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.

Once again, we have a winner!

— Pete Rauske (@peterauske) October 6, 2017

Game 1: 63/88 (72%)

Game 2: 65/88 (74%)

Game 3: 64/88 (73%)

Game 4: 44/57 (77%)

Game 5: duh

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.

I’ve always felt that statistics like this are bogus for a couple of reasons. First, the assumption is that winning Game 1, by itself, is a causal reason that the team wins the series. But all sweeps mean that the team that won Game 1 won the series, which skews the statistics. Some of those teams might have won the series even if they had lost game 1. I wonder what the statistics would be if you took away sweeps. Second, why is game 1 more important than game 2? If a team loses game 1 but wins game 2, what difference does it make? Obviously, if you win the first game, you have fewer games you need to win but, other than that, there is nothing especially important about game 1, it seems to me.

Using a 57 count for Game 4 means the person is only using LDS and excluding 1981.

*

Game 4: Teams trailing 2–1 in the series go 30–27 (b-ref play index for potential elimination games), teams trailing 2–1 must go 17–13 in Game 5 if 44–13 is correct (27 series win for Game 4 winners from 3–1 series, requires 17 more series wins from teams trailing 2–1 in Game 4).

*

Game 3: Teams trailing 2–0 in the series go 21–31 (b-ref play index for potential elimination games), eliminating the 31 sweeps the series winning team is 33–24 in Game 3 if 64–24 is correct.

*

Game 2: Teams trailing 1–0 must go 36–52 (to have 52 teams down 2–0), eliminating the 31 sweeps those teams are 36–21 in Game 2.

*

Game 1: Eliminating the 31 sweeps, the series winner is 32–25 in Game 1.

Who exactly plays Paper, Scissors, Stones? Is that some kind of weird locally trademarked version of rock, paper, scissors. I am a 43 year old man and in my life I have never heard it called that. Somebody help me out here. Where and when is this the common way to say that. I’m shaken to my core right now.

Darrel,

You’ve missed out. I won a ticket to see Led Zepplin in 1977 at the Richfield Coliseum playing Rock, Paper, Scissors. I went rock, which of course breaks scissors. Great night.

I’m impressed. You almost never see a non-mathematician get probability right the way Joe did.

It’s a meaningless stat. Reminds me of the ones that this team has a 92-1 record when leading after 8 innings. That sample is too big. What is their record when they lead after 8 by one run or whatever the current game situation is? Even then, baseball is a crap shoot. Lousy teams win about 40% of the time, good teams about 60%. So the Padres can beat the Dodgers 3 of 4 in September.

There’s no such thing as too big a sample size. The larger the sample size, the more accurately it reflects the population.

The only advantage of a smaller sample size is that it reduces cost.

You are correct. I think Marco meant that the sample was not adequately defined (i.e., the sample was too large because it included games that shouldn’t be in the sample). The sample should be games in which they lead by one run after 8 innings, thus eliminating all the multiple-run leads which were a much higher probability of wins.

I think Marco is right, and his question illustrates his point perfectly. If your population is Florida, and your sample is 10000 people from Florida, then you would like the sample to be even larger, obviously. But if your population is Florida and your sample is 10000 people from across the USA, then you may want the sample to be smaller, to exclude all the non-Florida people. Or you may want to include everyone, because people are the same, right? Like a lot of statistical inference, it’s a judgment call.

Sorry Pete…..your reply is incoherent.

By definition, a sample is a subset of a population. If your population is Florida, the sample must be a subset of Florida’s population. The larger the the sample size of Florida’s population, the more accurately the sample would reflect the characteristics of Florida’s population. If your population is the United States, the larger the sample size of the United States’ population , the more accurately the sample would reflect the characteristics of the population of the United States. Similarly for the population of the United States excluding Florida. Ask anyone with a rudimentary understanding of statistics if a larger sample more accurately reflects the characteristics of a population.

But you are missing the point. If someone told you that x% of people in Florida would die in the next year, what does that tell you about your chance of dying? Without knowing how your age, for starters, compares to the average age of a Floridians, not much.

So the real point is, it is too broad a sample. Looking at “games where they were winning by 1 run after 8” is more useful than “games where they were winning after 8”.

Good column – but it is kind of odd that the obvious had to be pointed out in the 21st century. The basic mathematical logic was developed by Thomas Bayes. He died in 1761.

Please forgive me, but I can’t bear to read a claim that Bayes developed the rather enormous universe called “basic mathematical logic”. This was actually created by the great ancient Greek philosophers. I’m not aware that Bayes did anything monumental other than Bayes’ Theorem (which is indeed monumental, if rather obvious… it can be proven immediately after defining its terms, by any mathematical novice).

It IS odd that this obvious fact had to be pointed out. But it obviously did. People talked about the mystical Game 1 influence as it related to holding Kluber back for Game 2. I knew the Game 2 winner had an even better record in MLB best-of-5’s, which made me wonder just a little bit if Francona was secretly influenced by that factor. I kind of doubt it, just as I doubt those numbers accrued so far really mean anything, but anyway…

It is just incredible how often people see an “amazing statistic” and stop their curiosity right there, instead of asking any follow-up question.

Red Sox fan here: There is zero chance Terry Francona was influenced by any mathematical reasoning. I love the guy, but….

There was a similar statistical mis-use in Game 2 of the Dodgers-D’Backs NLDS. Referring to Rich Hill, the announcers compared his first inning ERA (6.28) to his ERA from the second on (2.something).

The problem is that ERA in any given inning is likely to be higher than ERA over multiple innings – the more outs you get, the lower the ERA is.

More comparable would be comparing the first inning ERA to the second inning ERA, to the third inning, etc. The first inning is likely to still be higher (you face better batters, starting with no outs), but it shouldn’t be as big a gap as when comparing one inning to multiple innings.

Joe alluded to this, but a big factor is that the home team in game 1, which is the stronger team based on their record (most times), tends to win more often. Not just winning Game 1, but the whole series.

My daughter’s (former) pediatrician once said something absurd to my 4-year-old daughter this way and I said to her “And thats why we have control groups.” The pediatrician looked at me funny.

I have to disagree with Joe’s comment about the “excellent Matt Vasgersian. I think he’s terrible. Every time someone hits a home run, he acts as if it’s the first one hit in the history of the game. He goes almost into hysterics. The other night, Bryce Harper hit a home against the Cubs and Ernie Johnson, Jr., got it perfect; he transmitted excitement without going completely over the top.

Many ages ago, I recall Tommy Lasorda talking about how important it was to win games in September. And I thought, if the Dodgers won every game from April to August, they probably wouldn’t need to worry too much about September, would they? As it turned out, the Dodgers almost pulled that maneuver this year: winning until late in the season and then hitting the skids. So if the Dodgers had gone into that losing streak without having done so well earlier, they might not be where they are now. Gee, that makes sense.

Oh, Joe. Time for an update here. Yes, the Browns posts are funny. But we need your exegesis of this latest chapter in the Cleveland Baseball Club’s post-War history…

By definition:

the series winner is victorious in 60% of all games in a 5-game series that go the distance (3 of 5)

the series winner is victorious in 75% of all games in a 5-game series that only go 4 games (3 of 4)

the series winner is victorious in 100% of all games in a 5-game series that only go 3 games (3 of 3)

Even without amassing historical statistics and doing a precise break-down, that gives you an idea that the win expectancy for any given game is probably in excess of 70%