I want to compare ratings of players from different leagues and predict rating of player in a league he/she didnt participate in. Rating of a player is estimated within a league where he was playing. There are some cross-observations which are players that have ratings estimated for more then one league.
For example there is a player P1 who has a rating 40 in league L1 and rating 55 in league L2. As you can see at the picture. There are distributions of rating in L1 and L2. Yellow line indicates the mean rating of a league and the green lines are cross-observations .
My question is if I know that player Px has a rating R in L1, what is his rating in L2?
Any ideas are appreciated!