Pythagorean expectation and the jeff shaw experience

Bill James’s Pythagorean expectation is a simple equation that takes the points scored by a team and the points scored against that team over a season and predicts their win percentage. Originally developed for baseball, it was adapted in the early 2000s for football, the other football, basketball, and hockey. In the interest of science I applied the same equation to our intramural Ultimate Frisbee team “The Jeff Shaw Experience”:

\[ Win\% = \frac{(Points For)^2}{(Points For)^2 + (Points Against)^2} \]
Our Ultimate Frisbee Team’s expected win percentage based on this formula is 36.9%.  Over a four game “season” this roughly translates to 1.5 wins.

This seems like a significant departure from our actual 0.500 record.  Of course, it’s impossible to win 0.5 games, so the only possibilities are winning 1 or 2 games (or 0 or 3 or 4). Still, there is something that we can learn about our team by our over performance.  When we lose a game, we lose by a lot, but when we win, it is often close.

As our team’s example makes obvious, a longer season would allow for better predictions. With enough games we could even set up an ELO system to predict the winners of individual games (like FiveThirtyEight does for seemingly every sport).  This also assumes 2 is the proper Pythagorean exponent for Ultimate Frisbee and this league, but that is a topic that is WAYYY too big for this blog.

Hopefully our first playoff game will give us a much needed data point to further refine our expected wins.  Hopefully our expected wins go up.