Posted by Neil Paine on February 10, 2011
Ken Pomeroy (of the outstanding college hoops stat site Kenpom.com) ran an interesting simulation last month with regard to the randomness inherent in single-game plus-minus scores:
According to Ken's simulation, a player with precisely average "true +/- skill" can show up with wildly variant observed +/- values over the course of a game, or even 20 games.
Just for fun, I re-ran this experiment for ten thousand games, tracking the observed +/- impact of the player through various checkpoints. Here were the results:
Even after 10,000 games, a massive sample that would never be possible to achieve in real life, our perfectly average "player" appears to be a half-point per 40 min worse than average by raw on/off-court plus minus. As Ken says, "respect randomness"!