Naive thoughts on Baseball

It turns out that there are a fair number of Red Sox fans in my neighborhood. I know becuase I could hear them cheering tonight. The last time I remember such an auditory signal with respect to a sporting event was when the Giants won the Super Bowl, whenever that was. The time before that was when NC State won the NCAA championship sometime in the mid-1980s (note that at that time I lived in Raleigh, not NYC).

For those of you who don't know, I live in Washington Heights in Manhattan. As I did until tonight, you might expect this to be a Yankees bastion but note: 1) the region of NYC that I live in has the largest Dominican population outside of Republica Dominica; 2) in thanking the fans of the Red Sox Nation, one of the executives listed places, Boston, California and the Dominican Republic; 3) Manny Rameriz grew up not too far from where I live (in NYC terms, "not too far" is measured in city blocks); 4) Pedro Martinez is also from the DR...

Perhaps more to the point with respect to this blog, the Red Sox completed tonight what no team in baseball has been able to do in post-season history, recover from being 3 games down in a 7 game series. Baseball being a game of statistics, I am wondering about this fact.

First of all, does the "post-season" history modifier matter. Are there examples in baseball history of teams going 4 straight to win a 7 game series in the regular season? I expect not, primarily because teams don't (rarely?) play 7 games in a row in the regular season.

Second of all, what are the statistics of baseball streaks like? Are they uncorrellated like coin tosses. Think about this, 3 consecutive coin tosses have yielded heads, what is the probablity that the next toss will be heads? (see A1 below). In baseball terms this would mean that the likelihood of winning and particular game is independent of whether you won or lost the previous game. It also means that the chances of a streak of length N is 1/2eN, so in an uncorrellated baseball universe the chances of winning 4 straight would be 1/16, not all that long odds in a sport that has a history of more than a century.

ahh but, that is more like the likelihood of sweep, doesn't the fact that the long suffering underdogs have lost 3 in a row (1/8 in a purely random world) have anything to do with it? I would say yes - it does suggest that the coin may be biased. That is that the chances of tails on the next toss are better than 50 - 50, in which case the odds of 4 in a row go down pretty fast. (if in fact after 3 games the odds are 75 -25, then the likelihood of 4 in a row is like 1/64).

Alternatively what if the chances of winning the next game depends on the outcome of the previous game. Statistics like that have a name that I can't drag up at the moment and I certainly can't write down. It opens a can of worms as well. If you won the last game is it more or less likely that you will win the next game? If you have won the previous 3 games what is the likelihood? The cool thing about baseball is that if you had the time and inclination, you could figure all this out. (If you do please let me know! I have the inclination, but not the time.)

The Red Sox and the Yankees are incredibly evenly matched these days. They had the two best records in the American League this year. That is the second place team in the American League East (Boston) had a better record than the winning teams in the other two divisions. Before tonight they had played each other 50 times in recent history and each won 25 games. The difference in their run scoring was 2 (I am quoting Tyler Kepner of the NYTimes (sorry can't be bothered with the link tonight) - Tyler didn't say which way it went, but given that fact and his allegiance, I am guessing it was advantage Boston.

OK - it is late, I am out of gas. Any thoughts on the probablity that the Red Sox will win the World Series?

Aside
A1 - 50%
End