Recently, ESPN offered a new single metric statistic for NBA basketball: Real Plus Minus (RPM). This metric measures how well a team does offensively and defensively with any given on court, and compares it with how well the team does at each with that same player off the court. RPM also uses logistic regression to account for the influence of the other players on the court at the same time.
Player Efficiency Rating (PER), the long time-standard single metric at ESPN created by John Hollinger, instead relies purely on things that can be measured in box scores.
Each stat has pros and cons. RPM measures intangible like setting hard screens, good defensive rotations, and creating offensive spacing with 3-point shooting. It suffers from higher variance when a player gets limited minutes, the de-aliasing of the effect from other players is a mathematical "best guess," and is an indirect measurement.
Conversely, PER is a direct measurement, and measures more tangible things that allow you to identify why an individual player is or isn't helping your bottom line (winning). However it doesn't measure the intangibles mentioned above. Nor are all stats inside the PER created equal:
While stats geeks will argue (a lot) about which metric is better, like a true statistician and analyst, my answer is "it depends." Both have value in particular circumstances, and when analyzed together, provide other unique insights. The following observations are based on the PER and RPM scores of the 336 NBA players who played 500 or more minutes during the 2013-2014 regular season.
1. PER is a better predictor of minutes played than RPM
When PER and RPM are converted to standardized and concerted to z-scores (by position played) and then treated as independent variables for predicting minutes per game played, both have significant predictive value. However, of the two, PER has a significantly stronger predictive value. This suggests teams give more weight to box score effects when determining who to play.
2. But RPM is a better predictor of winning percentage
When you examine the effect of the interaction terms of PER * minutes played, and RPM * minutes played, and use them to predict team winning percentage, only the RPM interaction term has any significant predictive value (p < .05). If you didn't follow any of that, though: winning teams tend to play high RPM guys more, and pay less attention to what a player's PER is.
3. Not all positions are equal under PER
This chart demonstrates why all the other analysis I did reduces PER to a z-score calculated by position. RPM showed a somewhat similar, but less pronounced, pattern. As a result, it was divided by position when converting it to a z-score.
4. Age (barely) matters
Do coaches play guys less as they age to preserve them, even if they're still producing on the court? The answer is yes, but only a little. When you estimate MPG based on PER and RPM, and then compare actual vs. estimate by age, you get a graph that looks like this:
The result is significant, if only barely (p < .05). But, yes, there is evidence to suggest that coaches do indeed give their older players less minutes than they have earned, or might be capable of handling.
Oh, and that diamond on the far right falling off the bottom of the chart? That's Manu Ginobili.
5. Position matters to minutes played (sometimes)
Using the same step-wise regression, it turned out that players who are power forwards and centers play significantly less minutes (~2.5 MPG for both PFs and Cs) than would otherwise be predicted. It is strongly suspected (based on previous work) that personal foul rate acts as a constraint on how many minutes they can play. Typically those players who are affected by this constraint are power forwards and centers.
6. Players who put up the numbers, but don't help as much in the final score
When standardized PER and RPM are compared, here are the top guys with the biggest differentials between the two (where PER z-score is greater than RPM z-score).
1. Amare Stoudemire (2.8)
2. John Henson (2.7)
3. Demarcus Cousins (2.3)
4. Kevin Durant (2.3)
5. Anthony Davis (2.0)
7. Players who help you the most on the scoreboard, but not in the box score
Similarly, going the other direction looking at the players with the biggest differential between standardized PER and RPM, where RPM is greater than PER, the top five intangibles players are:
1. Nick Collison (2.8)
2. Patrick Beverly (2.2)
3. Iman Shumpert (1.9)
4. Matt Bonner (1.9)
5. Epke Udoh (1.9)
8. Players who deserve more playing time
Based on previous models of expected playing time using standardized PER and RPM, some players are predicted to get a lot more minutes than they actually do. Usually this is because a player is a good back-up behind one of the top players in the game (Brandan Wright, Jeff Withey, Patty Mills). In Ginobili's case, it seems to verify that Popovich is indeed saving him for the post season.
1. Manu Ginobili (Model indicates he should get 16.1 MPG more than he actually does)
2. Brandan Wright (15.4)
3. Steve Novak (13.6)
4. Jeff Withey (13.1)
5. Patty Mills (13.0)
9. Players who don't deserve the minutes they're getting
This is often due to being a rookie on a bad team (Ben McLemore), being the only option available (Jimmy Butler, Brandon Jennings), or the team feeling like they can't sit you when they're paying you so damned much (Andrea Bargnani). Thus, the top five guys who get the most unearned playing time are:
1. Ben McLemore (13.2 MPG more than expected by the model)
2. Michael Carter-Williams (11.6)
3. Brandon Jennings (11.6)
4. Andrea Bargnani (11.0)
5. Jimmy Butler (10.9)
10. The all-overpaid list
The combination of PER and RPM allows for a different sort of look at value: in short, how much are you paying for your talent? If you treat PER and RPM as equal (and standardized by position), add them, and standardize salary, you can estimate the difference between on-court value and cost. This gives an idea of what the best (and worst) deals are in the NBA. We'll start with everyone's favorite: the worst deals in the NBA. These are the players where you're paying big money for guys who don't help you on the court, or on the salary cap.
1. Amare Stoudemire (Most overpaid)
2. Kendrick Perkins
3. Carlos Boozer
4. Joe Johnson
5. Andrea Bargnani
11. The All-Underpaid List
Conversely, players who have a big (positive) difference between standardized production and cost represent talent you're getting on the cheap. Thus, the best values in the NBA are typically players still on a rookie scale contracts. But not always...
1. Isaiah Thomas (Most underpaid)
2. Chris Andersen
3. Patty Mills
4. Eric Bledsoe
5. Manu Ginobili
12. What's the verdict on RPM and PER though?
It's another tool in the statistician's toolbox, and it has good predictive value in a number of areas. However, given the observed value of PER both as a stand-alone statistic, and of the value of PER used in conjunction with RPM in modeling and forecasting, both should be tracked by ESPN going forward.