I am trying to create ratings/skill scores using ranking systems like Elo, TrueSkill, and OpenSkill. All of these systems are similar in that they have a distribution that represents players' skill and that the update after a match is dependent only on the parameters of the distribution.

Are there similar methods that also incorporate some exogenous measure of victory, so that the update is dependent on the distribution parameters of the players, but also margin of victory, aka how much a player won by?

  • $\begingroup$ See also stats.stackexchange.com/questions/592572/… (so far without answer) $\endgroup$ Nov 18, 2022 at 1:25
  • $\begingroup$ @kjetilbhalvorsen Thanks, I will keep an eye on that too. $\endgroup$
    – GBPU
    Nov 18, 2022 at 1:31
  • $\begingroup$ Can you explain what scoring systems you have in mind? A few examples may help. $\endgroup$
    – clp
    Jan 14, 2023 at 10:09
  • $\begingroup$ @clp Some things I have been looking at include Microsoft's TrueSkill and OpenSkill. The issue is neither of these take into account how much a player one a match by, simply whether they won or not. $\endgroup$
    – GBPU
    Feb 9, 2023 at 21:23
  • $\begingroup$ Sorry, but I meant the scoring system of the games involved. Is it like baseball, soccer, basketball, football? An example of game scores would also help. Question 592572 has been answered, and could include clues. $\endgroup$
    – clp
    Feb 13, 2023 at 15:16

1 Answer 1


Moderated paired comparison might be an option. It's an adaptation of the Bradley–Terry model for a setting with a continuous outcome, based on fitting a penalized likelihood model to the observed margins of victory.


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