The thing I'm having trouble figuring out is how to calculate this if each player doesn't have a constant number of plate appearances. For example, what if player 1 only has 200 PA, while player 10 has 700? We can calculate the average OBP of the group either by averaging the OBP of each player in the sample, or just sum the PA's and times on base for every player and calculate OBP that way. I'm guessing the latter would be better, because doing it the former would result in player's with lower PA's having larger relative weight in the average. For example, a player with only 100 PA having an OBP of .400 would skew the average upwards.

So when we go to calculate variance(observed), we run into the same problem if we do (OBP(observed)-OBP(average))^2. That is, we are giving equal weights to each player in the sample, even though some may have significantly more PA. So I guess my question boils down to how we weight variances when they are based off of different sample sizes?

Hope that makes sense - if I need to clarify anything let me know. Thanks!