Elo Ratings: Expected Score and How Ratings Change After a Game
October 29, 2026
The Elo system, created for chess, assigns each player a number so that the difference between two ratings predicts the expected result. The expected score of player A against player B is E_A = 1 ÷ (1 + 10^((R_B − R_A) ÷ 400)). A score of 1 is a win, 0.5 a draw, and 0 a loss, so the expected score is the win probability when draws are not possible.
A rating gap of 200 points gives the stronger player an expected score of 1 ÷ (1 + 10^(−0.5)) = 1 ÷ 1.316 = 0.76.
Skip the math and get your answer instantly:
Open the Percentage Calculator →Expected Score by Rating Gap
Equal ratings give 0.50. A gap of 100 points gives 0.64, 200 gives 0.76, 300 gives 0.85, and 400 gives 0.91. The scale is designed so that each 400-point gap multiplies the odds by 10. The expected score is for a match, not for one game's exact outcome. In chess, a 200-point gap means that the stronger player is expected to score about 76% of the points in a long match, which includes draws.
| Rating gap (stronger minus weaker) | Stronger player's expected score | Weaker player's expected score |
|---|---|---|
| 0 | 0.50 | 0.50 |
| 100 | 0.64 | 0.36 |
| 200 | 0.76 | 0.24 |
| 300 | 0.85 | 0.15 |
| 400 | 0.91 | 0.09 |
Updating Ratings
New rating = old rating + K × (actual score − expected score). The K-factor controls how fast ratings move; it is 32 for new or low-rated players in many systems, 20 or 16 for established players, and 10 for top-rated players. Using K = 32, A (1600) versus B (1400) with E_A = 0.76: if A wins, A gains 32 × (1 − 0.76) = 7.7 points, rising to 1607.7, and B loses 7.7. If A loses (an upset), A drops 32 × 0.76 = 24.3 points and B gains 24.3. If they draw, A loses 32 × (0.5 − 0.76) = 8.3 points. The system is zero-sum between the two players when both use the same K. Upsets cause larger swings than expected results.
Where It Is Used
Chess federations, online chess platforms, Go, esports, table tennis, and some sports leagues such as the World Football Elo ratings. Video games use variants (such as Glicko, which adds a rating deviation, and TrueSkill for teams) to deal with uncertainty and team play. Home leagues can use Elo in a spreadsheet to rank players over time.
Limits
Ratings are relative to the pool and drift if players enter and leave. The 400-point scale and the logistic curve are assumptions that fit some games better than others. Rating inflation or deflation can occur, and new players need several games to stabilize. Treat ratings as estimates with an uncertainty of dozens of points.
Frequently Asked Questions
What is the Elo expected score formula?
E_A = 1 ÷ (1 + 10^((R_B − R_A) ÷ 400)).
How much does a 200-point favorite expect to score?
About 0.76.
How are ratings updated?
New rating = old rating + K × (actual − expected).
What is the K-factor?
A parameter controlling how fast ratings change.
Why do upsets change ratings more?
Because the actual score differs more from the expected score.