Expected Score in Elo Chess Ratings

Expected score is calculated using the formula: E = 1 / (1 + 10^((Opponent Rating − Your Rating) / 400)). When two players are equally rated, expected score is exactly 0.50 for each player. For every 400-point rating advantage, the stronger player's expected score rises to approximately 0.91. If you want to test the idea with real inputs, try the Test expected score with the calculator.

An expected score of 0.75 does not mean you will win 75% of the time. It means that across many games against this level of opposition, you would be expected to average 0.75 points per game — a mix of wins, draws, and occasional losses that collectively average to that figure.

Consider a 1800-rated player who draws against a 1400-rated opponent. The expected score was approximately 0.91, meaning the system expected nearly a full point. The actual draw scored only 0.50, which is 0.41 below expectation. With K=20, this produces a painful loss of about 8 rating points from a draw.

Now consider the same 1800-rated player drawing against a 2200-rated opponent. Expected score here is approximately 0.09. The draw scored 0.50, which is 0.41 above expectation. Same K=20, same draw, same rating gap — but this time the player gains 8 points. The result label is identical; the expected score context makes them polar opposites.