The Sinker Paradox

Two things are very much true in modern baseball, and they’re in seemingly direct contradiction with one another. The first hardly requires any introduction: fly balls are leaving parks like never before. There’s almost no point in linking to a story about it, because there’s no way you haven’t heard if you are reading this website, but what the heck, here’s Ken Rosenthal talking about it. Baseball in 2019 is a game of home runs — allow fly balls at your own risk.

At the same time, the two-seam, sinking fastball is going extinct. The trend started a while ago, and it doesn’t look like it’s stopping anytime soon. Cutting sinkers has worked, kind of, and progressive teams like the Astros and Rays are leaning into it. Heck, overhand arm slots and high-spin four-seam fastballs are the hallmarks of modern pitching. Teams are looking for them in draft picks and getting young pitchers to throw more of them.

Think about those two things for a second. Fly balls are more dangerous than ever, but the pitch that is best at avoiding fly balls is on the decline. It’s a mystery worthy of Sherlock Holmes, and today I’m throwing on my deerstalker hat. The first thing we need to do is confirm that fly balls really are worth more than ever. This might seem trivial, but it’s worth doing, if only to figure out just how much more fly balls are worth these days.

Here’s one way to think about batted balls: when you put a ball in play, that’s the result of the plate appearance. Maybe it’s an out, or maybe it’s a double, but that plate appearance is over as soon as a fair ball happens. You can think of the value of a given batted ball as the difference between that batted ball’s value and the value of a random plate appearance. Because of the way wOBA is defined, it’s easy to work out the run value above average of a given event — you simply subtract league average wOBA from the event’s wOBA and divide by a yearly constant called wOBA scale. Take a look at the average value of each batted ball type in every year since 2002:

Boy, line drives sure are valuable, so much so that they wipe out the scale. Let’s look at ground balls and fly balls in isolation:

One quick note on the units: I chose to represent it in runs above average per 100 balls in play. It would be totally fine to look at this per single ball in play, but I liked having whole numbers. It’s kind of intuitive, too — in 2019, if you replaced 100 random PA from a league average player with 100 random fly balls, that would be worth just under seven runs. In 2014, 100 fly balls were worth a mere two runs above average. Want the ingredients for an offensive explosion? There you go.

Looking at this data, it’s clear that the new ball is massively changing the relative value of different batted balls. Line drives and ground balls essentially haven’t moved. Meanwhile, fly balls are pure baseball gold now, and they were mere trash as recently as 2014. That brings us to our next question: why are we seeing the decline of the pitch best suited to avoid fly balls at the same time that fly balls are most important to avoid?

First things first — what if sinkers just aren’t generating the same amount of ground balls as before? There’s been a lot of talk about newly designed swings that lift sinkers into fly balls. If that’s the case, maybe the changing value of fly balls doesn’t matter, because some of the ground balls sinkers are trying to get are transforming into home runs. Let’s take a look at the batted ball rates of sinkers over the last twelve years:

It looks like not much has changed in the past few years. There appears to be some bleed-through between line drives and fly balls, but aside from that switch, things have been quiet. Even in that case, rates have stayed pretty constant since 2015.

What do these rates mean in terms of run scoring? We can combine the batted ball percentages with the value of each batted ball type we calculated up above and work out the amount of runs above average sinkers allow per 100 balls in play, accounting for the different batted ball distribution and value in each year. Here’s that result, with four-seamers in the graph for comparison’s sake:

Curiouser and curiouser. Sinkers were more valuable than four-seamers in 2008, but their advantage narrowed somewhat as batters turned more of them into line drives. The recent fly ball value explosion, however, has made sinkers significantly better for the pitcher again. Why, then, aren’t we seeing more of them?

There are at least three huge effects that I haven’t addressed so far, without which no analysis would be complete. First, consider that 17% fewer sinkers were thrown in 2018 than in 2008. It stands to reason that getting rid of those presumably bad sinkers would flatter the overall sample. We can handle that by slicing up the data and focusing on one segment. Next, there’s something even more obvious: not every pitch results in a ball in play. Just 20.3% of sinkers thrown this year have ended up in play, compared to 15.8% of four-seam fastballs. We can work out rough values of balls, strikes, and fouls and add those values to our analysis. Finally, who’s to say that fly balls hit off of sinkers and fly balls hit off of four-seam fastballs are created equally? We can check that as well.

First let’s equalize our samples. In each year from 2014-18 (the start of the downtick in two-seam fastballs), I looked at the pitchers who accrued the 51st-75th most value from their sinkers, per Pitch Info’s run values. Then I looked at the batted ball results those pitchers had in the subsequent year. In this way, there’s no selection bias problem — if I simply looked at the 51st-75th best sinkers in a year and took those batted ball rates, I’d be contaminating our data, because we already roughly know how valuable those sinkers are. Why 51st-75th? Well, I’m not convinced there’s much value to be gained from looking at the singular greatest sinker throwers. Maybe they’ll follow the population as a whole, but then again, maybe not. I’m looking for pitchers who have reason to keep throwing the pitch, but who aren’t outliers. We’ll repeat the process for four-seam fastballs to end up with a comparable group.

There doesn’t appear to be anything when it comes to batted ball splits. The sub-population of 51st-75th best pitchers with both fastballs are worth about the same as the overall group, easily within a margin of error, from 2015 to 2019. Two-seamers put in play are better for pitchers, relative to four-seamers, than they were in 2014, and it’s not just a selection effect. If we’re going to find an answer, it’ll be somewhere else.

Next, let’s add in balls and strikes. One reason that four-seam fastballs are gaining prominence is because balls in play are increasingly dangerous. Four-seam fastballs generate more swings and misses, which means that putting the two pitches on an equal axis of balls in play isn’t telling the whole story. Take a look at swinging strike rate, called strike rate, and foul ball rate for the two types of fastballs since 2008. Of note, I calculated but am not going to show these splits for the sub-sample from the previous section, because they’re indistinguishable from the overall population.

With these results in hand, it would be tempting to work out the average run value of a strike, foul, or ball. Then we could just apply those values and go from there. The only problem with this analysis is that it doesn’t quite work that way. The average value of a strike is heavily influenced by turning, say, a 3-2 count into a strikeout. But the called strikes in our sample aren’t distributed evenly. Batters take a lot more strikes 0-0 than with two strikes. Instead, I’m going to focus on results when the batter swings. This comes a lot closer to a fair representation of pitch value.

This analysis is enlightening. The edge that two-seam fastballs produce on balls in play is real, but four-seam fastballs are so much better at producing whiffs and foul balls that they more than make up their contact disadvantage. Even though it seems like getting grounders is all you need to make a pitch worth it in this era of Death Star-level fly ball production, the rest of the outcomes matter too.

I have a confession to make. I just spent 1,500 words showing that sinkers aren’t more valuable than four-seam fastballs in a world where batted ball results are random. There’s just one problem: batted ball results aren’t random. Take a look at the wOBA value of fly balls hit off of two-seam and four-seam fastballs, respectively, since 2008:

Oh. That looks like it might make a difference. Let’s redo the study from above, only plugging in the specific wOBA allowed for each pitch type/batted ball combination. First, the value of 100 batted balls:

Four-seam fastballs have been particularly bad for pitchers on balls in play this year, but for the most part this analysis makes sinkers look worse than they did before we segmented the batted ball results. Let’s finish the thread by throwing these new batted ball values into a calculation of runs per 100 swings:

I’m usually hesitant to say “there you have it,” but… there you have it. Even when balls in play were less onerous for pitchers, the swing-and-miss properties of four-seam fastballs gave them an edge in overall value. That edge appears to still exist, even as fewer pitchers throw two-seam fastballs and the ball carries further and further.

The sinker paradox is fun to think about. Grounders are good, but sinkers are bad. What gives? I posit three reasons in this article. First, batted balls off of sinkers aren’t as advantageous as you might think. Second, batters do more damage when they put a sinker in the air than when they put a four-seamer in the air. Third, sinkers induce very few whiffs relative to four-seamers, and in the lively ball era, getting an out without allowing contact is paramount.

These aren’t the only possible reasons for the decline of sinking fastballs, of course. Matt Trueblood did some interesting analysis that points to sinker pitch tunneling being less favorable than four-seam tunneling. More specifically, curveballs have been regaining popularity relative to sliders, and four-seam fastballs pair better with curves than two-seamers do. Batters may have changed swings to more effectively target sinkers, though that hasn’t really showed up in the data in any obvious way.

There are, in other words, many reasons you might expect sinking fastballs to decline in popularity. Getting more grounders isn’t enough. Two-seamers need to get enough more grounders to offset their disadvantages in several other categories, and thus far, it doesn’t appear that they have. This is a lesson in baseball, but it’s also a lesson in logic. Two effects work in offsetting directions all the time (more grounders, less whiffs). If you want to know the net effect, it’s not enough to say that two things point opposite ways. You have to go in and work out the differences if you want to be able to say anything more than “well it’s confusing, that’s for sure.”

When it comes to baseball, it looks like the league has done an excellent job working out the net costs and benefits of various fastballs. This is subject to change, of course, as swings and run environments change. For now, it all makes sense: two-seamers are worse, all-in, and so they’re getting thrown less. If only every cost-benefit analysis had such a clean answer.