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ELO Rating - Player EXP gains/PVP


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I've noticed that a lot of online game companies use the ELO rating system

Anyone on CE using the ELO rating system at their game ? If so what's your experience with it ?

Info regarding ELO in games:

In many computer role-playing games, the played game character has an experience (which can be compared to the rating of a chess player), which grows exponentially as the character evolves (while the Elo rating of a chess player grows linear as the player evolves).Therefore, in a morpg with pairwise battles, it can be a desirable feature to have an experience attached to each character which resembles the Elo rating of a chess player, but grows exponentially to better match the experience of a character in other rpg's.

Let's call a character's experience Q, and define it as


where R would be the Elo rating of the character. We then have a bijection between R and P, where R = 400log10(Q / C). Notice that the experience will always be positive, while the rating can be any real number. Imagine we have two characters, A and B, with the experiences QA and QB. In a battle between A and B, the expected score of player A can be calculated using the exact formula


So, we have


and the corresponding expression for player B that is


When the battle is over, by using the formula for updating the rating of a character, we can also update the expereince of the character:




where F = 10K / 400. A low K values corresponds to an F values close to 1. However, while the K value is lower for stronger chess players, the F value is often left unchanged, to enable the system to be more dynamic (which is a requirement for making a game fun).In opposite to a chess player, a character of a single player rpg is made to evolve through out the entire game, as he encounters new and better items, develops his skills, learns new spells, etc. In a morpg on the other hand, the creators often continuously develop the games and create new patches, such as in World of Warcraft. As each patch is released, the environment of the game is changed; this makes the game more chaotic.

For low F values, the formula for updating the experience can be approximately estimated by


where 59ac54b4948928c89ccf8eb4b4700e1b.png . Using players A and B as referrals again, and inserting the formula for the expected score, we can substitute E and obtain


Now, since S = 1 at win, but 0 at loss, the experience gain is


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