Take plus minus from boxscore and adjust it.
We need to do adjustment because teams are not equal. Most GSW players have amazing plus minus. The pros of a plus minus based stat is that they are largely an unbiased measure of a player's effectiveness. Who cares what kind of numbers you put up or don't put up as long as your team is +20 pts per 100 possession with you playing.
APM: you take the basic plus/minus that you see on boxscores, solve a system of linear equations that takes into account the teammates and opponents on the court. Why? See above sentence. It doesn't do a good job at doing this because basketball is not a 1v1 game.
The obvious idea is:
-- Assume everybody has a "true" +/- score.
-- Take every unique collection of 10 guys on the court, look at the actual +/-, and use that as an estimate of the overall sum/difference of the 10 guys' true stats.
-- Fit this data with the best estimates for "true +/-" you mathematically can.
Weighting all that for minutes played would be straightforward. Weighting it for various late-game/end-of-quarter tactics is less so, but such flaws are shared by almost all statistical approaches, so let's ignore it.
Why doesn't that work?