February 26, 2014
Introducing the Attackability Score
Sometimes you just want to see a table.
A couple weeks ago, writing about Yasiel Puig, I noted that, contrary to the common narrative about Puig chasing sliders, it was really his fastball whiff rate that was out of control. Relative to his whiff rates on breaking and off-speed pitches, it made him particularly attackable with fastballs. Dan Brooks pointed out afterward that each type of pitch has a different baseline whiff rate. So if, for instance, a batter has a 10 percent whiff rate on fastballs, 20 percent on breaking balls, and 30 percent on changeups, it looks like a significant difference. But if the league-average whiff rate is 10 percent on fastballs, 20 percent on breaking balls, and 30 percent on changeups (it’s not), then this hitter is essentially just as strong (or weak) on fastballs as on off-speed pitches. Relatively speaking, the 10, 20, and 30 are essentially equal.
We knew all this while we were writing or reading the piece, of course, but Dan provided me a clearer way of expressing each hitter’s relative tendencies: z-scores for each batter’s whiff rate on each type of pitch. Example: Tyler Moore’s whiff rate on fastballs (26 percent in 2013) was 1.5 standard deviations higher than the league average. His whiff rate on off-speed pitches (36 percent) was 0.4 standard deviations higher than league average. And his whiff rate on breaking pitches (41 percent) was 0.9 standard deviations higher. Ignoring for a moment the game theory involved—pitchers presumably identify his weakness and throw more of that, with diminishing returns—we would say this about Tyler Moore: He’s terrible at making contact on fastballs, pretty bad at making contact on breaking balls, and not great at making contact on off-speed pitches. If you were attacking Tyler Moore, you’d attack him with fastballs, though he’s got swing-and-miss in his game no matter what you throw.
So now we have three z-scores for each hitter. Again, all pretty intuitive. But what we really wanted to do was figure out how attackable Puig (or Moore) is. When he steps up to the plate, is it an easy decision which pitch to throw to him? Of the three categories of pitches, is there one that he is especially helpless against? Does he, in other words, make it easy on opponents by being great at one thing but terrible at another?
So there’s one more step Dan took: He found the standard deviation for each hitter’s three z-scores; and then found the z-score of that standard deviation, relative to other hitters, to see how attackable he is. We're going to call this an Attackability score.
So, to demonstrate, we'll go back to Moore: His three z-scores were 1.5, 0.4, and 0.9. The standard deviation of those three numbers is 0.57. And relative to all other hitters, 0.57 is .14 standard deviations higher than average—his Attackability score is 0.14. In other words, he’s just a little bit more attackable than average. In other other words, he’s not particularly easy to attack, because he doesn’t have one weakness that’s far out of line.
Desmond Jennings, by contrast, is easy to attack: His whiff rates are 24 percent (fastball), 19 percent (off-speed), and 26 percent (breaking); relative to the rest of the league, those rates are 1.2 standard deviations high (fastball), 1.2 standard deviations low (off-speed) and 0.7 standard deviations low (breaking); and the variance of those three figures is very high: 2.3 standard deviations higher than average. He’s a contact hitter on some pitches, and he's Drew Stubbs on others. When Desmond Jennings is up, the plan is simple: Throw fastballs.
We’ll get to the table soon. But why does this matter? Well, let me demonstrate. I asked twitter.com to name a player who is particularly susceptible to one pitch. Particularly susceptible. Thirty-five player/pitch combinations were named: Carlos Gonzalez and sliders, Drew Stubbs and curveballs, Yasiel Puig and fastballs, etc. Thirty-one of the 35 answers were breaking balls. So many hitters are so susceptible to breaking balls, our eyes and experience tell us. More people named Ryan Howard+Sliders than named any hitter+fastballs.