The simulator uses as input each team's home and road winning percentages and then uses a formula I first saw in one of the Baseball Abstracts to calculate the winning percentage of the home team in each game. For example, if you had teams A and B team A's winning percentage in home games would be:
A = (A.HomeWPct - (B.AwayWPct * A.HomeWPct)) /
((A.HomeWPct + B.AwayWPct - (2 * A.HomeWPct * B.AwayWPct)))
The simulator then uses these percentages with some randomization to "play" each game in 2-3-2 series format.
In any case my results were that the White Sox would win the series 64.2% of the time and the Astros 35.8% of the time. The outcomes are shown in the following graph:

I certainly think the Astros have a better chance than this given the strength of their big three but it will be difficult for them to score runs. The Sox bullpen may also be rusty having thrown just 2/3 of an inning in the ALCS.
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