One of the big ongoing questions in NBA stats and player valuation is where to set “replacement level”. I believe an empirical approach to determining that level is best.
Jeremias Engelmann has produced an outstanding resource in his 12 year average RAPM data. Since so many years are used, it is quite stable; however, one simply gets an “average” view of the players.
It is wonderful, though, for looking at broad trends–and perfect for looking at replacement level. Remember–RAPM will regress all players toward a uniform prior, so for very-low-minutes players, the results are biased toward that value. However, once, say, 1500 minutes are played, the results stop being biased toward the prior significantly. This is visible in the graphic below.
So what is replacement level? I would define it as a player that can easily be obtained at a minimum salary. This likely would mean playing only some games (perhaps 30-40) at 8 or so minutes per game.
Using RAPM, we can identify a fairly linear relationship between MPG and RAPM performance, and thus derive an estimated replacement level for RAPM.
In this case, I would estimate replacement level at about -3.35 for overall, -2.65 for offense, and -0.70 for defense.
