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An incomplete description of the algorithm. Our attorney friends tell us that we should not go into any detail about the algorithm itself, so we won’t. In the numerical examples, we do not give the actual numbers that are produced by the algorithm, but instead give “representative” ones. Basically, if team A has rating A, and plays team B with rating B, then the algorithm takes the score of the game (actually, the goal differential) and the difference in the ratings of the teams, and decides how many points are exchanged between the teams. For instance, if A is 500, and B is 300, the ratings difference is 200 points. Suppose A beats B 2-1. Then the algorithm would figure out how many ratings points are exchanged between the two teams. Say this is 10 points. This would be the same rating exchange if the score were 3-2, or 17-16. Then the new rating of A is 500 + 10 = 510, and the new rating of B is 300 – 10 = 290. If A beats B by more than one goal, the number of points exchanged increases with each goal, but each goal is “worth” fewer rating points, with a maximum exchange occurring when A beats B by 6 goals. So if A beats B by 7-1, or 23-1, the rating exchange would be the same. If the scores were reversed, so the lower rated team (B) beats the higher-rated one (A), then the rating point exchange is considerably greater. For instance, if the ratings were as given, and B beats A 2-1 (or 3-2, or 5-4, …), then B might gain 30 points, which A would correspondingly lose. Then the new rating of A is 500 – 30 = 470, and the new rating of B would be 300 + 30 = 330. As the rating difference increases, the number of points exchanged when the higher-rated team beats the lower-rated team decreases, becoming 0 when the ratings difference is around 700 points. Conversely, as the rating difference increases, the number of points exchanged when the higher-rated team loses to the lower-rated team increases, up to a maximum of about 75 points if the ratings difference is 700 points, and the lower-rated team beats the higher-rated one 6-0 (this has not happened yet). It is important to understand that the rating is a statistical thing. Teams whose ratings differ by about 75 points or fewer should be considered essentially equal in strength. If you play a team rated 400 points higher than you, they would be expected to win about 90% of the time. But you would be expected to win 10% of the time, and this does, in fact, happen. So you still have to play the game. Generally, the odds are like this. If the ratings difference is as given below, the higher-rated team should be expected to win the given % of the time:
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