## Grand Slam, First Career At-Bat June 15, 2010

Posted by tomflesher in Baseball.
Tags: , , , , , , ,

On Saturday, Daniel Nava hit a grand slam in his first at-bat (hitting ninth for Boston). Needless to say, the odds against this are exceedingly long.

So far in 2010, there have been 1786 home runs hit in 73122 Major League Baseball plate appearances, for a rate of about .024 home runs per plate appearance. The American League has a league on-base percentage of .331 and the National League’s OBP is .329. That means that the prospect of any plate appearance ending in an out is (using .330 as the average OBP) .670. The likelihood of the bases being loaded at any point in an inning is the sum of three probabilities – three on base with 0, 1, or 2 outs.

$p[bases loaded, 0 out] = .33*.33*33 = .036$

$p[bases loaded, 1 out] = .33*.33*.33*.67 = .024$

$p[bases loaded, 2 out] = .33*.33*.33*.67*.67 = .016$

$p[bases loaded] = .036 + .024 + .016 = .076$

Note that this slightly overestimates the probability, since it ignores the likelihood of an extra-base hit. Obviously an extra-base hit would increase the chance that three people made it to base but one or more scored, leaving the bases unloaded.

Now, with a home run probability of .024, and a bases loaded probability of .076, the (again, slightly overestimated) probability of a grand slam is about .002, or .2%. That is, about one in every 500 at-bats should be a grand slam.

Since 1920, there have been only 10 people who have hit a home run and had 4 or more RBIs in their first game. The list is here. Of those games, six (including Nava’s) involved any player hitting a grand slam (including three hit by the rookie in his first game – Nava, Kevin Kouzmanoff on September 2, 2006, and Jeremy Hermida on August 31, 2005). Incredibly, both of them hit grand slams in their first career at-bats, with Kouzmanoff in the lineup as the DH in the #8 slot and Hermida pinch-hitting in the #9 spot.

Also interesting is that Hector Luna played with both Kouzmanoff and Hermida when they hit their grand slams, and that in 2009, the Red Sox had no home runs with runners in scoring position by the #9 hitter. Quite a turnaround.

(I should point out that Bill Duggleby also hit a grand slam in his first career at-bat in 1898, but that the searchable data doesn’t go back that far.)

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