The Determinants of Multi-Run Homers

This investigation begins with a simple frustration. I was recently watching the Rays and, after a few solo homers wandered over the fence, I asked myself, “How can a team with such a solid on-base percentage hit so few multi-run homers?”

It makes sense that, if’n a team can matriculate men down to first and second and even third base, they can get more bang for their homer bucks. My frustration reminded me of Jeff Sullivan’s frustrations in 2012, when he wrote the epic monkey’s paw game recap, wherein he bemoaned the Mariners’ solo homeritis.

But, to me, it made sense the Mariners had solo homeritis. The 2012 Mariners had a .296 OBP — worst in the majors by a Deadball Era or two.

So I began a quest, a quest that has lasted several months. I have scaled SQL cliffs, journeyed deep into Pivot Table mines, and waded through the blogger depression swamps. With the support of some eclectic friends, such as Jeff Zimmerman, Matt Hunter, and Steve Staudenmayer, I have concluded that OBP and runs per home run do indeed have a relationship, but that relationship is severely diluted by randomness and unpredictability.

This is not a new idea, the idea that production is subject to the whims of context. In fact, with LOB%, we are able to somewhat obliquely analyze how a pitcher has been lucky or unlucky with respect to the timing of events.

But investigating the relationship between OBP and multi-run homers is not as simple as dividing a team’s run total by their home run total. Nor is it as simple as looking at the HR run expectancy on the Guts page — because those numbers are “runs through the end of the inning,” not scored specifically on the homer.

So, if we appeal to data mining spirits, we can gather the following, a list of team’s OBP, their OBP less their HR-rate, and their runs scored via HR:

When you finish filtering and fumbling around with these numbers, consider the surprisingly small correlation between OBP and homer runs:

The first things we should observe:

1. The correlation between OBP-less-HR% and homer runs is around an R-squared of .10, which is to say OBP explains 10% of the variation in homer runs. That’s not a strong correlation by any stretch.

2. Holy cow, the 2013 Detroit Tigers are about to break the runs-per-homer scale.

3. The bottom 8 teams in runs per HR are playing in the 2013 season. What?!

Barring a possible data error, it appears the league as a whole — at least since 2007, where this data set begins — has produced fewer and fewer runs per home run:

And this makes sense given the league’s descending OBP, but still, the drop in 2013 seems quite dramatic — especially given the Tigers’ current insanity.

So far, it all seems pretty random. But when we mush together all the teams in the league, we see a more useful, intellectually palatable connection:

Here we find a 60% correlation. Obviously a .999 R-squared would be great, but 60% can still satisfy my intellectual expectation. Because here’s what’s tricky: Managers are constantly attempting to predict when and where homers will occur and adjust their lineups according to that expectation. That’s why they do not bat their heavy bopper, long-ball men No. 1 or 2, but instead No. 3 and 4.

But baseball has a lot of randomness. Sometimes, Adam Dunn only hits 11 homers and sometimes Brady Anderson hits 50. Managers cannot anticipate breakout seasons, breakdowns seasons, or fluky seasons with any great certainty.

So for us, we have to accept the formulas above (such as: R/HR = 2.57 * OBP + 0.74) as our basis for expectations, but simultaneously accept the matter of multi-runs homers as nearly pure chance.

To simplify this, let’s talk in terms of specifics: The aforementioned Rays had a .331 OBP entering play on Sunday, August 25. According to the basic formula above, we’d anticipate 1.60 runs per homer from the 2013 Rays if they manage to maintain their .331 OBP moving forward. Presently, they have a 1.41 homer runs rate — one of the worst rates of the last six seasons.

We would be engaging in the Gambler’s Fallacy if we said, “Oh, so they will have a lot of grand slams over the final month in order to bring that season number up to 1.60.” First of all: No, we expect 1.60 going forward, not as the final result. Furthermore: As we’ve already suggested, the world of runs per homer is a cruel, unforgiving world of randomness and chaos. Their already epicly bad number could get worse just as much as it could get better.

Another likely component behind the discontent between OBP and homer runs is the uneven spread of talent in the lineup. For instance, Giancarlo Stanton’s 16 homers leads the Marlins offense. So does his .360 OBP. Stanton is an incredible hitter, but it would be a spectacular accomplishment for even him to hit a two-run or three-run homer with himself on first base and second base.

So perhaps the next level of this study would be to examine the spread of hitting talent throughout the roster. The steady terrifyingness of the Tigers lineup (9 players above 100 wRC+, min. 100 PA) may help indicate how they’ve managed a bizarre runs-via-homer rate. But at the same time, these thicker lineups should be producing more back-to-back and back-to-back-to-back homers, which necessitate at least one solo homer despite the preceding player improving his OBP.

As for now, though, the determinants of multi-run homers are murky with random variation. We have to ascribe much to luck, chance, and the curses of monkey paws.