## Adjusted Point Differential and Pythagorean Wins

More terrific statistical work from Citizen BelgianClipper, who apparently has a little too much time on his hands and some truly mad Excel skillz. Dude, step away from the keyboard. Maybe go see the sights. I hear the canals in Bruges are nice. Steve

Fellow citizens,

This is a follow-up fanpost on this fanshot which Steve so graciously promoted to the front page (thanks) - (you're welcome).

First off, I'm adding the Adjusted Point Differential for all NBA teams. I have also added this to the original fanshot but some of you might not have seen so:

the 76ers have a actual point difference of 9.11 but the average team would be expected to have a point diff of 1.41 against their opponents. Thus their adjusted point difference is 7.70. The last 2 stats are the difference between their actual points and points expected for and against. This has the nice effect of dividing the Adjusted Point differential between offence and defence. Thus the Sixers have an Adjusted Point Diff of 7.70 which is composed of 2.11 points of offence and 5.59 on defence.

Secondly, Citizen Bandany wondered how this would effect Pythagorean Wins.

I'm using Basketball-reference.com method to expand this topic

W PythPythagorean Wins; the formula is G * (Tm PTS14 / (Tm PTS14 + Opp PTS14)). The formula was obtained by fitting a logistic regression model with log(Tm PTS / Opp PTS) as the explanatory variable.

this leads to the next table

Act pyth is the Pythagorean Wins calculated using the actual point difference. Act/exp pyth is the Pythagorean Wins calculated by dividing the the actual point per game for and against by the respective expected values. Using this measure you get a corrected Pythagorean Wins which takes in account the strength of the opposition. If we compare both calculations you see that the Clips would be expected to have won 0.807 games more if we use this last calculation. the last 2 columns compare these calculations with the actual number of wins. it is a bit weird that the Clips get harped because of their point differential whilst OKC, even without adjustments, have by far the greatest difference between their actual wins and Pythagorean Wins.

Well now I went completely mad: using the expected points values I calculated the Pythagorean Wins the average team would have against the opposition each team faced (exp pyth). In golf terms: par for the course. Then I compared them to the actual wins and the adjusted Pythagorean Wins. To counteract the difference in number of games I divided those comparisons by the number of games each team has played. "W vs exp pyth" per game essentially gives an indication by how much a team exceeds their expected Pythagorean Wins. "Act/exp vs exp" compares the adjusted Pythagorean Wins against the expected Pythagorean Wins. This could be seen as some sort of "objective" evaluation of a team results. The "mean" in the regression to the mean idea.

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