Fabulous Adventures In Coding
Eric Lippert is a principal developer on the C# compiler team. Learn more about Eric.
No tech today, but a little basic math.
In baseball, a sport I know little about, apparently the Boston Red Sox have recently come back from a three game deficit to win a best-of-seven series against their traditional rival team, the New York Yankees.
Baseball is a game which attracts statisticians, and many have noted that this is the first time in major league baseball history that a team has won a best of seven series after being down three games to none.
However, it has happened twice in hockey.
I have a modest proposal. Suppose once a year, the National Hockey League and Major League Baseball decide all their various championships without going to all the trouble and expense of playing the game. Rather, they could simply hold a best-of-seven coin-flipping championship. (Call it the Numismatic Hockey League if you'd like.)
Suppose Boston calls heads. The odds of Boston flipping T T T and then coming back to win with H H H H are one in 128.
Therefore, there should be one such occurrence on average every 128 series. There are four such series a year: the American and National League finals, one "world" series (for which only North American teams are eligible, strangely enough), and one Stanley Cup. You'd expect to wait 128 / 4 = 32 years on average between occurrences.
We've been playing pro baseball and hockey, what, about a hundred years in North America?
Three such series, in about a hundred years -- or, roughly one every 32 years. It seems like the math works out rather nicely. Maybe they have been deciding the games via coin flipping and just not telling anyone. Hmm...
Is Boston's victory really that impressive? I mean, the last time I played Risk I rolled three sixes on three dice and England crushed Iceland -- odds of that are 1/216, almost twice as long as Boston coming back from a three tail deficit in the National League Coin Flipping Championship. That's because my blue plastic army guys really worked together as a team and gave 110%!
And yet it didn't make headlines in even the local paper.
In related news, if Houston wins their championship, and it ends up being Texas vs. Massachussets in both baseball AND the presidential election, that's going to be freaky weird. What are the odds of that?