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Winning the Division = Statistically Improbable

The Red Sox have been playing some great baseball lately. Over the last 10 games, they are 9-1. Some Red Sox fans are starting to believe that the division is within sight.

I hate to be the bringer of bad news, but it is very unlikely that the Sox catch the Yankees and win the AL East.

The Yankees have a 95-55 record at present, with 12 games left in their season. The Red Sox have a 89-59 record and 14 games left. To win the division outright, the Sox have to close a 5 game gap by winning 6 games, and then hold off the Yankees. But let's say the Sox and Yankees finish the season with a tied record. In that case, the division winner is determined by tie-breakers, starting with head-to-head record and then record against the whole division (see here, 10th and 11th paragraphs). The Sox lead in both of those categories right now, so if they can tie the Yankees in record, they ought to win the division.

After the jump, I detail how this plays out practically.

To win the division, it's likely that all the Sox have to do is tie it. Below, I've listed the combination of Sox wins and the maximum Yankee wins in the remaining games that allow a tie of their final records. The numbers in parentheses are the teams' final win totals given those figures.

Sox Wins :: Maximum Yankee Wins

14 (103 wins) 8 (103 wins)
13 (102 wins) 7 (102 wins)
12 (101) 6 (101 wins)
11 (100) 5 (100)
10 (99) 4 (99)
9 (98) 3 (98)
8 (97) 2 (97)
7 (96) 1 (96)
6 (95) 0 (95)

So, if the Sox win every remaining game (14), the Yankees can still hold them off by going 9-3 the rest of the way. If the Yankees play .500 baseball the rest of the way, they'll win 6 games and Boston will have to win 12 to tie them.

Someone more mathematically gifted than myself can run the numbers on these scenarios and give likelihoods. If you assume that the chance the Yankees lose any game is 50%,* the odds of the Yankees losing each of their last 12 games is 1/2^12, or 1 in 4096, or a 0.02441% chance. Every Yankee win going forward, and every Sox loss, astronomically reduces the chances of the Sox winning the division. currently gives the Sox odds of winning the division as 9.6%. It will take a combination of an utter collape by the Yankees and a miraculous run by the Sox for the latter to win. Dice-K, Wake would have to be superb, the pen would have to hold leads, and our offense would need to be on a tear. It could all happen, but don't bet on it.

*This is pushing it, because the Yankees are a better than average team, so their odds of losing should be below 50%.