We want to predict how many points per game LeBron James is going to get per game. Assume there is some underlying theta that does not change game to game, that predicts how many points he will get. For previous information, we have NBA league averages, and we have Lebron James points per game for previous years and games.
How do you choose a prior here?
It would be easy to get say a league average of points per game on all starters who play roughly the same minutes as Lebron. And it is easy to get Lebron's point per games for previous games. The main question is, if I am using a beta distribution to describe the prior, how do I decide what level of sureness to assign the prior? How do we combine Lebron's previous years of points, the league average, and a beta distribution into an accurate description of a prior for Lebron and how sure we are of it (without making arbitrary decisions). Thanks for any thoughts!!