A week ago, Sam Miller and Dan Brooks over at Baseball Prospectus unveiled a new metric that they termed the "attackability score" -- the pitch or pitches that you would throw certain players in order to attack them, based on their standard deviation above or below a baseline whiff rate for that pitch.

Each type of pitch has a baseline whiff rate no matter who's throwing it: Fastballs tend to have the lowest whiff rates, changeups the highest. What Brooks developed was a z-score for these for each pitch and also each player as a whole, so we can compare different players to a league average whiff rate. I'll let Sam Miller explain it:

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.

Clear as mud, right? As Sam says at the beginning of the piece: "Sometimes, you just want to see a table." I agree, so I went ahead and built a table for all the 2014 Cardinals that had a qualified number of plate appearances in 2013:

Here's how to read this:

The first column is the sample of pitches (n)

The next three columns are the whiff rates for those players on fastballs (fawswing), offspeed (owswing), and breaking balls (bwswing) based on Pitch F/X data.

The next three columns are the z-scores of those whiff rates: In other words, what pitch is the hitter most susceptible to in terms of whiff rate? I've bolded the highest score for each player.

The last two columns measure the hitter's attackability: How easy is it to decide what to throw a certain hitter? The first is the raw z-score, the second is the "Scout", where 50 is exactly league average: Less than 50 means you're more attackable than league average, greater than 50 makes you less attackable.

The first thing that sticks out like a sore thumb: Why are there negative numbers? Well, remember that we're comparing these hitters based on standard deviations to league, and it turns out that all but two of the 2014 Cardinals had above average attackability rates in 2013: Jhonny Peralta and Yadier Molina. Peralta really struggles with off speed pitches, and if you go by this, you should basically never throw Yadier Molina a breaking ball, as he will likely square it up and crush it. Announce your presence with authority, Laloosh.





So why is Matt Adams the second least attackable despite having above average whiff rates against everything? Because "attackability" is trying to find out whether you have a specific pitch you are vulnerable to and Adams really doesn't have one -- he democratically whiffs at just about everything at a slightly above league average rate. That also means he likely hits everything too, however, meaning that if you leave any of these pitches in a zone where Adams can handle it, you're going to be walking around the mound shaking your head on a regular basis.





You can see why our lineup causes pitchers so many fits -- few Cardinal hitters have any one pitch that you can throw to consistently and get them to miss it on a regular basis. And Matt Carpenter....I have no words. Only one qualified hitter out of the 442 measured had a lower attackability score and lower z-scores than Carpenter in 2013: Nori Aoki. Carpenter rarely swings and misses, and when he does it's not on one certain pitch.





Game theory clearly applies here (if a hitter is susceptible to a certain pitch, pitchers should throw him more of that pitch), but not as much as you might think. It's pretty clear that Peralta struggles with changeups, but only 10% of the pitches he saw last year were of that variety. The last pitch you'd want to throw him, per whiff rate z-score, is any sort of breaking ball, yet pitchers threw him sliders nearly 20% of the time last season.





Sample size caveats certainly apply here, and one season's worth of data probably isn't enough to draw definitive conclusions about hitters against certain types of pitches. Whiff rate also isn't only one way to measure effectiveness of pitches either: Peralta might slug .600 on offspeed pitches, which would demonstrate why he doesn't see them as often as his whiff rate z-score might suggest. I just thought this was interesting on a number of levels and hope that Sam and Dan decide to extrapolate this further to tell us more about player performance against certain pitches in the future.