i'm creating a fantasy basketball model (could be used in other games too) where we can project how well a player will do against another team even when the player hasn't played against a certain team before. i have a statistics question about what i'm trying to do.
i have broken down each team into the 5 positions and have compiled data for how many fantasy points/minute a team gives up to their opposition in that position. so for example, the Lakers give up .984 fantasy points a minute to opposing teams centers which is above average (league average is .925). i have also compiled how many points every player in the league scores on average per minute. for example dwight howard, a center for the Rockets, scores on average 1.111 fantasy points/minute which is way above average (the league average is still .925)
now the tricky part where i need help is when i combine the two numbers. i'm trying to see if Player X plays vs Defense Y, how many points should i expect from that player assuming he plays a constant amount of minutes. so in this hypothetical example let's say i'm trying to project Howard's points vs the Lakers assuming he plays 30 minutes that game
what i've thought of is finding the deviation about the mean for each player relative to the average of all the other players' points/minute and then figuring out the deviation about the mean of how many points/minute an opposing team gives up to each specific position.
the problem with this is i dont know what to do next. i'm trying to find a way to use this data to create a somewhat accurate projection assuming i know how many minutes a player is going to play. i feel like this would involve a non-linear curve where top players and top defensive teams would be extremely effective while average players and defensive teams would produce marginal results and poor players and defensive teams would would give bad results.
any ideas on how i can further my model specifically with evaluating a player vs defense for position considering i know both of their averages vs the entire league? thanks in advance i've been thinking about this and playing with this for the last week!