In last week’s column, I took an initial look at the question of whether pitchers in general-or specific pitchers-are able to successfully tailor their approach to be more effective in certain game situations, or to be exact, during double-play (DP) situations and situations with a runner on third and fewer than two outs (R3). To do this, I performed some cursory analysis of pitching data for the 2005-09 seasons to see whether ground-ball, walk, and strikeout rates differ in these situations compared to the norm. The numbers I ran for the DP situation showed an increase in ground balls (which are often, but not always, good for the pitcher in double-play situations), a decrease in strikeouts (which are always good for the pitcher in any situation) and a decrease in walk rate. Lastly, I looked at individual pitchers to get some idea of which ones improved the most during the DP situation, based on a quick and dirty measure I called **PRIDE**, which summed the changes in ground-ball and K rates and subtracted the change in walk rate.

Baseball Prospectus readers being the insightful group that they are, the article spawned a series of terrific suggestions on how this first-cut analysis could be improved. Therefore, instead of moving on to the R3 situation, this week I’m going to incorporate some of these suggestions and take a deeper (and better) look at the DP situation.

To start off with, commenter Drew Miller pointed out a solid (and obvious) improvement to the sample I was working with-exclude all plate appearances for pitchers. Given the frequency with which batters in the eight-hole will be pitched around, showing up as “unintentional” walks that set up DP situations, pitchers likely make up a disproportionately large percentage of plate appearances in those situations, thus pitcher PAs are not included in the data for this article. Reader Brian Kopec and others suggested comparing the DP situation numbers not to all non-DP situations (which would contain the R3 situations where ground balls are not necessarily wanted), but rather to base situations that don’t lend themselves to situational pitching. With that in mind, the chart below shows data split into four different situations: DP, R3, R2 (runner on second base only, fewer than two outs), and BASE (two outs or bases empty). All “change” columns compare numbers for that situation to the BASE situation-a time when any out will do. Lastly, I’ve removed all sacrifice bunts from the calculation of ground-ball percentage and GB/PA-these had been skewing ground-ball percentages. Here are the new numbers:

Situational Pitching Splits, No Pitcher PAs, 2005-09 Change Change HBP+ Change Change Split PA* GB% GB% GB/PA GB/PA BB/PA BB/PA K/PA K/PADP 163,903 43.68% -0.51% 33.47% +0.94 8.05% -1.03 15.33% -1.98 R3 21,168 44.47% +0.29% 32.38% -0.15 11.51% +2.43 15.70% -1.62 R2 41,368 46.35% +2.16% 33.75% +1.22 11.22% +2.15 15.96% -1.35 BASE 646,205 44.18% -- 32.52% -- 9.08% -- 17.31% --*: Excludes intentional walks and sacrifice bunts.

Looking at the double-play situation, we still see a decrease in both strikeouts and walks, but not as substantial a change as seen in last week’s chart. Most significantly, however, the GB% (i.e., the percentage of balls hit in play, including home runs, that are hit on the ground) now actually decreases slightly. The GB/PA percentage goes up a little, but this is entirely due to the reduction in walk and strikeout rate. There may be a small selection bias here-batters asked to sacrifice are likely lesser hitters who may be more prone to “lose” the strike zone battle and whiff or hit a ground ball had they been allowed to swing away. Even so, it would appear that pitchers in aggregate aren’t able to increase GB% significantly, if at all, in situations when it would be beneficial for them to do so. But attempting to do so seems to result in a small reduction in walk rate and a greater reduction in strikeout rate.

Taken together, do these changes result in any benefit for the pitcher’s team, or does the batter come out on top? To determine that, we need to calculate the actual effect that ground balls, strikeouts, and walks (and hit batsmen; in this article, any chart showing walk rates are actually showing rates of walks and HBPs together) have on run prevention. Another reader recommended trying to calculate the run expectancy changes that occur for each of these events-a good approach, so that’s what I’ve attempted to do below.

Run Expectancy (RE), as shown on BP’s Run Expectancy Matrix, calculates the average number of runs scored in an inning after a certain number of outs and a certain set of runners on base (i.e., the base/out state) have been achieved. These are calculated each year; since my data set is from 2005 to present, I’ve averaged the run expectancy for each of the eight double-play situation base/out states for the charts below. To determine how effective, say, a strikeout is in the double-play situation, we need to look at each of the eight base/out states and determine what the situation will be after the play-comparing the run expectancy for the base/out state before and after the play will show us how many runs on average that play will have saved or produced. Weighting these RE changes by the frequency with which that state occurs during a game, then multiplying the final RE change by the percentage change in strikeouts during the double-play situation compared to the BASE situation, will give us an idea of how much the change in strikeout rate in the double-play situation will affect how many runs are scored. This may sound complicated, but the charts below should make it pretty clear.

First, we need to take the DP numbers above and break them into the eight double-play base/out states (many thanks to BP intern Dan Malkiel for slicing the data thinner):

Base/Out States in DP Situations, 2005-09 Change Change HBP+ Change Change State PA GB% GB% GB/PA GB/PA BB/PA BB/PA K/PA K/PA0 OUT 66,321 44.34% +0.16% 34.40% +1.88 7.57% -1.51 14.87% -2.45 100 46,414 44.12% -0.07% 34.35% +1.82 7.53% -1.55 14.62% -2.69 103 4,560 43.40% -0.78% 34.19% +1.66 7.83% -1.25 13.40% -3.91 120 11,722 45.82% +1.63% 34.79% +2.26 7.96% -1.12 16.21% -1.11 123 3,625 43.78% -0.41% 34.15% +1.63 6.43% -2.65 15.53% -1.78 1 OUT 97,582 43.21% -0.97% 32.83% +0.30 8.38% -0.70 15.65% -1.67 100 56,071 42.93% -1.25% 32.76% +0.23 8.29% -0.78 15.39% -1.92 103 9,846 44.74% +0.56% 34.76% +2.23 8.09% -0.98 14.22% -3.10 120 22,801 43.60% -0.58% 32.34% -0.18 8.93% -0.15 16.88% -0.43 123 8,864 42.32% -1.86% 32.41% -0.11 7.78% -1.29 15.66% -1.66 Total 163,903 43.68% -0.51% 33.47% +0.94 8.05% -1.03 15.33% -1.99

Even before trying to calculate the Run Expectancy change, slicing the data into these distinct base/out states reveals some interesting things. As you can see, the ground-ball percentage during the double-play state goes up slightly with one out, and goes down with two outs-mostly because of a +1.63 change in GB% in the “runners on first and second” state. Perhaps this is just noise, because I don’t have a rational explanation for it; I’d love to hear what BP readers think. The other standouts are the large reduction in strikeout rates with runners on third, especially first-and-third situation-apparently batters are successfully trying to put the ball in play to plate a run without a hit.

Now that we have numbers for each base/out state, we can use them to calculate run expectancy changes. Even Minard would have difficulty showing that in one easy-to-read chart, so I’ve broken it up into pieces. First the easy ones, strikeouts and walks:

Run Expectancy Changes in DP Situations for K and BB, 2005-09 Begin % of DP Begin Post-K Post-K Post-BB Post-BB State Situations RE RE RE Change RE RE Change0 100 28.32% 0.907 0.545 -0.362 1.515 +0.609 0 103 2.78% 1.795 1.186 -0.609 2.324 +0.529 0 120 7.15% 1.515 0.925 -0.590 2.324 +0.809 0 123 2.21% 2.324 1.586 -0.739 3.324 +1.000 1 100 34.21% 0.545 0.232 -0.313 0.925 +0.381 1 103 6.01% 1.186 0.499 -0.686 1.586 +0.400 1 120 13.91% 0.925 0.457 -0.469 1.586 +0.660 1 123 5.41% 1.586 0.777 -0.809 2.586 +1.000Weighted RE Change Post K: -0.435 Post BB: +0.567

The “no outs, runner on first” state (or 0 100) makes up 28.32 percent of double-play situations, and has a run expectancy of 0.907. After a strikeout, the state will be “one out, runner on first”, which has an RE of 0.545. Thus the RE change after the strikeout is the difference: -0.362. Each state is calculated and the frequency percentages are applied as weights, giving the results at the bottom: a strikeout decreases RE by 0.435 runs, while a walk increases RE by 0.567 runs.

Ground balls are more complicated. First, I calculated the percentage of ground balls that ended in a double play (36.75 percent), a fielder’s choice out (35.01 percent), or in no out at all (28.24 percent). To determine the base/out state after each of these events, I had to apply some generalizations. For double plays, the runner at first and batter will be out, while all other runners advance. For fielder’s choices, the runner at first is out (i.e., a DP was attempted but not completed), except in bases-loaded situations, where I assumed a force at home. The results:

Run Expectancy Changes in DP Situations for FC and DP, 2005-09 Begin % of DP Begin Post-FC Post-FC Post-DP Post-DP State Situations RE RE RE Change RE RE Change0 100 28.32% 0.907 0.545 -0.362 0.108 -0.798 0 103 2.78% 1.795 1.545 -0.250 1.108 -0.687 0 120 7.15% 1.515 1.186 -0.329 0.370 -1.145 0 123 2.21% 2.324 1.586 -0.739 1.370 -0.945 1 100 34.21% 0.545 0.232 -0.313 0.000 -0.545 1 103 6.01% 1.186 1.232 +0.046 0.000 -1.186 1 120 13.91% 0.925 0.499 -0.426 0.000 -0.925 1 123 5.41% 1.586 0.777 -0.809 0.000 -1.586Weighted RE Change Post FC: -0.356 Post DP: -0.820

The wonders of math show us that double plays are twice as good as strikeouts, but only make up slightly over a third of all ground balls. Fielder’s choices are a little less good than Ks, and make up another third. What about non-outs? To help calculate this, I made a few more assumptions: I counted singles and batters reaching on error as the same event, always with runners advancing a single base, with the exception of runners scoring from second in the “first-and-second” situation. These account for 92.25 percent of non-outs on ground balls. Doubles (7.37 percent) advance runners two bases, while triples (0.38 percent) are self-explanatory.

Run Expectancy Changes in DP Situations for FC and DP, 2005-09 Begin % of DP Begin Post-1B Post-2B Post-3B Weighted State Situations RE RE RE RE RE RE-CHG(92.25%) (7.37%) (0.38%) 0 100 28.32% 0.907 1.515 2.028 2.434 1.556 +0.650 0 103 2.78% 1.795 2.515 3.028 3.434 2.556 +0.762 0 120 7.15% 1.515 2.515 3.028 3.434 2.556 +1.041 0 123 2.21% 2.324 3.324 4.028 4.434 3.380 +1.056 1 100 34.21% 0.545 0.925 1.429 1.972 0.967 +0.422 1 103 6.01% 1.186 1.925 2.429 2.972 1.967 +0.781 1 120 13.91% 0.925 1.925 2.429 2.972 1.967 +1.041 1 123 5.41% 1.586 2.586 3.429 3.972 2.653 +1.067Weighted RE Change, Post Non-Out GB: +0.697 Weighted RE Change, All GB = -0.229

Applying weights to the three ground-ball outcomes (DP, FC, and non-out) gives us this final result-when a pitcher induces a ground ball in a double-play situation, on average the run expectancy will be reduced by 0.230 runs. While adding grounders helps pitchers, losing strikeouts (-0.435) hurts them almost twice as much, so trading grounders straight-up for strikeouts is a losing proposition, unless there’s also a significant reduction in walks.

Now that we know the Run Expectancy changes associated with each event, we can use them to calculate the change in RE between the ground-ball, strikeout, and walk rates that pitchers accrue in the BASE situation and the DP situation:

Total Run Expectancy Changes in DP Situations, 2005-09 % of DP Change Change Change Change Change Change Total Weighted State Sit. GB/PA BB/PA K/PA GB RE BB RE K RE Change RE Change RE0 100 28.32% +1.82 -1.55 -2.69 -0.004 -0.009 +0.010 -0.004 -0.0011 0 103 2.78% +1.66 -1.25 -3.91 -0.002 -0.007 +0.024 +0.015 +0.0004 0 120 7.15% +2.26 -1.12 -1.11 -0.005 -0.009 +0.007 -0.008 -0.0006 0 123 2.21% +1.63 -2.65 -1.78 -0.005 -0.026 +0.013 -0.018 -0.0004 1 100 34.21% +0.23 -0.78 -1.92 -0.000 -0.003 +0.006 +0.002 +0.0009 1 103 6.01% +2.23 -0.98 -3.10 -0.005 -0.004 +0.021 +0.013 +0.0008 1 120 13.91% -0.18 -0.15 -0.43 +0.000 -0.001 +0.002 +0.001 +0.0002 1 123 5.41% -0.11 -1.29 -1.66 +0.001 -0.013 +0.013 +0.001 +0.0001Total Change in Run Expectancy per PA: +0.0002

It looks as if in double-play situations, any change in approach by pitchers (and batters) winds up in a tiny net win for batters. But there are individual pitchers who do seem to realize a significant benefit when trying to get ground balls, and others whose numbers suffer:

Best Run Expectancy Changes in DP Situations, 2005-09 GB% Change Change Change Total Pitcher Change GB/PA GB/PA BB/PA BB/PA K/PA K/PA RE ChangeRamon Ortiz +5.34% 37.46% +4.96 5.92% -2.18 11.83% +0.76 -0.0270 Jeff Suppan +3.84% 40.68% +5.21 6.36% -3.32 10.36% -1.11 -0.0260 Brian Moehler -2.27% 35.98% -0.42 3.14% -3.86 12.76% +0.70 -0.0240 Jason Jennings +5.01% 38.22% +6.12 7.59% -2.94 12.30% -1.99 -0.0221 Adam Eaton +6.15% 33.59% +5.36 8.33% -1.63 13.80% +0.10 -0.0219 Scott Kazmir -2.10% 23.82% -1.76 9.47% -2.03 26.11% +3.07 -0.0209 Jon Garland +1.00% 38.87% +2.05 4.19% -2.60 11.52% -0.09 -0.0191 Jake Peavy +1.65% 29.22% +1.66 5.96% -1.95 25.84% +0.85 -0.0186 Kevin Millwood +2.45% 36.29% +2.79 5.87% -2.01 16.37% -0.02 -0.0177 Andy Pettitte +3.43% 38.43% +1.96 6.30% -0.59 19.02% +1.82 -0.0157

Some pitchers (Ortiz, Jennings, Eaton) appear here primarily due to an increased GB%, while others (Moehler, Suppan) joined the club via large walk reductions. Scott Kazmir manages to get significantly more strikeouts and fewer walks when pitching in double-play situations; I’d be interested to see if he has better control when pitching from the stretch in general.

Worst Run Expectancy Changes in DP Situations, 2005-09 GB% Change Change Change Total Pitcher Change GB/PA GB/PA BB/PA BB/PA K/PA K/PA RE ChangeBartolo Colon -4.09% 31.40% -1.88 7.99% +2.17 11.57% -5.43 +0.0403 Kevin Correia -3.96% 28.49% -2.18 11.40% +2.51 11.97% -4.58 +0.0392 Woody Williams -5.00% 26.01% -3.92 9.25% +2.67 10.12% -2.97 +0.0371 Joel Pineiro -4.79% 39.25% -2.07 7.00% +0.65 8.19% -4.55 +0.0282 Kyle Davies +1.50% 31.48% +3.95 11.99% +0.46 8.99% -7.68 +0.0270 Matt Morris -2.63% 37.80% +0.08 7.34% +0.49 7.34% -5.58 +0.0269 John Danks -6.94% 27.82% -4.15 9.19% +0.60 15.75% -3.09 +0.0264 Sidney Ponson +0.98% 43.56% +1.79 10.52% +2.14 7.73% -4.02 +0.0256 Wandy Rodriguez -1.34% 31.45% -0.50 10.60% +1.90 15.21% -3.04 +0.0251 Chad Gaudin -4.00% 30.00% -2.32 12.33% +1.25 16.98% -2.34 +0.0226

Increased walks and reduced strikeouts hurt these pitchers far more than their reduced ground-ball rate. This explains the absence of Brian Bannister, whose incredible 11.96 percent reduction in GB% dragged him to the bottom of the list in last week’s article. However, using Run Expectancy to compare shows that Bannister overcomes this by reducing his walks and increasing his strikeouts. One loyal reader suggested that the crafty and self-aware Banny may be fooling hitters by pitching them high in the zone during situations when they might expect the ball to be down. I don’t know if that’s what PITCHf/x would show, but I’d be tickled if it were the case.

Thanks to all for the input that lead to this improved comparison method. Now that we’ve walked through the calculations, next week I’ll look at the R3 state and a few other details.