What Is the ELO Rating System?
The ELO rating system was developed in the 1960s by physicist Arpad Elo to provide an objective numerical measure of chess player skill. It has since become the foundation for ranking systems across chess, football leagues, baseball, competitive video games, and many other head-to-head competitions. The core insight is that a rating difference between two players implies a predictable win probability, and that actual game results should update ratings proportionally to how surprising the outcome was relative to expectation.
The ELO Formula Explained
Step 1: Calculate expected score — E = 1 / (1 + 10^((opponent_rating − my_rating) / 400)). A 400-point rating advantage gives roughly a 91% win expectation; equal ratings give 50%. Step 2: Calculate rating change — ΔR = K × (actual_score − E), where actual_score is 1 for a win, 0.5 for a draw, and 0 for a loss. The 400-point scale and the use of base-10 power is a design choice by Elo; some systems use base-e (natural logarithm) or different divisors for finer calibration.
Choosing the Right K-Factor
The K-factor controls how quickly ratings move. FIDE (the international chess federation) uses K=40 for new players (first 30 games or under age 18), K=20 for players rated below 2400, and K=10 for established Grandmaster-level players. A high K-factor makes the system responsive to current form but produces more volatility. A low K-factor provides stability but makes it slow to correct rating errors. Most online competitive games use K=32 as a sensible default that balances responsiveness and stability.
Frequently Asked Questions (FAQ)
Q. If I beat an equal-rated opponent, how many points do I gain?
A. Against an equally rated opponent your expected score is 0.5. Win and you gain K × (1 − 0.5) = K/2 points. With K=32 that's +16 points, and the opponent loses 16 points.
Q. What's the difference between ELO and Glicko?
A. Glicko extends ELO by tracking a Rating Deviation (RD) alongside the rating itself. RD measures how confident the system is in the current rating. Long inactivity raises RD, making subsequent games produce larger swings. This addresses ELO's weakness of treating all players' ratings as equally certain.
Q. Does ELO work for team games?
A. ELO was designed for 1v1 competition. Team game adaptations exist (TrueSkill, OpenSkill, etc.) that assign individual ratings adjusted for team wins. Some platforms use a simplified team ELO where the whole team shares a rating, but individual-contribution modeling is inherently more complex.