# The National Coin Flipping League Championship Series

### The National Coin Flipping League Championship Series

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?

• And assuming that a dollar spent equals a dollar in talent, the Yankees would only have 54-46 advantage. Anyway, time to go home.
• Besides, we always herald the first, and this is a first in MLB. I'm sure there's been plenty of cases of someone rolling 3 6's to win as an underdog (heck, it probably happens every game).
• Really? I'd be surprised? OK, I'll bite. What percentage of teams that are down 3-0 end up down 4-0?

If it were coin flipping, I'd expect it to be 50%. Given that being down 3-0 is evidence of being the worse team, in reality I'd expect it to be slightly lower.

I'd be surprised if it were, say, 25%.
• Whether this was your intention or not, it would seem that your analysis is a classic proof by contradiction that Baseball is much more than coin flipping.
• If I'm reading this correctly..

"The Red Sox were the 26th team in Major League history to fall behind 3-0 in a seven-game series. They are just the sixth to avoid a sweep, and now just the third to win two straight after dropping the first three."

I'd say that 20-26 teams in baseball lost 4-0 after going down 3-0.
• So it's about 20%. I am surprised!

:)

• Yep, I think he was feeling feisty and just wanted to post a major troll. The "modest proposal" should have given it away.

Score : -1, Flamebait
• I'm shocked, shocked that you'd think I'd do such a thing. Shocked!
• :D
• The reason why no team had been down 0-3 and then won 4 straight games is because the team that won the first 3 games *is a lot better*, so of course they will almost always win 1 of the remaining 4 games. You need to make your coin weighted on one side to have the analogy hold. ;)
• If only 25 people playing ball were as reliable as flipping coins...
• If you take into consideration W vs. L over the course of the season, the Yankees are approximately 2 percent better than the Red Sox (ultimately W vs. L is a better gauge of a team's prowess than salary). So if the teams play any seven games together in a closed environment (not counting previous years because the teams were different back then) it ***should*** be split 3-4 one way or another.

That being said, numbers lie and Damon is my boy.
• Well, sure, but that's not the issue -- given a 3-4 split, there are 35 equally likely ways to distribute the wins and losses.

Which raises an interesting point. Winning a series with HTHHTTH is every bit as unlikely as TTTHHHH, but no one ever makes a big deal out of it.

People make big deals out of things that seem particularly _dramatic_, not particularly _rare_.
• you should check out a wonderful novel by robert coover titled "universal baseball association, j. henry waugh, prop." it's a hilarious exploration of almost this exact idea (and provides nice parallels to the job of the fiction writer).
• > The odds of Boston flipping T T T and then coming back to win with H H H H are one in 128.

This is not true. Since the series ends when one team reaches 4 wins, there are not 2^7=128 valid combinations of wins and losses. In fact, there are only 50 valid combinations -- 1 way to win a series in 4 games, 4 ways to win in 5 games, 10 ways in 6 games, and 35 ways in 7 games. So, you'd expect 1 occurrance every 50/4 = 13 years. It is surprising then that we don't see it more often.
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