Probability distributions for predicting basketball players' points scored?

Rather than attempting to model scoring by the sum of three independently varying random variables, have you considered simply modeling it as a single random variable and ignoring the underlying 1, 2, and 3-point contributions?

That would be much easier, and I suspect if you've gotten reasonable results on rebounds and assists, you will for total points as well.

Would you suppose that a normal distribution for total point output might work? I know normal distributions are not discrete, so that you might get predictions like 15.2874 as an answer to some question.

It would probably be easier not to worry about where the points come from (1,2, or 3 points), but just look at overall point production. There is an average and a stan dev, and I could easily see how from there it would have a normal-like distribution. Very high scores would be highly unlikely, though not impossible.

I suppose you would have to make some adjustments, since negative scores are not possible. There must be some model for normal-like distributions in which negative values are not possible, such a population distributions or something like that.

I hope this helps.

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You have already solved your own problem (the way you analyzed and framed the problem already have the answer in it).

It is 3 poisson processes. 1 point process, 2 point process, 3 point process; each has its own lambda. (count by basket)

Total point is just the sum of 3 processes (1x 1pt basket + 2x 2pt basket + 3x 3pt basket). Good job, good application.

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