This week, I collected the stats of NBA Regular Season (2017-2018) for the Eastern 15 teams, and the following variables:

W – the number of games won
L – the number of games lost
W/L% – the win-loss percentages {W/(W+L)%}
PF – the number of points (or runs, goals, etc) scored by the team
PA – the number of points allowed by the team

The Pythagorean formula (described first by Bill James in the context of baseball) says that    W/K = (PF/PA)^k,                                                                                                                                    where k is a constant that is dependent on the particular sport.                                                Taking logs, we can reexpress this formula as                                                                            Log(W/K) = k*Log(PF/PA)

From the above plot, on the top of it, it is the scatterplot of log(W/L) against log(P/PA). Also, I add the best line by adding a smooth with the “lm” method. It shows that the slope of this line is 15, which indicates that the estimated best fitting choice of k based on my collected dataset is 15. Thus, the Pythagorean formula claims that, for any team in NBA, the ratio of its “W” and “L” is approximately 15 powers of the ratio of its “PF” and “PA”.

On the bottom of the graph, it is the residual plot of the fitted line I added. 4 teams are labeled as the unusual points. It is clear that Bulls, Cavaliers, and Hornets are the unlucky teams which could not be well predicted by the Pythagorean formula. Conversely, Wizards seems to agree with the formula immensely.

Data Resource: https://www.basketball-reference.com/boxscores/#site_menu_link