Bloggo’s Number Crunch- Odd Odds

Odds that Phillies or Yankees Share Birthdays

Posted By: David Gassko
What are the odds that two players on a major league team’s active roster—the 25-man squad a team plays for most of the season—have the same birthday? You might imagine that they are fairly low—there are, after all, 365 days in a year, but just 25 active players on a baseball team. If you made that assumption, however, you’d be falling prey to a common statistical fallacy.
The odds that two players on a major league active roster will have the same birthday are in fact better than even. How can that be? It is all a matter of combinations.
1911 photograph of Fred Luderus, first baseman...

Image via Birthday-probabilities_leaderIf the question had been, what are the odds that you share a birthday with, for example, a Philadelphia Phillies player, the odds would be fairly low—about 1 in 15.09, in fact. But the odds that two players in the Phillies clubhouse have the same birthday are significantly higher, because we’re not comparing just one person to the whole clubhouse, we’re comparing the whole clubhouse to itself.Image via Image via Wikipedia

The graph above shows how the odds of two people having a matching birthday increase as the number of people being compared goes up.

In groups of 40 people—the size of a complete MLB team—the chances of a birthday match are about 90%. It’s no surprise, then, that the Yankees’ 40-man roster yields 2 matches (Edwar Ramirez and Mark Melancon on March 28 and Christian Garcia and Brett Gardner on August 24) and the Phillies’ 1 match (Clay Condrey and Ryan Howard will both celebrate their birthday on November 19).

Native American baseball player Ben Tincup of ...

Image via Wikipedia

A 25-person major league clubhouse happens to have just enough people to go over the breakeven point—the odds are half-and-half with a 23 person group. Luckily, that coincides with the size of many common groups—classrooms in high schools, small offices, and bars in off hours, if you’re the betting type. Few people would guess that in all of those settings, the chances that two people will have a matching birthday are so high, but as is often the case, that only illustrates how strange and unintuitive statistics can be.

In other words, instead of having 1*25 = 25 combinations of dates to check, we suddenly have 25*24/2 = 300 combinations to check. With 300 possible combinations, you can see how the odds two players on the same active roster share a birthday will be pretty good—1 in 1.76 (57%) to be exact.As luck would have it, neither the Phillies’ nor the Yankees’ active rosters actually holds two players with the same birthday. But a comparison of the two teams’ 25-man rosters (25*25/2=312.5 combinations) does reveal one match: Yankees catcher Jorge Posada and Phillies pitcher Brett Myers were born exactly nine years apart—Posada on August 17, 1971 and Myers on August 17, 1980.

From the Book Of Odds

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One thought on “Bloggo’s Number Crunch- Odd Odds

  1. Pingback: Let’s Try This Again Next Year- And Get It Right This Time | Bloggo Schloggo

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