Posted by Neil Paine on April 20, 2010
As if everyone isn't already tired of this debate (one which will never be satisfactorily settled, I'm sure), here's a final note on who contributed the most to the 1995 Rockets' offense during the playoffs, Hakeem Olajuwon (mega-high usage, average efficiency) or Clyde Drexler (mid-to-high usage, mega-high efficiency)...
My last post attempted to create a simple model of team offensive efficiency using Dean Oliver's Offensive Rating, Possession %, and what Dean called "Skill Curves", or the relationship between changes in individual usage and efficiency rates. In general, both Oliver and Eli Witus found a quantifiable inverse relationship between increases in usage and predicted offensive efficiency -- in other words, there's diminishing returns to increasing your usage, and as you add more usage you become less and less efficient (which only makes sense to anyone who's ever played basketball).
This model -- based on a ton of real-world evidence, not mere hunches and beliefs -- predicted that the 1995 Rockets' starting lineup would actually be better off on offense by taking some possessions away from Hakeem and re-allocating them to Drexler, and it implied that Drexler was in fact the player who added the most on a per-team-possession basis to the Rockets. In essence, when the Rockets' starting 5 was on the court together, Drexler was their most important offensive player and should have even taken a bigger role in the offense if the Rockets wanted to maximize points per possession.
However, although the model holds for all players in general, there's always the chance it could be flawed for specific players with specific playing styles, and Olajuwon/Drexler could certainly be one of those cases. When I was putting together a WARP-style stat based on Skill Curves, APBRmetrician Dave Lewin once warned me that a player's impact on team offense is not entirely explained by his offensive rating and possession rate, and that a regression between an on/off points per possession metric and box score stats could surprise me in the sense that its outcomes would not always match the general Skill Curve model.
But luckily for us, in 2005 Lewin's mentor Dan Rosenbaum actually did run a regression using boxscore numbers to predict his Adjusted Offensive +/- metric. If you're unfamiliar with adjusted offensive +/-, it's the same as regular adjusted +/- but it only deals with the team's points scored per 100 possessions when a player is on the court vs. off, adjusting for the quality of his teammates, backups, and opponents. The results?
The SAS System 14:08 Wednesday, August 10, 2005 63 Model: MODEL1 Dependent Variable: OFF1 Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 12 9291008.6501 774250.72084 118.118 0.0001 Error 1081 7085843.2932 6554.8966634 C Total 1093 16376851.943 Root MSE 80.96232 R-square 0.5673 Dep Mean -0.42353 Adj R-sq 0.5625 C.V. -19115.86189 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 -7.056284 0.61411305 -11.490 0.0001 PTS 1 0.702730 0.06387650 11.001 0.0001 TSA 1 -0.525243 0.06276998 -8.368 0.0001 FTA 1 0.083834 0.06323568 1.326 0.1852 TA 1 0.327152 0.04249266 7.699 0.0001 AS 1 0.640857 0.04863086 13.178 0.0001 OR 1 0.733202 0.10084425 7.271 0.0001 DR 1 -0.138614 0.05560930 -2.493 0.0128 TO 1 -1.042591 0.14327755 -7.277 0.0001 ST 1 0.713849 0.14956205 4.773 0.0001 BK 1 -0.111075 0.10316250 -1.077 0.2819 PF 1 -0.093128 0.08545434 -1.090 0.2760 MPG 1 0.043603 0.01161761 3.753 0.0002 Where: PTS = points per 40 minutes TSA = true shooting attempts per 40 minutes FTA = free throw attempts per 40 minutes TA = three point attempts per 40 minutes AS = assists per 40 minutes OR = offensive rebounds per 40 minutes DR = defensive rebounds per 40 minutes TO = turnovers per 40 minutes ST = steals per 40 minutes BK = blocks per 40 minutes PF = personal fouls per 40 minutes MPG = minutes per game
So now we can look at what Dave was talking about -- perhaps Hakeem and Clyde are a situation where the skill curve model works on paper but is contradicted in the real-life results...
(Note: Minute-weighted sum of team OPM was forced to equal tmOrtg - lgORtg.)
...Or not. Using a completely different method, one which takes into account how each player plays, the interaction effects of those styles, and one which was also built using real-life evidence and a large sample of real NBA results, we once again see that Drexler had a bigger positive impact on Houston's offense than Olajuwon. I realize this fairly overwhelming amount of evidence will still not convince a large number of you, dear readers, but I just wanted to put it out there. No bias, just more cold hard numbers derived from real NBA data.