November 29, 2016
The World Series of Coin Flipping
Let’s have our own World Series, you and I. A World Series of coin flipping. First to four wins. Your call, heads or tails. Ready? Let’s go.
There are four ways you can win. First, you can win four flips in a row. Since the odds of winning any one flip are 50/50, your chance of a sweep are ½ x ½ x ½ x ½, or ½4, which equals .0625. You have a 6.25 percent chance of winning four straight flips.
There are a few ways you can beat me 4-1. I can win the first flip, you the next four. Or you can win one, I win one, then you win three. Or you win two, I win one, and you win another two. Or you take three, I win my one flip, and then you finish me off. The odds of each of those sequences, since there are five coin flips total, is ½5. But there are four ways for you to win, so 4 x ½5 = .125. You have a 12.5 percent chance of winning our World Series 4-1.
I’ll spare you the narrative, but you have a 15.625 percent chance of beating me 4-2. And our series will go to seven games, with you victorious, 15.625 percent of the time as well.
We can double those amounts and figure the chances that our World Series will last a given number of flips. If you have a 6.25 percent chance of winning in four straight, so do I. There is a 12.5 percent chance of a sweep. Similarly, there’s a 25 percent chance that one of wins in five. There is an equal 31.25 percent chance that our series goes to six or seven flips.
Why did I bother telling you all of that? Because it’s relevant as we look back on seven-game postseason series. Let’s look at only the divisional era, beginning in 1969. Since then, there have been 47 best-of-seven World Series (every year, 1969-2016, excluding 1994) and 62 best-of-seven Championship Series (every year beginning in 1985—the LCS prior to then was best-of-five—excluding 1994). That’s 109 best-of-seven postseason series. How have they shaken out?