# NBA: How do PER and win percentage correlate?

The player efficiency rating, or PER, is a widely used metric in professional basketball to quantitatively determine how "efficiently" players play. For example, shooting a low percentage, being on the court but not collecting any stats, or high turnover rates all make a player less efficient. More information can be found here.

Notably, PER is an individual metric, not a team metric. Adding up the PER for every player on a team may say something about the team, but it also misses everything about the effects of teamwork, coaching, team defense and so on. Despite this, does team PER explain anything about a team's success?

First, we can graph each team's median and mean PER. As of February 1st 2014, the teams on the left have the highest win percentage; the teams on the right the lowest. If team PER highly explained a team's win percentage, we'd expect a cleanly decreasing line: as team PER declines, so does win percentage. Not what we see, however:

Some interesting observations: the Jazz have a higher median PER than the Thunder and Pacers. Dallas leads the league in mean PER. The majority of teams have a fairly normally distributed set of efficient players. And of course, Kevin Durant's PER (the only observation above 30) is absurd relative to a league average of 15.

There doesn't look like there is a great relationship between team PER and win percentage, but we can get more precise. We can regress team PER on win percentage data found here and get:

So there's clearly some sort of relationship, but how strong is it?

```lm(formula = team.data\$WIN_PCT ~ team.data\$PER)

Coefficients:
EstimateStd. Error t value Pr(>|t|)
(Intercept)-0.73201 0.24308 -3.011 0.00546 **
team.data\$PER 0.08203 0.016125.087 2.19e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1171 on 28 degrees of freedom
Multiple R-squared: 0.4803, Adjusted R-squared: 0.4618
F-statistic: 25.88 on 1 and 28 DF, p-value: 2.185e-05```

The relationship is significant between PER and win percentage (ie. "something is definitely going on here"), but our model only explains about 48% of the data, so it's not great for predictions. How does team PER correlate with a team's offensive efficiency or defensive efficiency? We can graph that as well:

The relationship is significant and, here, PER explains about 79% of the variation in a team's offensive efficiency. For defensive efficiency:

This time, the relationship is insignificant with a p-value of .806 and PER explaining only .2% of the variation in defensive efficiency. In other words, the model is extremely poor and PER says nothing about how a team performs defensively.

Intuitively, this makes sense. PER not only captures more offensive stats, but offensive stats are easier to come by. How tight Andre Iguodala plays an opposing player isn't recorded but his field goal percentage is. PER would naturally do a better job at explaining a team's offensive success, and this offensive success leads to a higher win percentage (so, PER is correlated with a higher win percentage). However, the reason it doesn't do a better job explaining win percentage (only 48% vs. 79% at explaining offensive efficiency) is because defensive efficiency is (as shown above) almost completely unrepresented. So, if defensive efficiency is important to a team's success, PER is clearly missing something in explaining win percentage. And, as you can guess, defensive efficiency is very important to a team's win percentage:

For its high win percentage, Indiana has a very mediocre offensive efficiency, but as apparent on the second graph, its defensive efficiency is anomalistically high (a lower number is better). Milwaukee is exactly where we would expect it: very poor offensive and defensive efficiency and therefore the lowest win percentage. Miami is the opposite of Indiana: very high offensive efficiency (along with Portland), but mediocre defensive efficiency. One final interesting fact: Portland and Miami have virtually the same offensive efficiency and win percentage, yet Portland is somehow significantly worse on the defensive end. I'm not sure how you can explain this observation besides the fact that these are imperfect metrics.

To summarize, team PER is definitely correlated with win percentage and a team's offensive efficiency, but does nothing to explain what happens on a team's defensive end.

Code and .csv's can be found at http://bit.ly/1fMYJQY.