
23.03.2004 
ERatingEach Rating has AntiRating Letter "E" may mean "Economic" or "Enhanced" or something other proper word. While working with ERating I saw that I have two absolutely equivalent ways to calculate rating. Usually we calculate rating as measure of strength. But in the same way we could calculate "antirating" as measure of weakness. For this we have to replace "win" with "loss" and "loss" with "win". As a result of this operation we will obtain another ranklist. Ranking by antirating will not exactly be congruent with the Ranking by rating. I think that "rating mirror" could be calculated for all ranking systems. As well as both ranklist are equivalent the problem is how to join ranklists by "rating" and "antirating". It depends on rating system. In general case we have to calculate two probabilities to win using both rating and antirating and then calculate mean value.
This way gives us probabilities but it does not give unit ranklist. Another way is to create artificial value such as sqr(Ra/ARa). Kenneth Massey proposed it when we discuss this problem. Economical approachLet's forget mathematical point of view on ranking problems and try to solve it on other way. Let's think that results of matches are goods. If teams wins it means that this team buys a game. If teams lose it means that it sells a game. Naturally that price for win and loss depends on strength of team.
