Have much appreciated your +/- analysis. Great stuff. Want to run an idea by you and any other statisticians on the Board.
If I were approaching a problem like this in some areas I have worked in professionally, I would take a data set that has a record for each NU possession and have a variable for the type of shot that was made, a 3, 2, 1 or 0 and a dummy variable for each player who played in the game, NU and the opponent. I would then regress the player variable, essentially on the floor or not, with the points outcome of the possession. The resulting coefficients for each of the dummies would indicate their relative contributions to scoring process. This method would have the virtue of controlling for the player composition of our opponent's defense on each possession as well - shooting the ball well matters, but who is trying to block the shot also matters. I think this calculation would address offense.
For defense, you could either reverse the process for the opponent's possessions, or set up the data base for all game possessions and add -3, -2, or -1 for the outcome variables to represent the opponent's scores. This should result in a coefficient for each player describing their combined contribution to NU scoring and their association with however much the opponent scores for a net player value.
I can imagine some problems getting meaningful estimates for guys who play 40 minutes or for 1 or 2 minutes. If there were enough of the 40 minute guys, it might blow up the equation as can happen in a regression where the dependent values don't align at all with one or more of the independent variables. But there might be some work-arounds. Interested in people's thoughts/critique.
I'm glad you like my +/- breakdowns and appreciate the interest!
It seems like you're proposing an improvement on what I call "Raw +/-"
The first thing I should mention is that if you are going to look at the capabilities of defenders on the other team, your data requirements just exploded by a factor of 1000 or so - because you have to do every player for every team for each of their games! I don't look at anybody but the players on our team. There are stats/programming guys like Evan Miyakawa who (I believe) are doing the whole universe - breaking every game down based on a possession, a result and what 10 players are on the court. Its very ambitious, but certainly impressive. I don't think Torvik and KenPom are doing their analytics based on which 5 guys were on the court at any given time (though I could be wrong). My impression is that they deal in total points and total possessions, which is much, much simpler.
If you look only at the results of a possession (4,3,2,1,0 points) and who was on the court for us, it seems to me that you are implicitly assuming that everybody shares equally in success or failure AND that any combination of 5 guys is just as likely to succeed as another.
So if Nicholson, Hunger, Fitzmorris, Barnhizer and Martinelli were deployed together and we got outscored 15-0, that would reflect poorly on each of them, when really it was just a crazy move by the coach.
So you have to try to assign credit or blame. Who missed the shots? Who turned the ball over? Who hit the 3 pointer? (Thats what I try to do with my Player +/-)
Admittedly what you are proposing would be an improvement - I'd probably look at defense as a 5 man unit instead of 5 individuals - but there is a lot of noise in the data, so all that extra complexity might not get you much.
