The count is 2-2, and the pitcher sets, winds, and delivers. It's a high fastball, and the batter swings—

The most successful end to this plate appearance, from the pitcher's perspective, is a strikeout. All but the rarest of strike threes result in outs, and strikeouts typically don't afford the runners any chance to advance. Strikeouts build confidence, get pitchers out of jams, and may also cause fist-pumps.

But what's the second-most successful end to the plate appearance? You might be tempted to say a double play—in fact, that might be better even than a strikeout—but the trouble is you'll end up relying on your defense, so we can do no better than to call this outcome a ground ball. Ground balls are pretty good. They tend to have low run values despite the fact that batters sport a decent average when hitting grounders.

No, the second-most valuable way to end a plate appearance is with a popup. In the mortgaged-backed security of pitching lines, pop ups are the mezzanine tranche. They may not get the AAA rating that strikeouts do, but they pay out not long after. A very high percentage—more than 99 percent—of popups are translated into outs. Some popups, thanks to the infield fly rule, are translated into outs automatically. Along with walks, strikeouts, and home runs, popups are the sometimes-y of true outcomes. If a pitcher can repeatably generate pop-ups, he's going to outperform expectations based only on walks and strikeouts.

Let's talk about skills for a second. We know, for example, that certain pitchers are very good at inducing ground balls. Put differently, certain pitchers demonstrate the ability to lower the average angle of the ball off the bat down toward the ground. Say the average ball in play is about zero degrees (and I don't know that it is, but let's just say), ground-ball pitchers might cause the average hitter to hit balls in play at a negative five-degree angle. Those worm burners add up, even if the average result isn't dramatically different from the average pitcher. Can we make a similar point about fly balls? On one view, the opposite of the ability to induce ground balls is the failure to induce ground balls, and guys who average (again, say) positive five degree batted-ball angles are less valuable than their ground-balling counterparts.

But what if the skill of influencing the angle of the ball off the bat went further than simply affecting the average angle? What if, instead of pushing the ball up or down, pitchers could induce specific types of contact? It's a tricky proposition, to be sure, particularly because the data we have on batted balls is so colored by park and other effects. But the answer has broad implications. If certain pitchers are much better at inducing pop flies than their ground-ball/fly-ball tendencies would suggest, then they have a material advantage over their competitors.

Whoa, Dream Weaver!

The funny thing about Jered Weaver is that he has, ever since he entered the major leagues, been better than he was expected to be. His minor-league numbers were fine but not spectacular, and when he reeled off 10 straight victories to begin his career, many were surprised that Jeff even had a younger brother. Since then, he has posted good strikeout numbers, but never spectacular ones, and he has done a fine job of limiting his walks. For several seasons now, his peripherals have marked him as a solid No. 2, while his outcomes have looked more like those of an ace. Since John Lackey is no longer an Angeleno, Weaver has taken over at the front of the Angels' rotation, and some pretty interesting things have begun to happen.

First, as of Monday, Weaver leads the league in strikeouts. Go ahead, I'll wait for you to check. Yep, there it is—107 punchouts in 94 2/3 innings pitched. He leads the league in strikeout rate (K/PA) among starters with 40 IP, too, with a 28 percent mark. For the first time since his rookie season, he has a K/BB ratio over 3 (4.65, in fact) and he looks to lead the Angels—who nearly always perform ahead of expectations—into at least a decent shot at the playoffs. So that's weird.

But things were weird with Weaver before this year, and it has a lot to do with pop-up rates. Did you know, for example, that Weaver has never finished out of the top 20 in pop-up rate? It's true: he has ranked fourth, 19th, 10th, and first in POP% from 2006-09 (minimum 120 IP). He also ranks 10th in the majors this year among pitchers with at least 40 IP.  I think this is deeply interesting. In a world where pop-up rates are simply a function of fly-ball and ground-ball rates, we'd expect the top of the pop-up charts to be populated by an exclusive club of fly-ball specialists. After all, a popup is just a funny kind of fly ball, isn't it? One way to answer this question is to check out how well fly-ball rate predicts pop-up rate. The chart below takes all pitcher seasons with at least 100 IP and plots fly-ball rate against pop-up rate.

Notice the apparent, but relatively weak, correlation. In fact, the adjusted r-squared for this relationship is just 0.3, suggesting that fly-ball rate doesn't do a particularly good job of explaining pop-up rate. So that's weird, too, but maybe not so weird. After all, there is a threshold between fly balls and pop ups: If a batter hits a pop up far enough, it's going to be classified as a fly ball. To some degree, we're measuring the relationship between two things that draw on the same pool of balls in play. Nevertheless, the fact that the correlation is positive suggests there is some degree to which pitchers who put the ball in the air a lot get more popups.

What about grounders? Well, it turns out they are much better correlated with popups (or at least they are in the sample I used). Here's the match:

Here the relationship is negative, which is just what we should expect. But now the adjusted r-squared is much higher, at 0.61. Remember that we are using park-unadjusted numbers here just to get a sense of the relationship between the ball types. It turns out that ground-ball rates do a pretty nice job explaining pop-up rate.

What happens if we put it all together? Well, things get a little tricky. The trouble with batted balls is that there is a fixed pie of them: There is a hard maximum on the number of fly balls, or ground balls, equal to the number of balls in play. When a pitcher induces one more ground ball, there is one less ball that could be a fly ball. So as I try to create a model to predict pop-up rates, we have to keep in mind that we could achieve perfect fit by including all the other batted-ball types: popups would just be whatever was left over. To see what I’m talking about, take a look at this chart of fly balls versus ground balls:

Note that the adjusted r-squared for this relationship is 0.75. Take away a ground ball, and chances are you’ve added a fly ball. It's a tricky problem, and it limits the amount we can do with the data.

But running a regression on batted balls isn’t entirely pointless. After all, if there is a separate skill to inducing pop ups, we should expect a simple model based only on ground-ball and fly-ball tendencies to make consistent mistakes for those pitchers who markedly possess or lack that skill. For the sake of going down swinging, let's try it. I ran a multiple linear regression on pop-up rates, using ground-ball and fly-ball rates as the independent variables. I then created a predicted pop-up rate using the resulting equation, which has an adjusted r-squared of 0.67. What do we find? First, some of Weaver's seasons have been of a sort that we expect a high pop-up rate: in 2009 we predict a 12-percent pop-up rate, for example (league-average rates are between 7-8 percent). But in 2009, his actual rate was 15.5 percent. Here are his predicted and actual rates from 2007-10:















Weaver does in fact generate more popups than we would expect based just on his fly-ball tendencies, which are already rather pronounced. That difference, although relatively small, is important because those extra popups are almost always outs.

If you’re curious, here are the pitchers who have been outpacing their expected pop-up rates so far in 2010, as measured by the difference between expected and actual POP%:



Clayton Kershaw



Hiroki Kuroda



Ted Lilly



Jeff Niemann



Colby Lewis



Jered Weaver



CC Sabathia



Ryan Dempster



Evan Meek



Mat Latos



These are all pitchers who are pitching quite well this season, and whether descriptive or prescriptive, the rate of popups they have induced undoubtedly has a lot to do with it. Other pitchers who have consistently beaten predictions in the past include Chris Young, Cole Hamels, and CC Sabathia. Clayton Kershaw finished just behind Weaver in outpacing his prediction in 2009 as well.

One reason why all this might be somewhat repeatable is home park, particularly since popups have a lot to do with the dimensions of the infield. But as a quick and dirty check against this, we can see that although the Angels finished first as a team in POP% in 2009, they finished last as a team in 2008. The Dodgers, too, have bounced around a fair bit as well. Again, it’s not slam-dunk evidence, and this is really important: no sound house can be built from the shaky foundation of untranslated batted ball data. But what evidence I have suggests that not only has Jered Weaver found a way to strike out guys at a higher level, but he also features a hidden weapon in his arsenal. Next time you watch him pitch, see if he doesn’t get a few extra popups over the course of the start. Next to strikeouts, they’re a pitcher’s best friend.

Question of the Day

Is the ability to induce popups a pitcher skill? Is it separable from fly-ball or ground-ball rates?