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Elo rating system possibly in Halo?


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The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. It is named after its creator Arpad Elo, a Hungarian-American physics professor.

The Elo system was originally invented as an improved chess rating system over the previously used Harkness system, but is also used as a rating system for multiplayer competition in a number of video games. 

The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to score an equal number of wins. A player whose rating is 100 points greater than their opponent's is expected to score 64%; if the difference is 200 points, then the expected score for the stronger player is 76%.

A player's Elo rating is represented by a number which may change depending on the outcome of rated games played. After every game, the winning player takes points from the losing one. The difference between the ratings of the winner and loser determines the total number of points gained or lost after a game. If the high-rated player wins, then only a few rating points will be taken from the low-rated player. However, if the lower-rated player scores an upset win, many rating points will be transferred. The lower-rated player will also gain a few points from the higher rated player in the event of a draw. This means that this rating system is self-correcting. Players whose ratings are too low or too high should, in the long run, do better or worse correspondingly than the rating system predicts and thus gain or lose rating points until the ratings reflect their true playing strength.

An Elo rating is a comparative rating only, and is valid only within the rating pool where it's established.

https://en.wikipedia.org/wiki/Elo_rating_system ]

Elo hell (also known as MMR hell) is a video gaming term used in MOBAs and other multiplayer online games with competitive modes. It refers to portions of the matchmaking ranking spectrum where individual matches are of poor quality, and are often determined by factors such as poor team coordination which are perceived to be outside the individual player's control. This ostensibly makes it difficult for skilled players to "climb" up the matchmaking ranking (and out of Elo hell), due to the difficulty of consistently winning games under these conditions. Its existence in various games has been debated, and some game developers have called it an illusion caused by cognitive bias.

https://en.wikipedia.org/wiki/Elo_hell ]

Understanding Elo might lead to a better understanding on advantageously playing with it, or just playing in general. A more relative derivative is TrueSkill (which is currently on its second adapted version or third as of Halo 5: Guardians) 

TrueSkill is a skill-based ranking system developed by Microsoft for use with video game matchmaking on Xbox Live. Unlike the popular Elo rating system, which was initially designed for chess, TrueSkill is designed to support games with more than two players. 

On Xbox Live, players start with 3  always increases after a win and always decreases after a loss. The extent of actual updates depends on each player's wow variable and on how "surprising" the outcome is to the system. Unbalanced games, for example, result in either negligible updates when the favorite wins, or huge updates when the favorite loses surprisingly.

Factor graphs and expectation propagation via moment matching are used to compute the message passing equations which in turn compute the skills for the players.

Player ranks are displayed as the conservative estimate of their skill. This is conservative, because the system is 99% sure that the player's skill is actually higher than what is displayed as their rank.

The system can be used with arbitrary scales, but Microsoft uses a scale from 0 to 50 for Xbox Live. Hence, players start with a rank of 3. This means that a new player's defeat results in a large sigma loss, which partially or completely compensates their mu loss (in mathmatical equation not examplified on the site). This explains why people may gain ranks from losses.

https://en.wikipedia.org/wiki/TrueSkill ]

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