Stat Geek Perspective: Luck In College Football

August 11, 2011 - by Austin Link

It can be tough to look at the college football projections and see that your team’s outlook is not as good as you’d hoped. As a result, I recently had an argument with a friend over the projection for the Northwestern Wildcats. Last year Pat Fitzgerald’s crew won 7 games, and they are returning 17 starters, so it’s reasonable to question their projected win total of 5.7 games.

Curiously though, the projected preseason ratings do foresee an improvement in the Wildcats’ power rating in 2011. The lower win total comes from two other factors: a harder schedule and a probable return to average luck*, after outperforming their rating last season.

*For the purposes of this article “luck” is defined as [actual wins – expected wins]. Expected Wins is the number of wins a team would be expected to have based off of our power ratings, which are in turn based off of margin of victory and quality of opponents. Many other aspects of luck affect games (fluke injuries, bad calls, lucky tips) but those are harder, though not impossible, to quantify.

Luck? Or Grit?

A harder schedule obviously makes a difference, especially for a team that routinely plays one of the Big Ten’s easiest. But my friend argued that Northwestern’s extra wins were due not to luck but “a gritty quarterback who makes the necessary plays to win close games”. Being a stats guy, I figured I’d do a test to see if there’s any correlation in luck between seasons, or if it really is just chance.

I collected the data on each team’s luck over the past four seasons in college football, then did a regression test. The results were shockingly clear, only about 5% of “luck” carries over from season to season. There was enough error in the data that the correlation between seasons in luck is consistent with random chance. If you win 2 more games than expected one year, you should still probably win the expected amount next year.

Is Northwestern Special?

Despite that analysis, it’s still possible that a few specific teams buck the trend and are consistently “lucky”. Which team has outperformed its expected win total the most over the past four years? Of course, the Northwestern Wildcats. They’ve had at least one win more than expected each season, and 5.4 extra total. For comparison, the second luckiest team, East Carolina, had only 4.4 extra wins.

Here are the top 5 and bottom 5 teams, in terms of actual wins compared to expected wins, from the last four years:

Team	2010 Extra Wins	2009 Extra Wins	2008 Extra Wins	2007 Extra Wins	Average Extra Wins
Northwestern	1.2	1.4	1.6	1.1	1.3
East Carolina	1.3	0.7	1.3	1.1	1.1
Mississippi State	1.1	0.6	0.1	2.5	1.1
Florida Atlantic	0.9	0.4	1.1	1.9	1.1
Utah	1.0	0.8	2.1	-0.3	0.9
Southern Mississippi	-0.6	-1.5	-1.4	-0.8	-1.1
Arkansas State	-2.1	-2.0	-0.3	-0.2	-1.1
Clemson	-1.8	-0.9	-1.5	-1.2	-1.4
Northern Illinois	-0.9	-1.2	-1.8	-1.7	-1.4
Western Kentucky	-1.6	-1.5	-2.1	-0.7	-1.5

Using the distribution of teams’ luck, it’s possible to calculate the odds that a team has 5.4 extra wins in four years by chance alone (Stats Geeks: that technique should work here, because no year-to-year correlation was found earlier). It turns out there’s only a 0.5% (1 in 200) chance that an individual team would be that lucky through randomness.

Normally 0.5% would be considered statistically significant, but it’s important to remember that there are 120 teams in the Football Bowl Subdivision. With that many teams, even just by chance you’d expect there to be at least one team in the same percentile as Northwestern.

Final Take

What does this mean for my debating skills? I still stand by the projected 5.7 wins for Northwestern. I think the regression shows that what we call “luck” is just that, luck. I don’t think it has any predictive value from year to year.

I do have to concede though that if there is one permanently “lucky” school in college football, it’s the Northwestern Wildcats. If they outperform expectations again, I may have to rethink the idea that “luck” is not a skill for some.