What Is the Elo Rating System?
The Elo rating system is a method for calculating the relative skill levels of players in competitive games. Originally developed by Hungarian-American physics professor Arpad Elo for chess in the 1960s, it has since been adopted by dozens of sports, video games, and competitive platforms worldwide.
At its core, Elo answers a simple question: given two players' ratings, what's the expected outcome of a match? And after the match, it adjusts both players' ratings based on whether the result matched expectations.
The Core Concept: Expected Score
Every player has a numerical rating. Before a match, the system calculates an expected score for each player using this formula:
EA = 1 / (1 + 10(RB − RA) / 400)
Where RA and RB are the current ratings of Player A and Player B. The result is a probability between 0 and 1:
- 0.5 means both players are equally likely to win
- 0.76 means Player A is expected to win ~76% of the time
- 0.24 means Player A is expected to win only ~24% of the time
How Ratings Change After a Match
After the game, ratings are updated with this formula:
RA (new) = RA (old) + K × (SA − EA)
- SA = Actual score (1 for a win, 0.5 for a draw, 0 for a loss)
- EA = Expected score (calculated above)
- K = K-factor (sensitivity of the rating change)
Understanding the K-Factor
The K-factor controls how dramatically ratings shift after each game. A higher K means bigger swings; a lower K means more stability.
| K-Factor | Used For |
|---|---|
| K = 40 | New players or beginners |
| K = 20 | Most established players |
| K = 10 | Top-level / grandmaster players |
A Practical Example
Suppose Player A has a rating of 1600 and Player B has a rating of 1400. Player B pulls off an upset win. Here's what happens:
- EA = 1 / (1 + 10(1400−1600)/400) ≈ 0.76
- EB = 1 − 0.76 = 0.24
- Player A loses (SA = 0): New rating = 1600 + 20 × (0 − 0.76) = 1585
- Player B wins (SB = 1): New rating = 1400 + 20 × (1 − 0.24) = 1415
The underdog gains 15 points; the favorite loses 15. The bigger the upset, the bigger the swing.
Where Elo Is Used Today
- Chess: FIDE uses a refined Elo system for official world rankings
- Video Games: League of Legends, Dota 2, Overwatch, and many others use Elo-inspired MMR (Matchmaking Rating)
- Football: The World Football Elo Ratings track international teams
- Dating Apps: Some platforms reportedly used Elo-style desirability scores
- Academic Rankings: Used to rank research papers and even images in comparative studies
Limitations of Elo
Despite its elegance, Elo has known weaknesses:
- Inflation/Deflation: Rating pools can grow or shrink over time as players join or leave
- Inactive Players: Ratings don't decay, so returning players may have outdated scores
- Team Games: Elo was designed for 1v1 — applying it to team-based games requires significant modifications
- New Players: Early ratings are unreliable until enough games are played (the "provisional" period)
Beyond Elo: Modern Alternatives
Systems like Glicko-2 (used in many online chess platforms) and TrueSkill (developed by Microsoft for Xbox Live) address some of Elo's limitations by tracking rating uncertainty alongside the rating itself. But Elo remains the foundational reference point for understanding competitive ranking systems everywhere.