When to walk (Part 2)

Remember that in Part 1, we were trying to determine whether the actual intentional walks issued by AL managers (from 1998-2007) in the sixth inning or earlier reduced the batting team’s run expectancy for that inning as opposed to letting the batter hit away.

Our assumption was that if the run expectancy (RE) of the batting team was reduced early in the game, its win expectancy (WE) would be reduced as well, and if the run expectancy was increased after an intentional walk, the win expectancy would also increase. In other words, early in a game, we can use RE as a proxy for WE, and thus use RE to analyze what it takes for an intentional walk to be profitable for the issuing team. Later, we’ll see if that assumption is true.

Remember also that after a team issued an intentional walk with one out and runners on second and third, in the sixth inning or earlier, the batting team went on to score an average of 1.722 runs, about what you would expect with the bases loaded and a good hitter at the plate. In fact, we determined that the batter coming up after the intentional walk had a wOBA of .357, after adjusting for the fact that the pitcher has the platoon advantage more often than would be typical of an average batter/pitcher matchup.

Interestingly, if we look at the RE tables for the No. 4 and No. 5 hitters in the AL, we find that the number of runs scored with the bases loaded and one out is 1.772, and 1.634 runs, respectively, for an average of 1.703, just about exactly how many runs are scored after an intentional walk (with runners on second and third and one out). The average wOBA for the No. 4and No. 5 hitters are .362 and .347, respectively, or .355 combined, also right around the platoon adjusted wOBA of our “next batter” after the intentional walk.

So, basically, managers are not accomplishing anything special in issuing the intentional walk. They don’t seem to know anything that we don’t know about the pitcher or the next batter that reduces the expected runs scored after it. Given the overall quality of the player at bat after the intentional walk, we expect around 1.7 runs to score, and that is almost exactly how many runs did, in fact, score.

We also mentioned in Part 1 that when the manager issued the intentional walk, the pitcher was more likely to be able to induce a double-play grounder (about 6 percent) and the next batter was more DP prone than the average batter, but that is mostly because he tends to be right- handed and hit in the middle or bottom of the order (and thus is slow). In fact, the GIDP rates of batters who were intentionally walked were the same as those who were not.

Batters who were intentionally walked were also a little less strikeout prone than batters who were not walked (by around 2 percent), but their walk rate was actually higher. So K and BB rates don’t seem to be much of an issue for the deciding manager.

The only thing left to do is to compare the 1.722 runs to how many runs we think would have scored had the intentionally walked batter been allowed to hit. There are several ways to do that.

One way is to look at various RE tables and see what the run value is with runners on second and third and one out. The league average tables say that 1.487 runs should score, but that is based on a bunch of league average hitters. We know that our intentionally walked batter is a well-above-average hitter, likely with the platoon advantage, and we also know that the next batter is a very good hitter, even though he tends to not have the platoon advantage (he is a good hitter because he tends to be the No. 4, 5 or 6 hitter in the lineup, and because managers like to bunch up good hitters for “protection”).

If we look again at the average RE tables by batting order position, we see that the No. 3 batter, the best in the order, followed by the next best batter in the lineup, has an RE of 1.574 runs (with the bases loaded and one out), still significantly short of the 1.722 runs that are scored after the intentional walk. The No. 4 batter has an RE of 1.597, a little better but still short.

But, the intentionally walked batter, after adjusting for platoon advantage, is a better hitter than an average No. 3 or No. 4 batter, so we would expect that his RE, when hitting away with runners on second and third and one out, would be greater than 1.574 or 1.597.

Let’s try another way to estimate that illusive, hypothetical RE. We can plug the intentionally walked batter’s expected component numbers into a semi-Markov chain simulator and see what we come up with. I’ll skip most of the boring math, but here is what I did:

I used the intentional walked batters’ overall “career” (three-year actually) component batting line, and adjusted it for the platoon advantage he likely has. Then I converted that to an equivalent batting line given that there are runners on second and third and one out (batters and pitchers have different approaches in that situation which changes the component rates). That is the batting line for the first batter that I plugged into the sim. After that, I simply used the actual average run expectancies for the next batter after an intentional walk. Here is what I got:

1.556 runs. Well, that doesn’t seem to work either. Obviously you’d rather pitch to a guy who is going to produce 1.6 runs or so than one who we know is going to produce 1.7 runs.

Let’s see if we can get a better estimate for how many runs would score if we let our intentional walked batters swing away. To do that, we’ll take a page out of the social and medical sciences’ experimental playbook. We’ll set up sort of a controlled, randomized experiment. In one group, we’ll have our intentional walked batters being walked, and in the other group we’ll have the same batters being pitched to. Since we can’t actually set up an experiment like this (and even if we could, we’d need to run it several thousand times to get any kind of data reliability), we’ll go back over the database and we’ll match up every intentional walked batter’s plate appearance with another PA when he wasn’t intentionally walked. We’ll also check to make sure that the pool of pitchers in each group is about the same. It is a daunting task, but for you, the curious and demanding reader, it is worth it.

To be a little more specific, here is what I did:

A Hardball Times Update
Goodbye for now.

I created a list of all players who were intentional walked, and how often. For example, from 1998 to 2007, in the sixth inning or earlier, Rafael Palmeiro was intentionally walked with one out and runners on second and third eight times, Bernie Williams 12 times, and Manny Ramirez 19 times.

Then I created a list of all players who were not intentionally walked given the same base/out state, also in the sixth inning or earlier. For these players, I computed how many runs were scored on the average, when they batted, and to the end of the inning (combined, they scored 1.510 runs). So, for example, Palmeiro was not walked 35 times, and his team scored an average of 1.343 runs starting with his at-bat to the end of the inning. For Manny, it was 53, and 1.849 runs, and with Bernie at the plate, it was 26, and 1.308.

Then I simply went through the intentional walk list and computed a weighted average of the runs that were scored when these batters were not intentionally walked, weighted by the times they were actually walked. So, for our three players above, we would have 1.343 * 8 + 1.849 * 19 + 1.308 * 12, all divided by 8+19+12.

If we do that for all of our intentionally walked players, we get a grand total of 1.528 runs, which is a little lower than expected, but certainly in the same ballpark as our previous estimates. What about the pitchers on the mound? Could it be that there are better pitchers on the mound when these batters are not intentionally walked, as opposed to when the same batters are walked? Or could there be a home/road discrepancy (visiting team batters are more likely to not be walked)?

As it turns out, when an intentional walk is issued, the batting team tends to be the home team, but only by a slight amount—not enough to really affect the batting line one way or the other. Pitchers, however, tend to be a little worse (their overall three-year wOBA against) when they don’t issue the intentional walk (to the same batters who are walked in the study). The “wOBA against” for all pitchers with runners on second and third and one out when the intentional walk is not issued, was .345. The league average wOBA for all pitchers in our study years is .343. When batters were intentionally walked, the pool of pitchers on the mound had a wOBA against of .342.

So, overall, pitchers who issue the intentional walk are better than pitchers who don’t, but that is based on the overall linear weight values that go into the wOBA formula, and not the adjusted values, for the base/out state we are talking about, second and third and pme out. The component profiles of these two pools of pitchers do differ, as you might expect.

When a pitcher walks a batter with runners in that situation, he tends to be a slightly low-walk, low-strikeout, ground ball pitcher. In other words, the manager is not confident in his pitcher’s ability to strike out the batter who is being intentionally walked, yet he knows that that same pitcher has a greater than normal ability to induce the DP after the walk.

When the manager chooses to pitch to these same batters, his pitcher tends to be a higher walk and strikeout (slightly) pitcher, and a little less of a ground ball pitcher (he induces fewer GIDPs). Keep in mind that the primary reason for not issuing the walk to these same batters who at other times were issued walks was the score of the game. Even though I didn’t control for score, my guess would be that if we looked only at the times when the score indicated that an intentional walk might be warranted, but the manager chose instead to pitch to the batter, we would find greater differences in the profiles of the two groups of pitchers.

So, all things considered, the pool of pitchers was not a whole lot different whether the intentional walk was issued or not. Here is the collective “batting line against” of the pool of pitchers when batters were walked, and that of the pool of pitchers when those same batters were not walked, all per 500 PA:

            s       d       t       hr      bb+hp   so      GIDP
IBB         82.1    24.7    2.28      14    42.5    79.3    12.1
No-IBB        81    24.2     2.3    14.4    45.6    80.2    11.4

So, I think that the 1.528 runs is a reasonable estimate for what our intentionally walked hitters would have produced had they been pitched to.

That means we are still stuck with anywhere from 1.5 to 1.6 expected runs when we pitch to our intentionally walked batters, as opposed to 1.722 runs, which were actually scored after the intentional walk. That’s a .1 to .2 run difference, multiplied by 508 times in 10 years, which is a “waste” of 50-100 runs (we’ll call it 75), or .5 runs per year per team.

Now, since most intentional walks tend to be issued in somewhat higher leverage situations (I think), even in the early and middle innings, that .5 runs might be the equivalent of .6 or so, still not much to get excited about, I must confess. But, as our friend Rob Neyer likes to occasionally remind us, “Why do something that is clearly wrong?”

I’ll add to that, “Every little bit helps, especially when this is just one of dozens of strategy decisions.” At the end of the year, the difference between lots of right and wrong decisions may add up to a win or more.

Finally, let’s look briefly at WE rather than RE, in the sixth or earlier innings. As we showed you in Part 1, these walks almost always occurred when the batting team was ahead (68 percent), or the game was tied (23 percent).

First, let’s see what the run scoring distribution looks like in an average second and third, one out situation, and an average bases loaded, one out situation, in a 5.0 rpg environment:

Second and third, one out

Runs            0       1       2       3       4     5+
Frequency   30.2%    28.5    22.4     9.9     5.3     3.7

Bases loaded, one out

Runs            0       1       2       3       4     5+
Frequency   31.8%    25.3    15.5    10.7     9.7       7

As you can see, the chances of the batting team not scoring goes up, but only a little. If managers think that loading the bases is a ticket to getting out of the inning unscathed, they are clearly mistaken. Now, obviously, if the batter being pitched to with the bases juiced is particularly strikeout or double play prone, the gap will be larger. And of course the larger the difference in the overall quality between the batter being walked and the one being pitched to, including platoon advantage, the larger the gap as well.

The biggest difference in the two distributions above, interestingly, is the chance of scoring exactly two runs, which is significantly reduced with the bases loaded. Also, you increase the chance of your opponent scoring exactly three runs by less than 1 percent by putting that third runner on base. Of course, you increase his chances of scoring three or more runs by almost 9 percent. So maybe, walking the bases loaded is a good thing when your team is winning by exactly one or two runs?

If we look at the WE charts, we see that if you are winning by two runs in the bottom of the fifth inning, and you walk the bases loaded (since we are using standard WE charts, we are assuming that these are all average batters, given the base/out situation), you decrease your chances of winning the game by 2.7 percent, which is a lot. Up one run, and you reduce your chances of winning by 1.9 percent, a little better, but still a lot. If you are down one or two runs, however, and you walk the bases loaded with one out, you reduce your chances of winning by .8 and .6 percent, respectively. So, no, it does not appear to be a good idea to issue the intentional walk when you are ahead.

What about with the score tied? You lose 1.4 percent in win expectancy after the walk. Better than with a lead, but not nearly as good as when you are down.

Of course, it makes sense that when you are losing, especially as the game goes on, putting on extra baserunners is not going to hurt you much. Imagine you are losing by 10 runs in the eighth inning. You could intentionally walk two or three batters in a row, and it won’t much change your win expectancy, which is going to be less than 1 percent no matter how many runners are on base.

So, while adding a baserunner when you are losing, especially when you are losing by more than one or two runs, doesn’t hurt you much, it isn’t going to help much either, even if the batter you walk is very good as compared to the next batter, or the next batter is particularly strikeout or GIDP prone.

If we look at these same WE charts, as we would expect, the further along in the game, the less the cost of an intentional walk to load the bases with one out. In the top of the first and the game tied, you give up 1.6 percent in WE. In the bottom of the sixth, and the game tied, you give up only 1.1 percent (still quite a large number for one strategic decision). If you are already down two runs in the top of the first, and you issue an intentional walk (to a random batter—since we are still using the standard WE tables), you lose 1.0 percent in WE. Bottom of the sixth, same situation, and you lose only .4 percent.

So while it is conceivable that even in the sixth or earlier, an intentional walk with runners on second and third and one out, might increase your WE, given the ideal batter and on-deck batter, it seems unlikely, given the fact that we just don’t see much of a hitting reduction, if any, after the intentional walk, as compared to what we think would happen if the walked batter were allowed to hit away.

My recommendation to any manager would simply be to never worry about walking anyone intentionally, at least in the early and middle innings. Pitch to everyone. One, except perhaps in rare, ideal situations, you are probably reducing your team’s chances of winning. Two, it is not worth the time and effort, and perhaps a little stomach acid and a few extra gray hairs worrying about it.

On the other hand, a manager knows that he will get crucified by fans and in the press, and perhaps even in his own organization, if he doesn’t walk an opposing team’s elite batter, the game is on the line, and he ends up getting beaten (you know the old, and silly, axiom, “Never let the other team’s star hitter beat you”).

Usually, if he issues the expected walk, he is on safe territory (from criticism), whether his team ends up winning or losing. So maybe it’s not worth the grief that might ensue. His call, I guess. Now, if managers want to make protection of their derrieres part of their decision-making process, it’s fine by me. I only wish that they would do it using the right information in the first place, so as to make an informed choice.

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