Elo Win Rate Calculator

Rating of Player A: Rating of Player B:

Enter the ELO ratings for both players to see their expected win rates.

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Understanding the ELO Win Rate Calculator

The ELO rating system is a method for calculating the relative skill levels of players in competitor-versus-competitor games such as chess. It's widely used in competitive gaming and esports to create fair matchmaking and track player progression.

How ELO Works

At its core, the ELO system is based on the idea that the difference in ratings between two players serves as a predictor of the outcome of a match. When a player wins, they gain ELO points, and the loser loses points. The number of points exchanged depends on the difference in their ratings:

If a higher-rated player wins against a lower-rated player, the point exchange is small.
If a lower-rated player wins against a higher-rated player, the point exchange is larger.
If players with very similar ratings play, the point exchange will be moderate.

The ELO Win Rate Formula

The probability of a player winning can be calculated using a logistic curve. The formula for the expected score (which represents the probability of winning) for Player A against Player B is:

E_A = 1 / (1 + 10^((R_B - R_A) / 400))

Where:

E_A is the expected score for Player A.
R_A is the ELO rating of Player A.
R_B is the ELO rating of Player B.

Similarly, for Player B:

E_B = 1 / (1 + 10^((R_A - R_B) / 400))

Note that E_A + E_B = 1, meaning the probabilities sum to 100%.

The expected score is often expressed as a win percentage. For example, an expected score of 0.75 means Player A is expected to win 75% of their games against Player B.

Using the Calculator

To use this calculator, simply input the current ELO ratings of the two players into the respective fields. The calculator will then determine the probability of each player winning the match, based on the ELO system's mathematical model. This is a powerful tool for understanding the matchup dynamics in competitive games.

Example Calculation

Let's say Player A has an ELO rating of 1600 and Player B has an ELO rating of 1400.

The rating difference is 1600 – 1400 = 200.

Using the formula for Player A:

E_A = 1 / (1 + 10^((1400 - 1600) / 400))

E_A = 1 / (1 + 10^(-200 / 400))

E_A = 1 / (1 + 10^(-0.5))

E_A = 1 / (1 + 0.3162)

E_A = 1 / 1.3162

E_A ≈ 0.760

So, Player A has an expected win rate of approximately 76.0%. Player B would then have an expected win rate of 100% – 76.0% = 24.0%.