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# The odds of not winning a world series from 1909 to 2012

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### #1 OCCubFan

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Posted 30 August 2012 - 08:15 PM

Bric wondered what the odds were of not winning the World Series for over a hundred years. Making a few assumptions, I calculated that the liklihood of not winning a World Series for the 104 years from 1909 to 2012 was 1 in 235. Alternatively, the probability of being so "unlucky" was 0.0043.

One of the assumptions was that if there were N teams in the National League then the probability of the Cubs winning the pennant was 1/N. The subsequent probability of winning the World Series was 1/2. So the probability of not winning the World Series in one year is 1-1/2N. Then, just multiply together the probability for each of the 104 years. Take into account that the National League had 8 teams for 53 years, 10 for 7 years, 12 for 24 years, 14 for 5 years, and 16 for 15 years.

This calculation assumes that every team in the league had an equal chance to win each year and furthermore that year's probability was not correlated with what had happened the previous year. Because the Cubs are a major market team, one would expect them to be above average most of the time. The big unaccounted-for variable is management of resources. That is why the Yankees (and Cardinals) have done so well and the Cubs have not won the World Series in 104 years.

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Posted 30 August 2012 - 10:00 PM

The one potential problem with calculating it this way is autocorrelation: the Cubs' chances of making the WS in 1950 are going to be similar to their chances of winning in 1949 and 1951. That's because the 1950 Cubs are a slightly modified version of the 1949 Cubs and the 1951 Cubs are a slightly modified version of the 1950 Cubs.

This makes it more probable that teams will have long dry or hot spells: you get "dynasties" of the same very good players making a team competitive in consecutive years (and thus greatly elevating the probability of more than 1/Nth of the pennants in that stretch), and "dudesties" of teams with bad players being bad (or being replaced by equally bad) players year after year.

The other thing to take into account is that when you have multiple teams, you have a range of expected outcomes even if all teams are equal. So, let's forget about the autocorrelation part: each team has a 1 in 16 chance of winning the WS. (This obviously applies only to pre-1961 baseball). Here are the expected number of teams to win X WS in 25 and 50 years:

WS 25 50
0 3 1
1 5 2
2 4 3
3 2 4
4 1 3
5 0 2
6 0 1

So, even at this level, you expect one team in 16 to fail to win any WS in half a century even if it was just as good as every other team!
Gods don't play dice with the universe, they are the dice of the universe: our job is to figure out how many sides and dice!

### #3 Brett

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Posted 13 February 2013 - 07:50 PM

I know this is a crazy old thread, but I actually stumbled upon it while performing a similar calculation on my own.

A question for Doc: if you would expect 1 in 16 teams to fail to win any WS in a half century, wouldn't the math be 1/16 * 1/16 for the same team to fail to win any WS in two half centuries?

That comes to 1 in 256 - obviously it would be a bit lower for that second half century because of expansion, but it makes me wonder whether that 1 in 235 figure is actually quite right, even after considering the range of expected outcomes.

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