## Homers leading off the game: more or less likely?

Posted by Andy on May 27, 2009

When Jimmy Rollins homered on the first pitch of the Phillies game with the Yankees on Friday, I got to wondering whether leadoff homers (not necessarily on the first pitch) happen more or less freqeuently than all homers in the game.

Here's what I mean.

In 2008, there were 52 leadoff homers. This counts only the visiting team batting in the top of the first, and not the home team batting in the bottom. In 2008, there were 2428 games. That means that 52/2428 = 2.14% of games featured a leadoff homer, and since each game has exactly one leadoff plate appearance, there was a 2.14% chance of a player hitting a leadoff home run in 2008. Now, checking out the major league batting totals for 2008, we see that there were a total of 187,614 plate appearances and 4878 home runs. That works out to 2.60%, meaning any plate appearance (including the leadoff spot) had a 2.60% chance of ending up as a home run.

That means that, very roughly, the leadoff batter of a game has roughly a 20% lower chance of hitting a homer than for any other average batter during the game. This result is not surprising given that leadoff hitters usually want to try to simply get on base by any means possible and swinging for the fences is usually not the first choice.

By comparison, let's look at walks in 2008. There were 165 walks to lead off games in 2008. Coming in those 2428 games means the leadoff batter waked 6.80% of the time. Looking back at the league-wide data, we see that there were 16,337 walks in those 187,614 plate appearaces. That means that on average, batters walked 8.70% of the time. So, again, leadoff batters were about 20% less likely to walk.

Incidentally, on the league-wide page, you can see data on the first batter of the game right here. In this case, that's first batter of the game *for each team*, so it includes the guy batting first in the bottom of the first inning.

May 27th, 2009 at 9:47 am

So then which hitter had the highest percentage of their homers being of the lead-off kind?

Soriano's 27.18% ratio (53 out of 195 in the leadoff spot) is lower than Ricky Henderson's 27.64% (81 of 293) and Biggio's 29.28% (53 out of 181).

Secondarily, why would their rate of homers in their 1st AB be so much higher than the percentage overall? Soriano (23.1%), Biggio (24.7), and Henderson (26.6%) of their AB came out of the leadoff spot, so why would their power be so frontloaded? Those ratios all approach 20-22% if you look at it from a per plate appearance level.

May 27th, 2009 at 10:08 am

What might be more interesting is to compare the rate of game-lead-off home runs to the overall rate of home runs hit by the #1 spot in the order; or even better, to the overall rate of homers hit by the players who started the game in the #1 spot in the order (thus eliminating pinch hitters, defensive replacements, etc.) This way you'd be eliminating the bias of counting cleanup hitters (and #9 hitters), etc. and only looking at whether leading off the game has an effect.

May 27th, 2009 at 12:29 pm

Good point, Tomepp, and that data is easy to find right on the 2008 MLB summary page (linked in my post above.)

So in 2008, the #1 slot in the batting order hit 466 HR in 22946 PAs, which is 2.03%. That, of course, includes the first PA of the game, which came in at 2.14% itself. I'm guessing, then, that there's no particular difference. Keeping in mind that through double-switches pitchers occasionally bat in the #1 hole later in game, it looks like homers are not more or less likely at the start of the game than otherwise.