# Compare ratings of players over different leagues

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!

Thank you

An existing way to do this is to use modified Elo ratings.

Video game servers sometimes use a similar scoring system called Glicko or Glicko-2 which might be better for your purposes.

My understanding is that you want to understand the rating of each player relative to every other player and that each in-league rating is essentially the rating of each player in that league relative to each other player in that league. If this is true then there are two ways I can think of to help you work out the hypothetical rating of player X in league L2 based on their performance in league L1:

• Generate global ratings based on one of the methods mentioned above and use them to insert the new player in the right place in the ranking
• Calculate am in group rating based on the methodologies described above and then calculate the new players ranking by stimulating the score he/she would accumulate if they played each of the players in L2 that they could be compared to in L1 and achieved the expected outcome (i.e. beat all the players they were ranked better than and were beaten by all the players they were ranked worse than)

You might also be interested to check whether the rank correlation between leagues is strong based on players that are ranked in both leagues.

• Thanks for the answer Nicholas. I feel like the methods you suggested are not using the cross-observations. I feel like its an important part that help calibration on the new league rating. Am I wrong? Is there a way to include those cross-observations? Apr 14, 2020 at 11:20
• Making an edit! Bear with me :) Apr 14, 2020 at 12:39
• Thank you for the edit! I am going to try the first approach using the global ratings. The second approach would be more problematic since players are in teams. Apr 15, 2020 at 11:56