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I have gathered data on a set of certain contests. The contests are in the form of single-elimination. That is, there are $2^n$ competitors in $n$ rounds. In each game, two players face each other, and the loser gets eliminated, until only one player remains who is the winner.

Now, the data I have is of multiple such contests, taking place annually. One caveat is that once a player wins, they don't play in these contests anymore. I want to ask for recommended rating systems for such a contest.

I considered Elo Rating System, but as some winners play less matches than those who have never won, and Elo depends more on matches won, it wasn't as effective.

I didn't understand Glicko, but I feel this won't work, as well.

I currently just use the victory percentage, which I calculate as $S=100 \times \frac {1.0\times v + 0.5 \times d} {m}$ where $v$ is victories, $d$ is draws and $m$ is the number of matches.

One thing is that the players get a score in each match (which generally ranges from 100 to 10000, but isn't limited by anything), which I think can be used in some way.

S_H_
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  • If you didn't understand Glicko, why do you feel like it won't work? – jtb Oct 18 '22 at 14:56
  • One thing to think about is why you are doing this. Do you want a rating system that is most predictive of wins/losses? Do you want a rating system that accurately reflects the score differential in a new (unseen) game? Your choice should reflect what you want to measure, and you haven't quite clearly stated what you are trying to measure. – jtb Oct 18 '22 at 14:58
  • @JoshBone because while I didn't get how to implement it, I have used Glicko systems before (chess.com, for example). It works sort of like Elo, in that more matches won will have better rating than all but lesser matches won. In my data, the first contest winner has 10 victories, 0 losses, but wouldn't be as highly rather as a player that has 18 victories, 2 losses. – S_H_ Oct 18 '22 at 15:49
  • Have you considered using average tournament rank? I.e., if the team reaches round $n$ every time, they recieve a rank of $n$. It sounds like you want your rating system to align with how well teams do in the tournament specifically. – jtb Oct 18 '22 at 15:52
  • @JoshBone I just wish to put the players in a sort of ranking. Essentially, I want a system that takes in score, and given two random players, predict what the score would be if these were to play each other. Then, using these predictions for all possible pairs of players, I want to rank them in such a way that a player would be more likely to win against all players below them. – S_H_ Oct 18 '22 at 15:52
  • You may have some slightly contradictory goals here then. Using your previous example: "the first contest winner has 10 victories, 0 losses, but wouldn't be as highly rather as a player that has 18 victories, 2 losses." Are you confident that the first contest winner didn't get lucky and play 10 easy opponents? In your most recent comment, it sounds like Elo is exactly what you are looking for, but due to the inherent stochasticity of single-elimination tournaments, the highest Elo player will not win every tournament. – jtb Oct 18 '22 at 15:55
  • @JoshBone so I count the rounds a player goes further into a contest, and then average them out? It would be good, but there could be a better player that gets eliminated before another. Like, if a tournament winner W wins against player A in round 2 by score 5000-4900 but the next matches W wins quite one sided, then player A would be a better player than others W faced, as A gave a better fight. – S_H_ Oct 18 '22 at 15:56
  • Let us continue this discussion in chat. – S_H_ Oct 18 '22 at 15:57

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