MethodI assume players scores are added linearly and that the line effects are primarily caused by pairs (this method can be extended to 3's, 4's or even 5's). Before going into the details I'll provide some quick short had I12 = I12 = total ice time player 1 and player 2 spent together, S1 = score - goals/hour for player 1, G12 = G21 - expected goals (based on shots for/against) while player 1 and player 2 were on the ice. Now I assume that I12*(S1+S2)/2 ~ G12 that is to say that the average between the two players goals per hour multiplied by ice time should be approximately the number of goals for/against. So if one player is very defensive and the other is terrible defensively they should be average defensively together. Now I know G12, that is to say I know how many (expected) goals for and against for any combination of players and I also know how much ice time every player has spent with any pair. But, I do not know S1 and S2, these are the individual scoring statistics (units: goals/hour). Now depending on the team there are 30 or so players who have played a game with the team so there are 30!/(28!*2!) = 435 equations, with 30 unknowns. Using these variables I can simply calculate the coefficients using a regression (no constant though). I wrote my own regression code for this matrix and as such I don't have error details: I don't know how well it performs.
- The benefit is that this algorithm will not alter the actual statistics significantly so if, for example, one Sedin has 1 extra goal compared to the other they will still be rated equally.
- It also allows significantly different scores for players who do spend significant time together given significant scoring differences, due to the fact that: a lower S1 can be made up by a higher S2.
- It doesn't chase low minute players statistics as the coefficients will be small and will have a smaller squared error.
- It produces extremes periodically (negative goals for/against), you can't score negative goals for...
- The scoring rates solutions (S1, S2) aren't very comparable between teams or even fully understandable how they got there.
- Since S1 and S2 aren't very logical, this leaves me multiplying by ice time to get an approximate "individual plus minus" statistic.