The question was posed today on twitter by a few associates of mine at SNY in New York. How likely is it that the Patriots win as many September games as the Red Sox?
Let’s use the Patriots record last year (14-2, 87.5%) and the Sox September record last year (7-20, 25.9%) as baseline probabilities.
The Patriots have 4 September games, the Red Sox have 21 games left
59% chance of Patriots winning 4 games, 33% chance of Sox winning 4 games or fewer
33% chance of winning 3 games, 17% chance of Sox winning 3 or fewer
7% chance of winning 2 games, 6% chance of Sox winning 2 or fewer
<1% chance of winning 0 or 1 game.
That leaves us with .59*.33+.33*.17+.07*.06 = appx 25%.
Thus, the probability of the Patriots finishing the month with as many wins as the Sox is roughly 25%.
Not bad, although admittedly the Patriots and Sox winning percentages are a bit of a stretch. Maybe that’s why Bobby V was so mad?