The Determinants of Multi-Run Homers

Let's get digging.

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:

OBP less HR%

OBP

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:

Homer Runs Over Time

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:

League-Wide Correlations

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.



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Bradley writes for FanGraphs and The Hardball Times. Follow him on Twitter @BradleyWoodrum.


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Jaack
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Jaack
2 years 9 months ago

It would be a spectacular accomplishment for Stanton to hit a two run home run with anyone on first AND second. But if anyone could fail like that, it would be the Marlins….

rusty
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rusty
2 years 9 months ago

Yeah, that could only happen if there are fewer than two outs and Stanton misses a base during his HR trot — and considering how much practice he has with said trot, it seems unlikely.

Note: this is based on my best recollection of that play a couple years ago where a would-be walk-off homer was ruled an inning-ending force-out because the guy on first missed second base (it was featured in that “you don’t know the rules of baseball” quiz espn hosted earlier this season).

dennis
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dennis
2 years 9 months ago

Actually, this would be a 2-run single (or double, or triple depending on where he crossed up) if the batter-runner was out for running ahead. What would have to happen is that the trail runner would have to pass the lead runner. Then the trail runner is out, and the other to runners score on account of the home run.

I’m sure the Marlins could pull it off.

RMR
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RMR
2 years 9 months ago

It would seem to me that a key part of the variation among teams is the factor of who specifically is hitting homers and who is getting on base?

Considering that homers counts as being on base, but don’t actually create a multi-run homer opportunity, if you have the same guys driving your OBP as hitting your homers, you haves less opportunity for multi-run homers than your curve would predict.

Sandy Kazmir
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2 years 9 months ago

Sounds like you have a ridiculously tough undertaking ahead. May want to build something that looks at when the home run was hit and the 3-4 batter’s OBP that are ahead of the home run. Would be incredibly difficult with changing lineups, but it sounds like you’ve rounded up a great team that loves to delve into this sort of thing. Godspeed.

The Slugger Formerly Known as Fielder
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The Slugger Formerly Known as Fielder
2 years 9 months ago

Did anyone consider that maybe the 2013 Tigers are clutch and other 2013 MLB teams are not clutch?

frank
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frank
2 years 9 months ago

i think you dont know the definition of clutch

Scraps
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Scraps
2 years 9 months ago

I think you don’t the meaning of sarcasm. Or maybe you do, and he doesn’t. Or maybe both of you do. Or maybe both of you do, but the meaning is reversed, which means both of you think that sarcasm is being employed, but really both of you are serious. Or maybe one of you is being a troll, but is really bad at it. Or maybe both of you are secretly presenting what “clutch” is but are very bad at explaining it — secretly — because you’re trying to get rid of the whole concept. But maybe one of you is actually holding up the concept as worth trying, and figures the other one will not notice. I figure one of those is worth getting behind, and the other is maybe also, but I’m not sure it’s sarcasm. I am sure that both of you know the meaning of “clutch”, “sarcasm”, and “Tigers”.

Justin Bailey
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Justin Bailey
2 years 9 months ago

Could batting order be a factor?

jaysfan
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jaysfan
2 years 9 months ago

Lineup construction seems like it should be a very important factor. Solo home runs by the three hitter with two out in the first inning are very frustrating (well, as frustrating as a home run can be).

nj
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nj
2 years 9 months ago

Or how about if your HR hitters are top heavy at 3-4-5 (hitting back-to- back more often) as apposed to having a more balanced approach.

Douglas Brouwer
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Douglas Brouwer
2 years 9 months ago

Another factor contributing to the Tigers multirunner home runs is that they do not play small ball for the most part. They are not ceating outs with steals or by bunting. Thus, their hitters have more outs to use trying to hit homeruns with people on base.

Thor
Member
Thor
2 years 9 months ago

Wow did not expect the mets to be #2 this year considering that their best hitter right now is Marlon Byrd. But maybe thats just a result of a really low opb.

Matt
Guest
2 years 9 months ago

Great writeup. And I hate to even think about diving into more batting order analyses, but this post makes me wonder if spreading out power hitters with high OBP between them could yield benefits.

Has anyone ever seen or done an analysis such as this?

Sam
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Sam
2 years 8 months ago

I think in general, you’re going to offset any increase in multi-run homers by a decrease in run production simply because some people aren’t getting as many at-bats.

As I’m sure anyone who reads fangraphs knows, lineup construction has only a small amount to do with overall performance (the best and the worst lineup arrangements are separated by only 2-3 wins over a season). But the ‘best’ arrangement is close to sorting the lineup by OBP. So if you move them around, and put them lower in the order, then you give up a few runs.

The way this would work is if you had power hitters roughly in the right spots anyway – i.e. two good on-base guys, then a power hitter who was also a pretty good on-base guy, then two lesser on-base guys, then a power hitter who wasn’t that good of an on-base guy, then the weaker hitters. But even then, I suspect the difference would be minimal.

Joseph
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Joseph
2 years 9 months ago

Nitpicking, but you might want to flip the axis labels for the OBP/runs-per-HR and OBP-HR%/runs-per-HR graphs. Took me a few seconds to figure out what happened. Shame there isn’t much point to leaving the 2013 Tigers on those graphs, haha. Outliers are fun to observe.

JKB
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JKB
2 years 9 months ago

Maybe The Relstionship Is Moderated By Organizational philosophy. The Tigers Might Be Trying To Hit Home Runs With Runners On, While The Rays Might Be Trying For Singles And Doubles In The Gap. Also Speed Might Be A Significant Covariate. Faster Teams Might Have A Higher Runs Per Double Rate.

x
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x
2 years 9 months ago

I can’t get through this article. I don’t know if the perpetual “homer runs” error was intended or not, but it drives me insane and wrecks an otherwise interesting article.

Kelly L.
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Kelly L.
2 years 9 months ago

Pretty sure it’s not an error and refers to “runs that are scored via homers.”

MGL
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MGL
2 years 9 months ago

From the city of “Picayune”…

“Here we find a 60% correlation.”

Typically “correlation” refers to “r” and not r squared (coefficient of determination). So the correlation with an r squared of .6093 is around .78, which is quite high. R squared is the “proportion of the variance in the output data that is accounted for by the regression model.” It is usually not that high (since even a high number less than 1 becomes a low number when squared!) simply because the outputs we usually deal with have a lot of random variation since the data points are usually based on a limited sample size. That is why you usually want to look at “r” and not r squared when looking at how one data set “explains” another.

Bill
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Bill
2 years 8 months ago

R squared “is usually not that high simply because the outputs we usually deal with have a lot of randiom variation since the data points are usually based on a limited sample size.”

Or maybe it’s not that high because OBP really does only a small proportion of the variance in runs per HR. :)

You can’t automatically blame a low R squared on lack of data. It MIGHT be due to a lack of data, but it might also be due to the fact that there really are other things affecting runs per HR that you haven’t accounted for.

If you really believe it’s a sample size issue, then you should get more data. But if in fact you haven’t accounted for other relevant variables, then increasing your sample size won’t help much. Still, trying to account for other relevant variables AND increasing your sample size are better approaches than simply asserting/pretending that you have a strong relationship by citing R instead of R squared.

AJ
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AJ
2 years 9 months ago

I don’t think you can simply look at Team OBP, because not all OBPs are created equally. For example, the #8 hitter’s OBP has a much less significant impact on a team’s R/HR than the #3 hitter’s OBP (because the #4 hitter hits more HR than the #9 hitter). One reason why the Tigers have such a high R/HR is because their HR are clustered in the top of their lineup, behind guys with high OBPs.

Michael
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Michael
2 years 8 months ago

In Minnesota a “Plouffe Bomb” has become synonymous with a solo HR. I have no idea what the data on him is, but it seems he only hits solo shots.

anonynous
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anonynous
2 years 8 months ago

Obviously the reason we’re not seeing any many multi-run homers as expected is because pitchers “bear down” with men on base! Great pitchers like CC Sabathia and Jack Morris pitch to the situation which is how they pile up so many wins even while sporting mediocre ERAs.

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