By Austin Tymins

On April 9, Russell Westbrook broke Oscar Robertson’s purportedly-unbreakable regular season record of 41 triple doubles against the Denver Nuggets. Some have called the feat arbitrary while others say it is enough to guarantee MVP hardware. How important is a triple double if Russ is changing his on-court behavior to pad certain stats, as some suggest? Does Russell Westbrook push teammates away for rebounds and excessively pass for assists when he is close to a triple double? In this post, I’m going to use play-by-play data for the entire 2016-17 season to look for evidence of Russ stat-stuffing.

I’ll rely on the Basketball Reference play-by-play regular season database which includes Russ’s 867 total rebounds and 840 assists. I’m only going to look at the rebound and assist stat categories since Russ hasn’t had any trouble reaching double digit points in any game this year (unlike the Ricky Rubio/Draymond Green-style triple double). I’ll first analyze rebounds and assists up to 10 in each game since that is, of course the eligible level for a triple double. Later in the article, I’ll expand the analysis to test for discontinuities at the double-digit threshold.

In general, I’ll test whether Russ sped up his stat accumulation in situations in which he needed rebounds/assists to reach a triple double. So, unless otherwise noted, the dependent variable is the time since last stat (TSLS). A lower TSLS implies that Russ is achieving rebounds/assists faster than normal and a higher number means he has slowed down in that stat category.

The primary independent variable is Distance, or the number of rebounds/assists away from a triple double in that stat category. According to the stat-stuffing hypothesis, Russ is more likely to target rebounds/assists when he is close to achieving double digits in those categories. I also tested nonlinear transformations and interactions including Distance, but these were insignificant and did not add any predictive ability beyond the linear case.

I’ve also decided to control for the Time Remaining in the game since Russ is more likely to be on the court in late game situations. This control does not affect any of the results but does control for an important source of omitted variable bias. Even when excluding the Time Remaining control, the results don’t change meaningfully. I’ve also tested for multicollinearity between Distance and Time Remaining using the VIF and found that the variables are far from being collinear and thus the parameter estimates appear stable and have consistent standard errors.

__Rebounds:__

I’ll start by looking at Russ’s rebounding. In the simplest regression of TSLS on Distance (controlling for Time Remaining), the coefficient on Distance is positive and significant below the 1% level.

Constant | 6.31*** |

Distance |
0.87*** |

Time Remaining | -0.23*** |

This suggests that Russ is getting rebounds 0.87 of a minute (or 52 seconds) earlier for each rebound closer to double digits. For example, Russ is getting his 9^{th} rebound 52 seconds earlier than his 8^{th} rebound on average after controlling for time remaining. This effect is thus large and very significant. Interestingly, the coefficient on Time Remaining is negative and statistically significant, as expected. As the time remaining in the game decreases, Russ’s average time before his next rebound also decreases.

Next, I test the idea that Westbrook is more likely to stat-stuff in games in which OKC is far ahead or well behind. If his stat-stuffing behavior is dependent on game state, then maybe this behavior is innocuous from a competitiveness perspective. To test this, I include the absolute value of the score margin at the time the stat occurs and a binary indicator for losing/winning as control variables. I will also include the interaction of the absolute value of the margin with the losing/winning indicator to see if Westbrook’s behavior is asymmetric in an OKC blowout win vs. an OKC blowout loss.

In the results below, we see that the Distance and Time Remaining coefficient estimates have not changed when controlling for game state. Additionally, the absolute value of the score margin is significant below the 1% level. This result is robust in regressions without the Losing and Interaction terms as well.

Constant | 4.97*** |

Distance |
0.90*** |

Time Remaining | -0.21*** |

Abs | 0.10*** |

Losing | 0.24 |

Interaction | 0.00 |

It appears Russ isn’t more likely to stat-stuff rebounds in blowout games. In fact, Russ actually slows down his rebound accumulation when the game gets out of hand (as judged by the coefficient on Abs). Additionally, Losing and the interaction of Abs and Losing are relatively small and insignificant which indicates that Russ’s rebounding behavior is approximately the same in wins and losses.

__Assist Results:__

I’ll now perform the same analysis on assists. Interestingly, the results are extremely similar to the rebounding case in that there is clear evidence of Russ stat-stuffing with assists.

Constant | 7.88*** |

Distance |
1.04*** |

Time Remaining | -0.30*** |

This suggests that Russ is getting assists 1.04 minutes (or 62 seconds) earlier for each assist closer to double digits. For example, Russ is getting his 9^{th} assist 62 seconds earlier than his 8^{th} assist on average after controlling for time remaining. This effect is large and very significant.

Below I test the same game state variables for assists to see if Russ is conveniently stat-stuffing assists. Unlike rebounds, I find that the absolute value of the score margin is insignificant. This indicates that Russ may be backing off of rebounds in blowout games, but that the margin has no effect on his assist behavior. Like rebounds, the Losing dummy and the interaction of Absolute Margin and Losing are insignificant and small.

Constant | 7.99*** |

Distance |
1.02*** |

Time Remaining | -0.30*** |

Abs | -0.02 |

Losing | -0.13 |

Interaction | 0.03 |

The evidence from the rebound and assist data suggests that Westbrook is * significantly more likely to target rebounds and assists if he happens to be closer to completing a triple double in that statistical category.* Interestingly, Russ appears to stat-stuff more on assists than rebounds to the tune of ~6 seconds per stat away from double-digits.

__Discontinuity Over 10:__

I’m now going to include data beyond the double-digit threshold to test whether a discontinuity exists in the time it takes Russ to record his next rebound/assist after reaching double digits. To do this, I now turn to a variable I’ll call Game Total which is simply the total number of rebounds/assists Russ has in the game up to that point (essentially opposite of Distance), and a variable called Over 10 which is a dummy representing if Russ is over double digits in that stat category. Below, I’m regressing TSLS on Game Total and Over 10, controlling for Time Remaining for rebounds.

Constant | 13.99*** |

Game Total | -0.76*** |

Time Remaining | -0.21*** |

Over 10 |
1.02* |

The coefficient on Over 10 is positive and statistically significant at the 10% level. This means each rebound beyond 10 comes 0.26 of a minute (16 seconds) slower than the previous rebound (1.02-0.76), controlling for time remaining. Below, one can see that the assists data supports the same narrative.

Constant | 16.84*** |

Game Total | -0.91*** |

Time Remaining | -0.28*** |

Over 10 |
1.70*** |

For assists, the Over 10 coefficient is large, positive, and statistically significant below the 1% level. This means each assist beyond 10 comes 0.79 of a minute (47 seconds) slower than the previous assist (1.70-0.91), controlling for Time Remaining.

In conclusion, the continuous regression and discontinuity evidence both point toward Russell Westbrook advantageously targeting rebounds/assists to produce a triple double. Though this isn’t necessarily damning evidence against the Westbrook MVP candidacy, it should be fodder against the myth of the triple double.

I like this a lot – but maybe it would be more meaningful as an anomaly from the NBA population mean! So, what I’m saying is that I think everyone “stuff the stats” when they think a triple double is close by! Maybe Westbrook was just better at it this season? 🙂

That is pretty hype my fellow Harvard grad