Should One Strike Make This Much Difference?

Jose Bautista takes as many 3-0 pitches as anyone in baseball. (via James G)

Jose Bautista takes as many 3-0 pitches as anyone in baseball. (via James G)

There’s no one perfect way to approach a plate appearance. There’s no magic formula to decode and apply. A plate appearance is a complicated and interdependent interaction without a clear solution. Think of all of the different variables. The pitcher decides on the pitch type and location, then has to execute it. The batter has to react to that decision and then execute his reaction. The catcher influences things. So does the umpire. There are base runners, the inning, the score, and the weather. And then there are more pitches if the plate appearance doesn’t end on the first one.

A single plate appearance itself is a scene in a much larger act in a much larger drama, but it’s a fundamental building block. There are hundreds of thousands of them every season and more than a million per decade. Some end in home runs and some end in three-pitch strikeouts. Baseball is difficult and the sheer number of opportunities means we’re bound to observe some unusual things. At any one moment, a pitcher could throw a foolish pitch or a batter could watch a perfect strike on 0-2 and no one would decide to study it.

Individual moments of confusion happen all the time in baseball. You’d be surprised if they didn’t. Yet over the course of hundreds of thousands of plate appearances, you would expect the madness to wash out. Sometimes batters whiff on meatballs, but they usually crush them. Despite the irrationality of a lot of baseball discourse, the game itself is painfully rational. Given a big enough sample, everything makes sense.

Or, at least, it usually makes sense. A few months ago, fellow Hardball Times writer Jon Roegele produced a tweet with the following table.

Roegele was particularly interested in the passivity of hitters on the first pitch of the plate appearance. He wondered if batters were being unreasonably cautious on the first offering, but something else caught my eye. Allow me to isolate it for you:

Count Avg. Distance From Center of Zone (ft) Swing% Fastball %
3-0 0.938  7.6% 81.7%
3-1 0.946 55.2% 70.8%

From 2007 to 2014, batters swung at 55.2 percent of 3-1 pitches. Those pitches were, on average, 11.4 inches from the center of the strike zone. Seven in 10 were fastballs. Presumably, you would think that as the probability of a pitch being near the center of the zone increases and the probability of a fastball increases (all else equal), batters would want to swing more often. That seems like a pretty safe bet, acknowledging that certain batters have location and pitch type preferences that are unusual.

We would also imagine that batters would be more likely to swing when they’re behind in the count as opposed to ahead in the count, all else equal. If they get a pitch they don’t like much, but think it’s probably a strike, swinging on 0-2 makes more sense than on 2-0 because of what happens if you take the pitch. Again, there are always exceptions, but as a general rule, that makes sense. So when you think about the difference between a 3-1 pitch and a 3-0 pitch, you might expect two countervailing forces. A 3-0 pitch is more likely to be a fastball and it’s more likely to be closer to the center of the zone, but there’s also one fewer strike.

Without knowing anything else, it might be hard to come up with a prediction about how batters will behave in one compared to the other, but if you just had to make a general prediction, you’d expect the batters would respond differently, but not dramatically differently. Except: In a 3-0 count, batters swing just 7.6 percent of the time compared to 55.2 percent when the count is 3-1. They see more fastballs and those fastballs are more likely to be in the strike zone, but they swing much, much less often.

As I said earlier, many factors influence a single pitch and plate appearance. We shouldn’t jump to conclusions, but on the face of it, this seems like a very irrational set of behaviors. I’m not the first person to wonder if batters should swing more often on 3-0 (examples here, here, here, and here) and there’s been work done on the value of strikes and balls by count, but there’s something very unsatisfying about the observed swing rate reality.

Let’s start with a basic comparison using 2-0 pitches and 2-1 pitches. Pitchers throw 2-0 pitches about half an inch closer to the center of the plate, on average, than 2-1 pitches. Fastball percentage increases by 12 percentage points from 2-1 to 2-0. Swing rate drops about 18 percentage points. Clearly, the extra strike matters a lot to hitters. Even though they are likely to get a better pitch to hit on 2-0, they are less likely to swing, by a decent margin. That’s not a confusing outcome, but when you compare to the difference between 3-0 and 3-1, things look strange:

3-0 / 3-1 COUNTS VS. 2-0 / 2-1 COUNTS
Count Avg. Distance From Center of Zone (ft) Swing% Fastball %
3-0 0.938  7.6% 81.7%
3-1 0.946 55.2% 70.8%
2-0 0.979 41.0% 67.3%
2-1 1.014 59.2% 55.8%

The impact of the extra strike influences the pitcher pretty predictably when it comes to the average distance from the center of the zone. Fastball percentage is also relatively predictable, except for the huge spike when you jump from 3-1 to 3-0. The pitcher’s response to the count, on average, is easy to understand. As pitchers get further behind, essentially, they throw more fastballs closer to the center of the plate.

If you rank the batter’s swing percentages without the actual rates, it doesn’t look unusual. Clearly batters get more aggressive with two strikes and/or as the pitcher throws more pitches. It’s odd that 0-2 is below 1-2, perhaps, but we can also imagine hitters expecting waste pitches more in those situations. It’s not perfect, but the order isn’t so out of whack that you can’t explain it with some basic psychology. Batters don’t want to go down looking, but also try to follow the pitchers’ behavior when they can.

The oddity is the magnitude of the differences, as Roegele noted on 0-0 pitches, and as I’ve noted on 3-0 pitches. The drop from 1-0 to 2-0 in swing percentage is less than one percentage point. The drop from 2-0 to 3-0 is more than 33 percentage points. Something else is governing this decision. The 3-0 pitch has been removed from the normal realm of baseball operations. What’s going on?

There are a few questions worth answering. The first concerns the intentional walk. Most intentional walks start 3-0, but not all 3-0 pitches happen within intentional walks. Let’s remove intentional walks and see what we have, using 2014 data from Baseball Savant, as we’ll be diving in further on 2014:

Count 2014 Swing Rate
3-0 8.4%
3-0 w/o IBB 9.4%
3-1 56.0%

So, naturally, things change, but they don’t change enough to really knock the inquiries off course. The other obvious factor is the idea of the 3-0 green light. Teams generally instruct hitters not to swing on 3-0 pitches unless perhaps it is the exact pitch they’re looking for or if the batter is one of the select few who gets “turned loose” with a green light. There’s obviously no way to know who had green lights when, but we can compare the population of 3-0 swinging hitters to the average population.

It’s not a perfect way to measure it, because the green light is a “may swing,” not “shall swing” situation. To give you an idea, weighting by the number of times a player swung 3-0, batters who swung 3-0 in 2014 hit for a .330 wOBA over the entire season while the league average position player hit for a .315 wOBA. Over a full season, the type of hitter who swings 3-0 might produce six to eight more batting runs than the average player. It’s a difference, but it’s not like the nearly 700 swings at 3-0 pitches were taken by Jose Bautista and Miguel Cabrera exclusively.

Now that we have the two primary complications taken care of, let’s move to the difference in outcomes. What happens when a batter swings 3-0 compared to 3-1. What’s the difference in outcome?

The problem here is that it’s not exactly that simple. It never is. Roughly speaking, about 55 percent of 3-0 pitches are in the strike zone and among the pitches at which batters swing, about 80 percent are in the zone. If you take every single 3-0 pitch, you will walk about 45 percent of the time on that very pitch and you will move to a 3-1 count 55 percent of the time. Taking a context-neutral approach, that walk is worth roughly 0.3 runs. Being in a 3-1 count is worth roughly 0.13 runs, as batters hit for about a .480 wOBA after 3-1 counts in 2014.

So if a batter takes every 3-0 pitch, assuming the other factors wash out, the expected value is 0.21 runs. If we round up a bit and say batters swing 10 percent of the time at 3-0 pitches, we can work out another expected value, this time of the observed results from last year.

Batters put the ball in play about 300 times on 3-0 pitches in 2014, and they posted roughly a .420 wOBA when doing so. That means they put the ball in play on about 45 percent of their swings. If we break this down, that means that 4.5 percent of the time their outcome is the .420 wOBA, 55 percent of the time it’s a 3-1 count, and 40.5 percent of the time it’s 0.3 runs (walk). Mix that all together and you have an expected value of about .19 runs. Another way to say this is that batters produced roughly a .550 wOBA after getting into a 3-0 count last year.

In other words, you might make the case that, on average, a batter should never swing on 3-0. After all, never swinging gave us a higher expected value than the 10 percent of the time we have them taking a hack. Except this ignores a really important angle that’s difficult to explore. The pitches and batters aren’t all created equal. We know there are a ton of fastballs and that they’re all closer to the center of the zone than the average pitch, but the 3-0 green light/red light is a huge problem for this type of analysis.

And it’s a theoretical problem that’s hard to solve. There’s virtually no other situation where batters are instructed to take with such frequency. Imagine there are 100 random 3-0 counts in front of you. Let’s say managers give the green light about 20 percent of the time and batters swing about half the time once they get the green light. There’s a huge problem in any analysis stemming from this data-generating process. We can only observe what happens on the 3-0 swings in which the manager has given the green light and the batter has chosen to swing, which means we don’t know how hitters would do if they were allowed to make the decision for themselves.

Do 3-0 green lights occur at random? Do they occur against certain pitchers or in certain situations? Do batters respond to them in a predictable manner or is it idiosyncratic? Unfortunately, no matter the sample size, we can’t answer these questions because we don’t know when the green lights occurred, which is obviously rather frustrating.

It seems like swinging at 8-10 percent of 3-0 pitches isn’t enough. It seems foolish to let such a large number of hittable pitches fly past, but in reality, it appears as if hitters are doing a decent job given that the expected run value of swinging more is lower than not swinging at all. But it’s hard to look past the massive difference between the 3-0 and 3-1 swing rates and feel okay about that answer.

Which is why the answer to this puzzle, this irrationality at which we began, might be hidden in plain sight. What if batters are swinging too much in 3-1 counts?

Using the same methodology as before, we find that taking every 3-1 pitch results in an expected run value of 0.15 and the current model of swinging at about 55 percent of 3-1 pitches yields an expected run value of 0.13. It’s more complicated than this. It always is. But perhaps the argument could be made that the swing rate in 3-1 counts is too high. We are right to notice the large gap between 3-0 and 3-1, but the oddity might truly be on the side of the 3-1 count.

We have to recognize that these are small differences and that the pitcher-batter interaction is not a static, league average interaction very often.

There is something fundamentally different about 3-0 and 3-1 counts compared to all other counts. If you take a ball, you’re guaranteed to walk. That’s true in 3-2 counts, but taking a strike is an automatic out, which changes the game a bit. The value of taking a ball in a 3-0 or 3-1 count makes swinging at those pitches much less valuable than in most other counts. It might be different if pitchers could fire 90-95 percent strikes in these counts, but they do not.

I do want to note that this is more like the beginning of a theory than a strong conclusion. There are all sorts of variables that influence the results and you can’t look past the green light/red light question and the potential changes that could occur if batters started taking far more 3-1 pitches. But we started by knowing the swing rates in each count, and we have a pretty strong suspicion that 3-0 counts and 3-1 counts shouldn’t be as different from one another as they are.

Given that there doesn’t seem to be much obvious value in swinging more in 3-0 counts, it does make sense that swinging less in 3-1 counts could solve the puzzle. Honestly, I began expecting to suggest managers give the green light far more often in 3-0 counts, but I’m left wondering if they shouldn’t be giving the red light on 3-1 counts much more frequently.

It comes down to this. With three balls and fewer than two strikes, putting a ball in play has a much lower value than a walk, even when facing a relatively predictable pitch. The positive outcome of taking a pitch is very high and the negative outcome is relatively small. A swing and miss or foul ball provides the same negative outcome as the take, but the positive value that occurs when the ball is put in play is much lower than the value of the walk. If pitchers could hit the zone more frequently with three balls, the game would be different. But they don’t, which means hitters are right to be cautious in 3-0 counts.

Somehow, the lesson hasn’t made its way into 3-1 counts. It’s very likely psychological and based on tradition. No one wants to make an out on a 3-0 count, so batters are correctly patient. When it’s 3-1, the batter is more comfortable with the risk of the swing, but that is perhaps not the right strategy. As I said earlier, there are lots of potential complications, but it’s worth exploring further. Fewer balls in play might not be popular with a lot of fans, but the 3-1 red light might be a winning strategy.

Neil Weinberg is the Site Educator at FanGraphs and can be found writing enthusiastically about the Detroit Tigers at New English D. Follow and interact with him on Twitter @NeilWeinberg44.
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8 years ago

This article makes my blood boil. As a former college player the most selfish thing you can do for your team is swing 3-0. Granted there are some circumstances where you might do it it is not something that should be done more often like the article states. For once, if you get to a 3-0 count it means the pitcher is having trouble locating his pitches, and while there is a high chance the next pitch will be a strike (the pitcher does not want to walk you) it might not be the strike you are looking for. Also, getting to 3-1 by taking a strike is not a bad strategy because if the pitcher is struggling to find the zone the next pitch could very well be a ball. Another factor is that by taking a pitch 3-0 you make the pitcher was more pitches, if this is against a starter it is a good strategy to get his pitch count up. Sure you can swing 3-0 and pop up to 2B or you can take one pitch and that could turn into a 10 pitch at bat. Lastly, game theory. MLB is so advanced in this day of age that if a team knows you are swinging 3-0 they might throw a curveball or a change-up and get an easy out (because you the hitter is expecting a fastball). On the other hand taking a pitch 3-1 is even worse when game theory applies. My recommendation to all writers and readers alike, if you have not played the game please join an adult league somewhere, it will help you understand why things are the way they are.

J. Cross
8 years ago
Reply to  baseballfan123

“This article makes my blood boil. As a former college player the most selfish thing you can do for your team is swing 3-0.”

Ah, yes, as a former college player you’re clearly the leading expert. Did you even read the article? Your comment suggest that you either didn’t read it or didn’t take the time to try to understand it.

8 years ago
Reply to  baseballfan123

Agreed with Jared. “Swinging 3-0 is the most selfish thing you can do.”

The ironic thing is that it is EXACTLY that mindset by “actual players” that causes them to act sub-optimally. Most sub-optimal play in baseball is caused by “cognitive errors” or by improper training that occurs at a young age. Such as, “If you swing at 3-0 and make out, the team and manager is pissed at you,” or, “You must protect the plate with 2 strikes, even at a 3-2 count, and no one likes to be called out on strikes (if you DON’T get called out on strikes a significant % of the time on 3-2 counts, you are probably swinging too often).”

8 years ago
Reply to  baseballfan123

I hope you are aware that he reached the exact opposite conclusion that you are arguing against…

Further, you reference game theory but do not work through the logic / payoffs of the analysis. I would love an additional post with your findings.

As far as the incredibly insulting “recommendation” at the end of your post, I might recommend to YOU that if you have not gotten a job at a website to regularly publish insightful baseball analytics that you do so as it will help you understand how to effectively think through problems, arrive at interesting conclusions and communicate these conclusions in a reasonable manner.

8 years ago
Reply to  baseballfan123

You clearly didn’t finish reading the article


J. Cross
8 years ago

Good stuff, here and like you say, I think this raises lots of questions.

“Roughly speaking, about 55 percent of 3-0 pitches are in the strike zone and among the pitches at which batters swing, about 80 percent are in the zone. ”

Is this based on a generic zone? Since the strike zone is larger on 3-0 and 3-1 counts than its typical size, I’m wondering if this analysis somewhat overrates the value of the “always taking” strategy on 3-0 and 3-1 counts. It would also be interesting to see whether hitters who are known to employ “always take” see a higher percentage of strikes.

8 years ago

Great article Neil. I hadn’t thought about the big gap in swing rate between 3-0 and 3-1 counts this way, especially the possibility that batters might be swinging a little too often on 3-1 counts.

I think you’ve laid out a great case for someone to do some analysis on this using the delta method, to normalize the comparison between the two counts.

8 years ago

Good job Neil.

I never thought about the 3-1 count. I think it is very possible that batters swings too often. However…

The behavior on counts is extremely context dependent. To be honest, without looking at that I think you’re going to run into a little bit of a brick wall, which you did. The four most important contexts, in no particular order, are:

1) Score late in a game. If you are down and not the tying or go-ahead run, base runners are important and it is probably correct to always take at 3-0 and often at 3-1.

2) The power of the batter. The less power the batter, the less he should swing, as getting a hit is not worth much more than a walk. In order to want to swing at 3-0 (and again, to a lesser extent at 3-1), you MUST be able to generate power for an extra base hit or HR.

3) The pitch recognition skills of the batter. If you are going to swing at 3-0, you MUST be able to swing at mostly strikes.

4) This might be the most important – the base runners and outs. Looking at generic run values is not nearly enough. You must look at context specific run values. For example, with runners on base and first base open (and especially with 1 or 2 outs), the value of the walk is very low, so you should be much more likely to swing. Another example is runner on third and less than 2 out. Other than bases loaded, the value of just putting the ball in play is so high that taking a decent pitch at 3-0 is probably a terrible strategy.

Basically, wrt baserunners and outs (and score/inning), the key to green light/red light at a 3-0 count is the relative difference between and frequencies of the walk and a ball in play.

In fact, that is ALWAYS the case, and that dictates whether to auto take or not. That incorporates all the factors above. The more power the batter has, the higher the value of the ball in play. Same with his pitch recognition skills.

For example, in the Texas, San Diego game last night, in the 4th inning it was 0-0 with a runner on second and 1 out. The count was 3-0 on Solarte. He was taking all the way. That is a terrible play. How do we know that?

Well, the generic value of the walk is around .31 runs and the single is .47 runs. Not much difference. But with a runner on second and 1 out? The walk is worth only .22 and the single .82. Now the single is worth almost 4 times the walk! Of course you don’t take! And in a 0-0 game, the differences in win value are even greater.

Neil, if you ever want to take the time to expand this analysis, it would be fascinating to see the swing rates by the difference between the win value (run value early in a game is fine) of a walk and a ball in play for each specific batter. We should see very different swing rates and we should see increasing swing rates as the difference in value increases.

8 years ago
Reply to  MGL

Insightful reply and I hope this continues!

A few (hopefully not naive) questions:

1. If Neil’s starting premise was that 3-0 and 3-1 swing rates should be similar, wouldn’t a lot of your context concerns drop away? Said differently, wouldn’t most of your context concerns when applied to 3-0 and 3-1 counts result in similar strategies? if that’s the case, you are still left with the answer of 3-0 counts result in too few swings or 3-1 in too many.

2. Wouldn’t your #1 context (scoring late) be offset by two conditions: 1) it impacts all counts, just these more so due to the probability of a walk outcome and 2) you are just as likely to add much less WPA late in a game (wide score gap) and therefore the value of a walk in these contexts are LESS than early in the game? Doesn’t this basically all wash out?

3. Your #3 context (pitch recognition skill) seems like less of a context and more of a… something else. I don’t know the data, but I could see a scenario whereby for players WORSE at pitch recognition the lower variance in pitch distance from the center could result in a much GREATER boost in expected value given that their specific weakness is being more dampened than the average player?

If these are dumb / irrelevant, I apologize!

8 years ago
Reply to  ReuschelCakes

At 3-0 and 3-1 counts, the approaches should be similar, but certainly not exactly the same. I don’t think that the swing rates should be THAT close to one another. Probably closer than they are, but exactly how close, I don’t know. A strike at a 3-0 count doesn’t change the run/win expectancy as much as at 3-1. 3-0 to 3-1 loses around .129 on the average, and 3-1 to 3-2, around .153. That is a small but important distinction.

I don’t understand your next question/comment about my context #1. Late in a game when you are down a few runs, a walk is worth almost as much as a hit or even a HR, so there is no need to swing at a 3-0 pitch. You are just trying to get on base. The reason to swing at 3-0 is when a hit or batted ball is worth a lot more than a walk.

#3 can be explained with this example. Let’s say that the pitcher throws 20% strikes and 80% balls. One batter has a perfect eye and will only swing at all strikes and never at the balls. Would you want him taking or not taking? Batter #2 has a terrible eye and swings at everything. Would you want him taking or not?

8 years ago
Reply to  ReuschelCakes

My comment on your context #1 was pointing out that it is just as likely that late in a game the opposite is true — 1 run games a HR is worth much more and in 10-run games neither are worth that much. With Neil’s data picking up both of these contexts together, they likely offset each other in some way.

On the hitters’ eye… it’s hard to think through that example because if a pitcher actually threw 80% balls your expected walk rate would be 90% if you just stood there. You’d need a very high BABIP to counteract that! If you use a more likely ratio of balls/strikes I was suggesting that a) batters with comparable skills and worse plate discipline probably make up for that in quality of contact or power; and b) if we know that these pitches are much more likely to be strikes (and closer to the center of the plate) than others, we are mitigating on some level our “bad eye” batter’s weakness. Meaning that our odds of a hit go way up.

8 years ago

Neil, when you found that just taking a 3-0 or even 3-1 pitch is worth around the same or even more than hen they swung at it, using the generic run values of the various events, those are deceptive numbers.

Swinging occurs disproportionately when the value of the hit and batted ball is much higher than the walk and vice versa. So you would have to take into consideration the bases/outs state and use RE24 values not generic run values of the various events. If you do that, I guarantee that you will find that when batters swing at 3-0 they generate a lot more runs than if they just took all the way.

8 years ago

Regarding 0-0, I assume batters want one pitch to pick up the release point. That said, what’s the average expected run value of BIPs on 0-0?