Elo Rating Update

This update rule changes a rating by comparing what actually happened in a game with what the rating system predicted. If the result is better than expected, the rating rises; if it is worse, the rating falls, and the size of the change is controlled by the K-factor. The formula comes from iterative rating systems in which each match is treated like a small correction to a player's estimated strength.

Use this when you need to update rankings after head-to-head competition, such as chess, esports, online matchmaking, or league play. It is especially useful when you want ratings to reflect both recent results and the difficulty of the opponent.

• Using 1 for a draw and 0.5 for a win instead of the other way around
• Forgetting that E is an expected score between 0 and 1, not the opponent's rating
• Applying the formula without checking whether the K-factor is meant to be fixed or changed by the system