How Accurate is the Pythagorean Theorem in College Football?

by user Leftyloon

In baseball, the Pythagorean Theorem is a often a better indicator of team strength and usually a better predictor of future performance than a team's actual record. Is this also true in college football? Only one way to find out. I wanted to know which variable was a better predictor of each BCS school's 2005 winning percentage: their 2004 winning percentage or their 2004 Pythagorean winning percentage.

R squared for 2004 win %: .4070

R squared for 2004 Pythagorean win %: .5108

Both variables explain a significant portion of the variability of the 2005 record. However, the Pythagorean winning percentage is a better predictor as it explains roughly 25% more of the variance than the standard winning percentage.

It should be noted that most teams' winning percentages are close to their winning percentages as predicted by the Pythagorean Theorem. Now let's shift gears and focus on those teams who had a significant disparity in their winning percentage and their Pythagorean winning percentage. The cutoff point for 'significant disparity' is an arbitrary one, but I chose .100. That means if a team had a winning percentage of .750, but only a Pythagorean winning percentage of .64, they are included in this portion of the study. 22 teams from 2004 fit this criteria. If you're curious, those teams are listed at the bottom of this article. Using the same methodology as the previous study, I looked to see how well the 2004 winning percentage of these teams predicted their 2005 winning percenatage and then how well their 2004 Pythagorean winning percentage predicted their 2005 winning percentage. Here are the results.

R Squared for 2004 win %: .0428

R Squared for 2004 Pythagorean win %: .3097

When we examine only teams with a significant difference in actual and expected winning percentage the predictive power of their actual record practically disappears. The predictive power of the Pythagorean method is much smaller as well, but a relationship can still be deciphered.

The final study is the same as the first, but this time with the 22 teams with significant differences removed.

R Squared for 2004 win %: .5750

R Squared for 2004 Pythagorean win %: .5826

This result is pretty logical. When a team's actual record closely matches its predicted record, both do a pretty good job of predicting the team's record the next year.

With this data, we can conclude that the Pythagorean Theorem is applicable to college football, and when prospecting forward it is best to look at a team's ratio of points scored to points allowed rather than their actual record.

Date

Fri 06/23/06, 5:24 pm EST

JfwiiiLittle Leaguer

1254 days ago

Score 0

Daryl Morey of STATS, Inc. did some research a few years back to apply Bill James' baseball version of the Pythagorean theorem to other sports, given each sport's distribution of points scored. It's also important to note that James actually found that 1.82 was the proper exponent for baseball (rather than 2, although squaring is easier).

Here were the results for the proper exponent to use for each sport: 2.37 for the NFL 13.91 for the NBA

For college sports, the numbers might be somewhat different, but not by a lot. Since college football games have a wider distribution of scores and potentially higher scores, I would expect the correct exponent to be slightly higher than the one for the NFL. Similarly, for college basketball, the correct exponent is probably smaller than the one for the NBA, since the games have lower scores.

Still, this is a useful analysis to perform from year to year, and it's always encouraging to see these mathematical principles holding strong. I'd be interested to see how those R^2 values look if you use a higher exponent, like the one for the NFL.

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LeftyloonJV Squad

1253 days ago

Score 0

Thanks for the comment. I should have clarified, I know Pythagorean illcits thoughts of the #2, but I actually used the exponent of 2.37 in my analysis.

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