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July 17, 2008

Attack! Attack! Attack!

A New Metric with Merit?

by Eric Seidman

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A3P: Attacking With Efficiency

While speaking to Max Scherzer not too long ago I learned about his interest in statistics and sabermetrics. His interest began while pitching at the University of Missouri when pitching coach Tony Vitello stressed the importance of "A3P percentage." Attack in three pitches, as explained by the Diamondbacks flamethrower, refers to a pitcher retiring a batter within three pitches, or having two strikes on him following the delivery of the third pitch. As an evaluative tool, it helps pitchers focus on getting ahead, and improves their aggressiveness on the mound.

According to Max, the results were cut and dried: regardless of "stuff," those with the highest A3P percentage were the most effective pitchers. He experienced these results firsthand as his collegiate numbers and success improved as his "attack percentage" increased. Intrigued by this idea, I decided to investigate whether or not it held true at the major league level in any way.

I focused on starting pitchers with 15 or more starts in the last season and a half. After coding my Pitch F/X database to number each pitch in a plate appearance, the numbers of interest became the total pitches thrown meeting the aforementioned criteria: two strikes after three pitches, or the batter retired with one, two, or three pitches. The 'or' clause ignored duplicates where the pitcher had two strikes after two pitches and retired the batter on the third. The total for each pitcher was then divided by his total number of batters faced during the study's span-April 1, 2007 to July 13, 2008-to find his attack percentage.

For starters, here are the top ten in A3P percentage:


Pitcher          A3P%
Derek Lowe      65.9%
Johan Santana   65.6%
Josh Beckett    65.4%
John Smoltz     64.3%
Kevin Slowey    63.8%
Jair Jurrjens   63.4%
Cole Hamels     63.2%
Paul Byrd       63.1%
Greg Maddux     62.9%
Zack Greinke    62.4%

And the bottom ten over the same period:


Pitcher           A3P%
Mike Maroth      49.5%
Jeremy Sowers    49.7%
Tom Glavine      49.8%
Kyle Davies      50.7%
Andrew Miller    50.7%
Mark Redman      50.9%
Miguel Batista   50.9%
Julian Tavarez   51.4%
Mike Pelfrey     51.5%
Phil Dumatrait   51.6%

Max found that the pitchers with the best A3P percentages were usually the most effective. But what constitutes effectiveness, and how is it quantified? Were those with the highest percentages also atop the ERA and ERA+ leaderboards? Or maybe the best in terms of K/BB ratio? Did they have the lowest opponent OPS counts? Effectiveness can be measured in a variety of ways depending on whom you ask; since there are so many different views, here are the correlations between A3P percentage and a number of different statistics:


Metric   Correlation
K/BB       .641
BB/9      -.609
OBP       -.595
FIP       -.515
ERA       -.501
OPS       -.496
AVG       -.392
SLG       -.328
K/9        .245
E-F       -.234
HR/9      -.148

E-F: ERA minus FIP

According to these results, A3P's quantified aggressiveness correlates quite strongly to K/BB, BB/9, OBP, FIP, ERA, and OPS. In industry terms, anything with a correlation of 0.80 or higher should be written about extensively. In sabermetrics, however, it tends to be a bit different. The DIPS theory, for instance, was based on walk and strikeout correlations around 0.70 and home runs around 0.35. A discussion with a few colleagues resulted in a general consensus that anything 0.50 or higher is pretty strong for our purposes, with moderate strength beginning around the 0.30 or so mark.

From an intuitive standpoint, K/BB, BB/9, and OBP should have the strongest relationships with A3P because, by definition, the batter is either retired within three pitches or he has two strikes on him after the third. A pitcher would have to lose the batter after going 0-2 or 1-2 for a walk to even take place. Regardless of strikeouts, pitchers with good A3P percentages are just not likely to walk as many batters.

Something to keep in mind, however, is that correlation does not necessarily equal causation. Just because A3P percentage has a strong correlation to FIP does not mean high A3P percentages will always result in better FIPs. With the large sets of data we have at our disposal in baseball, it will be very easy to find correlations between two given columns, but it does not mean they are directly related; it just means the numbers share bonds. For example, theoretically it could be discovered that bunt hits allowed correlates strongly to walks, but from watching a game of baseball, it becomes evident that these two events realistically have very little to do with one another.

So, while we could take the next step and run a linear regression to predict a metric using A3P percentage as one of the independent variables, the question of whether or not it matters would then come into play. Suppose this regression is run to try and predict K/BB, using A3P percentage and BB/9-the following formula would result from this dataset:

K/BB = 8.219(A3P%) - 0.476(BB/9) - 1.042

That would be the K/BB regression line based on its correlations to A3P percentage and BB/9, all of which share strong relationships. Regressions aren't the end-all solution, however, and even though K/BB correlates moderately to opponents OPS and ERA, it isn't necessarily strong enough to merit intense inspection. Additionally, the whole batter/pitcher matchup comes into play with this attack percentage in that the likelihood of a positive result from the batter is already going to lessen when the count is in the pitcher's favor. Even without a metric to explain this, it is largely understood that an 0-2 count is worse for a hitter than a 2-0 count. Despite A3P percentage sharing strong relationships at first glance with measures such as ERA, FIP, K/BB, and OPS, it really just attempts to measure working ahead of the hitter or challenging him in the strike zone.

A problem with the number, especially when trying to determine if it holds up as a useful tool at the major league level, is that it isn't consistent with itself. By measuring the components individually perhaps results would make more sense, because combining two unrelated but possible scenarios can cause a mathematical headache. Here's the first problem. Consider: What if a pitcher gets a hitter 0-2, throws a ball, and then gives up a home run? That would qualify the at-bat for A3P percentage inclusion as a positive result, even though the ultimate result is negative.

Then again, the more you work ahead, the less likely something like that would result. If this statistic was created by the coaches at the University of Missouri in order to stress working ahead of the hitters, that's great (if obvious), because working ahead will keep the batter/pitcher matchup in favor of the guys on the mound. In that regard it is very interesting to know who works ahead, but the "retired in three pitches" component of A3P percentage does not stipulate the count; instead, a hitter could have a 2-0 count, get a ground-ball out, and the at-bat would technically credit the pitcher for working ahead and attacking the zone.

Ultimately, though, retiring a hitter within three pitches could be, and likely is, influenced by the randomness of balls put in play. Calculating it alongside working the count in your favor convolutes the results and therefore deems them less effective than we may expect. Working ahead of hitters has definitely been shown to have positive effects for pitchers, but I'm just not quite sure that is what A3P measures, even if it intends to. While working ahead of a hitter could be a controllable skill, getting outs (other than strikeouts) within three pitches is not. The stat could be further stipulated by only measuring the amount of times a pitcher has two strikes through two pitches and retires him on the third, and that might offer better results, but at that point why not just measure the percentage of 0-2 counts?

All told, if this statistic is supposed to work like a placebo in aiding the confidence level of pitchers in attacking the zone or working ahead when on the mound, then it's definitely worth preaching at the collegiate level, and even earlier than that among amateur pitchers. However, at the major league level it really does not seem to be anything more than a potential gimmick.

Eric Seidman is a contributor to Baseball Prospectus. He can be reached here.

Eric Seidman is an author of Baseball Prospectus. 
Click here to see Eric's other articles. You can contact Eric by clicking here

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