I run competitions, not in chess, but my question relates to chess Ranking systems, and will give an example of the issue I face. Game 1:

Alice scores 5, Bob 4, Chris 3.

I use the glicko-2 and elo Ranking system to break that down into two wins for Alice (over each other player) and one win for Bob (over Chris).

My problem is that if the result was:

Alice 10, Bob 4, Chris 3

That is a much bigger win for Alice, but the ranking system sees the result as no different from the first.

Has anyone come across a ranking system that takes into account margins of victory etc.?

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    How does one define a margin of victory in chess? With Glicko or ELO, the relative ratings of the players will change in accordance with the expected outcome. I have never seen a chess tournament that score on anything other than (wins + 1/2 draws). (I have heard of cases where draws were counted as .4 instead of .5 in order to reward 'fighting chess.') – Tony Ennis May 9 '16 at 23:16
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    It looks as though you had a potentially interesting question, but I do not understand the question as asked. Alice has 10? 10 of what, please? – thb May 10 '16 at 0:51
  • ELO is not a ranking system, it is a rating system. Are you talking about calculating tournament ranking or about calculating players' rating? – IA Petr Harasimovic May 10 '16 at 10:52
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    The querier is not talking about chess; he's talking about a different sort of competition in which scores are relevant, and is wondering whether there is a generalization of Elo that can takes score differentials into account. Alice has 10 generic points in this unspecified game. – dfan May 14 '16 at 14:21
  • @TonyEnnis I think there is a modification of Elo, that takes into account the margin of the victory, that is used for football. – Myungjin Hyun Dec 4 '17 at 11:02

If you're interested in use (more than in development), you should give a try to rankade, our ranking system that features rankings, stats, and more.

Rankade doesn't use Elo, but its algorithm (called ree algorithm), although more complex, is similar to Elo if you play 1-on-1 matches only.

Opposite to Elo and Glicko (here's a comparison), rankade can manage any kind of match (one-on-one, faction vs. faction (two teams, which may be asymmetrical), multiplayer, multi-faction, cooperative games, single player games, and so on), so you can insert one match with Alice 5, Bob 4, Chris 3 output (without breaking down one actual match in multiple fake matches). Anyway, rankade - like all aforementioned ranking systems - does not incorporate margin of victory (even if you can easily manage this issue using weight feature, and/or insert scores for stats).

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I think what you should do is, treat every pair of players like they played a match, and arrived at the given result. So for example in the second case:

Alice vs Bob 10-4 - 14 games

Bob vs Chris 4-3 - 7 games

Alice vs Chris 10-3 - 13 games

And calculate rating like that Although this will distort the ratings, because every point is counted double the times, more if there are multiple players. I think you can weight that in in the k factor in case of ELO, or you can just divide all the games and points with two - this should not be a problem, since performance is calculated from percentages, so a half game can be fine mathematically.

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Yes. But it depends what the competition is.

Vegas and all bookies use point spread or dollar odds to make bets come out even. They start with their estimates (unpublished) of the rankings of the teams.

Baseball has its own rankings which depend on the pitchers for the game.

You can (or used to) be able to see power rankings that were published. USA today used to (may still) print the power rankings for college football teams and also for basketball.

The guy who provided them had a system and I saw it described once.

Note that for football the ratings gain less the bigger the win is so that running up the score is not helpful for getting a bigger rating. This is to keep the power rankings meaningful as the football probability of a win depends on the difference in the power rankings. EG if one team is favored by 20 points they are 99% likely to win, if the spread is 3 points then it is about a 55% chance for the higher to win.

You should look at sports gambling and see how they do power ratings for something similar to the type events you are interest in.

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