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Tuesday, June 28, 2011
“Paradox”: Expectation of being favored to win - vs - Expectation of winning
I’m not sure that my title description is clear enough. And if someone wants to propose a better title to be clearer, please do so.
Someone sent me something like what I’m about to post, and he called it a “paradox”, but it is not at all a paradox. It’s a question of whether you average out binary numbers or average out the rates.
Suppose that Roy Halladay’s true talent level is such that the Phillies win .601 of their games with him on the mound against an average team at a neutral site. At home, the odds go up by +.050 (and on the road, it goes down .050). Against good teams, the odds go down by .050 (and up by .050 against bad teams). Against great teams, the odds go down by .100 (and up by .100 against terrible teams). So, Phillies with Halladay starting at home against a terrible team gives us odds of .751 that the Phillies will win. And on the road against a great team gives us .451 that the Phillies will win.
Count as “1” any time the Phillies have a greater than 50% chance of winning with Roy Halladay on the mound.
What percentage of the games are the Phillies favored to win? Is it exactly 60%? Or more than 60%? It’s not a trick question.
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