Writers of Pro Football Prospectus 2008

27 Aug 2007

Does Peyton Manning Break Pythagoras?

In this week's Scramble for the Ball thread, Chris wrote:

The Colts also winning more games than their expected or Pythagorean win total is also a testament of Manning giving them value at the margin.

Fellow FO reader pharmboyrick added:

...truly great QBs significantly raise the win total of their teams. Manning is a combination of a talented pocket passer with an innovative and opportunistic offensive coordinator.

While we can't prove those statements to be true or false one way or another, we can look at the available data and try to determine whether there's evidence such a trend exists.

First off, it's true that Manning and the Colts have exceeded their Pythagorean win projection almost every year. If you ignore Manning's rookie season (where he was by no means truly great, and in fact a disaster the first few weeks), the Colts have averaged one win in excess of what would be expected by Pythagoras. That being said, there's another factor to be accounted for here -- teams that win as many games as the Colts have under Manning often exceed their Pythagorean win total. For example, since the advent of the 16 game season, the average 12-win team has exceeded their Pythagorean projection by .76 games; in 2006, the Colts were 2.41 wins ahead of their Pythagorean projection, and 1.65 wins above the average 12-win team's Pythagorean projection. On average, the 1999-2006 Colts were 0.4 wins per season better than they would have been expected to according to the combination of their raw win totals and the expected boost for teams who win those number of games. Just for the purposes of this little XP, let's say that the Colts had 0.4 WAP (Wins Above Pythagoras) per season.

This doesn't mean that Pythagorean projections don't work, mind you. The reality of the situation is that very few teams have such strong differentials as to be projected to win twelve games, for example, based upon their projection alone. Inherently, a few things go their way during the season. Is this luck or a variable beyond simple PF/PA that we don't measure? Almost assuredly both.

Now, is there any evidence that the quarterback play of the Colts is the reason why they're exceeding their Pythagorean expectations? That's something we can attempt to measure. Let's take every team from 1978 on (scaling all seasons to a 16-game schedule), measure their Pythagorean wins as well as their WAP, and compare it to the quarterback rating of the team's leading passer. QB Rating is not a perfect stat by any means, but without DPAR data available for 1995 and earlier, it will do.

What I found was that the correlation between QB Rating and the difference between a team's Pythagorean wins and its actual record is a very slim .07 -- in other words, there's not a remotely significant relationship between QB rating and above-expected performance. Furthermore, QB rating had a -.23 correlation with a team's WAP. These weak correlations do not necessarily mean that Chris's point isn't true; instead, it means that the data we have available does not show the relationship to exist.

What if we take Rick's point that "truly great QBs" significantly raise the win total of their teams? Defining "truly great" quarterbacks is a difficult thing, but no one argues that great quarterback play isn't hugely important to a team -- since 1978, there's a .51 correlation between the starting quarterback's QB rating and a team's raw wins. Let's define "a truly great quarterback" to be the 50 best single-season QB ratings since 1978. Of those 50 teams, 38 exceeded their Pythagorean projection, the average team doing so by .61 games. The thing is, we already know excellent quarterback play leads to winning teams; we're looking to see if it raises the win totals of their teams above similar teams without the stud quarterback. We obviously can't separate quarterback play out entirely, but we can use WAP to determine how the average team did relative to the team with the stud passer and the same number of wins, and whether the All-World quarterback really made a difference.

The answer? Not at all. The 50 teams with excellent quarterbacks averaged -.21 WAP, or slightly worse than teams with average quarterbacks but the same number of wins did. Essentially, what the data we have available shows is that quarterback play has a lot to do with winning, but very little to do with exceeding a team's performance as recalculated by the Pythagorean Theorem.

Posted by: Bill Barnwell on 27 Aug 2007

38 comments, Last at 29 Aug 2007, 10:58am by admin


by hooper (not verified) :: Mon, 08/27/2007 - 11:28pm

Correct my interpretation of Pythagorean if it's wrong, but it's the use of the ratio of points for and points against to determine the approximate winning percentage, right?

What if the really strong teams tend to build strong leads early enough in games that they stop trying to score and start trying to run out the clock in the 4th quarter? Could we be seeing the "run when winning" concept damping the point differential in enough games to lower the Pythagorean prediction well below actuality?

by Len (not verified) :: Mon, 08/27/2007 - 11:50pm

Is Manning's example unique? Are there any other instances of a team beating Pythagoras for such a stretch as the Colts have? And if so, what kind of QB play did they have?

by The McNabb Bowl Game Anomaly (not verified) :: Mon, 08/27/2007 - 11:50pm


The FO research on GUTS vs STOMPS indicates that really good teams tend to win by substantial margins, rather than skating by narrowly.

In fact, the research from that study proves that teams which win a lot of games by a small margin are not as successful in the postseason as teams that win by a large margin, even if the large-margin teams are beating up bad opponents and the small-margin teams are edging out good opponents.

That's a long-winded way of saying that the Pythagorean wins concept works very well in football. As noted in this piece, Pythagoras underestimates very good teams, but not by all that much (less that a game for 12-win teams).

by throughthelookingglass (not verified) :: Mon, 08/27/2007 - 11:52pm

Part of what makes Manning so great is his ability to pick up enough for a first downs (very few wasted yards). This causes his DPAR to be higher than an approximation based on his normal stats.
So, it may be more accurate to find the qbs whose performance exceeds their y/a, td/int, and see if their teams outperform Pythagoras.

by footballprofessor (not verified) :: Tue, 08/28/2007 - 12:04am

I think if you look a little further back in history you'll see that the Colts' streak of beating their Pythagorean estimates began back in 1989. Since then they've exceeded their Pythag estimate 13 out of 18 years, and from 1989 to 1996 they never finished below their estimate.

I think it has a lot more to do with management than quarterback performance, etc.

by BD (not verified) :: Tue, 08/28/2007 - 12:23am

Does anyone know if this trend holds in other sports?

One thought that occurs to me that is unique about football is that teams adjust their strategy (except for Mike Martz) when they have the lead. They are more likely to run the ball and use up time on offense (resulting in less points). On defense, they are more likely to play prevent, which prevents quick scores but results in more yardage allowed (and therefore points allowed).

In that way, even in a "STOMP", teams will probably score less points than expected given their skill level, etc.

Of course, by restricting the range to only 12+ winning teams, any correlations will tend to be suppressed. More advanced analysis of this question seems to be necessary.

by Dan (not verified) :: Tue, 08/28/2007 - 12:58am

I think that the reason for that .76 game "boost" for 12-win teams is the same as the reason for regression to the mean. Many 12-win teams got an extra dose of good luck in some of their close games. The set of 12-win teams includes lots of teams that should have been 10-6 or 11-5, but got some good luck that gave them an extra win or two (while only adding a fraction of a pythagorean win). (Luck has a bigger effect on real wins than on pythagorean wins - that's one of the main reasons why it's useful to keep track of pythagorean wins.) Of course, there are also a few teams in the 12-win set that ought to have won 13 or 14 games but had bad luck, which partially cancels things out, but there aren't nearly as many of those teams so they don't even out. Manning's Colts, are consistently exceeding their pythagorean projection, though, which makes good luck a less likely explanation, since it's unlikely that the same team would keep having all this good luck.

Instead of comparing the Colts to other teams with the same record, I think it would be better if you defined the comparison set as all of the teams whose pythagorean winning percent was about the same. (That gets closer to looking at the set of teams with the same true ability.) How many wins above their pythagorean total would you expect the Colts to get if they played like these teams?

by DGL (not verified) :: Tue, 08/28/2007 - 1:18am

"...Pythagoras underestimates very good teams..."

Yeah. One of his lesser-known theorems states, "Persia is ranked too low because Cyrus just wins. Orphism is way better than this. Akousmatikoi rulez!!

by Richie (not verified) :: Tue, 08/28/2007 - 1:37am

Footie Award to #7!

by Dan (not verified) :: Tue, 08/28/2007 - 2:23am

I just ran the numbers, and it looks like my suspicion was correct. I looked at every team since the last strike, 1988-2006. First, I looked at 3 stats: wins, pythagorean wins, and excess wins (wins minus pythagorean wins). As we'd expect if luck has a big effect on wins and excess wins, but only a small effect on pythagorean wins, there was a strong relationship between wins and excess wins, r=.50, but only a very weak correlation between pythagorean wins and excess wins, r=.10. So if we pick out good teams based on how many wins they have, we're going to tend to get teams with excess wins, but if we pick them out based on how many pythagorean wins they have then we're going to get teams that are much closer to 0 in excess wins.

The next thing I did was to pick out a bunch of comparison teams, with similar pythagorean wins to each of Manning's Colts teams, to see if they also tended to get lots of excess wins. The short answer: they didn't. They averaged very close to 0 excess wins. The long explanation: for each Colts season (1999-2006), I chose 14 comparison teams, the 7 closest in pythagorean wins that had more pythagorean wins and the 7 closest in pythagorean wins that had fewer pythagorean wins. (Since the 2000 and 2003 Colts were close together in pythagorean wins, 10.61 and 10.51, and I didn't want duplicates, I ended up with fewer comparison teams near them). I ended up with 101 comparison teams, in total (14 x 8 - 11 lost due to the 2000 & 2003 Colts). On average, the comparison teams had 0.037 excess wins, while the 8 Colts teams averaged 1.040 excess wins.

So Manning's teams are getting about 1 Win Above Pythagoras, on average, whether you just look at the raw excess wins or you compare them to other teams with similar pythagorean projections.

Is this difference statistically significant? Yes, it is. Looking at all teams since 1988, excess wins has a standard deviation of 1.23 (and it's almost the same if you just look at teams in the comparison group). For 8 years to average 1 excess win, just by chance, has a p value of less than .01. (That's the p value for the one-sided test; the two-sided test gives p less than .02.) So Colts' tendency to finish with more wins than their pythagorean projection is something that would be unlikely to happen due to chance.

by Yaguar (not verified) :: Tue, 08/28/2007 - 8:39am

I'm almost sure that a consistently good-to-great team like Indianapolis will exceed its Pythagorean win total over an extended period. I bet it's especially true of good-to-great teams that are great because of their offenses.

Here's why:

A very good team sometimes blows its opponents out, but rarely gets blown out by another team, unless that team has Ty Law or Maurice Jones-Drew.

After reaching a certain point margin, teams stop trying to score points as fast as possible. A team with a great offense, especially, is likely to achieve high point margins over its opponents several games per year. Meanwhile, teams playing against a great offense will probably not play conservatively unless they have a truly monstrous lead, because a great offense can come back and win a game at any time. Another quality of the good team is that it might rest starters once it has clinched some sort of playoff seeding.

Think about the 2004 season. There was a stretch where the Colts had 4 straight wins with 41+ points on offense and a 27+ margin of victory, including a game where Manning threw 6 touchdowns in two and a half quarters. against Detroit. (Seriously, two and a half quarters.) Jim Sorgi took over midway through the third quarter, and threw three passes for the rest of the game. Let it suffice to say that Manning could have thrown for nine touchdowns if necessary.

At the end of the season, they played Sorgi, Dominic Rhodes, and Brandon Stokley against the Broncos because they had already clinched their playoff position. They lost by 29 points. Then they played the Broncos again in the playoffs, and they hung 49 points on them.

I believe Chris is right, and Manning does break the Pythagorean wins system, in that he creates a disproportionate number of games that simply aren't remotely competitive. In those games, the scoreboard doesn't reflect the true strength of teams as accurately as it usually does, because one team has stopped trying to score.

by hooper (not verified) :: Tue, 08/28/2007 - 9:18am


I think Yaguar (#10) did a more thorough job of explaining what I meant in my first post. I agree that good teams tend to rack up larger margins, but I think that is precisely why they can afford to quit scoring in the last quarter of many games.

If the great teams were to continue their scoring pace throughout the entirety of the game, the margins would likely be even larger than we see, and the Pythagorean Wins of the great teams would likely be higher (and more closely match the records of the great teams). That would seem reasonable for great teams in general, though it wouldn't entirely explain the Colts.

by pawnking (not verified) :: Tue, 08/28/2007 - 9:38am

Let's remember what's going on with this kind of analysis. Although DRAP and such are good at analyzing success in specific plays, it's not as good at predicting wins (although still a fine system and better than most). The writers admit there are things contributing to wins and losses they cannot put into a formula.

Therefore, is it not surprising there may be great players, especially ones as cerebral and experienced as Manning, who can contribute more to wins than his mere physical skills? That is, we can measure to an extent how much his passing can contribute to the wins, but what about his game management?

The post which started this whole this by pharmboyrick raised this very point, although I would have put it differently.

DVOA, as far as I know, doesn't measure the impact of good OCs vs. bad OCs to wins and losses, except as much as each individual play will contribute to a win or loss. A great OC can not only design a good offensive system, but can call plays appropriate to the situation, which sometimes involves doing things other than scoring points. The effect of this would allow a great OC to outperform the team's overall Pythag win %.

Thus the point is a valid one. We can capture how great a QB Manning is through DVOA. We can't capture how great an OC he is except through peripheral stats such as wins above Pythag.

One last thought, can we evaluate other OCs (or playcallers) on this stat?

by footballprofessor (not verified) :: Tue, 08/28/2007 - 9:51am

"In those games, the scoreboard doesn’t reflect the true strength of teams as accurately as it usually does, because one team has stopped trying to score."

Yeah, that's very true of estimating wins according to final margin of victory. If you build a 49 point lead and then take your starters out and win by 20, you don't see everything in the final margin.

That's why I use three stats in my estimated wins formula - Highest High, Lowest Low, and Closing Margin. That way the 49 point lead you had in the game doesn't disappear.

by Bill Barnwell :: Tue, 08/28/2007 - 11:19am

Excellent work Dan. I think we can't necessarily link that, though, with Manning being the reason why, since there's no real relationship with QB rating.

by Rich Conley (not verified) :: Tue, 08/28/2007 - 11:28am

"If the great teams were to continue their scoring pace throughout the entirety of the game, the margins would likely be even larger than we see, and the Pythagorean Wins of the great teams would likely be higher (and more closely match the records of the great teams). That would seem reasonable for great teams in general, though it wouldn’t entirely explain the Colts."

There was a game against the 49ers last year (IIRC) where it was 41-0 at the half. The final score was 41-0, because the Chiefs played their 3rd string in the 2nd half.

Its still a blowout, and satisfies the guts/stomps thing, but doesnt accurately show the real difference in talent that day.

Teams definitely become more conservative in the second half when they have a large lead, and this is pretty much unique to Football (doesnt happen in baseball/basketball..does in soccer)

by Rich Conley (not verified) :: Tue, 08/28/2007 - 11:32am

Maybe theres something with teams who have extremely skewed offense/defense not working properly with pythagorean wins.

I'd be interested to see if teams with high offensive/low defensive DVOA continually overperformed, and if teams with low offensive/high defensive dvoa continually underperformed.

IE, is having a good offense more important than having a good defense?

by Cmos (not verified) :: Tue, 08/28/2007 - 12:49pm

Could we get some sort of DVOA for Qb's in short passing systems and Qb's in Deep throwing systems to see if one system produces a higher win total?

Maybe the same for zone blocking teams versus man blocking schemes?

by MJK (not verified) :: Tue, 08/28/2007 - 12:50pm

I read this EP last night, and went to bed thinking about it, and now first thing in the morning I find out that a lot of people have had a lot of the same ideas I have had. My fault for living on the West Coast, I guess...

I find it useful to think about this issue in reverse...i.e. rather than considering how many wins a given point differential predicts, think about what point differential you would expect an N-win team to have. That is, invert PW = f(PS,PA). So if we know a team has 10 wins, and we suppose it scored X points, we can estimate how many points it should have given up.

Next, remember that Pythagoras isn't a fundamental relation...there's no mathematically provable reason why it should hold...but rather it is a fit of a function to a large block of empirical data. In other words, we know from how many, many teams have done in the past that there is a relationship that usually holds between wins and [PS,PA], characterized by an exponent parameter that is fit to the data.

With these two thoughts in mind, consider an "average" 12-win team. Each win or loss is either a blowout, a close game, or something in between. Maybe the average 12-win team gets two blowout wins, five close wins, five 8 point wins, three close losses, and one blowout loss. This will correspond to the point differential that, when plugged into Pythagoras, will indicate about 12 wins.

So the only ways the Colts could be out-performing pythagoras in a season where they win 12 games is if more of their wins are "close wins" than your average 12-win team, or if more of their losses are blowouts than your average 12-win team, or some combination thereof.

Two hypotheses immediately jump out--either the Colts are strucutred in such a way that they tend to win more close games than most teams, and hence a larger percentage than normal of their wins are "close", or their losses occur in such a way that when they lose, they lose big.

My first thought had been that the second case was true, along the "playoff spot clinched, resting starters" idea that Yaguar suggested. This initially makes sense--a team that is as successful as the Colts will generally clinch their playoff seeding before Week 17, and hence will rest their starters and lose big in their last game or two, skewing their Pythagorean projection lower than is worthy of their actual team skill. This hypothesis would be easy to check--just re-run the pythagorean numbers and the W-L numbers excluding all games where the Colts had clinched their seed. However, I suspect, from Dan's research and from thinking about it, that this will not be the case, because if it were, we would expect ALL successful teams to show this phenomenon, but they apparently do not. Of course, it is possible that the Pythagorean fit just doesn't work well in the 12+ win regime, so any team out in the tail is going to not be well predicted by Pythagoras (especially because, with so few losses, it only takes one screwy game to screw up the Pythagorean projection for that season). But I have to think more about that.

So that leaves us with the second hypothesis. Are the Colts somehow winning more close games than expected? If so, that could have something to do with Manning...I know it has been shown statistically that Brady performs much better in close games (when the score is within a TD either way)--this may be true of Manning as well. Alternately, the Colts have traditionally had a powerful offense and a suspect defense, leading to high scoring shootouts. It runs against my intuition, but maybe shootouts tend to be closer than your "average" football game...

I don't have the time at work today to do any real research on this, so I just leave it to provoke thought and discussion...

by Joseph Adler (not verified) :: Tue, 08/28/2007 - 1:26pm

Good comments by MJK.

"Pythagorean Wins" is based on a formula that Bill James developed for baseball. It's a simple model that does a good job estimating the number of wins, but it's not perfect. Subsequent work by Clay Davenport of Baseball Prospectus led to something called the "Pythagenport" formula that is more accurate.

There isn't anything magical about this formula; it's a model that works reasonably well at predicting wins. As this article notes, the model is not perfect.

I think it makes more sense to try to calculate a better formula, perhaps by using a logistic regression model to estimate winning percentage.

by Marko (not verified) :: Tue, 08/28/2007 - 1:40pm

"There was a game against the 49ers last year (IIRC) where it was 41-0 at the half. The final score was 41-0, because the Chiefs played their 3rd string in the 2nd half."

That 41-0 halftime score was the Bears over the 49ers. I remember the announcers saying that the 41 point halftime margin was tied for the second highest in NFL history. The final score was 41-10, as the Bears pretty much tried to run out the clock rather than run up the score in the second half.

by OMO (not verified) :: Tue, 08/28/2007 - 1:44pm

"You really shouldnt believe everything sportscenter tells you."

Well played, sir. Well played.

by Andrew (not verified) :: Tue, 08/28/2007 - 1:56pm

Left unconsidered in this is that high-win teams are frequently out-performing their Pythagorean win totals.

Since 1978 and excluding 1982 and 1987, 100 teams have had 12 or more wins, but only 50 teams have had 12.00 or more Pythagorean wins.

The results are especially skewed at the high end. 46 teams have had 13 or more wins, but only 8 have had 13.00 or more Pythagorean wins. And 21 teams have had 14 or more wins, but only 1 has had over 14.00 Pythagorean wins.

This isn't to say good quarterbacking is not important. The following R squared values say it is. But it doesn't need to be Manning level play, just good.

R-squared value for Pythagorean Wins to various QB driven stats:

Yds/Att: 0.3111
Passing TD's: 0.2481
Offensive Int's: -0.1654

And just as helpful is a pass defense that gets interceptions, and a run defense that limits yards and rushing touchdowns.

Defensive INT's: 0.2054
Rushing TD's Allowed: -0.2902
Rushing Yards Allowed: -0.2880
Yds/Att Allowed: -0.2183

by Cmos (not verified) :: Tue, 08/28/2007 - 2:19pm

#24 Andrew
So yards/Att is important but that could still be masked by short passes going long and long pass being stopped at catch, right? System still isnt as much a factor?

by Tracy (not verified) :: Tue, 08/28/2007 - 2:23pm

Also left unconsidered is that a team that on average wins by a score of 42-28 will have a lower pythagorean projection than a team that on average wins by a score of 21-7, even though each team has an average 14 point margain of victory. Since the Colts seem to fit the profile of the former, this may be why pythagorean projections seem to be under-projecting the Colts.

by Vern (not verified) :: Tue, 08/28/2007 - 2:48pm

I think the pythagorean wins concept (PF/PA) suffers in football because football has a clock. In baseball, your opponent always has the same chance to score as you - the same number of outs. Very rarely is it wise to trade runs for outs and so PF and PA pretty much dominate.

In football, eating clock aka "managing the game" can be just as important to winning because it can determine how many chances you get to score compared to your opponent. Not as a side factor either, but as a central strategy you see in probably a third of all games.

I suspect strongly that something like PF per Offensive possession and PA per Defensive possession would work better. Either way, what is needed is something that values a TD on a 10 minute drive that effectively removes an opponent's possession as much as 10 points scored in only 4 minutes giving the opponent an extra possession or two to make it back.

by MTR (not verified) :: Tue, 08/28/2007 - 2:49pm

Don't forget than humans and Pygathorian wins don't see things the same way. People talk about a "10 point win" but the formula will give very different results if it was 10-0 or 40-30. Usually high scoring games impress the formula less, so it's easy to see how the Colts might look like overachievers to it.

by Cisco (not verified) :: Tue, 08/28/2007 - 2:54pm

If the differential between pythagorean wins and actual wins is a function of great QB play, it should be easily testable by looking at the consensus great QBs of the last 20 years. Since QB rating is meaningless and historical DPAR and DVOA data may not be available, why not just check the P-wins vs Wins of say John Elway, Dan Marino, and Joe Montana in their primes?

by Dan (not verified) :: Tue, 08/28/2007 - 3:08pm

Teams with a good passing offense do consistently outperform their pythagorean projection. There have been 49 teams since 1998 that had a Passing DVOA of at least 20, and they've averaged .50 Excess Wins.

by Rich Conley (not verified) :: Tue, 08/28/2007 - 3:34pm


Have you looked at offense in general?

I think you'll find the same thing.

And I think you'll find that teams that have high defensive DVOAs underperform.

The formula is essentially


Points Allowed is more important than points scored in the formula, because points scored is "cancelled out" essentially.

Winning 10-0 is much more impressive than winning 40-30. Why? Because scores are much more significant in a 10-0 game than in a 40-30 game.


Teams with better defenses will underperform, teams with better offenses will overperform. Teams that are really scewed one way will be off by more.

by Bobman (not verified) :: Tue, 08/28/2007 - 3:37pm

Wow, where to start? Yaguar, very nice. MJK, too. Vern above suggests points per poossessin as a way to nullify the clock, but clock management is important. However, if we apply this to last year's totals, when Indy had in effect 2.18 FEWER GAMES in terms of offensive drives than the Saints (holy crap--that's 35 fewer possessions!), we begin to see how the Pythag Wins might be better suited to baseball than football, where "possessions" or scoring opps are equal (except for home teams winning after the top of the 9th foregoing their last licks). That's why Manning's DPAR is so stratoshperic and their Pythag wins are not--one measure is better suited to football than the other. Not to say Pythag is bad, but it's not as refined as some of FO's home-cooked metrics.

Rich Conley, I think you are on to something too.

Especially with Indy--many is the time I saw them build a 21-28 point lead only to "prevent" themselves down to a 3-10 point win over the past 9 seasons. I am a tooth-grinder and this is one reason why. This probably affects their Pythag wins projections down below where they "should" be.

REAL POINT OF POST: But are we really measuring the right thing? Shouldn't we be measuring a hypothetical Pythag wins for Indy with a replacement level QB, and then compare it to the with-Manning actual win totals? Then we'd see them outpacing their Pythag total BY FAR.

This should hold for any team with an above-average QB, but I suspect Manning's contribution to the Excess Wins Over Pythag (EWOP) is the largest around the league.

Much as I love Manning, Tom Moore, & Co, I see no reason this won't hold to some extent for a super-dominant player at another position. Ray Lewis in 2000? There are fewer measurables for a LB, but if his presence so skews the playcalling, the options, the approach, that another team has so little room for error, well, his PAR adds a few wins to the Pythag total.

Taken to its logical conclusion, conceptually every team's dominant player is responsible for a certain portion of their wins (and their most glaring weakness, whatever it might be, is responsible for a negative win number). I think that Manning's Wins contribution is very very large, enough to counterbalance a below-average D as well as outperform their Pythag total.

by James G (not verified) :: Tue, 08/28/2007 - 4:00pm

21 - I think you're on to something with the pythagenport. I linked the glossary page for that in my name.

One thing to note is that he says, "the more runs per game, the higher the exponent [in the Pythagorean winning percentage approximation]." That would suggest to me that high-scoring good teams with porous defenses will often outdo their Pythagorean projections, and really bad teams, but that have good offenses, will often under perform in total W-L.

Follow the link on that page, and find an article that talks about baseball stats borrowing from football!

by Dan (not verified) :: Tue, 08/28/2007 - 5:03pm

I ran the numbers, and it looks like teams with good offenses do also tend to outperform Pythagoras. The 50 teams since 1988 that scored the most runs averaged .54 excess wins. Similarly, the 50 teams that allowed the most runs averaged -.58 excess wins. In other words, Pythagoras rates teams that play in high scoring games too close to average.

Just looking at run differential (assuming that a team that wins 10-0 and one that wins 40-30 are equally good) goes too far in the other direction, though, and overall run differential does slightly worse than Pythagoras at predicting a team's record (r=.912 vs. r=.911). If you use both of them at once to predict wins (with regression) then you get a better prediction than with either one (r-squared=.834, which is equivalent to r=.913), and both variables are statistically significant (p

by James G (not verified) :: Tue, 08/28/2007 - 6:04pm

Trying to comment this again. Follow the link in my name and see that Dan's observation holds for baseball and that Clay Davenport discussed this his pythagenport formula that Joseph Adler mentions.

by Mr Shush (not verified) :: Wed, 08/29/2007 - 7:23am

"Teams definitely become more conservative in the second half when they have a large lead, and this is pretty much unique to Football (doesnt happen in baseball/basketball..does in soccer)"

Just to screw things up even further, I suspect that whether and to what extent this happens is heavily dependent on coaching philosophy (think of Cowher's Steelers vs. Martz's Rams for extreme examples which also conveniently prove that either approach can be highly effective, given Martz's astonishing record when playing with a significant lead). In soccer, the same holds true: Mourinho's Chelsea will invariably seek to simply shut the game down at 2-0 (sometimes even 1-0), while Ferguson's United will often set out to turn a win into a rout.

by Andrew (not verified) :: Wed, 08/29/2007 - 9:26am

Cmos #25:

So yards/Att is important but that could still be masked by short passes going long and long pass being stopped at catch, right? System still isnt as much a factor?

I checked all the easily measurable factors - passing and rushing yards, total yards, yards per attempt, yards per rush, offensive touchdowns, passing touchdowns, rushing touchdowns, completion percentage, interceptions, etc., and those were the factors that correlated the best to pythagorean wins.

Yards/Attempt is a proxy for play efficiency in the passing game.

The other interesting correlation is the strong negative correlation to opponents rushing yards and rushing touchdowns. It seems that teams almost invariably allow around 3000-4000 passing yards per year regardless of their win total. Bad teams allow 2000-3000 rushing yards, while good teams keep that closer to 1500. However, all teams allow rushing to occur at about a 4 yards per rush clip, with little variation or correlation.

What this means is that winning is correlated with rush attempts made (0.2111) and opponent rushing attempts allowed (0.3283). This makes sense because you run to drain the clock at the end of the game to seal the win. If you've forced your opponents to pass a lot, they are behind, and passing a lot gives more opportunities for interceptions. Additionally, if you are a good team, you are forcing your opponent away from an activity where all teams are pretty much around league average - rushing - into an activity where bad teams are highly inefficient - passing.

The correlatiosn would say that good QB play on offense and a good rush defense and pass defense = lots of wins.

by James G (not verified) :: Wed, 08/29/2007 - 10:24am

The comment by 21 is insightful. I looked up the pythagenpat formula on BP and found a discussion about adjusting to run environment. Good stuff. I would link it, but I think the link is causing my comments to be swallowed by the anti-spam filter.

by admin :: Wed, 08/29/2007 - 10:58am

This is a great discussion. It's too bad we now have to close off comments because people decided to turn it into yet another Brady vs. Manning argument. Those are the rules, kids.