April 21, 2015

Baseball Therapy

Should They Pitch to the Eighth Hitter?

by Russell A. Carleton

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Last week, we talked about National League strategy. Because the Senior Circuit still hasn’t figured out the whole DH thing, teams have to ask questions like where should the pitcher bat in the lineup? The gambit of hitting him in the eighth spot, a strategy that’s been tried on and off, actually doesn’t end up helping a team. All the advantages that you get from having a “second leadoff hitter” are cancelled out by the occasions when you have to either let a pitcher hit in a key situation too early or sacrifice him for a pinch-hitter.

This week, there’s another question to ponder. It’s a close game, and there are runners in scoring position, but first base is open. The no. 8 hitter is strolling to the plate. If you wanted to, you could politely let him take first base free of charge and take your chances with the pitcher behind him. Should you?

Warning! Gory Mathematical Details Ahead!

For now, we’re going to assume that as the eighth batter walks to the plate, there is a runner at third (and third only) and two are out. At the time that the manager makes this decision (walk the eighth guy or pitch to him) he has no knowledge of what is about to happen, so he has to base his decision on some reasonable probability estimates. It’s possible that he walks the eighth-spot guy, pitches to the pitcher, and watches the pitcher hit the only home run of his career. It’s possible that the eighth-spot guy strikes out. Sometimes you do everything right and it doesn’t work, but the choice is between first and third, two outs with the pitcher hitting or third only with the eight-hole guy hitting.

I used data from 2010-2014, and looked at how eighth hitters hit in the sixth inning or earlier, two outs, a runner in scoring position, and the game within three runs either way. (I also made sure that the pitcher’s spot hadn’t been previously double-switched out.) In these situations, the eighth hitter was intentionally walked 36.8 percent of the time. When he was pitched to (taking away those IBBs), he walked 11.8 percent of the time, which is a really high number. In similar situations, but where the bases are empty, the eight-spot hitter hitting in front of the pitcher walks a mere 6.9 percent of the time. We can look at that and say “Ah… the unintentional-intentional walk” where pitchers nibble and try to get the hitter to chase a bad pitch, but if he walks, so what. We were thinking of doing that anyway. Just to double check, I looked to see whether hitters in this specific situation were more likely to walk than their walk rate (and the pitcher’s walks allowed rate) would indicate. (Gory details: log-odds ratio method, binary logistic regression) The answer, which will shock no one, is yes. For now, we’re going to leave those unintentional-intentional walks in there, since it will likely be part of the pitcher’s strategy anyway if the manager decides that they are pitching to the eight-spot guy.

First let’s look at what happens when the eighth hole hitter hits in this sort of situation. (We’ll use actual data outcome data from this very situation. It pretty much mirrors the composite no. 8 hitter line over time, with the exception of the extra walks. Expected runs on the play is simply how many runs we expect to score on the play involving the eighth hitter. For example, if he makes an out, no runs will score. If he walks, no runs will score, but if he singles, one run will score. Run expectancy afterward is sometimes just a natural corollary (if he makes the third out, then there is no further run expectancy for this inning). In other cases (the eighth hitter doubles, now the pitcher is up with a runner at second and two out), I can’t just use the standard run expectancy matrix, so I used the results of similar situations (the run expectancy from other situations in which a pitcher hit with two outs and a runner at second, again, from 2010-2014). For errors, I put the batter on first and let the runner on third score (effectively a single).

Outcome	Percentage of time it happens	Expected runs on this play * percentage	Run expectancy after (this inning) * percentage
Out in play or strikeout	66.0%	0	0
Walk or HBP	12.4%	0	0.028
Single or error	15.3%	0.153	0.016
Double	4.8%	0.048	0.009
Triple	0.4%	0.004	0.001
Home run	1.0%	0.020	0.004
Total	100%	0.225	0.058

If the manager chooses to pitch to the eight-spot hitter in this two-out, runner on third situation, we can expect something on the order of 0.283 runs over the rest of this inning.

Now, let’s take a look at what pitchers do in these sorts of situations. Assuming a runner on first (the eighth batter who was intentionally walked) and a runner on third. Since there are two outs, I’m assuming an extra base of advancement on a single or double from the runner on first, for the sake of simplicity. If the pitcher does something other than make the third out, I’m going to assume that the rest of the inning run expectancy is going to be in line with the overall 2014 run expectancy chart.

Outcome	Percentage of time it happens	Expected runs on this play * percentage	Run expectancy after (this inning) * percentage
Out in play or strikeout	83.9%	0	0
Walk or HBP	3.8%	0	0.024
Single or error	9.6%	0.096	0.042
Double	2.0%	0.004	0.006
Triple	0.2%	0.004	0.001
Home run	0.5%	0.015	0.0004
Total	100.0%	0.119	0.074

So, if the manager elects to walk the eighth spot hitter and face the pitcher instead, he can expect 0.193 runs in the rest of the inning. Compare that to the .283 runs expected from pitching to the eighth hitter. So clearly a win for walking the eighth hitter, right? Well, not so fast. If a manager pitches to the number eight hitter and he makes an out, then the next inning, the pitcher leads off. If the manager walks the eighth spot hitter, even if the pitcher makes an out, the next inning will start with the leadoff hitter at bat. Not surprisingly, innings that start off with the leadoff hitter batting yielded .556 runs from 2010-2014, while those starting with the pitcher at bat yielded only .415 runs, a difference of .14 runs. But in fact, there could be more. You can make the case that by issuing a walk to the eighth spot hitter, you’re actually giving an extra plate appearance to another hitter later in the game, so there might be knock on effects later. Let’s look.

Here’s a side-by-side comparison of how many runs a team scores over the rest of the game (NL rules games only), as a function of whether the pitcher or the leadoff hitter is the first batter in that inning.

Inning	Pitcher Leads Off	Leadoff Hitter Leads Off	Difference
2nd	3.66	4.19	0.54
3rd	3.23	3.37	0.14
4th	2.47	2.68	0.21
5th	2.19	2.42	0.23
6th	1.72	1.93	0.21

By walking the eight-hole hitter and pitching to the pitcher, even if the pitcher makes an out, it guarantees that the opponent will get to start afresh next inning with the leadoff hitter (or potentially the no. 2 or no. 3 hitter) at-bat, something that is worth roughly .20 runs.

And you really only give up .09 runs fewer runs on average within the inning from walking the eighth batter. So, walking the eighth batter actually loses you .11 runs, mostly from the fact that by walking the eighth batter, you take away the possibility of forcing the other team to lead off an inning with the pitcher. But wait. If you pitch to the eighth hitter, 34 percent of the time he’s not going to make an out, so you still have some chance of incurring the .20 run penalty for “clearing” the pitcher’s spot even if you pitch to the eight-hole hitter, so that’s a .07 run punishment on average. That means that walking the eighth batter loses you .04 runs on average.

That figure, .04 runs, rests on a lot of assumptions, particularly that a team has a “normal hitting” eighth hitter and a normal hitting pitcher. It’s the sort of decision that, if you use a little more specific input, like a particularly good (comparatively) guy in the eighth spot, the mathematically correct decision could be (slightly) in favor of walking the eighth hitter. Because there’s a runner in scoring position, increasing the eighth hitter’s chances of getting a hit has a greater return than normal. It’s more likely to knock in a run, and score the .20 bonus because his hit will guarantee that the pitcher’s spot will be cleared before the end of the inning. So if you are facing someone who is a little better than an average eighth hitter, you should probably walk him.

If you put runners on second and third (remember, above we were only looking at a runner on third), the payoff tilts in favor of walking the eighth hitter by about .10 runs. Not surprisingly, in that particular situation, the eighth hitter gets walked 56.6 percent of the time (and when they pitch to him, he walks at a 15.3 percent rate!) Again, those numbers will wiggle a bit with the exact situation at hand, but more times than not, it’s going to make sense to put the batter on first via walk than give him the chance to do any damage.

The Game at Equilibrium
It’s entirely possible that most teams have run this calculation before me, although it’s worth noting that when I looked at the early 1980s ('80-'84), well before most teams were interested in running any sort of statistical analyses, rates of intentional walk in these RISP with the eighth hitter coming up in close-game scenarios were only slightly below where they are now. (In the '80s, with any runner in scoring position, two outs, and the pitcher on deck, an IBB was issued 25.5 percent of the time vs. 36.8 percent of the time today, and in the specific situation of a runner on second and third with first base open, the IBB came out 53.3 percent of the time vs. 56.6 percent of the time now.) This is a complex decision that isn’t clear cut either way, and yet baseball kinda figured it out and got it right back when the Apple IIe was the most powerful personal computer on the market. There’s a lot of implicit knowledge in the game and we need to respect that.

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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