Elo Calculator

A simple command line interface for calculating elo rating.

Usage

$ elo rate PLAYER_RATING OPPONENT_RATING SCORE [-k] [--round/--no-round]

Where

PLAYER_RATING

an integer representing the rating of the player

OPPONENT_RATING

an integer representing the rating of the opponent

SCORE

• win or 1
• loss or 0
• draw, tie or 0.5

--k

The K factor, a constant that impacts how the rating will change in a single match.

--round / --no-round

Round results to the nearest integer.

Examples:

$ elo rate 1800 1750 win

> Player rating: 1809
> Opponent rating: 1741

$ elo rate 2100 1900 loss -k 64 --no-round

> Player rating: 2051.4
> Opponent rating: 1948.6

How the ELO rating is calculated

The first step is to compute the transformed rating R for each player. This step will simplify further calculations.

R_i = 10^{r_i/400}

Then we calculate the expected result E for each player.

E_1 = \frac{ R_1 } {R_1 + R_2}

E_2 = \frac{ R_2 } {R_1 + R_2}

After the match is complete we can compute the rating variation \Delta r_i for each player.

\Delta r_i = K (s_i - E_i)

Where:

K

the K factor is a constant that regulates by how much the ratings will vary in a single game.

s_i

is the score of the player i in the game.

• s_i = 1 if the player wins,
• s_i = 0 if the player loses and
• s_i = 0.5 if the match is a draw.

And E_i

is the expected result of the match

Finally the new rating r'_i can be calculated by:

r'_i = r_i + \Delta r_i