🏅ELO System

The Elo System is using K-factor to calculate the outcome Elo. We're not using Glicko-2 for ELO formula.

Modified Elo System:

• DeChess employs a modified version of the traditional Elo rating system. This modification includes adjustments to the standard Elo formula to better fit the specific needs of DeChess users and game types.

Varying K-Factors:

The K-factor, which determines the sensitivity of rating changes based on game outcomes, varies depending on different factors:

• Player Rating: New or less experienced players typically have a higher K-factor, allowing their ratings to change more rapidly based on game results. This helps them quickly achieve a rating that more accurately reflects their skill level.

• Game Type: Different K-factors may be applied to different types of games or formats. For instance, faster time controls like bullet and blitz might have higher K-factors compared to slower formats like classical chess.

• Activity Level: Active players who frequently engage in games might experience different K-factors compared to those who play less often.

Rating Calculation:

• The expected score and new rating calculations follow the general principles of the Elo system but with adjustments to the K-factors. The basic formulas used for updating ratings are:

Formula A (The first formula tells you how to predict the outcome of the game)

$$NewRating = Rating + K(Score - Expected Score)$$

Formula B (The second formula tells you how to update your rating depending on the outcome of the game)

$$E_A = \frac{1}{1 + 10^{\frac{R_B - R_A}{400}}}$$

If Player A has a rating of 𝑅 𝐴 ​ and Player B has a rating of 𝑅 𝐵 ​, the precise formula for determining the expected score of Player A is:

$$E_B = \frac{1}{1 + 10^{\frac{R_a - R_b}{400}}}$$

Similar to A and you can predict outcome elo of Player B :

$$E_A = \frac{1}{1 + 10^{\frac{R_b - R_a}{400}}}$$

For example

Example: If the probability of winning is 1, you are certain to win the game. If the probability of winning is 0, you are guaranteed to lose the game.

Important: When the probability of winning is 0.5 (or 50%), you will win approximately as many games as you lose. Essentially, this means the outcome will be a draw on average.

Win	Lose	Draw
1	0	0.5

Rating of 𝑅_𝐴: 1200 (Game Draw)

$$E_A = \frac{1}{1 + 10^{\frac{1200 - 1400}{400}}} = \frac{1}{1 + 10^{-0.5}} \approx 0.76$$

Rating of 𝑅_𝐵: 1400 (Game Draw)

$$E_B = \frac{1}{1 + 10^{\frac{1600 - 1400}{400}}} = \frac{1}{1 + 10^{-0.5}} \approx 0.24$$

If Player A Wins:

• New Rating (A) = 1400 + 32 × (1 - 0.7597469266) = 1407.68

If Player A Loses:

• New Rating (A) = 1400 + 32 × (0 - 0.7597469266) = 1375.68

If Player A Draws:

• New Rating (A) = 1400 + 32 × (0.5 - 0.7597469266) = 1391.68

If Player B Wins:

• New Rating (B) = 1200 + 32 × (1 - 0.2402530734) = 1224.32

If Player B Loses:

• New Rating (B) = 1200 + 32 × (0 - 0.2402530734) = 1192.31

If Player B Draws:

• New Rating (B) = 1200 + 32 × (0.5 - 0.2402530734) = 1208.31

Application in Different Game Formats

DeChess may apply specific rating adjustments for various game formats, such as rapid, blitz, or bullet games, ensuring that the rating system accurately reflects performance in each type of game.