Nebraska and Football’s Pythagorean Theorem

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Nebraska and Football’s Pythagorean Theorem

“It’s not about yards, ma’am, it’s about points.”

Bo Pelini wasn’t talking about football’s Pythagorean Win Theorem when he said that, but he could have been. The theorem, first invented for baseball by stat god Bill James in the 1980s and then adapted by current Houston Rockets general manager Daryl Morey for other sports in the 1990s, provides a formula for calculating expected wins based only on points.

The equation is beautiful for it’s simplicity. Only two things matter: 1) How many points you score, and 2) how many points you allow. That’s enough, based on historical trends, to come up with an expected winning percentage and, from that, expected wins. Once you have both of those, you can see if teams are over- or underachieving. In a piece Monday, Grantland staff writer and former Football Outsiders contributor Bill Barnwell listed the Pythagorean Win Theorem as one of the four “new-school” stats poised to make an impact in football in the years to come.

That, of course, piqued my interest in how Nebraska looked against one of the fundamental ideas of advanced statistics, so I ran the number for the past 20 seasons of Huskers football. But before we get to that, here’s the formula itself:

Points Scored^2.37 / (Points Scored^2.37 + Points Allowed^2.37) = Expected Win %

(Note: The exponent of 2.37 is constantly under debate and varies from sport to sport. The current number is the standard for NFL teams and football at large but if you poke around even a little you’ll find that stat heads love to argue about it, the real number is probably different for college football, and nobody has seemed to find that better number for the college game yet. There is a lot of gray area here, but, using the 2.37 number, I think the results are still illustrative.)

In 2011, Nebraska scored 379 points while allowing 304 for an expected win percentage of .628 or 8.16 wins over a 13 game season. The Huskers actually won nine games last year (.692 win %), meaning that the team overachieved by nearly a full win (0.84). Or, the way you’ll most often see it written by people tracking Pythagorean Expectation, Nebraska was lucky. Based on the points they scored and the points they allowed, Nebraska stole nearly a full game. For comparison purposes, Nebraska’s Pythagorean Expectation for the past 20 seasons is below (negative numbers in red, click to enlarge):

Some quick historical observations on that data:

–Remember the narrative of Nebraska’s 2009 season? That the Huskers had a national championship caliber defense and no help from the offense? Wrong, at least according to the Pythagorean Win Theorem. Nebraska had enough offense. The Huskers underperformed by nearly 2.5 wins that season, the largest variance, either good or bad, of the last 20 years. Depending on when those two extra wins happened, the Huskers are almost assuredly in a BCS bowl.

–Teams with a large negative Pythagorean margin typically improve the following year. That didn’t happen for the Huskers in 2010. Nebraska won 10 games, the same as 2009, although they did perform closer to statistical expectations (-1.15 Pythagorean margin). If you still feel like Nebraska missed a huge opportunity to take home a conference title during those two years, this definitely shouldn’t change that feeling.

–Unless you give up zero points all season, it’s impossible to have an expected win percentage of 1.000 so Nebraska’s national championship seasons will always come up as statistically “overachieving.” That said, it’s interesting to look at the national title years in comparison. The 1994 and 1997 squads both won nearly one more game than was to be expected. The 1995 squad only won half a game more than expected.

–The 20-year trend, which admittedly includes too many variables to be anything more than a curiosity, shows that Nebraska lost about 12 more games than it should have. Between 2002 and 2011, the last 10 years of Nebraska football, the Huskers were expected to win .654 percent of their games and actually won .631. In the previous 10 years, the win expectation was .908 — yes, better than 90 percent — while the actual winning percentage was .881.

Moving on from the historical perspective, what does this mean for the future? Here’s the Pythagorean Win Theorem applied to the Big Ten last year, using only conference games to remove the varying strengths of non-conference schedules, sorted by largest Pythagorean margin:

Using that table, you’ll see that Nebraska was the fifth “luckiest” team in the Big Ten last year. It also shows that, based on the Huskers’ overall Pythagorean margin of 0.84 last year, Nebraska’s luck came primarily in the conference portion of the season. Penn State was far and away the luckiest team last year. The Nittany Lions were outscored in conference play but somehow made it to 6-2. Michigan, a team many people viewed as lucky last year (myself included), was pretty close to earning what they got based on points with a Pythagorean margin of -0.44. The scariest prospect for Nebraska fans and the Big Ten in general? Wisconsin was in a near dead-heat with Ohio State for lowest Pythagorean margin, with the Badgers winning one full game less than they should have. (Cue the back-to-back Hail Mary losses, on the road no less, now.)

So what does it all mean for Nebraska in 2012? There aren’t reliable numbers for the college game in terms of predicting future results, but go back to that Barnwell piece and you’ll find 27 years worth of NFL data. Between 1983 and 2010, teams with a positive Pythagorean margin between 0.5 and 1.0 won an average of 0.9 fewer games the following year.

But it could be worse. Teams in Penn State’s position had an average of 2.5 fewer wins the following season.

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