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“PF + PA) / G) I was poking around in the data the other day, though, and found that the so-called “Pythagenpat” variant actually correlates slightly better with teams’ actual won-lost records since the NFL-AFL merger. That formula suggests for each team an exponent of”
This is mostly a huge end-of-regular-season data dump, but I’ll explain a little before the table…
PFR’s Simple Rating System can be broken into offensive and defensive components, which represent the number of points per game the team scored/allowed per game compared to the league average, after adjusting for the strength of opposing offenses and defenses faced. If you want to derive an expected winning percentage from that, you have to “back out” to total points scored/allowed again. To do that, you just add OSRS (or subtract DSRS) to the league’s average PPG, then multiply by the number of games the team played. This will give you adjusted points scored/allowed totals for the season.
To get that into a winning percentage-like form, you then need to plug those totals into the Pythagorean Formula. It usually takes the form of
(Pts Scored ^ x) / (Pts Scored ^ x + Pts Allowed ^ x)
where x was determined to be around 2.4 for the NFL in the 1990s, when current Houston Rockets (yep, basketball) GM Daryl Morey researched it for STATS, Inc. Last year, Football Outsiders decided to employ a “floating” exponent that varies with the scoring environment in which a team played, recognizing that a single point is more important to winning in lower-scoring environments. To that end, they used what’s known as the “Pythagenport” method of determining the exponent, which is
1.5 * log10((PF + PA) / G)
I was poking around in the data the other day, though, and found that the so-called “Pythagenpat” variant actually correlates slightly better with teams’ actual won-lost records since the NFL-AFL merger. That formula suggests for each team an exponent of
((PF + PA) / G) ^ 0.2466
This gives you a 1.204 RMSE vs. wins since 1970, a very slight improvement over the 1.205 RMSE you get using FO’s formula.
At any rate, I applied the Pythagenpat exponent to each team’s schedule-adjusted points scored/allowed totals since 1970, and tweaked the pythagorean win/loss totals up/down at the league-season level to match actual league-wide win/loss totals. The result was a definitive set of pythagorean ratings for every team since the merger:
Now, as an aside, I wouldn’t go plugging those directly into the log5 formula to predict this weekend’s games just yet. You first need to regress to the mean to account for the uncertainty we see in any observed result. To do that, just add about 17.65 games of .500 performance to each team’s pythagorean Wpct, and you’ll get a “true talent” number that should yield more accurate probabilities regarding future outcomes.
