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Wednesday, June 23, 2010
Reader Mail of the Day: Historical Win Rates
What do you do when the result of a positive act results in a negative value in win expectancy? e.g. Bottom of 5th, runners at corners, 1 out, home team up by 5: win exp = 98.6% (137/139). Next batter singles and runner on 1st goes to 3rd, making situation the same, but home team up by 6: win exp = 96.7% (87/90) (numbers from winexp.walkoffbalk.com - if there is another source, I imagine that somewhere in the list of possibilities that the above situation has occurred)
A win PROBABILITY is a probability, or an expectancy, or a future outcome.
What the reader is quoting here are TWO POOLS of past historical win rates. In one case, teams found themselves in one situation 139 times and won 137 times. In another case, a better situation to be in, COMPLETELY DIFFERENT teams found themselves in that situation 90 times and won 87 times.
You cannot simply compare the two, and come up with a delta win expectancy. This is why I am completely opposed to looking at win expectancy charts based solely on the empirical / actual / historical. You get hundreds, if not thousands, of such inconsistencies. Don’t do it. This is why Markov chains are far more preferable.
It’s important to make the distinction between past win rates of a bunch of unrelated game states, and future win probabilities of game states that are completely dependent on each other.
I hope I explained that well enough.
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