baseball stoopidstats: who has won their share of world series?

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What last I yammered about this stuff, I was looking at the lengths of World Series droughts. That was inspired by the Cubs victory, which ended their streak of more than 100 years. And I was thinking about the Mets (my team of choice) and the fact that they haven't won in 30 years.

But although 30 years is a long time, it's not really an extraordinary drought, since there are 30 teams. With 30 teams, we can really only expect a team to win once every 30 years (on average). This led me to wonder about the Mets: Have they won their share of World Series? The answer isn't entirely obvious. There have been 54 World Series since they were enfranchised. With two wins, they've won more than 1 in 30. But for most of the time they existed, there were fewer teams.

To answer the question (and the analogous question for each other team), I came up with a statistic (which I will call a team's Wins per share ratio). The goal is to calculate how many World Series a team has won, divided by the number they would have been expected to win if wins were evenly distributed among the teams. For a given team, this statistic is taken by adding 1/Nt for all years, t that the team existed (and a World Series was played, where Nt is the number of teams existing in year t. To take a simple example, if a team has existed for six years, during which there were 30 teams, and they won 1 World Series, then their statistic is 1 / (6 / 30) = 5. This means that they have won 5 times as many World Series as their share.

The accompanying table shows the 30 existing franchises and their ratios. By way of background (for those not into MLB history), the modern World Series began in 1903, and has been played every year since then except for 1904 and 1994. For the years in that span, the number of teams was as follows:

• 16 teams through 1960
• 18 teams in 1961
• 20 teams from 1962 through 1968
• 24 teams from 1969 through 1976
• 26 teams from 1977 through 1992
• 28 teams from 1993 through 1997
• 30 teams from 1998 onward

I am not considering Federal League teams, since the FL did not participate in the World Series.

 It should come as no surprise that the Yankees sit atop the list, having won nearly five times as many World Series as their share. My Mets have won just fewer than their share.

One quick anecdote about this. When I did my first draft of these calculations, I made a mistake and had the Yankees winning 4.80 times their share. I IM'd a friend at work about it. Then when I realized I had made a mistake, I IM'd him to say it was actually 4.74. His response? "I thought 4.80 looked a little strange."