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 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.

And yet, of those 31 suggestions, only four actually identified a player whose Attackability score was more than one standard deviation worse than average. And of those four, none is most attackable with breaking pitches. All four have whiff rates on fastballs far worse (relative to their peers) than whiff rates on breaking balls. Thirty-one players were said to be particularly susceptible to breaking balls, and you can argue that not one of those 31 actually is.

In fact, the players who were identified as swinging and missing at the most breaking pitches swing and miss at the most pitches, period. Justin Ruggiano had a terrible whiff rate on breaking balls last year—1.0 standard deviations worse than average. He was also 1.0 standard deviation worse on fastballs, though, and 1.1 standard deviations worse on off-speed pitches. Ruggiano is, in a sense, one of the least attackable hitters in baseball. (Which is not to say he's good. He's Justin Ruggiano! He makes this parenthetical's point all by himself.)

The point being: Our eyes can badly mislead us. Sliders and splitters are swing-and-miss pitches, and we associate certain players with flailing away wildly at them. But most of the guys you think of as whiffing at sliders actually whiff at everything; in a lot of cases, pitchers are quite possibly better off throwing whichever pitch they control best, or that the situation calls for. The batters who should see the most sliders aren’t Howard, Cruz, Soriano, Arencibia. Rather, they're Jonny Gomes, Asdrubal Cabrera, Michael Bourn, Stephen Drew, Chase Utley, Brendan Ryan, guys who are much worse against breaking pitches than against other pitches.

So who were truly the most attackable hitters last year? Finally, the long-promised table, of the 25 most attackable hitters in the game. The last column, z-attack, shows how high each player's Attackability score is—essentially, how easy it is to decide what to throw him. The bolded number shows the pitch type he is most susceptible to—FAz for fastball z-score, Oz for offspeed z-score, or Bz for breaking ball z-score:

fname n FA Whiff O Whiff B Whiff FAz Oz Bz sdv z-attack
Jonny Gomes 637 0.1058 0.505 0.4963 -1.0 1.8 2.0 1.7 3.6
Omar Infante 777 0.068 0.4124 0.3256 -1.6 0.9 0.0 1.3 2.3
Desmond Jennings 1025 0.2375 0.1927 0.2632 1.2 -1.2 -0.7 1.3 2.3
Miguel Montero 960 0.2774 0.2697 0.3158 1.8 -0.5 -0.1 1.2 2.2
Paul Konerko 883 0.1003 0.4135 0.4136 -1.1 0.9 1.0 1.2 2.1
Jeff Francoeur 656 0.2519 0.25 0.2877 1.4 -0.7 -0.5 1.1 1.9
John Buck 838 0.2813 0.3605 0.3097 1.9 0.4 -0.2 1.1 1.7
David Lough 617 0.0811 0.3868 0.3333 -1.4 0.6 0.1 1.0 1.7
Avisail Garcia 529 0.2765 0.3214 0.3246 1.8 0.0 0.0 1.0 1.6
Matthew Joyce 866 0.1224 0.4575 0.3851 -0.7 1.3 0.7 1.0 1.6
Asdrubal Cabrera 1040 0.1803 0.1905 0.3889 0.2 -1.2 0.7 1.0 1.5
Jason Castro 916 0.2729 0.2913 0.3818 1.7 -0.3 0.6 1.0 1.5
Andy Dirks 862 0.1753 0.2297 0.4259 0.2 -0.8 1.1 1.0 1.5
Jose Lobaton 574 0.2486 0.2683 0.3109 1.3 -0.5 -0.2 1.0 1.4
Chris Carter 1119 0.3157 0.3761 0.491 2.4 0.5 1.9 1.0 1.4
Pablo Sandoval 1202 0.1797 0.2018 0.1844 0.2 -1.1 -1.7 1.0 1.4
Michael Bourn 952 0.1383 0.4274 0.4409 -0.5 1.0 1.3 1.0 1.4
Chris Iannetta 740 0.205 0.5816 0.4351 0.6 2.5 1.3 1.0 1.4
Justin Morneau 1280 0.1799 0.1517 0.2919 0.2 -1.6 -0.4 0.9 1.3
Logan Morrison 552 0.159 0.1558 0.3361 -0.1 -1.6 0.1 0.9 1.2
Mark Reynolds 1007 0.3109 0.3905 0.4133 2.4 0.7 1.0 0.9 1.2
Carlos Gonzalez 812 0.2697 0.3333 0.3414 1.7 0.1 0.2 0.9 1.1
Prince Fielder 1260 0.108 0.3839 0.37 -0.9 0.6 0.5 0.9 1.1
Stephen Drew 943 0.1431 0.36 0.4433 -0.4 0.4 1.4 0.9 1.1
Jarrod Saltalamacchia 957 0.296 0.3636 0.4198 2.1 0.4 1.1 0.9 1.0

So that’s a table! (Here’s the full table with 442 players ranked.) There are interesting things in that table. Jeff Francoeur, for instance: When you die, and the movie of your life plays in your final moments, there will be about eight different scenes of you watching Francoeur flail at sliders; yet it’s his inability to hit the fastball, not the slider, that sets him apart. Jonny Gomes, a high-strikeout hitter, turns into Elvis Andrus on fastballs. Avisail Garcia is basically a contact hitter—except that he turns into Kelly Shoppach on fastballs.

Interesting! Useful? Ehhh. On first glance, you would say opponents don’t think so. Here’s how they pitched Gomes and Garcia last year:

  • Gomes: 65 percent fastballs, 23 percent breaking, 12 percent offspeed
  • Garcia: 66 percent fastballs, 25 percent breaking, 9 percent offspeed

So even though Gomes is totally attackable on anything but fastballs, and Garcia is attackable only on fastballs, there's practically no difference in how many fastballs they saw. And this is where we come up against the limitations of our cursory look at this topic. Whiff rate is only one way of measuring how well a batter does against a pitch, for instance, and Gomes slugged .542 on off-speed pitches—102 points higher than on fastballs—when he did connect; Garcia, meanwhile, slugged 40 points higher against fastballs than against off-speed pitches. Further, there's context to the pitches a batter sees, sequencing and counts and the opponents he faces. Gomes, for instance, saw nearly twice as many lefties as Garcia did, and lefties were significantly more likely to throw him fastballs than righties were. If we just looked at how righties pitched these two batters, we would conclude that opponents did avoid giving him fastballs. We've got the noise of a one-year sample: Gomes' whiff rate on fastballs was 11 percent and on offspeed 50 percent in 2013, but in 2011 those rates were 17 and 41 percent—so one year is strongly suggestive but not the final word on a player's abilities. And in this case the size of the samples is particularly important: Because we’re measuring variability, the small-sample fluctuations are not just noise—they’re actually part of what we’re measuring.

Like I said, I just wanted to see the table. I didn’t promise anything from it—though I'm sure I'll write more readable follow-ups, now that some groundwork is laid. It does point toward hitter weaknesses in a way that my simple look at Puig’s whiff rates couldn’t.

Thanks to Dan Brooks for doing all of this.

Thank you for reading

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Isn't there more to this than whiff rate? I have no data before me, but if Jeff Francoeur for example swings and misses frequently with fastballs but hits for significantly more power *when* he makes contact, that would alter the attackability equation.
Sam mentioned that in the penultimate paragraph.
Yikes. I look dumb, must have read right over that sentence. Anyway, it would be really interesting to see the same sort of charts for batters' OPS against different pitches.
? "I asked to name a player ..."
I hope you follow up on this from 10 different angles. I love this.
Love this. Really well done.
Very interesting. I'd love to see a way to try and quantify the game theory aspect of this. Jonny Gomes might be a good test case for this as well. Sure, pitchers still throw him 65 percent fastballs, but what's the fastball rate for most players - 70%? 75% And unless you're Doug Jones or Randy Choate, what's the minimum fastball percentage you would expect to see (to "keep hitters honest" and maximize the effectiveness of the offspeed/breaking pitches)?

I think another interesting aspect of this would be the interplay between the hitter's susceptibility and the pitcher's arsenal. I mean, sure, Miguel Montero is (relatively) horrible against fastballs and very good against offspeed, but if my heater is only 89, am I still better off going fastball, or does the offspeed pitch become the one I should be using?
Interesting...Mark Reynolds is a little less legally blind against offspeed pitches.
This would be cool to see while paired with release points. Like does a certain hitter hit fastballs relative to location.

I wonder how granular with the data you could get. Getting scores for pitch type, location, delivery method.
We could get extremely granular.

I think this was a first-pass reply to something that Sam wrote, and once Sam clears out all of his other topics, like, "Would it be better to put a pit between second base and third base or between home plate and first base?" and "Would catcher-runner collisions be better if players wielded jousting lances that they received from the third base coach?", we'll probably examine it in greater depth. =)

But seriously, I would expect more stuff about this kind of thing.