Elo in sports and esports

Elo was built for chess, but anything with head-to-head results can use it. FIDE notes that it has been used in football, baseball, basketball and other sports.^[1] The World Chess Hall of Fame mentions collegiate and professional two-player competitions and online games such as World of Warcraft.^[2] Here are some well-documented examples and how each changes the basic formula.

Football: FIFA's men's world ranking

Since August 2018, FIFA's men's world ranking has used a method called "SUM". It adds or subtracts points after each match instead of averaging results over a period.^[3] The formula is Elo with football-specific settings:^[4]

• Scale of 600, not 400, so a given points gap means a smaller edge than in chess.
• Match importance I acts as K. It's 5 or 10 for friendlies, 15–25 for Nations League, 25 for qualifiers, 35–40 for continental finals, and 50–60 at the World Cup.
• Penalty shoot-outs: the winner scores W = 0.75 and the loser W = 0.5.
• Knockout protection: in the knockout rounds of a final competition, a team never loses points.

FIFA's own example: a team on 1300 points wins a qualifier (I = 25) against a team on 1500. It gains 17 points and the other team loses 17.^[4] Our calculator gives +17.07 before rounding. The win probability calculator has a 600-scale option to check W_e.

American football: FiveThirtyEight's NFL Elo

FiveThirtyEight's published NFL model shows three common changes to Elo for team sports:^[5]

• Home advantage: 65 Elo points are added to the home team's rating before the expected score is worked out, except at neutral sites.
• Margin of victory: K = 20 is multiplied by ln(point differential + 1) × 2.2 / (winner's Elo edge × 0.001 + 2.2). Blowouts count more, but less so when a heavy favourite wins big. A 14-point win by an even team gives a multiplier of 2.71.
• Between seasons: each team keeps two-thirds of its rating and is pulled one-third of the way back toward 1505.

Video games: TrueSkill on Xbox

Many online games need ratings for teams and free-for-alls, which plain Elo doesn't handle. Microsoft Research built TrueSkill for Xbox Live matchmaking. It's been used in games from Halo 3 to Forza Motorsport 7.^[6] The 2006 paper presents it as a generalisation of Elo that tracks uncertainty and can infer each player's skill from team results.^[7] Read more in Elo vs Glicko-2 vs TrueSkill.

AI models: Chatbot Arena

LMSYS's Chatbot Arena ranks AI chatbots by asking people to vote between two anonymous answers, which makes each vote a head-to-head "game". It started with online Elo ratings. By December 2023 it had collected over 130,000 votes on more than 40 models, and it moved to the Bradley–Terry model, which fits all votes at once and gives more stable ratings for models whose ability doesn't change.^[8]

Dating apps: Tinder moved on

Tinder's "Elo score" was, in Tinder's words, "a hot topic among members and media alike". In 2019 the company said Elo was "old news" at Tinder, "an outdated measure", and that its technology "no longer relies on it". It now uses activity, Likes and Nopes, profile details and location.^[9]

What these examples have in common

Each one keeps Elo's core idea: an expected result from a rating gap, then an update toward the actual result. Each also tunes it for its sport, with home advantage, margin of victory, match importance, a different scale, or reversion between seasons. You can set up a simple version for your own group with the free league tool.

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