Elo Rating Calculator

Formula

The formula to calculate the new Elo rating is:

\[ R_{\text{new}} = R_{\text{old}} + K \times (S - E) \]

Where:

\(R_{\text{new}}\) is the new Elo rating
\(R_{\text{old}}\) is the old Elo rating
\(K\) is the K-factor
\(S\) is the actual score of the player
\(E\) is the expected score of the player

What is an Elo Rating?

The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. Named after its creator, Arpad Elo, a Hungarian-American physics professor, the Elo system is based on the concept that the performance of each player in a game is a normally distributed random variable. The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to win an equal number of times.

Example Calculation 1

Let's assume the following values:

Old Elo Rating (R_old) = 1500
K-Factor (K) = 32
Actual Score (S) = 1 (win)
Expected Score (E) = 0.75

Using the formula:

\[ R_{\text{new}} = 1500 + 32 \times (1 - 0.75) = 1500 + 32 \times 0.25 = 1500 + 8 = 1508 \]

The New Elo Rating is 1508.

Example Calculation 2

Let's assume the following values:

Old Elo Rating (R_old) = 1600
K-Factor (K) = 24
Actual Score (S) = 0 (loss)
Expected Score (E) = 0.6

Using the formula:

\[ R_{\text{new}} = 1600 + 24 \times (0 - 0.6) = 1600 + 24 \times -0.6 = 1600 - 14.4 = 1585.6 \]

The New Elo Rating is 1585.6.