Friday, January 12, 2018

CFB Pythagorean Records Revisited

A couple months ago, I published an article discussing the use of Pythagorean expectation to evaluate CFB teams and taking it a step further by using differentials not just in points, but in yardage and yardage efficiency. If you're interested, that article can be found here. Today, I will be revisiting the concepts discussed in that article, and taking it a step further, looking at the year to year trends in Pythagorean expectation and how that relates to overall win percentage.

The idea of a Pythagorean Record in baseball is that a team tends to regress to their Pythagorean Record. For example, if a team finishes 10 games above what their record would be for a given season, that same team the next season (barring major personnel changes) would finish closer to their Pythagorean Record for the previous year than to their overall record for the previous year. It's called regression - if you flip a fair coin 10 times and it comes up heads 9 times, it's unlikely that the next ten times that you flip it, it will come up 9 times again.

Does this notion hold ground in football? The answer initially appears to be no.

The relationship between Pythagorean Expectation in 2016 and Win Percentage in 2017 is almost non-existent, with an R^2 of 0.01.

This makes a good amount of sense - unlike MLB teams, college teams lose approximately one-quarter of their team every year and replace them with an entirely different group of players. Personnel changes can also dramatically impact a program - see Lane Kiffin's arrival at FAU as an example. As a result, the overall strength of CFB teams from season to season varies dramatically, and Pythagorean expectation from the previous season is not indicative of

Does luck automatically regress year to year? Our data from 2016-2017 fails to support that conclusion as well.

In general, we see that luck does not correlate from season to season. In general, a team that outperforms their Pythagorean Expectation is just as likely to outperform it again as they are to underperform it by the same margin the next season. In addition, if we look at the average of residuals for CFB teams since 2014, it becomes very obvious that it's difficult to consistently overperform or underperform.

You'll notice that the data is largely normally distributed, but skewed a little to the right - I would believe that this results from the fact that it is easier to consistently lose close games than it is to win them. Hence, if you lose more close games than you win, you'll post a negative residual.

But over the past 3 seasons, very few teams have outperformed their Pythagorean expectation consistently, and those that have only did so did not do so by extreme margins. The "luckiest" team in this span, Georgia Southern, outperformed their expected record by winning about 2.6 games more than they should have over the stretch, which is by no means a huge margin. The "unluckiest" team, Washington, lost only about 4.4 games more than they should have. In the longer run, I would expect this differences to become only marginal, and I would avoid calling Washington's spate of bad luck (or GaSo's spate of good luck) anything other than a fluke.

Ultimately, we can conclude that without context, Pythagorean Record does not predict future performance. We can also conclude that college football teams do not really possess the means of consistently outperforming or underperforming their Pythagorean Expectation over long periods of time, indicating that teams will trend towards their pythagorean expectation in the long run.

To view the updated CFB 2017 advanced records, click here.

To view the CFB 2016 advanced records, click here.