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Wednesday, May 23, 2007

Pythagorean Projection - Nebraska and Expected Wins

The Pythagorean projection is an approximation of a team’s wins based solely on points scored and allowed. This concept was made famous by baseball analyst Bill James who discovered that the record of a baseball team could be very closely approximated by taking the square of team runs scored plus the square of team runs allowed.

Later statistician Daryl Morey of STATS, Inc. attempted to apply the formula to many sports. The basic Pythagorean projection formula looks like this:

What Morley found was the formula worked best for other sports if the exponent was tweaked. For example, for the NFL, the exponent is 2.37 instead of 2. The Pythagorean projection works remarkably well for the NFL. According the 2006 Football Prospectus:
"Out of 18 Super Bowls played since the 1987 strike season, 11 were won by the team that led the NFL in Pythagorean Wins, while only seven were won by the team with the most actual victories".
Using this information as a starting point, I have attempted to examine the Expected vs. Actual Wins for Nebraska from the Osborne era through Callahan’s first three years. For my analysis I utilized the 2.37 figure of the NFL. The results of the analysis are listed in the table below.

CoachYearGamesPoints For Points Against Expected Wins Actual Wins
Callahan 2006 14 428 256 10.89
2005 122962527.138
Osborne1997 1356519712.0113

Some have since utilized the formula as a crude measure of whether a team has over- or under-achieved. From this perspective if actual wins < than expected wins a team has “under-performed”. Likewise, if actual wins > than expected wins that team has “over-achieved”. Notre Dame blog The Blue-Gray Sky completed a similar analysis of their team last year. Like BGS, I tend to see the formula more as a measure of a team’s luck over the course of a season. As BGS states:
“...because what the Pythagorean method really measures is how many games you were supposed to win based on a strict measurement of points scored and points given up; it's not a measurement of how good a team really is. Perhaps another way to talk about it is in terms of Fate: which teams were "luckiest", and which teams were snakebitten.”
So we could see the 2006 Huskers as a team that under-performed according to this measure. After all, the team’s expected wins were 10.8 and their actual wins were 9. Or we could think about the luck or lack of break’s the team experienced. Like say a 22-20 loss to Texas on a late fumble or a 17-14 loss to Auburn that included a “risky” fake punt.

But whichever way you choose to view the Pythagorean projection (and there are many), it is an interesting statistic in college football. I continue to hope that CFB moves toward the statistical analysis that is now commonplace among the MLB blogosphere. My plan is to continue to help usher Nebraska football coverage into the “Moneyball” era with pieces such as these.

As it stands, the analysis was hardly earth-shattering, but was an interesting undertaking nonetheless. Some things of note:

  • Check out how consistent Nebraska was during the 1980s and early 90s. Even managing to score 421 points three straight years.

  • One of the first things I did was jump to some years I felt the Huskers under-achieved (1987,1992,1998). Lo and behold, the formula agrees!

  • I don't see a whole lot of "over-achieving" going on. Have we really been that unlucky through the years?

  • You can read more about the Pythagorean projection at:
    Pigskin Pythagoras
    Football Outsiders