APBRmetrics

I have a question about how APM and RAPM get calculated. Hypothetical:

Player A and Player B play together 90% of their minutes: Team is +10 with them together

In the 10% they are not together:
Player A is +5
Player B is -5

Does APM/RAPM assume that player A is a true +5 player while B is a -5 player? Does APM/RAPM give 1/5 of the credit for the +10 to both player A and B or does it give basically all the credit to player A and assume that player B is holding player A?

Somebody more knowledgeable can correct me, since I'm pretty new to this, but APM is trying to account for ALL teammates and ALL opponents on the floor by doing a simple regression, which gives each player a different amount of credit. Basically, you're trying to give each player a certain amount of credit for the +/-. This credit is assigned to minimize the difference between the actual outcomes of all matchups and the expected outcomes for those matchups based on the credit you gave them.

RAPM uses ridge regression, which is quite complicated (and out of my league) to explain the calculations.

I'm not sure if I really understand your questions though. It's not just a matter of simple arithmetic when it comes to APM/RAPM.

colts18 wrote:I have a question about how APM and RAPM get calculated. Hypothetical:

Player A and Player B play together 90% of their minutes: Team is +10 with them together

In the 10% they are not together:
Player A is +5
Player B is -5

Does APM/RAPM assume that player A is a true +5 player while B is a -5 player? Does APM/RAPM give 1/5 of the credit for the +10 to both player A and B or does it give basically all the credit to player A and assume that player B is holding player A?

There are other players involved, so this is a bit complicated.

But lets simplify this to a 2-on-2 tournament, with the opponents always the same:

90% A+B: +10
5%, A+C: +15
5%, B+C: +5

APM would get A = +10, B = +0, C = +5.
RAPM would assume a prior of, perhaps, 0, with some weight to it. You would get A= +6, B = +3, C = +3 (or something of the like). The outliers are brought together, and the whole summation is biased toward the prior somewhat.

If players are collinear, APM ignores that part of the sample. RAPM, the way I think of it, does more of the "1/5" thing in effect...

There is no real answer to this question. APM and RAPM are just solutions to minimization problems, nothing more in actuality. They will distribute credit such that the error is minimized.

The fact of the matter is that APM can 'cheat', assigning stupid values to players whose input in the sample is very sparse. RAPM cannot do this due to additional constraints on the minimization.