K-Factor

The K-Factor is defined as follows. If two players with identical ratings are playing a game where each side has no intrinsic advantage over each other, then after the game is finished and there is a victory by one player and a loss by the other, then the ratings of the players will move relative to each other by a K-Factor amount with each player getting an equal adjustment. More specifically, the winning player's rating will go up by half of the K-Factor and the losing player will go down by half of the K-Factor.

Determining the correct K-Factor can be difficult and has its own body of research that I have not yet had time to explore. My belief is that some of this fudging is unnecessary and a K-Factor of 40 will work well enough in most scenarios as long as you make adjustments to the ratings to account for low alphas. As a specific example, the K-Factor used for chess players over 2400 is set to a less optimal low value of 16 in order to fix issues with undesired rating spread (or low alpha values).

As an example, if two players have a rating of 1600 and the current K-Factor is 32 (a typical value), then the winner will have a rating of 1616 after the win, and the loser will have a rating of 1584 after the loss.

If the player's ratings are not identical, then the rating adjustment increases if the lower rated player wins and decreases if the higher rated player wins. Assuming that there are no issues that make one player special, each player gets an identical but opposite rating adjustment. As an example of a special player, a player that has only played a few games is given a provisional rating which will get a much larger adjustments with each win or loss.

The amount the rating adjustment changes is dependent on the model used to emulate chances of wins and losses. Generally if the model says that I have X percent chance of winning and K is my K-factor and I win, then I should get (1 - X)⋅K improvement in my rating and the loser should have the same amount subtracted. For example, if player A has a rating of 1700 and player B has a rating of 1600 and the current model says that there is 64% chance of player A winning and player A wins then if we assume the K-factor is 32, then the rating for player A will become 1700 + (1 - .64) ⋅32 = 1712 (rounding floating point values to nearest integer) and the rating for player B will become 1588.

The most typically used model for predicting winning percentages based on differences in ratings is the logistic curve exponential decay model used in implementing the Elo rating system.