Introducing Relational Plus Minus
Summary
Regularized Adjusted Plus Minus (RAPM) underpins many of the advanced analytics that are publicly available for player evaluation in the NBA. RAPM itself is very noisy and returns one number for offense and one number for defense which is not very descriptive. This research presents a variation to the RAPM methodology that explicitly accounts for the impact of two players playing together and in doing so creates a tool that is more stable than RAPM and more descriptive. Through considering players as a set of values denoting the RAPM of every pairwise connection the player can have with their teammates, every player earns multiple different coefficients that can be understood as individual observations of that players abilities.
To express a player’s ability in one number, the mean of the various connections can be taken. I’ve called this Relational Plus Minus (RelPM) because the impact a player has on the point differential is derived through their relations to others. Like RAPM, RelPM has an offensive and defensive component and RelPM is the sum of both components.
When trained on data from two seasons(two year RAPM), the offensive component of RelPM is more predictable of future RelPM than RAPM is of RAPM, the defensive component is only minimally less predictive (difference of 0.006) than RAPM, and the sum of both components is slightly more predictive.
Data
I created the matrix for the ridge regression through my own code but a special thanks goes to Matthew Barlowe for making nba-scraper. Without it I wouldn’t have been able to get all the play-by-play data and this wouldn’t have happened.
Feature Matrix
Below is the feature matrix I designed for RelPM
| Variable | Type | Description |
|---|---|---|
| Offensive Pairs | Categorical | If the two players defining the pair are on the court set to 1 if one or both are off set to 0 |
| Defensive Pairs | Categorical | “ |
| Possession Difference | Categorical | Offensive team is x possessions ahead/behind -5,-4,-3,-2,-1,0(tied),1,2,3,4,5+ |
| Home Team | Binary | If the offensive team is also the home team |
| Start With Ball | Binary | If the offensive team started that observation with the ball |
And the Label
| PTS/100 | Numerical | The points the offensive team scored per possession times 100 |
RelPM compared to RAPM
The last paragraph of the summary mentions that two year RelPM is slightly more predictive of future RelPM that RAPM is of RAPM. Here are correlation coefficients I took. The first two years are the 15-16 and 16-17 seasons and the next two are the 17-18 and 18-19 season.
| Component | RelPM | RAPM |
|---|---|---|
| Offense | 0.471 | 0.407 |
| Defense | 0.372 | 0.379 |
| Total | .461 | 0.427 |
The actual connections between players have a correlation coefficient of 0.273 across two year samples.
RelPM and RAPM have a correlation coefficient of 0.937 which makes sense considering that RelPM is simply a variation of the RAPM methodology.
Results
Best Offensive and Defensive Players by RelPM
Below is are the KDE plots for the offensive and defensive connections of the top ten offensive players by offensive RelPM in the 17-18 and 18-19 season
Below is the top ten defensive players by RelPM in the same span
And finally the top ten overall players in that span
Top Ten RAPM vs. Top Ten RelPM
| Player | RelPM Rank | RAPM Rank |
|---|---|---|
| Stephen Curry | 1.0 | 1.0 |
| Chris Paul | 2.0 | 2.0 |
| Joel Embiid | 10.0 | 3.0 |
| Kyle Lowry | 3.0 | 4.0 |
| Jrue Holiday | 23.0 | 5.0 |
| Kelly Olynyk | 4.0 | 6.0 |
| Danny Green | 12.0 | 7.0 |
| Otto Porter Jr. | 37.0 | 8.0 |
| Robert Covington | 21.0 | 9.0 |
| Damian Lillard | 8.0 | 10.0 |
| Player | RelPM Rank | RAPM Rank |
|---|---|---|
| Stephen Curry | 1.0 | 1.0 |
| Chris Paul | 2.0 | 2.0 |
| Kyle Lowry | 3.0 | 4.0 |
| Kelly Olynyk | 4.0 | 6.0 |
| Pascal Siakam | 5.0 | 11.0 |
| Kevin Durant | 6.0 | 15.0 |
| Al Horford | 7.0 | 22.0 |
| Damian Lillard | 8.0 | 10.0 |
| Victor Oladipo | 9.0 | 14.0 |
| Joel Embiid | 10.0 | 3. |
Special Thanks
A special thanks goes out to evolving-hockey for their amazing RAPM write-up and to Matthew Barlowe once again for nba-scraper and you should definitely look at his website The Seventh Man for actual basketball stats and not just posts about them.
RelPM CSV
CSV of RelPM values for each player with individual connections: github
If you have any questions, comments or inquiries you can reach me at my email: nathandelara1@gmail.com or on twitter @NathandeLara_