I've been playing around with my current NBA model over the last couple of days and I'm looking at injuries at the moment. Specifically, I want to automate the redistribution of minutes & other key stats for a matchup when a key player is out for whatever reason.
Taking one of tonight's games as an example, let's look at a SAS @ CHI matchup. Assume that Tony Parker is sick and won't play. He normally plays 32 minutes a game, and those minutes will obviously be redistributed among the rest of the team. My question is how to best go about redistributing those minutes.
Options:
1) Redistribute minutes among existing starter/bench players weighted by how many minutes they currently average (I'm currently using a general case of 5 starters and 5 bench players used in each game on average)
2) Weight the minutes by position. Should George Hill be receiving more minutes than Option (1) would give him because he is the backup PG for the Spurs?
3) Give the majority of the minutes to the other players as described in Option 1, with the remaining minutes given to an average replacement player derived from the remaining players on the Spurs bench that would otherwise not play.
I'm leaning towards the first option, however when the method is applied to injuries of less important players the model now tends to overestimate the team's edge. ie: MyDyess is out, but his 18 minutes gets redistributed to what are largely better offensive players, increasing the expected value of those minutes...
Does anyone have experience trying to model injury replacement in a similar way that could offer a suggestion as to which option is going to offer the best solution?