# Strikeouts and Pitch Counts

Back in the days when men were men, nobody worried about pitch counts. If you tried to take Ed Walsh out of a game after 100 pitches, he’d probably tell you he had at least another 200 pitches in him. Despite the current efforts of Nolan Ryan to go back ye olden days of not counting pitches, the current way of the world is that every other team does it, so we might as well pay attention to it.

These days, a pitcher is usually taken out after around 100-110 pitches, give or take a few. Often times, this means taking out a guy throwing a shutout in the 6th inning because he had reached the 100 pitch limit. There are two ways around this: letting the pitcher throw more pitches (which could potentially increase the risk of injury), or becoming more efficient (i.e., throwing fewer pitches per at bat). I’m here to talk about the latter.

The conventional wisdom goes something like this: It takes at least three pitches to strike someone out, but only one is required to get a groundball out. Therefore, a pitcher could decrease his pitch count by not attempting to strike out as many hitters as he can. That seems good enough for most people, but the astute readers of StatSpeak know that this can’t end there. A strikeout results in an out 100% of the time (ignoring the rare dropped third strike), but a ball in play results in an out only 71% of the time. That “other 29%” results in more batters coming to the plate, which results in more pitches having to be thrown to those additional batters. On one hand, we have more strikeouts leading to more pitchers per at bat, but also leading to fewer batters coming to the plate. On the other, we have more balls in play (fewer strikeouts) leading to fewer pitches per at bat, but also leading to more batters coming to the plate. Which of the effects is stronger?

Thanks to the work of Tom Tango, it has been shown that the average strikeout requires 4.8 pitches, the average walk takes 5.5 pitches, and if the plate appearance results in batter contact then it takes an average of 3.3 pitches (the data he used are all publicly available, by the way). Before you say “but so and so is different,” these numbers have been tested against extreme pitchers here. So these averages apply very well to all pitchers, whether they follow the norm, or if they are unusual cases like Randy Johnson and Brad Radke. We can use these estimates to see how an increased strikeout rate affects a pitch count.

How about a real-life test of the estimator? Joba Chamberlain has received some criticism from mainstream media-types about needing to be more efficient with his pitches, so he’s as good an example as any (and since he’s a Yankee, I know this will get on Pizza Cutter’s nerves). Joba has faced 256 batters this year, striking out 55 and walking 28. Plug those numbers into the formula (remember to subtract K’s and BB’s from the total batters faced when using the formula), and you get just under 989 pitches thrown. How many has he actually thrown this year? 984. I hope that difference of only 5 pitches helps to ease your concerns about accuracy.

Now back to the question at hand. Prorated to 9 innings, this is a fairly typical pitching line: 9 innings, 6 strikeouts, 4 walks, and one home run. If 30% of balls in pay fall in for hits, that also means that there are 10 hits allowed in those 9 innings. In that “typical” game, a pitcher is expected to throw 153.1 pitches in 9 innings. What about games that aren’t normal, like one where the pitcher racks up a ton of strikeouts?

Here’s an extreme example: Take the exact pitching line from above, but change strikeouts from 6 to 27. So the new pitching line is 9 IP, 27 strikeouts, 4 BB, 1 HR. Using the formula above, the pitcher would be expected to throw 154.9 pitches. The effect is actually smaller than that, and here’s why: If a pitcher strikes out 27 batters, would you really expect the ONLY guy to make contact to hit the ball over the fence? When a pitcher is that dominating, what are the chances that he’d give up a home run at a rate of one per 9 innings? I’d say very slim. Fewer balls in play means fewer fly balls, which in turn means fewer home runs, and fewer pitches. So the real pitch count would be lower than 154.9, but for simplicity’s sake I’m going to call it even.

Let’s look at the other extreme–a pitcher who doesn’t strike out a single batter all game. Such a pitcher would be expected to allow a little over 12 hits per game. His expected pitch count for a game that included 4 walks, no strikeouts, and 12 hits including one home run would be 151.2 pitches. The caveat above about home runs also applies here, but in the opposite direction–a pitcher who has ever batter put the ball in play on him would likely allow more than one home run per 9 innings, so he’d likely throw slightly more than 151.2 pitches.

So what did we learn from this exercise? Even in the most extreme cases, striking out lots of batters will not increase your pitch count by any noticeable effect. Even when comparing two pitchers with polar opposite strikeout tendencies, the difference comes out to fewer than four pitches per 9 innings, with the real-life effect likely being even smaller than that due to the home run issue mentioned above. Next time you hear someone saying that a pitcher needs to “pitch to contact” in order to decrease his pitch count, you’ll know that it makes no difference.

### 4 Responses to Strikeouts and Pitch Counts

1. Dave Allen says:

Great idea Dan. It got me thinking, the idea should be minimizing pitches per out. A strike out is 4.8 pitches per out. Now consider a guy who just gets balls in play. How many pitches does he need to throw to get one out, assuming .300 BABIP? He throws the first 3.3 but then there is a 30% chance he needs to throw 3.3 more, and a 30% chance he needs to throw 3.3 more and so on. So he needs to throw:
3.3 + 3.3*0.3 + 3.3*0.3^2 + …
= 3.3 *(1+ 0.3 + 0.3^2 + …)
= 3.3 / 0.7 = 4.71
So just as you said a strikeout pitcher throws just marginally more pitches per out. A strikeout takes only 0.1 more pitches per out than a BIP.

2. Dan Novick says:

I wouldn’t have thought of that on my own, but that seems to be correct.
But that difference of .1 pitches is negated by the fact that fewer balls in play means fewer home runs (and fewer pitches).
I calculated hits above as .3*BIP. If you count HR as X*BIP, then you would get more accurate numbers than what I had above after I changed the K-rate. The “X” in the previous sentence is the rate of home runs per ball in play. I don’t know what that rate is, so in the article I just said “we’ll call it even” and left it at that.