Elo for ranking anything
If you can say "A beat B", or "I prefer A to B", you can rate it with Elo. Arpad Elo himself called his system "applicable to any type of competitive activity in which individuals or teams engage in pairwise competition".[1] Here are three common uses and the settings that work for each.
1. Pairwise comparisons: rank a list by picking between two
Ranking 30 things from best to worst at once is hard. Picking the better of two is easy. Ask for enough pairwise choices, treat each one as a "game", and Elo ratings sort the list. A standard statistical model for this is Bradley and Terry's 1952 model of paired comparisons.[2] The same idea powers Chatbot Arena, which ranks AI models from human votes between two answers.[3]
Try it: free pairwise ranker
Which do you prefer?
Tips: aim for about 3–5 comparisons per item. Our ranker pairs items with similar ratings so each choice tells it more. Random pairs work too but need more votes. If the "true" order doesn't change, as with photos, products or AI models, you can refit all the votes at once with Bradley–Terry. That way, the order of the votes doesn't matter.[3]
2. Office ping pong, foosball and club ladders
A league is the classic use. Everyone starts on the same number, results go in, and the table sorts itself. Our free league tool does this in the browser. These are the settings we suggest. They're our own recommendations, not a standard:
- Start everyone at 1000 or 1500. The number doesn't matter, only the gaps do.
- K = 32 for a casual office league where people play a few times a month. Use 20 if people play daily. FIDE uses 40 for new players and 20 or 10 for established ones.[6]
- Enter matches in the order they were played. Elo depends on order.
- Make the leaderboard a ladder, not a trophy. Some players stop playing to protect a top rating. A minimum number of games, say 5 in the last month, before someone appears in the top spots keeps people playing.
- Doubles: either rate each pair as a "team", or give both partners the same change based on the average of the two players' ratings. Plain Elo can't tell who carried the team. TrueSkill was designed for that.[4]
3. Matchmaking
A rating's other job is setting up fair games. The TrueSkill paper lists three uses for skill ratings: matching players of similar skill, giving the public something to follow, and qualifying for tournaments.[4] Microsoft built TrueSkill to identify and track gamers' skills so it could match them into competitive games.[5] With plain Elo, the simple version is to pair players whose ratings are closest, since a gap near 0 means an expected score near 50%. The win probability calculator shows how fast games get one-sided as the gap grows.
Pitfalls
- Too few comparisons: ratings with only one or two games behind them are mostly noise. Show the number of games next to each rating.
- Isolated groups: if group A never plays group B, the two sets of ratings can't be compared.
- Changing K mid-season changes everything after that point. The league tool replays the whole history so it stays consistent.
- Inflation and deflation: with equal K, points only move between players. When players leave, the points they won or lost leave with them.
Sources
- Elo, A. E. (1978). The Rating of Chessplayers, Past and Present (2nd ed.), Preface to the First Edition. New York: Arco. — Book
- Bradley, R. A. & Terry, M. E. (1952). Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons. Biometrika 39(3/4), 324–345 — Biometrika
- Chiang, W.-L. et al. (7 Dec 2023). Chatbot Arena: New models & Elo system update — LMSYS Org
- Herbrich, R., Minka, T. & Graepel, T. (2006). TrueSkill™: A Bayesian Skill Rating System. Advances in Neural Information Processing Systems 19 — Microsoft Research
- TrueSkill™ Ranking System (project page) — Microsoft Research
- FIDE Rating Regulations, effective 1 March 2024 (with the 400-point rule as amended from 1 October 2025), sections 7–8 — FIDE Handbook