The Daily Parker

Politics, Weather, Photography, and the Dog

What are the odds for a losing streak?

A couple of days ago at work, we were talking about stupid things sports commentators say. In any sport, but much more so in baseball and U.S. football than others, you hear some commentator say "Well, Bob, with runners on first and third on a night with a 10-knot breeze out of the northeast, when the pitcher's name starts with 'M', there's only a 1-in-65 chance a left-handed batter with six toes on his right foot will fly out to center." Who cares, right?

But being in Chicago, there is a huge question in that category that we should answer: What are the odds that a baseball team can fail to win the World Series for 104 years?

Of course, given the Chicago Cubs' history, the odds are observably certain that one baseball team can do it. But, all things equal, what is the probability this can happen?

Here's how we figured it out. First, in any given year, all but one team does not win the World Series. For example, there are 30 teams right now, but only the San Francisco Giants will win the World Series. (Tonight, in fact, unless Detroit suddenly turns into a different baseball team.) So the basic formula for the probability of losing the world series is:

...where t is the number of teams and y is the number of years with that number of teams.

Since the Cubs last won in 1908, Major League Baseball has expanded six times, from 16 teams (in 1908) to 30 teams today. With 30 teams, the probability of losing the World Series is 0.9667, that is, 29 in 30. In 1908, the probability of losing was much smaller, 0.9375, or 15 in 16.

But here's the problem. The probabilities are multiplied together, like this:

Since 1908, there have been 103 World Series (there wasn't on in 1994, remember), so the data going into the formula are: from 1908 to 1960, 16 teams and 53 Series; in 1961, 18 teams, 1 Series; 1962 to 1968, 20 and 7; 1969 to 1976, 24 and 8; 1977 to 1992, 26 and 16; 1993 to 1997, 28 and 4; since 1998, 30 and 14. Doing the math, we come up

The probability that the Cubs would lose all 103 World Series contests since last winning in 1908 is 0.00441, or 1 in 227.

I will now go cry.

And just for giggles, the probability that they would fail to play in the Series (i.e., win the pennant) since their last appearance in 1945 is 0.04798, or 1 in 21. So there's hope.

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