; the Houston Texans, footnote 11.
4 Indianapolis Colts (1984-2005). For the Baltimore Colts, see footnote 12.
5 St. Louis Rams (1995-2005). For the Los Angeles Rams see footnote 8.
6 Oakland Raiders (1995-2005). For the Los Angeles Raiders see footnote 9.
7 Tennessee Titans (1997-2005)
8 Los Angeles Rams (1983-1994)
9 Los Angeles Raiders (1983-1994)
10 St. Louis Cardinals (1983-1986)
11 Houston Texans (2002-2005)
12 Baltimore Colts (1983)

I'll let you guys comment on the list, but there's one more thing to mention. The old NFC Central (1983-2001) and current NFC North is very well represented on this list: three teams in the top five, and two more in the top ten (of course Tampa Bay's in the NFC South these days).

There's probably a good bit of synergy on this list. If Green Bay is dominant at home and bad on the road, when Minnesota plays Green Bay, the Vikings will probably lose at Lambeau Field but win at home. That will artificially inflate the Vikings HFA factor. If all the NFC North teams have strong home field advantages -- and most fans probably think the Bears and Packers do -- that will drive all the NFC North teams up this list. The Bucs are an interesting study too. Tampa ranked in the top five in HFA factor from 1983-2001, with 34 more home wins than road wins. That's an average of 1.89 wins more per year playing at home. Since joining the NFC South, the Bucs have won only three more games in four years at home.

21 Comments | Posted in Home Field Advantage

Breaking down “Yards Per Carry” II

Posted by Chase Stuart on July 11, 2006

Reading yesterday's post on YPC, left me with the following question. Is it more impressive to rush 50 times for 250 yards, or 300 times for 1250 yards? That's a simple question with lots of complicated answers.

Let's first look at all RBs from 2002-2004 performed the following season.

In 2004, twenty-six RBs ran between 51 and 100 times, and as a group they averaged 4.18 YPC. Seven RBs had 250-300 carries, and that group averaged 4.19 YPC. I'm not sure exactly what you would say about the talent levels of the two groups. Are they similar because the players averaged the same YPC? Or is the high carry group better because those runners earned more carries, which is a reflection of how good they are?

You're probably expecting me to tell you that the low carry group averaged 5.0 YPC in 2005, while the high carry group averaged 3.0 YPC. Or maybe the reverse. Either way, I set you up for nothing. In 2005, the 26 members of the original low carry group averaged 4.15 YPC, and the original high carry group averaged 4.14 YPC. Here's the full chart:

	   2003	   2004	   2005
01-50 4.03 4.17 3.96
51-100 3.64 4.05 3.95
101-150 4.37 4.26 4.22
151-200 3.61 4.34 3.95
201-250 4.31 3.79 3.81
251-300 4.51 4.28 4.13
301+ 4.35 4.36 4.37

Remember exactly what this is saying. It means that all RBs with 151-200 carries in 2002 averaged 3.61 YPC in 2003 (on however many carries). The two high carry groups (251-300 and 301+) in Year N (2002, 2003 or 2004) averaged the most yards per carry in year N+1 (2003, 2004 or 2005). That's pretty interesting, although maybe not entirely surprising. It appears to reaffirm what we thought before: the best RBs get the most carries. And assuming that a player's ability remains relatively constant from year to year, then it makes sense that the RBs with the most carries one year would average the most yards per carry the next.

Here's the same table as above but with carries listed instead of YPC.

	   2003	   2004	   2005
01-50 2087 2131 1330
51-100 1116 1661 1997
101-150 795 1527 965
151-200 731 699 780
201-250 1414 1474 1386
251-300 2407 728 1278
300+ 2822 2866 2774

Don't be alarmed at the high number of carries from that first group. From 2002-2004, 251 RBs that were in the 01-50 carries group while only 31 RBs over those three seasons totaled 300+ carries. What's more important is that only three RBs with 01-50 carries in Year N then rushed for 900 yards in Year N+1. Here's the list, with the first year on the left and the second season on the right.

Player		Rush	Yards	YPC	Rush    Yards	YPC
Rudi Johnson 17 67 3.94 215 957 4.45
Reuben Droughns 6 14 2.33 275 1240 4.51
Willie Parker 32 186 5.81 255 1202 4.71

To be honest, I'm a bit surprised that only one runner per year came out of nowhere to have a big year. You probably want to temper your enthusiasm on any unproven runner unless you've got a really good reason to like him.

  • A couple more ways to look at YPC data

Yesterday I wrote that the RBs with the fewest carries having the lowest yards per carry average (as a group) was probably counterintuitive. But just because those runners as a group had a low average, that doesn't mean it's hard for individual runners to have a high average.

Over the four seasons, the top 26 runners in yards per carry all had fewer than 40 carries. On the flip side, none of the bottom 100 runners in yards per carry even had 50 carries. So yeah, you're going to get some extreme results when you look at these small sample sizes.

But we can still play around with the numbers a little bit. First, let's look at all RBs with a small number of carries one year, and a large number the next. There are thirty-three RBs in NFL history that rushed less than 100 times in Year N, and 250 times or greater in Year N+1.

Name			YearN	Rush	Yards	YPC	Rush	Yards	YPC
Lamont Jordan 2004 93 479 5.2 272 1025 3.8
Willie Parker 2004 32 186 5.8 255 1202 4.7
Reuben Droughns 2003 6 14 2.3 275 1240 4.5
Emmitt Smith 2003 90 256 2.8 267 937 3.5
Troy Hambrick 2002 79 317 4.0 275 972 3.5
Deuce McAllister 2001 16 91 5.7 325 1388 4.3
Fred Taylor 2001 30 116 3.9 287 1314 4.6
Shaun Alexander 2000 64 313 4.9 309 1318 4.3
Lamar Smith 1999 60 205 3.4 309 1139 3.7
James Allen 1999 32 119 3.7 290 1120 3.9
Jamal Anderson 1999 19 59 3.1 282 1024 3.6
Ahman Green 1999 26 120 4.6 263 1175 4.5
Stephen Davis 1998 34 109 3.2 290 1405 4.8
Duce Staley 1997 7 29 4.1 258 1065 4.1
Anthony Johnson 1995 30 140 4.7 300 1120 3.7
Garrison Hearst 1994 37 169 4.6 284 1070 3.8
Harvey Williams 1993 42 149 3.5 282 983 3.5
Erric Pegram 1992 21 89 4.2 292 1185 4.1
Barry Foster 1991 96 488 5.1 390 1690 4.3
Cleveland Gary 1991 68 245 3.6 279 1125 4.0
Gaston Green 1990 68 261 3.8 261 1037 4.0
Ottis Anderson 1988 65 208 3.2 325 1023 3.1
Greg Bell 1987 22 86 3.9 288 1212 4.2
Charles White 1986 22 126 5.7 324 1374 4.2
Curt Warner 1984 10 40 4.0 291 1094 3.8
Earnest Jackson 1983 11 39 3.5 296 1179 4.0
Curtis Dickey 1982 66 232 3.5 254 1122 4.4
Wendell Tyler 1980 30 157 5.2 260 1074 4.1
Terdell Middleton 1977 35 97 2.8 284 1116 3.9
Wilbert Montgomery 1977 45 183 4.1 259 1220 4.7
Otis Armstrong 1973 26 90 3.5 263 1407 5.3
Lydell Mitchell 1972 45 215 4.8 253 963 3.8
Ron Johnson 1971 32 156 4.9 298 1182 4.0
Totals 1359 5583 4.11 9440 38500 4.08

I'm not sure what you would have predicted, but the same runners that averaged 4.1 YPC on an average of 42 carries ran equally well with an average of 286 carries the next year. But that's misleading if it makes you place more value on small sample sizes.

Inside the group there wasn't much consistency: only one-third of the RBs averaged within half a yard per carry of their YPC average from Year N. The correlation coefficient, explained here of the YPC for the RBs in Year N and Year N + 1 was just 0.16. This means that the YPC average of the RBs in the second year can be "explained by" 3% their YPC average in the first year, and 97% other stuff. This is a longwinded way of saying a small bit of data (less than 100 carries) just doesn't tell you very much. What about a bigger piece of data?

There are 188 RBs in NFL history that recorded at least 250 carries in consecutive seasons. How do their numbers compare? The high workload RBs averaged 4.32 YPC in Year N, and 4.28 YPC in Year N+1. But as we saw above, that could be the result of lots of RBs cancelling each other out.

You'd expect the correlation coefficient to be higher than 0.16 here, and it is. But it's only 0.39; that means that even with RBs that we know a lot about, only 15% of each RB's YPC in Year N+1 can be "explained by" his YPC average from the previous year.

Before we get to the last way to measure the data, an analogy might help here.

Let's say you flip a regular coin ten times, and it lands on heads ten times in a row. You'd probably still say the coin is only 50% likely to land on "heads" on the next flip. Because even though a coin will only land on ten straight heads once every 1,000 times, the odds that your regular coin was actually a weighted coin is a lot less than one in a thousand.

But now assume you take a coin with heads on both sides and put it in a bag with two other coins. If you pull out a coin without looking, flip it twice, and it lands on two heads, you won't think the odds are 50/50 anymore that the next flip will produce a heads. Because even though getting two straights heads isn't very unlikely, it's more likely that you've grabbed the coin with two heads.

Once you think of football statistics like that, the following analogy is pretty simple. If Joe Runningback runs 75 times for 500 yards, you can either chalk it up to a combination of good luck and a small sample size, or you can rationalize the result by claiming that Joe Runningback's pretty good. It then becomes a question of what's more likely: that an average RB could do what Joe did, or that Joe's actually a very good runner? And that's why when you deal with small sample sizes, your own personal beliefs on a player become very important in how you interpret the data.

This gets us to the last idea for the day. There have been a few running backs in the NFL, so here's how I narrowed the list. Any RB that debuted before 1970, had fewer than 200 career carries or is still active was thrown out. I then looked at all RBs who had 51-100 career carries at the end of either their first or second season while averaging at least 4.00 yards per carry. That left us with 58 RBs who fit our basic profile: runners who had success on a small number of carries very early in their career.

What we'll add in is their draft position. Presumably, the round in which a player was drafted can serve as a predicate for "I think Joe Runningback is a good or bad runner."

I'll let you guys comment on the data. The numbers on the left represent the group's career-to-date totals after the season in which each RB passed the 50 carry mark (either their first or second); the second set of numbers show how the group performed for the remainder of their careers.

Round	# RBs	Rush	Yards	YPC	Rush	Yards	YPC
1 9 680 3,229 4.75 5,099 21,270 4.17
2-3 10 751 3,519 4.69 6,164 26,316 4.27
4-6 13 975 4,419 4.53 6,743 25,689 3.81
7+ 26 575 2,997 5.21 3,106 13,068 4.21
2,981 14,164 4.75 21,112 86,343 4.09

For those curious, the correlation coefficient of each RB's original YPC average to his YPC average for the remainder of his career was 0.43; the correlation coefficient for draft round (with the number 10 used for any undrafted player or player drafted after round 9) with his remaining YPC average was -0.23. We'd expect a negative correlation here: the lower (better) the round a player was drafted in, the higher his expected yards per carry average.

7 Comments | Posted in General, Statgeekery

Breaking down “Yards Per Carry”

Posted by Chase Stuart on July 9, 2006

If you only had one stat available and you had to pick between two different running backs, you'd probably want to know how many yards each runner averaged per carry. A player's rushing yards is largely a function of his total carries, and that number is dependent on certain things beyond his control (the quality of the other RBs on the team, his coach's philosophy, and the scoreboard, for example). But yards per carry helps to level the playing field, and gets at exactly what we want to know.

Fortunately, we have lots of statistics available, so we don't need to use only yards per carry. So if you were building an NFL team you'd take Clinton Portis before Rock Cartwright, despite Cartwright's 3.0+ advantage in yards per carry last season.

This gets us to the problem of small sample sizes. When Shawn Bryson averaged 5.28 YPC on 50 carries in 2004, it was easy to dismiss his success. Many would claim that achieving a high yards per carry average on a small number of carries is easy. (Of course, when Willie Parker rushed for 5.81 YPC on 32 rushes, those people probably said he wasn't as good as his numbers either.)

You'll hear this argument a lot: it's easy to record a high YPC if you don't have many carries. Maybe they don't really mean easy, but at least easier. But just because people say it, doesn't make it true. It's undoubtedly true that it is easier to get all sorts of extreme YPC numbers with a small number of carries, and that includes really high (and really low) YPC averages. And RBs that are running well usually get more carries going forward than runners that don't do so well. So what do the numbers say?


Carries 2002 2003 2004 2005
01-50 3.92 3.75 4.01 3.34
51-100 4.34 3.86 4.18 4.15
101-150 3.93 4.26 4.11 3.78
151-200 3.88 3.97 4.17 3.87
201-250 3.94 4.11 4.11 3.97
251-300 4.28 4.48 4.19 4.14
301+ 4.41 4.43 4.36 4.49

Average 4.15 4.18 4.19 4.07

The above table includes every RB's YPC average the past four years. If a RB had 87 carries, his totals were put in the "51-100" category. Some of these groups are really small -- in 2003, only three RBs had between 251-300 carries. The low carry group is by far the biggest, because about 80 RBs a year have 50 carries or less. Most of the other groups have between 10 and 25 players.

So what does this table tell us? The RBs with the fewest carries also have the lowest yards per carry average. Now be careful. This does not mean that it's harder for RBs with fewer carries to obtain a high YPC average. It just means that RBs with fewer carries also tend to average fewer yards per carry. They also may have a higher YPC average (more on that tomorrow).

As you could probably noticed, the NFL average jumps around a bit. The average YPC is relatively constant so it's probably not absolutely necessary to normalize each player's production by year, but it feels like the right thing to do. Here's the same data as above but instead of showing each group's average YPC, we're looking at each group's average YPC as a percentage of the league average yards per carry.


2002 2003 2004 2005
01-50 94.4% 89.6% 95.8% 82.1%
51-100 104.6% 92.2% 99.7% 102.1%
101-150 94.5% 101.8% 98.1% 92.9%
151-200 93.4% 94.9% 99.5% 95.2%
201-250 95.0% 98.2% 98.0% 97.6%
251-300 103.2% 107.2% 100.0% 101.7%
301+ 106.2% 106.0% 104.0% 110.2%

I think that table captures what we want a bit better. The runners with the fewest carries clearly average the fewest yards per carry. The RBs with the most carries also average the most yards per carry.

So what does this all mean? Well, it might not mean much. It's logical to assume that coaches give the most carries to the best RBs. Less talented RBs won't get as many carries, and we shouldn't expect them to do well just because they are only running two or three times a game. Something else might skew the data as well. If Joe Scrub is lucky enough to rush 120 times for 600 yards, his coach might give him an extra 40 carries. Even if he only averages three yards per carry on those additional touches, his YPC for the season will be 4.50, and he'll be in the 150+ bracket. So the RBs in the 150+ bracket will get a boost while the RBs in the 101-150 group will "lose" Joe Scrub's stats.

Now that we know it's not common for running backs to average a high number of yards per carry without a lot of carries, let's take a quick look at all RBs last year that averaged at least 4.5 yards per carry with fewer than 100 rushes.


Name Car Yards YPC
Rock Cartwright 27 199 7.37
Jason McKie 3 22 7.33
Dan Kreider 3 21 7
Aveion Cason 10 65 6.5
Darren Sproles 8 50 6.25
Michael Pittman 70 436 6.23
Michael Turner 57 335 5.88
Justin Fargas 5 28 5.6
Terry Jackson 2 11 5.5
Damien Nash 6 32 5.33
Maurice Hicks 59 308 5.22
Adrian Peterson 76 391 5.14
Ron Dayne 53 270 5.09
Ryan Moats 55 278 5.05
Bryan Johnson 1 5 5
Shawn Bryson 64 306 4.78
Leonard Weaver 17 80 4.71
Bruce Perry 16 74 4.62
Mack Strong 17 78 4.59
Chris Perry 61 279 4.57
B.J. Askew 13 59 4.54
Patrick Pass 54 245 4.54

Darren Sproles, Michael Turner, Justin Fargas, Maurice Hicks, Adrian Peterson, Ryan Moats, Leonard Weaver and Chris Perry are all young and talented runners that haven't earned much playing time yet in the NFL. All play behind some pretty good runners, but are only an injury away from seeing significant playing time.

Michael Pittman, Ron Dayne and Shawn Bryson are NFL vets that have seen some success after changing teams, but have had generally underwhelming NFL careers. Bryson and Pittman are both versatile RBs with career YPC averages of 4.0+ and soft hands, but neither looks to be a starter anytime soon.

There's only one RB on that list that is a projected starter in 2006, and it's Ron Dayne. Dayne's always been a controversial running back that seems to polarize NFL fans. Will he revive his career in Denver? Should we care more about the much larger sample size (most of his career in New York where he was a bust) or the significantly smaller but more relevant one (his success playing in Denver last year)? It's hard to say, and I don't think he was as impressive as his 2005 stats indicated, but the above data makes me think we probably shouldn't dismiss those numbers too quickly.

10 Comments | Posted in General, Statgeekery

Wide receivers, quarterbacks, and consistency II

Posted by Doug on July 7, 2006

Following up on yesterday's post. . .

I decided it might make sense to open up the investigation a bit. What I plan to do is to consider each team's coach, their main quarterback, main running back, top two wide receivers and top pass-catching tight end (I'd like to include offensive linemen, too, but don't have sufficient data). Ideally, I'd like to see what happens to the team's offensive output when each of those factors is changed one at a time. For example, is a team's performance more consistent if they change only the coach or if they change only the quarterback? Is a team's offensive output more variable, ceteris paribus, when they switch running backs or when they switch wide receivers?

This is fairly easy to do, but it turns out that we're going to run into sample size problems. Only four teams since 1978, for instance, have kept the same main quarterback, running back, and tight end, and top two wide receivers, but changed coaches. (How many of those four can you name off the top of your head? Two of them were Super Bowl champs; you will figure those out if you give it a moment's thought. I'll be impressed if anyone can name the other two without looking it up.)

But in a lot of cases, the team's "top pass-catching tight end" is a very minor part of the offense. The same could even be said of the team's second wide receiver in a lot of cases and even of the running back in extreme cases. I'd like to make the question a little more flexible, allowing the tight end, for example, to change if he wasn't a big part of the offense in Year 1. In other words, I want to try to see what happens if three of the four most important (skill position) parts of the offense stay the same and one changes. It's not exactly clear how to best implement that, but once I get it figured out I should have some respectable sample sizes and still stay within the spirit of the original question.

I'll think about it and get back to you on it in about ten days.

That's right. I'm taking next week off. I'll be traveling a bit and internet access will be spotty. But fear not, I have deputized my friend Chase, who claims to have five full days of posts ready for you. I'll be around enough to monitor what's happening, but Chase will be running the show.

12 Comments | Posted in General, Statgeekery

Wide receivers, Quarterbacks, and consistency

Posted by Doug on July 6, 2006

I recently picked up a copy of a book called The Wages of Wins, by David Berri, Martin Schmidt, and Stacey Brook. The authors are economists and they apply their economic outlook to the world of sports. I generally find this sort of thing interesting because the economist worldview has always struck me as very sensible. And because I like sports.

I want to make clear that this post is not a review of the book. I may or may not do that in a future post, but right now I have not read enough of it, nor have I read it carefully enough, to construct an adequate review. But I did get an idea while reading through it, and that's a sign of a promising book. The purpose of this post is merely to share the idea.

Most of the book is about baseball and basketball, but there is one chapter devoted to football. Its title is How are quarterbacks like mutual funds? It starts with a game-by-game look at Brett Favre's 2004 season, in which he threw 20 touchdowns and 4 interceptions in the odd-numbered games, and 10 touchdowns and 13 picks in the even-numbered games.

The title question is then answered:

The Favre story suggests that NFL quarterbacks are not quite as consistent as NBA players. Like mutual funds, past performance is no guarantee of future returns.

The authors then go on to build a metric of quarterback performance. The discussion will surely get sidetracked if I tell you exactly what it is, so I'm not going to do that. I'll just tell you that it includes passing attempts and yards, rushing attempts and yards, interceptions and fumbles. Using that metric, the authors measure the year-to-year consistency of quarterbacks and show that quarterbacks are, in fact, not very consistent. More precisely, quarterbacks' ratings according to this measurement constructed from yards, attempts, and turnovers are not very consistent. It's not uncommon, for example, to see a quarterback's rating go from the top quintile in the league to the bottom quintile --- or vice versa --- in consecutive years. I had not realized how variable quarterback stats are.

The authors observe that one reason for this inconsistency is that the rating they attach to a quarterback in a given year is dependent on the performance of a lot of players besides the quarterback himself. This point is well-known to all aficianados of football numbers; it is simultaneously the reason football is so fun to watch and the reason it's so hard to analyze. Any measure that penalizes Brett Favre when Donald Driver fails to get open or rewards Favre when Driver steals a sure interception out of the defender's hands is going to make Favre look more inconsistent than he really is. And that's not a criticism of Berri, Schmidt, and Brook's system in particular, because every system does it.

Favre's rating is a function of his performance, his teammates' performance, and random noise (yeah, there's some other stuff in there, too. I'm trying to keep it simple.). A rating of, say, Dwyane Wade, based on his stats would also be a function of his performance, his teammates performance, and random noise. But since Favre has 10 teammates and Wade has only four, it would be reasonable to suspect that Favre's rating is diluted by factors other than Favre's performance to a greater extent than Wade's is. Even if Favre's performance is rock steady from game to game and year to year, his rating, because there is so much other junk mixed into it, might still tend to vary a lot.

To summarize: Berri, Schmidt, and Brook do a very nice job of showing that quarterbacks' statistics are inconsistent (compared to those of basketball and baseball players) from year to year. But the open question is whether quarterbacks' performances are inconsistent from year to year, or if the variance in the statistics is due to the weak relationship between statistics and performance.

And the issue is not limited to quarterbacks, of course. In fact, quarterbacks might be the least affected by their teammates' performance. This is a wild guess, but I'd say that Donald's Driver's statistics are more influenced by Brett Favre's performance than Favre's are by Driver's performance. If Driver isn't doing his job, Favre can at least try find someone else to throw to. But Driver has no such option if Favre isn't holding up his end of the bargain.

I am going to shift the focus from quarterback to receivers now, and try to come up with a very rough estimate of a first pass at an extremely preliminary vague notion of an idea for how to maybe possibly determine how much of a wide receiver's production is attributable to the receiver himself, the quarterback, and everyone else on the team.

The idea goes like this. Look at all wide receivers who played at least 8 games in two consecutive seasons, and divide those receivers into three groups:


  1. those who were on the same team both years, and the team had the same starting quarterback both years;

  2. those who were on the same team both years, but with different starting quarterbacks each season;

  3. those who were on different teams in the two different years.

It'd be nice to also have a different-team-same-quarterback group, but history just doesn't provide us enough examples of that. Anyway, we press on.

The next step is to compute the year-to-year correlation in receiving yards per game for each of the groups. As many of you already know, a correlation coefficient is a number between -1 and 1 that measures the strength and direction of the linear relationship between two quantities. A positive correlation indicates two quantities that vary together (i.e. when one goes up, so does the other) while a negative correlation indicates two quantities that vary inversely. A correlation of 1 (or -1) means that the two quantities are perfectly linearly related. That is, one quantity can be predicted exactly if the other is known. A correlation of 0 means that there is no linear relationship at all between the two, so knowing one is of no use to you in predicting the other.

As this pertains to pairs of consecutive seasons of the same wide receiver, the correlation coefficient tells us roughly how easy it is to predict a receiver's stats this year using only his stats from last year. Here are the numbers:

Group 1 - same team, same QB: correlation = .75

Group 2 - same team, different QB: correlation = .64

Group 3 - different team: correlation = .44

What does this mean? The standard way to interpret these numbers is as follows (from the first statistics book I grabbed off the shelf):

[the square of the correlation coefficient] is the proportion of the total variation in the y's that can be attributed to the linear relationship with x]

Sometimes the square of the correlation coefficient is described in terms of "explanatory power": it's the percentage of the variation in y's that is "explained by" variation in x. The squares of those numbers are: .56, .41, and .19. So roughly speaking, what we have is this:


  • For receivers on the same team with the same quarterback, their numbers this year are "explained by" 56% their numbers from last year, and 44% other stuff.

  • For receivers on the same team but with a different quarterback, their numbers this year are "explained by" 41% their numbers from last year, and 59% other stuff.

  • For receivers on different teams, their numbers this year are "explained by" 19% their numbers from last year, and 81% other stuff.

I really don't know what that means, except in a strict mathematical sense. It's tempting, but not mathematically justifiable, to try to make some conclusions about the role of the quarterback and the rest of the team based on differences between some of the numbers above. I am, for now, just going to say what I know is true: that receiver's stats are definitely more predictable if they stay on the same team, and even more predictable if that team keeps the same quarterback. Not an earth-shattering revelation I realize, but hey, it's just a blog post.

It might be interesting to play this game with other factors too, like coaches for instance. That is, build a same-team / same-quarterback / different-coach group and compare it to a same-team / different-quarterback / same-coach group. I'll put that on the ever growing to-do list.

5 Comments | Posted in General, Statgeekery

Is less more?

Posted by Doug on July 5, 2006

A few weeks ago, footballoutsiders linked to my ten thousand seasons series. A general theme among the comments was that the simulation was inaccurate because it was based on season-long power ratings instead of last-few-weeks power ratings. Because teams' true strengths vary so much during the course of a season, I should have used a smaller but more recent sample instead of using all the data. Less is more. I thought about that for awhile and pondered the possibility that those folks might have a good point.

That caused me to try to build a power rating system based on at-the-time strength of schedule, which I was unable to do. But a by-product of the effort was this post about at-the-time strength of schedule. Interestingly, the majority of the respondents to it felt that taking a five-week slice of data introduced too much variability into the numbers. Use all the data. More is more. I thought about that for awhile and pondered the possibility that those folks might have a good point too.

So I decided to do a quick check. I looked at all games in weeks 10--13 during the years 1990--2005. For each game, I recorded the following information:


  • the difference between the two teams' full-season at-the-time ratings according to the simple rating system.

  • the difference between the two teams' last-5-weeks at-the-time ratings according to the same system.

So if it's week 12 of 2005 and San Francisco is playing Tennessee, we look at their week 1--11 ratings (which rate the Titans as about 5 points better) and their week 7--11 ratings (which rate the 49ers a couple of points better). I chose to look only at weeks 10 through 13 because week 10 is late enough to show some differentiation between the full-season and at-the-time ratings, and week 13 is early enough that most teams haven't given up or started to rest their regulars or whatever.

Now that we've got all the data collected, we run a logit regression to build a formula that will predict the winner of each game. Result: the at-the-time rating was not significant (in the official statistical sense). That means: if you know the full-season ratings, then there is not sufficient evidence to conclude that knowing the last-5-weeks ratings helps you predict the winners of this week's games.

If you build a formula that uses just at-the-time ratings, it will predict about 62% of the games correctly. If you build a formula that uses just full-season ratings, it will predict about 66.4% of the games correctly. If you build a formula that incoporates both, it will predict about 66.6% of the games correctly.

Interesting.

One problem here is that the simple rating system does not take home field advantage into account. It could be modified to do so, but I've never bothered because NFL teams always play the same number of home and road games during the course of a season. But that's not true in a 5-week stretch, so the last-5-weeks ratings have a bit of noise included in them. I'm not sure how much of a difference that makes, but it might make some.

Assuming the above paragraph doesn't invalidate the study, this looks like pretty clear evidence that, in this case, less is not more.

7 Comments | Posted in General, Statgeekery

At-the-time strength of schedule

Posted by Doug on July 3, 2006

The Steelers and the Saints had the same strength of schedule last year. The Steelers' opponents' record, after throwing out the games against Pittsburgh itself, was 121-119. The Saints' opponents' record was the same.

But it seems that Pittsburgh's opponents were playing a lot better at the time than New Orleans' were. If you look at each opponent's record in just the two weeks before and the two weeks after they played the team in question, you get a different picture of their strength of schedule.

For instance, here is Pittsburgh's:


1 ten beat bal, lost to stl
2 hou lost to buf, lost to cin
3 nwe beat oak, lost to car, lost to sdg, beat atl
5 sdg beat nyg, beat nwe, beat oak, lost to phi
6 jax lost to den, beat cin, lost to stl
7 cin lost to jax, beat ten, beat gnb, beat bal
8 bal beat cle, lost to chi, lost to cin, lost to jax
9 gnb lost to min, lost to cin, beat atl, lost to min
10 cle lost to hou, beat ten, beat mia, lost to min
11 bal lost to cin, lost to jax, lost to cin, beat hou
12 ind beat hou, beat cin, beat ten, beat jax
13 cin lost to ind, beat bal, beat cle, beat det
14 chi beat tam, beat gnb, beat atl, beat gnb
15 min beat det, beat stl, lost to bal, beat chi
16 cle lost to cin, beat oak, beat bal
17 det lost to cin, beat nor

Here's how you read that mess:

In week 1, Pittsburgh played Tennessee. In the weeks surrounding the Pittsburgh game, Tennessee beat Baltimore and lost to St. Lous. In week 14, Pittsburgh played Chicago. In the surrounding weeks, Chicago beat Tampa, Green Bay, Atlanta, and Green Bay again.

If you tally it all up, you'll find that Pittsburgh's opponents were 32-24 in the two weeks before and after playing the Steelers. Note in particular the last weeks of the season. From week 12 on, Pittsburgh's opponents were beating almost everyone except Pittsburgh (and other teams that Pittsburgh played during that stretch).

New Orleans' opponents, on the other hand, were not doing as well around the time they played the Saints.


1 car beat nwe, lost to mia
2 nyg beat ari, lost to sdg, beat stl
3 min lost to tam, lost to cin, lost to atl
4 buf lost to tam, lost to atl, beat mia, beat nyj
5 gnb lost to tam, lost to car, lost to min
6 atl beat min, lost to nwe, beat nyj
7 stl lost to sea, lost to ind, beat jax
8 mia lost to tam, lost to kan, lost to atl, lost to nwe
9 chi beat bal, beat det, beat sfo, beat car
11 nwe lost to ind, beat mia, lost to kan, beat nyj
12 nyj lost to car, lost to den, lost to nwe, beat oak
13 tam beat atl, lost to chi, beat car, lost to nwe
14 atl beat det, lost to car, lost to chi, lost to tam
15 car beat atl, lost to tam, lost to dal, beat atl
16 det lost to gnb, lost to cin, lost to pit
17 tam lost to nwe, beat atl

When you add it up, Pittsburgh's at-the-time strength of schedule was 32-24 and New Orleans' was 21-33. Even though their overall strengths of schedule were identical, it might be the case that the Steelers were actually playing a tougher slate.

Here is the full list.


TM YR Local Overall Diff
=========================================
sfo 2005 35- 20- 0 126-114- 0 +0.111
nwe 2005 33- 21- 0 124-116- 0 +0.094
pit 2005 32- 24- 0 121-119- 0 +0.067
dal 2005 31- 21- 0 127-113- 0 +0.067
jax 2005 30- 25- 0 115-125- 0 +0.066
nyj 2005 29- 22- 0 123-117- 0 +0.056
buf 2005 28- 24- 0 117-123- 0 +0.051
ind 2005 28- 25- 0 115-125- 0 +0.049
min 2005 29- 26- 0 117-123- 0 +0.040
nyg 2005 31- 26- 0 121-119- 0 +0.040
bal 2005 29- 25- 0 124-116- 0 +0.020
cle 2005 29- 27- 0 120-120- 0 +0.018
kan 2005 29- 26- 0 123-117- 0 +0.015
gnb 2005 28- 25- 0 124-116- 0 +0.012
sea 2005 25- 30- 0 107-133- 0 +0.009
det 2005 27- 27- 0 118-122- 0 +0.008
ten 2005 27- 28- 0 119-121- 0 -0.005
phi 2005 28- 26- 0 126-114- 0 -0.006
sdg 2005 29- 23- 0 136-104- 0 -0.009
den 2005 27- 26- 0 125-115- 0 -0.011
chi 2005 24- 29- 0 112-128- 0 -0.014
oak 2005 28- 27- 0 126-114- 0 -0.016
hou 2005 26- 27- 0 123-117- 0 -0.022
car 2005 23- 30- 0 110-130- 0 -0.024
stl 2005 23- 31- 0 114-126- 0 -0.049
mia 2005 22- 32- 0 110-130- 0 -0.051
was 2005 27- 28- 0 132-108- 0 -0.059
tam 2005 21- 33- 0 110-130- 0 -0.069
cin 2005 22- 32- 0 117-123- 0 -0.080
atl 2005 21- 34- 0 118-122- 0 -0.110
nor 2005 21- 33- 0 121-119- 0 -0.115
ari 2005 20- 33- 0 119-121- 0 -0.118

My original intent in looking into this was to develop a rating system that would use this kind of strength-of-schedule number instead of the full season number. I ran into some technical troubles, but I'll get them sorted out sooner or later.

17 Comments | Posted in General

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

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