### Red Sox rolling

In my last post I claimed that 4-2 is the single most likely World Series result if one team has between a 50% and 60% probability of winning each game. Well, now the Red Sox are up 2-0 in the Series. What's the single most likely result now, assuming that the Red Sox are only slightly favored to win each individual game?

Surprisingly, it's a 4-0 sweep.

Let's conservatively assume that the Red Sox have only a 51% chance of winning each game. We can then compute the probability of each possible result by looking at every possible win/loss sequence. For example, consider 4-2. If we take "CCBB" to mean Colorado wins games 3 and 4 and Boston wins games 5 and 6, then there are only three possibilities that lead to a 4-2 result: CCBB, CBCB and BCCB. The probability of each is 49% × 49% × 51% × 51% ≈ 6.245%, and multiplying by 3 gives the probability of a 4-2 result: 18.735%. Doing the same for the other possible results, we get

Red Sox 4-0 | 26.01% |

Red Sox 4-1 | 25.49% |

Red Sox 4-2 | 18.735% |

Red Sox 4-3 | 12.24% |

Rockies 3-4 | 11.76% |

Rockies 2-4 | 5.765% |

So, unless the Rockies are truly the better team, a sweep is now more likely than any other result, and the Red Sox have at least a 81.25% chance of winning it. (For the Rockies to have a 50% chance of winning the Series, they'd need to have a 68.62% chance of winning each game.)

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