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RAPM vs. MPG (A Look at Replacement Level)

October 30, 2012
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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.

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To-Do List

  1. Salary and contract value discussions and charts
  2. Multi-year APM/RAPM with aging incorporated
  3. Revise ASPM based on multi-year RAPM with aging
  4. ASPM within-year stability/cross validation
  5. Historical ASPM Tableau visualizations
  6. Create Excel VBA recursive web scraping tutorial
  7. Comparison of residual exponents for rankings
  8. Comparison of various "value metrics" ability to "explain" wins
  9. Publication of spreadsheets used
  10. Work on using Bayesian priors in Adjusted +/-
  11. Work on K-Means clustering for player categorization
  12. Learn ridge regression
  13. Temporally locally-weighted rankings
  14. WOWY as validation of replacement level
  15. Revise ASPM with latest RAPM data
  16. Conversion of ASPM to" wins"
  17. Lineup Bayesian APM
  18. Lineup RAPM
  19. Learn SQL