EvanZ wrote:
I guess this is a question I have for Jerry. In general, ridge regression reduces the variance of the ratings compared to APM (or just O.L.S.), but all else being equal, shouldn't we expect the ranking to be roughly the same (for the non-informed case)?
Roughly, yes. At least once you use a healthy amount of data.
But, sometimes, the regularization has the following effect:
say you have a team performing at +10 in a healthy amount of games. if you sum up APM*minutes for every player of that team it will have to add up to +10.
If you sum up RAPM*minutes for every player it will not add up to +10, but close (the more data, the closer). With a good amount of games it's probably something between 8 and 9. Let's say +9.
Now, APM has no constraints on player value, it is not afraid to ship all the credit to 1 single player and might say that he's a +15. The entire team will have to add up to +10, so the remaining players will have to add up to -5
RAPM does have constraints on player value, and subsequently will give the top player a lower rating, say +6. The entire team will have to add to +9, thus the remaining players will have to add up to +3
Mystic has cited the Young/Williams situation for Philly. With no constraints on player value APM gives Young a +19. I think we can agree that this is an unrealistic assessment. Because Young's rating is that high, and Philly's APM*minutes will have to add up an overall rating of +12, APM will then just give a (heavy) negative rating to some of it's other players, and Lou Williams ends up with a -15.
Things like that happen less often with more data, but they still happen.
Another example. Say you play two vs two with a friend, there are no substitutions. You two win games against average opponents by an average of 2 points. APM will give both of you a +1, RAPM does almost the same (maybe it says +0.9/+0.9). Now, your friend plays a single game without you, but instead with an average teammate against two average teammates, and wins the game by 2. APM will now give him a +2, you get a zero. RAPM will generally still rate you positive. It will give your teammate a higher rating than yours (the closer the more games you two played together), but it will probably say something like +0.92/+0.88