121

The White Sox played the best-record-in-baseball Rays even over the weekend, winning the second and fourth games of the four-game series.  What are the odds of that?  Well, it depends on what you mean by "that."

Before the series began, the likelihood of the Sox, with their .435 winning percentage, beating the Rays ,with their .667 winning percentage, in a single game on a neutral field was around 27%.  (I've explained the formula for calculating this before.  It's complicated and not worth doing again.)  The chance of winning the second and fourth games out of four is 73%*27%*73%*27%, which equals 3.88%.  So if that's what we mean by "that," then there was less than a 4% chance of winning the second and fourth game -- very unlikely. 

If what we mean is winning any two out four games (which is what I meant), then we don't care in which order the Sox win them.  There are six combinations of outcomes where the Sox could win two games (win games 1,2; 1,3; 1,4; 2,3; 2,4; 3,4), so we have to multiply 3.88% by 6, which equals 23.3% -- still unlikely, but not shocking. 

What would have been shocking is the Sox winning all four games, which had a probability of about 0.5%.  By contrast, the Rays sweeping was actually more likely than the two teams splitting -- a roughly 28% chance.  (Just for the sake of completeness, the Rays had a 42% chance of going 3-1 and a 5.7% chance of going 1-3.)

None of these calculations reflects the fact that the game was played in Tampa or that the percentages of winning a single game change a bit after each game is played, but I've got a lot to do today, so that kind of analysis will just have to wait for when I've got more time to play with the numbers.

In any event, the Sox are now 8.5 games back of the Twins, with a Magic Number of 121.  But now they're back home, where they have a somewhat better record.  Go Sox!