Marvelous Sounding Stats

On Thursday, during the Cleveland-New York playoff game, the excellent Matt Vasgersian and John Smoltz made a pretty big deal of a marvelous sounding statistic.

They pointed out that teams that win Game 1 of a five-game series win 72% of the series.

They were trying to amplify the obvious but essential fact that the winner of Game 1 in a five-game series has a HUGE advantage in the series. And this statistic certainly seems to amplify it; almost three-quarters of your first game winners go on to win the best of five series! Big deal!

King Kaufman caught it first. King is one of the most astute people in the sports business -- he has started this very cool new podcast called "Can't Win 4 Losing," which, in addition to using 4 in a way Prince would have approved, is all about losing in sports. It's superb.

Anyway, right away Kaufman made the point that while 72% of the winners of Game 1 will win the series, he was absolutely sure that the percentage was HIGHER for Game 2. In fact, as he thought about it, he was sure that the percentage of series wins was higher for EVERY SINGLE OTHER GAME in the series.

Ex-scientist and Hamilton fan Pete Rauske -- I divine these things from his brief but informative Twitter handle -- did the math and found that Kaufman was exactly right.

https://twitter.com/peterauske/status/916326482733039618

Obviously, the "duh" for Game 5 is that, obviously, 100% of the Game 5 winners win the series.

What's cool about Pete's percentages is that they pretty decisively show that every game is basically as important as every other game, with the obvious exception of the last. We love tying a certain significance to every game.

Game 1 is all about building momentum.

Game 2 is to either take control of or get back into the series.

Game 3 is the potential clincher or potential swing game.

Game 4 is about finishing the job or staying alive.

Game 5 is for all the marbles.

All of these labels -- and hey, I use them too -- are so ridiculous. In any best-of-five format -- a best of five series, a best of five set tennis match, a best of five Paper, Scissors, Stones duel for the front row seat -- each victory gets you exactly one-third of the way to the goal. Every second victory gets you two-thirds of the way to the goal. Every third victory finishes the goal. It doesn't matter the order of the victories and it doesn't matter the decisiveness of the victories.

Let me break down some fun math for you. You are flipping a perfectly weighted coin. On one side, is a picture of Cleveland's West Side Market, one of the great treasures in this world. That represents Cleveland winning. On the other side, is The Strand bookstore in New York, another of the life's wonders. That represents New York winning.

You will flip the coin five times. The first time, it comes up Cleveland.

So now, what are the chances the Yankees can win the best-of-five coin flip?

Well, flip a coin four times and there are 16 possibilities -- that 2 (heads or tails) to the power of 4 (number of coin flips).

Those 16 possibilities are easily broken down -- N is New York, C is Cleveland..

Five possibilities that New York wins the series.

NNNN

CNNN

NCNN

NNCN

NNNC

Obviously, there would be no fifth game in a couple of these possibilities but those are the five ways the Yankees would win.

There are, meanwhile, 11 possibilities for Cleveland to win the series.

CCCC

NCCC

CNCC

CCNC

CCCN

NNCC

NCNC

CNNC

NCCN

CNCN

CCNN

You can add those up if you want, but that's how it goes. There are eleven possibilities for Cleveland to win the overall coin challenge, five possibilities for the Yankees to win the overall coin challenge.

That, 11/16, is 69% ... or almost identical to the 72% that sounded so interesting when the announcers first said it. And remember that's with a coin flip which means that is assuming the two teams are exactly as good as each other. In most cases, I imagine, the winner of Game 1 is probably a little bit better than the other team because Game 1 is usually played in the better team's ballpark. Most people would probably say Cleveland is better than New York.

In other words, Cleveland is 72% likely to win the Yankees series not because of some mystical "winning Game 1 is so important" thing but because the Tribe has to only win two more games, while the Yankees have to win three. If Cleveland wins Game 2, the odds will shoot up. Back to the coin flip.

Possibilities for New York down 2-0 in the series.

NNN

Possibilities for Cleveland up 2-0 in the series.

CCC

CCN

CNC

NCC

CNN

NCN

NNC

That's seven out of eight or 88%. Again this assumes -- wrongly, probably -- that the two teams are exactly even.

And if the Yankees win Game 2? Sure, we'll talk about momentum and how important it was for the Yankees to steal a road win and future decisions with Corey Kluber and the opportunity for Luis Severino to redeem himself and all of that because it's fun and baseball is supposed to be fun.

But the pure math would be a 50% chance for each team.