ELO rating

The formulas for calculating user's ratings can be as follows:

Rn = Ro + K * (W - L) * log10(N + 1)

where:

Rn - the new rating of the player Ro - the old rating of the player K - a coefficient that determines the rate of rating change and can be chosen based on the desired level of variability (for example, 32 for chess, 20 for poker, etc.) W - the number of correct predictions made by the player L - the number of incorrect predictions made by the player (but not less than 0) N - the total number of predictions made by the player (both correct and incorrect)

Thus, the formula takes into account both the number of correct and incorrect predictions, as well as the total number of predictions made. The log10(N+1) coefficient allows for faster rating increase for players who make more predictions

log10(N+1) is the logarithm with base 10 of N+1, where N is the total number of predictions made by the player. Adding one to the formula helps to avoid division by zero error if the player has not made any predictions.

For example, if a player made 100 predictions, then log10(100+1) = log10(101) = 2.004. If a player made 10 predictions, then log10(10+1) = log10(11) = 1.041. The more predictions a player makes, the faster their rating will change when the number of correct and incorrect predictions varies.