The Elo rating system was created as a better chess rating system but is now used in other games as well. In it performance can’t be directly calculated but can be inferred from wins, draws and losses of other players. The rating given will depend on the rating of the player played against. Firstly the expected result of the game is calculated using players and opponents skill level:

is player A’s skill level and is player B’s skill level. This will be a number between 1 and 0 and reflects the probability of player A winning. If and are reversed in the equation, player B’s probability of winning can be obtained. Adding the two probabilities together will also equal one. After a game or series of games, the players’ new rating can be calculated with:

is the players’ new result. is the players existing result. as from before is the expected result and is the actual result of the match. The difference in the predicted and actual outcome is then subject to what is sometimes called the K-value. This is the maximum amount the players rating can change per game. In chess the most popular values used for K are 16 for masters and 32 for less skilled players. Here is an example to show a perceived weaker player winning against a higher skilled opponent given the values of 1119 for player A and 1507 for player B:

Player A jumped by 28 as this was an unexpected result. If player A had lost like predicted the rating jumps would not be as extreme.The United States Chess Federation uses its own rating system. The K-value in this system is based on how many games the players’ level is based on () and how many games they have played in the tournament ():

This seems the better approach of calculating the value as it is more dynamic at calculating the games played. The game Halo Wars uses the Elo rating system for assigning difficulties when you play against the AI. Their version is modified to generate numbers somewhere under 200. Ensemble Studios who made the game never did announce the limit of the rating so it is only an assumption.