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Player A wins 90% of matches

Player B wins 60% of matches

If they play each other what is the probability that;

Player A will win

Player B will win

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    dup: http://math.stackexchange.com/questions/44579/p-chance-of-winning-tennis-point-what-fp-chance-of-winning-game2012-06-22
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    @leonbloy I don't think that is at all the same question; that is much more straightforward. Games are made up of points. This question asks how to compare two players based on their previous records playing other people.2012-06-22
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    @leonbloy It isn't a duplicate because the probabilities don't add up to 1. The answer is indeterminate. If player A is the best in the world and player B is a decent 15-year-old playing for school teams, for example ... . Or player A could be a school champion, and player B a decent club player. Who knows?2012-06-22
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    @Mark I supposed there was an implicit assumption that $A$ and $B$ had accumulated these records by playing against the same pool of opponents.2012-06-22
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    @MarkBennet: I would put that in as an answer. I think it is the best we will get.2012-06-22
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    @MarkDominus I gave an extreme example to show that the answer would depend on the assumptions. How often have they played each other?2012-06-22
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    @Ross I think we can do better. This sort of problem is well-studied in sports statistics. For example, football teams $A$ and $B$ have the known won-lost records at the end of the season; whom do we expect to win when they are matched up in a postseason game? Someone who knows something about it could at the very least cite the existing literature.2012-06-22
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    @Mark (both) I agree that I was wrong, it's quite a different (and not well posed) question.2012-06-22
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    @MarkDominus: that would be true if they play some of the same people, but we aren't even given that.2012-06-22
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    @ross As I said, I supposed there was an implicit assumption that $A$ and $B$ had accumulated these records by playing against the same pool of opponents. Otherwise Mark Bennett's trivial objection holds. But why interpret the question in the least interesting way possible when there is a reasonable question lurking inside? Presumably OP is not interested in comparing Roger Federer against Joe Schlobb based only on their win-lose records.2012-06-22
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    Sorry to have caused so much confusion, I'm pretty new to this and still learning how to pose questions correctly. Part of the problem with not knowing how to figure something out is that I don't have the insight/experience to realise that the source of the records is important. I was indeed assuming that they had accumulated these records by playing against the same pool of opponets... should I edit the question to include this assumption? Many thanks for the Bradley-Terry model too, I had never heard of it. Sorry once again, and thanks to everybody that took time to respond to my question.2012-06-23
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    @MarkBennett Regarding your comment "How often have they played each other?" I now see this could be very important, are the resulting probabilities significantly different? Perhaps I should pose this as a separate question...2012-06-23

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