The 1995-96 NBA season saw the Chicago Bulls set a then-record of 72 wins, finishing with a final record of 72-10.  The league’s 29 franchises finished with win totals ranging from the Vancouver Grizzlies’ 15 wins to the Bulls’ 72 wins.  It would be interesting to see how the Pythagorean relationship, looking at the ratio between points scored and points against, does in predicting these win totals.  The relationship is:

where W = total wins in the season, L = total losses in the season, P = points for, PA = Points against, and k is some constant.  Below is the data for each team.

Below are the plots of log(P/PA) against log(W/L), along with the residuals plot for the fitted regression equation.

From the original scatter plot we can see that the regression line does a good job fitting the data.  The residuals plot confirms this; there appears to be no pattern and no significant outliers.  The fact that there are no significant outliers speaks to the predictive accuracy of this relationship.  The Chicago Bulls, while having 72 wins, also had an average point differential of +12.3.  On the other hand, the league-worst Vancouver Grizzlies had an average point differential of -10.0.  Teams with a log(w/l) of 0, in this season the Phoenix Suns and Charlotte Hornets, had point differentials of 0.3 and 0.6 respectively.  These two plots demonstrate that no team in the NBA this season was very “unlucky” or “lucky” in terms of the number of wins they got compared with their ratio of (P/PA).

The regression estimate for the constant k is 14.286, giving us a final model of

log(W/L) = 0.0062 + 14.286*log(P/PA) + error.

This estimate of the coefficient for k is very close to the ones Daryl Morey and Dean Oliver came up with in their initial application of the Pythagorean Expectation to basketball.