# A Strange Sentence About Grand Slams

From today’s Times, an article by David Waldstein called “Mets’ Stretch Without a Slam? Gone. Gone“:

The Mets had gone 299 games and 280 plate appearances with the bases loaded since their last grand slam, while their opponents had hit 18 during that span. So when the opportunity arose in the fourth inning Tuesday night — with Jason Bay at the plate, no less — the chance of a Mets grand slam was slim.

Was the chance of a grand slam really so slim?

If you flip a coin 10 times in a row and come up with 10 heads, is the 11th flip any more likely to be heads (or, for that matter, tails)?

Of course, it could be that such a long streak without a grand slam feeds into the Mets’ collective psyche and discourages them from hitting one.

It could also be that the Mets are simply worse than everyone else at hitting home runs in general (which they’re not, even though they’re pretty bad).

But more likely the streak was an essentially random run of bad luck.

Which finally ended with Jason Bay hitting a grand slam.

And then, seven batters later, Carlos Beltran hit another grand slam for the Mets.

Random is as random does. Which is why predicting the future is such a fool’s errand.

Question: how many at-bats until the Mets hit their next grand slam?

No fewer than 4.

#### MattieShoes

There's a distinction between at-bats and plate appearances. A plate appearance resulting in a walk does not count as an at-bat, so it's entirely possible to have grand slams in consecutive at-bats -- Grand Slam, Walk, Walk, Walk, Grand Slam.

#### Chris

Correction: No fewer than 1.

#### *daniel

As always, there's a Venn Diagram for predicting the future:

http://www.vennding.com/2010/11/prognostication-is-fools-game.html

#### Chris

Although it's true that the chance of a grand slam wasn't lessened because of the streak preceding it, it was still a pretty slim chance, particularly with Jason Bay at the plate.

Prior to yesterday's game, Bay had 3 homeruns in 192 at bats, giving him -- with some disclaimers -- about a 1/64 chance of hitting a homerun. Looking at his numbers with runners in scoring position going into the game, it's an even slimmer chance: Bay was 8 for 51 with RISP with no homers this year.

In his career prior to last night's game, Bay had 2 grand slams in 97 chances, but he's also fallen off considerably since his halcyon days, so it is more reasonable to look at a more recent sampling as opposed to career numbers.

The Mets will hit their next grand slam in 178 at bats. Mark my words.

#### Joshua Northey

I would look at:

MLB GS Rate (since new park)
Mets GS Rate (since new park)
Individuals Mets players HR rates and likelihood of encountering bases loaded

And make some sort of weighted average. You might also want to include the time of year and quality of upcoming opponents pitching/defense.

I am probably forgetting a lot of stuff, but this really isn't a hard question like most of the ones posted here. It has an approximation of a right answer.

#### dta

I think grand slams are not subject to random distribution; I would think particular hitter/pitcher combinations would affect the outcome greatly. Jose Bautista is much more likely to hit a grand slam off, say, me, than Tim Lincecum.

#### Bree

You have to consider that baseball players aren't coins, and their chances of hitting a grand slam are neither 50% each at bat nor equal for all players (or teams). Going nearly 300 games without a grand slam sort of implies that the team lacks the ability to do so--or rather that the probability of any at bat with bases loaded resulting in a grand slam for the team is very slim.

#### fraac

Important statistical point: if you get heads 10 times in a row, chances of an 11th head are slightly better than 50%. If you get heads 100 times in a row, the 101st is a virtual certainty. And in sport you don't have to look hard for self-fulfilling prophecies.

#### ORLY

Important statistical point: you need to enroll in a Statistics class.

#### fraac

No, really. Ask Levitt. It's one of those things that are almost too obvious to make sense.

#### jb

Let's not overlook that the probable outcomes in Mr. Bay's at bat. It's not simply HOME RUN/NOT HOME RUN. It's HOME RUN vs. TRIPLE vs. DOUBLE vs. SINGLE vs. FLY OUT vs. GROUND OUT vs. STRIKE OUT vs. WALK vs. HBP, and each of those possibilities have nearly infinite sub-possibilities. There were a few pitches to Mr. Bay before his home run. What if one of those hit him? What if one of those was a wild pitch, thus turning a grand slam into a three-run home run? The thing about baseball is that each pitch (not each at-bat with the bases loaded, which is a loaded situation to begin with) carries a very low probability for the scenarios listed above(outside of contact/no contact, which is 50/50.)

Now, even if you take the simplistic approach that the home run was simply a fly ball that went beyond the wall and was not foul; in this case, were the ball hit 50 feet or so towards center field, it would not have been a home run.

#### KevinH

I'll go out on a limb and say it'll be at least 4 at bats until they hit their next grand slam.

#### Skip

Well, if the Tigers pitch tonight like they did last night, chances are pretty good they'll hit another one very soon. It's not just how good the hitters hit, also how poorly the pitchers toss 'em up there.

#### SpacePirate

Well, it would require at least 4 more at bats unless the Met's had 3 guys on base as of this post.

#### AaronS

But hitting a baseball is not "chance" in the sense of flipping a coin. It's a matter of skill. Let's put it another way....

John has went 300 games against chess grandmasters and has never won a game. He is playing another grandmaster today. Is there now a 50-50 chance of his winning? Is he somehow "due" a win after losing so many times?

This is not simply a random stretch of bad luck. Yes, John might get lucky, but the chances seem very much against that happening. Did I mention that John is a baboon?

Same in baseball. The assumption seems to be that there is an equal chance of hitting a grandslam as not hitting one. Not so. A team that is really bad at homeruns, or that might be particularly susceptible to pressurized situations like "bases loaded," may be worse at hitting home runs just because they tend to suck.

So when you know just how bad a team is in that department, yeah, you can say that the chances are SLIM. Doesn't mean it won't happen. Doesn't mean that luck won't play a role. But the CHANCES are such that it is likely that a grandslam will not be hit.

And that's my take on it.

#### MW

Null hypothesis: when a grand slam occurs, it is equally likely to go to either team.
Observation: Of the last 18 grand slams to occur in a game where the Mets were playing, all of them went to the opposing team.
Chance of this occurring if the null hypothesis is true: 2^-18 = 1/262144.

However, this isn't a fair assessment: we chose the observation to make (18 grand slams, games where the Mets were playing, games prior to the one discussed above, Mets on losing side) after the event because it seems remarkable. It would have been equally remarkable had the Mets won all 18 of those grand slams, or if some other team had the same losing streak, or (perhaps) if the result came from games in one particular ballpark. At minimum, we need to multiply this probability by 2 (equally remarkable whether the one team is always winning or always losing) and the number of teams in the league* (which, as non-American, I don't know.) Probably one should also multiply by the number of other statistics which would seem impressive if a team had a streak of them (home runs, bottom of the ninth wins, no-hitters, etc etc.)

However, I think reasonable corrections will still leave you with a probability on the order of 1/10,000, so we can reasonably reject the null hypothesis that the teams are equally likely to score a grand slam, and conclude that over this period, the Mets were bad at getting grand slams, rather than simply unlucky. However, the Mets' grand slam odds are expected to drift over time, so the odds that the next grand slam in a Mets game will go to the Mets is not easy to calculate.

* It isn't quite as simple as this, as the odds of two teams having remarkable grand-slam win or lose streaks at the same time are not independent, but I expect this would cause only a minor correction.

P.S. fraac's coin toss scenario is a significant plot point in the play "Rosencrantz and Gildenstern are Dead".