Home Run Value, Revisited

Who knows?

Maybe it is because I was never really good at hitting them. Maybe it is because Billy Beane wrote that book about how on-base percentage smells better than home runs. Whatever the reason, here I am, trying to debunk the notion that home runs are worth more than what is already accounted for. Again.

I am not talking about entertainment value, of course. The wow factor of a Brandon Allen’s shot over the foul pole is off any chart I could ever make. But, that’s not the question. The question is, are HR – as a working tool for creating runs – underrated? Are they necessary? Can they be replaced with other tools of same quality?

In case you missed it back then, joined AN later or just don’t like my writings, I did a piece on succeeding without HR power. And for what its worth, it backed up the theory that it doesn’t matter what portion of your eggs is in the HR basket. But simulations made in mothers’ basements are one thing, real life baseball something completely different. Here is another attempt to answer the question – are HR new undervalued commodity?

Before something can be proclaimed to be overvalued or undervalued, it has to receive a value first. Enter wOBA*.

* If you are not really a stats person, don’t worry. I generally try to keep math simple and refrain from using many acronyms, because I like to understand what I am looking into. If you are, this might be boring for you.

How valuable is a home run?

That depends in which context you look at it. Imagine there are runners on 2nd and 3rd and two outs. The next batter either walks or homers. How much more valuable would that home run be when compared to the walk? Well, it depends on whether the next guy homers himself or grounds out. The difference can be anywhere between three runs and none.

The best would be if we could somehow keep track of all the home runs ever hit and all the bases on balls ever awarded. Under every imaginable circumstance. And then look at how many runs were really produced as the result of it. You know, some kind of spreadsheet on steroids, where every single event ever recorded on a Major League diamond was kept and and looked at. And then we could assign some values to it, to see how much value, on average, each hitting event brought to their real teams in their real games.

That’s wOBA in a nutshell. People actually did that.

And as for numbers, in 2010 a home run had a value of 2.07. Base on balls was worth 0.70. So, basically a home run does the same damage as three bases on balls.

Is wOBA any good as an indicator of offensive prowess?

OK, now we have our value. Naturally, not everyone will agree that linear weights (that’s the numbers attached to each event) that wOBA uses are a good way to estimate the quality of a batter or a lineup. To have a quick check on how telling wOBA is, let’s look at 2010 MLB hitting statistics and use correlation check.

A correlation is a single number that describes the degree of relationship between two variables. The higher the number (it maxes out at 1 or -1), the stronger that relationship is. Closer to 0, less significant the relation. So, as a goal of any offense is to score runs, we’ll look at how well does scoring runs correlate with different ways to qualify such offense.

What does this tell us? That batting average is a nice thing to have but that it only has roughly 50% of influence on run production (the R2 number or r-squared or coefficient of determination). Ditto home runs. Looking at OBP or SLG is a better way to evaluate offenses. Looking at both together even better. Looking at wOBA the best one. It has more than 0.90 R2, indicating a very, very strong relationship indeed.


Do HR heavy offenses outperform their wOBA?

So, wOBA seems to be excellent, yet not perfect. It is understandable that a perfect correlation of 1.00 can not be achieved, due to what some call luck, and some distribution. But, does it undervalue the home run? Would a team with high portion of HR-induced wOBA outperform its expected production?

One side says no. It doesn’t matter how you build your wOBA, as long as the sum is the same. If you have $100, who cares if it’s made of five $20 bills or two $50 ones? The other side says – try rolling five joints with two bills.

And indeed, some teams outperform their wOBA line, some score fewer runs than expected. But does it have anything to do with how many HR they hit? In short, not at all.

Year 2010 saw some drastic differences in how big a part HR played in offensive production of MLB teams. Bautista-led Blue Jays had 29% of their offense in the HR basket, whereas the A’s … well you know, you’ve been watching.

If wOBA indeed undervalued HR as offensive weapon, or if in general teams beneath certain HR threshold (and whatever that threshold might be, the Athletics were under it!) underperformed their wOBA expected line, we would see some correlation in the above table, between real life performance and HR percentage in the offensive production.

As it turns out, we are looking at the very definition of two things that have absolutely nothing to do with each other. Rather logically, teams that outperformed their wOBA lines were good on base paths. But whether they hit many or few home runs? Absolutely no difference.


Do HR heavy offenses outperform Pythagoras?

Well, sure, because Pythagoras can’t turn on that inside fastball as he used to anymore.

But, isn’t the secret in actually winning the damn ballgame? You know, coming through with a three-run shot against Felix in the ninth? So, perhaps HR-dependent teams don’t score more runs, but they score them when it counts.

If you’ve been paying attention, you know how to interpret this table by now. A negative number would normally indicate inverse relation, but such a minuscule one simply means – not related at all. On a side note, it is kinda depressing to make these charts and always have the A’s stick out in a negative way. Way to not hit at all, guys, create fewer runs than you should with your measly hits and then create even fewer wins than you should with your measly runs.


Are HR heavy offenses more likely to succeed against good pitchers?

So, a higher wOBA will lead to more runs, the lower one to fewer. HR participation in offense doesn’t make any difference whatsoever, neither on scoring runs nor on winning games. Now that we have that clear, let’s turn to what sounded like an intriguing idea.

Do HR heavy offenses perform better against aces? The idea is that it is easier to hit a home run off Felix*, than it is to string 3 hits of him or draw a walk against a guy of such good stuff. That aces are more likely to leave one pitch in the middle than throw four of them outside the zone that umpires will call ball and that Bobby Crosbys of this world will not swing at.

*It’s a bit funny, because A’s actually scored 6 runs off Felix in 2010, none on home runs.

As WaddellCanseco pointed out, the Aces create a lower scoring environment when they pitch, and the value of a HR in lower scoring environment historically increases. The counterargument is that it can not be assumed that good pitchers suppress scoring in the same way as moving the fences, juicing the ball, lowering the mound and similar exercises do. That it can not be assumed that they suppress walks and singles more than they do HR.

So, a final exercise. Aces are Top 15 pitchers in 2010, according to FanGraphs WAR. All of MLB pitchers and all of the hitting teams are the control groups. Top 6 teams (Top 3 in each league) in HR wOBA % are our High HR Group. Bottom 6 teams (Bottom 3 in each league) are our Low HR Group.

What we will look at is whether the Aces suppress the run production of Low HR Group more than they do when facing a High HR Group. If so, an argument can be made that HR have some value in itself, because they will give an otherwise equally valuable team a better chance to succeed in the postseason, when Aces take over.

As it turns out, Aces have it actually a bit easier when trying to shut down teams that more so rely on long ball (the sample size is roughly 1200 innings).


Summary (or the entry point for the tl;dr group)

All data, both from simulations and real life, strongly indicates that:

  • wOBA does an excellent job in evaluating offensive prowess
  • It doesn’t matter how much of each component there is in wOBA, HR included
  • Teams don’t need HR hitters. They need good hitters and it is completely irrelevant how their hitting qualities are distributed.
  • Having a higher portion of HR in your wOBA mix will neither help you score more runs, nor win more games nor beat great pitchers
  • You still can’t roll five joints with two bills

Preemptive caution – I will not look at Top 17 pitchers vs Mid 4 offenses in day games umpired by Dana DeMuth. If you want more data, you’re on your own.

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