Each pitch of a plate appearance can be grouped into four outcomes: a called ball, a hit-by-pitch, a called strike, or a swing. Swings can then result in three outcomes: balls in play, foul balls or misses. So, broadly there are six outcomes for each pitch. Looking at how these outcomes vary as a function of the ball-strike count has been an interest of mine for some time now. For example, how often do hitters swing in a 3-0 count? How often do hitters swing at the first pitch? These sorts of questions have received some attention (e.g., here, here, here and here). However, there are many more questions of this nature that can be asked.
For example, on a recent episode of the FanGraphs Audio podcast, managing editor Dave Cameron and host/author Carson Cistulli wondered about hitters protecting the plate when there are two-strikes. More specifically, they wondered if batter's swinging strike rate goes down with two strikes. Perhaps hitters are fouling off more pitches in an effort to protect the plate.
How hard is it for pitchers to get the third strike? An excellent analysis from Jon Roegele has demonstrated that the strike zone is not called as the perfect rectangle shown on television broadcasts. It changes with every pitch, and shrinks when a batter has two strikes on him. Umpires are seemingly hesitant to punch a batter out.
Now, if batters are aware of this reduction in the likelihood of a called third strike, it could reduce the rate at which they swing at pitches, perhaps leading to a coincident reduction in the swing and miss rate. Alternatively, batters may swing more with a protective swing that is intended to foul pitches off. As a result we would see more foul balls in two-strike counts. However, such protective swinging is not immune to misses and therefore the swinging strike rate may not change at all or it might even be higher.
It seems there is a reasonable hypothesis either way and without looking into the data it is too difficult to assess what has happened in these situations. Dave Cameron left it on the podcast as: "I am sure someone will figure it out". Well here's hoping that I am that someone (and that I have not overlooked someone else having already looked into this question).
PITCHf/x data is useful for responding to these inquiries. Using the Baseball-Savant PITCHf/x search tool, I gathered every pitch thrown in a major league game for the 2008-2014 seasons (through Sunday's games). Pitches were binned according to the 12 possible ball-strike counts, and by pitch outcomes: (1) called ball, (2) called strike, (3) swinging strike, (4) ball-in-play, (5) foul ball, and (6) hit-by-pitch. Please note that called balls include pitch-outs and intentional balls. Also note that, unfortunately, the way I gathered the data does not allow me to comment on how pitch location affects these outcomes. That will be something for another article.
To begin, here are the data for how often batters swing (outcomes 3-5) in all counts:
We see that regardless of the number of balls, batters have tended to swing more often in two-strike counts than in one-strike or zero-strike counts. So this looks like initial evidence in favor of the proposal that hitters swing more in two-strike situations in order to protect the plate. But how often do they swing and miss (i.e., a swinging strike)?
Here are the data:
Again we see that regardless of the number of balls in the count, the swinging strike rate is higher with 2-strikes. In fact there is a steady increase in swinging strike rate as the number of strikes in the count increases. Below is a table that shows swinging strike rate again, but this time only for instances in which the batter swings (outcomes 3, 4 & 5):
So, from these data we see that if a batter swings he has been more likely to swing and miss in a two-strike count than in a one-strike or zero-strike count. Again, there is the steady increase in swinging strike rate as the number of strikes in the count increases. This can be taken as additional evidence in support of the notion that hitters are attempting to protect the plate with two-strikes by swinging more. Interestingly, as the next two tables show, the higher swinging strike rate in two-strike counts comes primarily at the expense of putting balls in play, as the foul ball rate stays pretty consistent.
|Foul% of Swings|
|Ball-in-Play% of Swings|
Considering the pitch that is likely to be thrown in any given count is important when interpreting this analysis. Pitchers may be able to rely more on their secondary pitches (e.g., curveballs, sliders) when ahead in the count. Thus the type of pitch thrown could lead to the increased swinging strike rate, as it is more difficult to hit breaking pitches.
Looking at the three-ball counts, we can see that the swing and miss rate does not change as much across zero-, one- and two-strikes as it does in the zero-, one- and two-ball counts. This could be because pitchers are throwing more fastballs in three-ball counts in order to have more control and avoid walking the batter. But this allows batters to make more contact. An examination of pitch type thrown across count would help support or reject this idea.
Finally, even with the increased swinging strike rate in two-strike counts, getting the third strike has still been the most difficult. This is intuitive as there are fewer ways to get the third strike than there are the first or second. However, by combining the swinging strike and called strike rates we can see how often a pitch is a ‘true' strike (i.e., not fouled off or put in play). From the table below it is evident that getting the third strike has been the most difficult strike for pitchers to get.
We now have some responses to the original questions posed in this article. First, the swinging strike rate is higher in two-strike counts than in zero-, or one-strike counts. This is true when considering all pitches and when limiting consideration only to the pitches at which the batter swings. Batters are swinging more often in two-strike counts, likely in an effort to protect the plate (despite evidence of a shrinking strike zone in such situations). If the two-strike swings are protective with the intent of fouling pitches off in order to get a better pitch to hit, they are not working. Foul rates on swings remain consistent across counts, while ball-in-play rates actually decrease. Finally, while there is a strikeout scourge in baseball, getting the third strike is still the most difficult to get.
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Chris Teeter is a Featured Writer at Beyond the Box Score. You can follow him on Twitter at @c_mcgeets.