Grand Slam Goldschmidt: Arizona Diamondbacks Are Mathematically Impossible

Gil ImberAnalyst IIOctober 6, 2011

PHOENIX, AZ - OCTOBER 05:  Ryan Roberts #14 of the Arizona Diamondbacks celebrates with Miguel Montero #26, Justin Upton #10, and Willie Bloomquist #18 after hitting a grand slam home run in the first inning against the Milwaukee Brewers in Game Four of the National League Divison Series at Chase Field on October 5, 2011 in Phoenix, Arizona.  (Photo by Christian Petersen/Getty Images)
Christian Petersen/Getty Images

I could have just as easily called this article "Round Trip Roberts," but I needed to stress just how grand the Arizona Diamondbacks are right now.

First, a little confession.

I am a math maniac. A numbers nutcase. A statistics screwball.

I am also a baseball fan. I guess the two go hand in hand.

So if you don't want to see something spectacular, you might as well leave now.

Because the Diamondbacks have just defied logic. This 2011 Arizona team has just taken one plus one, put it in a hitting machine blender and made it equal four. By hitting four grannies in four consecutive home games, the Diamondbacks have destroyed all notions of normalcy.

Let me explain.

The grand slam is one of the most exciting offensive feats in baseball. To experience it requires the fusion of multiple elements, all of which must occur for a grand slam to be possible:

No. 1: A batter manages to get on base. With an average MLB on-base percentage of .333, we're already looking at a meager one-third chance of successfully accomplishing step one.

No. 2: A second batter manages to get on base while that first batter manages to remain on base. The probability of a second batter getting on base alone remains .333; and .333 times itself is .111. Though we're assuming a whole lot that the first batter has managed to safely advance to second or third base, .111 is still a fairly low probability.

The scoreboard: Where numbers go to play.
The scoreboard: Where numbers go to play.Justin Edmonds/Getty Images

No. 3: A third batter manages to get on base while batters one and two likewise remain on base: the bases are loaded. Multiplying .111 by .333 once more yields .037, a low probability for sure. Though .037 still fails to account for the whereabouts of runners No. 1 and No. 2, this figure clearly demonstrates the seldom nature of loading the bases.

No. 4: A fourth batter, with runners No. 1, No. 2, and No. 3 on base, hits a home run. To calculate this probability, we take 128—the average number of home runs hit every year with the bases loaded—and divide this by 166,608—the average number of individual at-bats in a season.

It comes out to .000768. That is a 0.0768 percent chance that any given at-bat will result in a grand slam.

Converting that to slams-per-game shows a probability of .0526. In other words, a grand slam ordinarily occurs once every 19 games.

Unless you're the Arizona Diamondbacks.

Even more improbable is how the four-in-four grand slam streak started in the first place.

On September 27, Ryan Roberts hit the most improbable of grand slams in extra innings to beat the Los Angeles Dodgers. Down 6-1 going into the bottom of the 10th inning, the Diamondbacks quickly had conceded two outs. It was over. Even the computer placed the Dodgers' probability of winning at 99.6 percent (Wait, didn't a computer also give the Red Sox a 99.6% chance of making it to the playoffs? Oh, my bad—wrong article).

D'Backs walk-off the Dodgers, starting an impossible sequence of events
D'Backs walk-off the Dodgers, starting an impossible sequence of eventsChristian Petersen/Getty Images

In that most improbable of come-from-behind victories—a first in MLB history—an impossible Diamondbacks streak began. Grand slam, game over. Diamondbacks win 7-6. Pandemonium in Phoenix.

September 28's regular season finale at Chase Field featured Cole Gillespie's four-run jack, and then came the Brewers.

Game 3 of the National League Division Series was a must-win for the snakes, and the boys from the desert certainly didn't disappoint. With rookie Paul Goldschmidt's fifth-inning grand slam, the Diamondbacks made the most exclamatory of statements: we're here.

Game 4 of the NLDS was another must-win, and another chance for someone to be a hero. After Milwaukee had plated a run in the top of the first, it was Arizona's turn to bat.

No. 1: Willie Bloomquist started the action with a lead off single. .333 chance of happening? No problem.

No. 2: Justin Upton walked, Bloomquist to second base. What's the big deal about one-ninth anyway?

No. 3: Miguel Montero singled, Bloomquist to third, Upton to second. So what? Teams load the bases. It happens.

No. 4: Roberts does it again. Something special is happening in Arizona.

Remember that slams-per-game probability? That measly .0526? Well, it just happened at Chase Field. Four consecutive times. That's .0526 x .0526 x .0526 x .0526.

Tatman just tatoo'ed 'em again
Tatman just tatoo'ed 'em againChristian Petersen/Getty Images

That's .00000765. That's a one-in-130,634 chance.

How can you even begin to try and explain something like that?

It must have been Roberts. Tatman is a freak of nature. The kid is a superhero. It's not just a conveniently placed pun. It's real.

It must have been Kirk Gibson. Anyone who hits one of the most famous home runs in World Series history must inspire greatness simply by being in the dugout.

Oh—I've got it now—it must have been umpire James Hoye. He worked the Dodgers-Diamondbacks series on September 27 and 28, and he's working the 2011 NLDS between Arizona and Milwaukee.

How else could a numbers nerd even begin to explain something so crazy as one-in-130,634?

As a diehard data devotee, I couldn't be happier about the Diamondbacks going to Milwaukee for Game 5. Us math folks have been through enough.

But as a baseball fan, I hope to watch another postseason game from Chase Field. After all, one-in-130,634 comes right before one-in-2,483,541. 

All statistics have been compiled and averaged based on data from the years 2006-2010, all calculations have been derived from this average. All raw data is from Retrosheet.org.