There's a certain theory from Greek philosophy concerning Forms. The Form of something is, more or less, the perfect idea of a thing. When you see a tree, you're seeing an imperfect reflection of the Form of a tree. We cannot perceive Forms; they exist in a higher reality of some kind (forgive me you philosophers for butchering wording). With all due respect to the ancient Greek philosophers (I read some of their stuff in ancient Greek), I'd say this strike 'em out, throw 'em out double play is about as close to the Form of that play as we can get.
The situation: 1st inning. Dee Gordon reached base on a bunt single to third; he was ruled safe after a challenge. It was a very close play with an awkward ricochet into Lucas Duda's glove, but Gordon's speed showed. Gordon is a very fast runner who stole 64 bases last year at a 77% success rate. It's not impossible to throw him out, but it's tough. Jacob deGrom was on the mound facing strikeout-prone Christian Yelich with Travis d'Arnaud catching. d'Arnaud has not shown himself to be a strong defensive catcher in terms of throwing out base stealers; his career CS% is 19.8 percent compared to a league average of 28 percent, but he had thrown out Gordon previously in the series. The table was set: a base-stealer on first with a strikeout-prone pitcher and batter combo.
A full count. A 94mph fastball up. A swing and miss. A good throw. A perfect tag. The Form, almost.
I decided to investigate the strike 'em out, throw 'em out double play. Using Baseball Savant, I gathered all stolen base attempts since 2008 with two strikes in which the pitch result was strike three. That unfortunately sounds a lot like one of those random telecast stats, "He's 15 for 34 with runners in scoring position in a day game against LHP with the wind blowing in." So it goes. What I've endeavored to compare are various PitchF/X attributes of successful DPs vs. unsuccessful DPs.
Overall, there have been 2,446 stolen base attempts on strikeouts since 2008. 62.4% of the time, the runner is safe. In the Form play above, deGrom threw a 94mph fastball. The first visual below displays the pitch type differences between the two outcomes, out or safe. The percentages are for each pitch type (I have hidden some pitch types-don't worry if your eyeballs don't add the percentages to 100). There shouldn't be anything unexpected.
As you would expect, harder pitches show up in greater proportions on unsuccessful steal attempts. It's harder to steal against faster pitches. However, since many pitchers use breaking and offspeed pitches to strike out the opposing batter, fastballs are underrepresented compared to the overall distribution of pitch types. Getting the strikeout is likely more important than throwing a pitch that allows greater odds of throwing out a runner.
The next aspect of the Form play above was pitch location. deGrom threw a middle-high fastball. Baseball Savant classified it into zone 11; their zone map is here.
Due to the nature of pop times, you would expect that unsuccessful steal attempts would have a higher percentage of pitches in those zone upper zones. The visual below compares the zone percentages between the two outcomes. I defined 'High' as zones 11,12,1,2, and 3. I defined 'Low' as zones 13,14,7,8, and 9. Zones 4,5 and 6 are 'Middle'. There are some pitches within zones 11-14 that could be classified as middle, and that is a confounding factor here. In theory, pitches thrown on the edge of the plate in the middle could be successful depending on the catcher handedness, batter handedness, and whether or not the batter is crowding the plate. Pitches thrown on the edge and up are unlikely to be swung at and are probably not well-represented in this data set.
Again, nothing unexpected. Catcher pop time is a factor when a runner is attempting to steal a base, and throwing a pitch higher reduces the pop time for the catcher. When StatCast data are available on catcher pop time, it will be interesting to see how pitch location affects catcher pop time.
The next element of the play, but not necessarily the Form, was whether or not the batter decided to swing; Yelich chased. The thought process is that a taken third strike would make it easier for the catcher to throw to second. A batter swinging is a batter putting things, whether the bat or his body, in the way of the catcher. The data don't really show a relationship here. The percentage of called third strikes is just about the same comparing whether the runner was out or safe (17.7% vs. 17.8%). The only difference, and it's a small difference, is that there is a higher percentage of blocked swinging strikes when the runner is safe (6.2%) compared to when the runner is out (1.6%). That makes sense; it's harder to throw out a runner if the catcher is blocking a curveball in the dirt.
There is a very high percentage of swings, though--about 82%. This article delves into older data about the thought process that swinging "protects" the runner; however, the dataset is more inclusive than strikeouts on steal attempts. One of the results found was that swinging didn't necessarily "protect" the runner. In fact, runners were safe at a higher percentage on non-swings than swings. The article and the comments delve further into explanations for that phenomenon, so I won't talk about that here. It's a different situation.
The other elements of the play that aren't necessarily quantifiable (yet): catcher pop time, time of the throw to second, and all the data about the runner like length of lead, first step, etc. With StatCast data, we could perhaps closer approximate what it is that makes up the Form of the strike 'em out, throw 'em out double play.
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