Does Peyton Manning Break Pythagoras?

In this week's Scramble for the Ball [1] 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 [2] 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.