What determines batters’ selectivity levels?

If you haven’t read my previous article “The influence of batters’ expectation on pitch perception” you might want to start there as this article is very much a continuation of that one. In that article I looked at what I believe is the influence of a batter’s expectations about the likelihood of a type of pitch being thrown on their ability to discriminate balls from strikes. We saw evidence that batters are aware of how frequently pitchers throw each type of pitch on each count and that these beliefs influence their approaches at the plate.

I’m back today to take a look at the other side of the story – selectivity. As a quick refresher, batting eye is a measure of a batter’s ability to discriminate between balls from strikes. It is maximized by a batter who swings at a lot of pitches in the strike zone and very few pitches out of the strike zone. Selectivity on the other hand is a measure of bias. It tells us whether batters are more concerned with misses (not swinging at a strike) or with false alarms (swinging at a ball). When selectivity is zero batters will make these errors at an equal rate. When it is positive the batter will swing less frequently overall and have a higher miss rate than false-alarm rate. Conversely when it is negative the batter will swing more frequently with a higher false-alarm rate and a lower miss rate. When you look at individual batters there does not seem to be much of a correlation between these two measures, though when you look at the league grouped by pitch count and pitch type there does seem to be a weak correlation between the two measures.


While this correlation is small it does make it more difficult to figure out exactly which measures are causally related to each other. Batting eye was most correlated with percentage of pitch type thrown, implying that batters take into account what type of pitch is coming and are better at judging the pitch types which are more frequent on that count. This also makes logical sense to me. We did see a break from the pattern in change-ups which is interesting and which we’ll come back to later.

Selectivity on the other hand is most correlated with percentage of strikes thrown – another link which makes logical sense. As pitchers throw more strikes it becomes beneficial for the batter to swing more often. Since there will be more opportunities to miss and less to false alarm, a batter would be smart to try to lower their miss rate at the expense of raising their false-alarm rate. They can achieve this by lowering their selectivity, which would lead to less errors overall. Below is a graph showing z-scores of percentage of pitches thrown for strikes compared to z-scores of selectivity broken down by pitch type and count. It does seem as percentage-of-strikes thrown relates closely to selectivity level.


There are, however, a small number of rather large outliers here. Looking at the data, I found a very similar phenomenon to one which we saw in the batting eye article – they all belong to one type of pitch. Here is the same graph without curveballs included.


While the lack of correlation in curveballs is puzzling, we see that there is an incredibly strong correlation for the other three pitches. I then went back to the batting eye article where change-ups do not demonstrate the expected correlation with percentage of change-ups thrown.


There is an almost perfect negative correlation between batting eye and percentage of change-ups thrown for strikes! This is puzzling and is not an adjustment which the batter would like to make. We know that batting eye on change-ups is not very heavily influenced by percentage of change-ups thrown so what is going on here? Perhaps it has something to do with the fact that change-ups are generally the slowest, straightest and easiest pitches to read? Batters might find it less important to sit on change-ups since they feel that they have more time to adjust to them. However the more they sit on the fastball the more effective the change-up becomes. Pitchers can take advantage of this fact by throwing change-ups later in the count when they are harder to read. Unfortunately I have not found a good correlation with curveball selectivity yet. Perhaps the difficulty that batters have in judging curveballs hinders their abilities to properly adjust their selectivity?

It seems to me that batters use both of these pieces of information (and probably other information as well) to adopt the approach they feel is most advantageous for that type of pitch. This could lead to batters applying different weights to their prior beliefs in order to best prepare for each count. I think this is a really interesting question, one which I don’t have an answer for yet.

I am looking forward to doing more research in this area and hearing feedback and theories from other people as well. I believe I have demonstrated that batters apply their knowledge of pitcher tendencies to alter their batting approach and that I have found a good way to measure these changes. The specifics are based on correlation and intuition but I do believe that there is strong evidence to support the conclusion. Looking at individual batters, individual pitchers, pitch sequences and other data should provide a clearer picture and an interesting insight to batters’ beliefs and approaches to hitting.

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  1. Northern Rebel said...

    You start showing these graphs, and even though I enjoy analytical baseball articles, I emmediately lose interest.

    When I looked at the title of the article, the word DUH! instantly came to mind.

    Hope tax dollars aren’t paying for this!

  2. Josh said...


    Can you point me to where you have properly defined batting eye and selectivity. We all understand what they mean in a general sense, how you describe them in this article and others, but to have a full understanding of what you are doing it would be helpful to know how they are calculated.

    For instance, there is a “Batting EYE” stat that is simply BB/K. Surely that is not what you are discussing. Is the formula Z-Swing #/O-Swing #? How do you measure selectivity? It appears to be a ratio as well. Is it Swings on Strikes/Swings on Balls ?

    Anyway, a glossary would be helpful. Thanks!

  3. Craig Glaser said...

    Sorry Josh… the best writeup so far is here: http://sabometrics.com/?p=242 which is also linked in the previous article.  I didn’t go that deep into the actual process but I’m planning to write something deeper on that end. If you are super interested you could look up Signal Detection Theory on google or wikipedia and find more of the science behind it.

    It’s tough to balance between folks who want more of the science and those who get completely turned off when any graphs are shown.

    And Northern Rebebl – I hope that not many tax dollars are being spent researching anything in baseball…

    As I said right now I’m trying to kind of establish what these measures mean.  The most interesting future questions from this article probably are regarding the weird patterns in change-ups and curveballs.

    I hope that I’m helping to show that the measures are actually showing what they should logically be showing.  I think once that happens they’ll be very interesting to some folks who want to understand the battle between pitchers and batters at a deeper level.

  4. dcs said...

    Sorry Craig…your link doesn’t answer Josh’s question. I looked at it and I’m still confused as to what the actual formulas are for your stats.

  5. Craig Glaser said...

    I hope I was clear that I had only had the time to write the theory up so far.  However, I have just written up a simple guide to the calculations of batting eye and selectivity. You can find it here


    I hope this answers your questions but if it doesn’t please feel free to contact me.  There’s also quite a lot of information on signal detection theory which you can find through wikipedia or google.

  6. Craig Glaser said...

    This link is probably not quite as interesting as the other but I think it’s pretty cool just how strong the correlation here is and that it (hopefully) demonstrates that the selectivity measure is measuring what it’s supposed to be measuring.

  7. Guy said...

    It’s great that you’ve explained the metrics.  Unfortunately, it’s not clear at all that the batting eye metric measures anything relevant to hitting.  In your example, you say it measures the “ability to judge balls from strikes” and that Scutaro and Uribe are equal on this dimension with these stats:
    MS:  Swing/strikes: 84%, Take/ball: 84%
    JU:  Swing/strikes: 98%, Take/ball: 50%

    Here are some problems you need to address:

    *The 2 hitters do not make the “right” decision with equal frequency.  With a 60-40 Str/ball ratio, Scutaro will be right 84% of the time and Uribe just 79% of the time.  Why is it better to convert these to standard deviations?  The result is to give more weight to extreme performances, like Uribe swinging at every strike.  The equal batting eye tells us that the two hitters are equally unlikely (or it would if you used the true distributions), not equally talented.  But who cares?  A .300 OBP and a .370 OBP are equally “unlikely,” but we never equate them.

    * Even worse, using the distribution gives more weight to swinging at strikes than taking balls, as your Scutaro/Uribe example illustrates.  But that’s exactly the opposite of what you want:  taking balls is, most of the time, much more valuable to the hitter than swinging at strikes. So your metric is less related to offensive talent than one that weighted the two decisions equally. 

    * As a result, I suspect that batting eye has either no correlation or a negative correlation with hitting skill.  In which case, why should we care about it?

    Selectivity clearly IS an important skill, though I’m not sure you’ve chosen the best way to measure it.  It’s worth trying to understand that in more depth.  But looking at the correlation between eye and selectivity, as you have, doesn’t seem very productive unless and until you can demonstrate that Eye measures something important, and measures it accurately.

  8. Craig Glaser said...


    There’s a few things I feel the need to point out

    1) This is not something I created.  This is a model of human perceptual ability which has been used for a long time and has a lot of research showing that it’s quite a good representation of human perceptual abilities.  I’m just applying it to a new area which I think will be extremely useful.  If you don’t think so, well, I can’t change that.

    2) It doesn’t weight swinging at strikes more than taking balls.  The reason you seem to think so is because the two batters are at very different parts of the distribution.  That is why 86-14 and 98-50 are the same batting eye measurement.  Not because of some weight being applied to one type of error vs the other.

    3) I think it has already shown to correlate quite strongly with some measures which make me believe that it is measuring what it’s supposed to.  Again I can’t control your opinion but I’ll be putting more time and effort in based on this.

    Now the one valid concern might be that the normal distribution doesn’t accurately describe the distribution of pitches.  That could in fact be why Juan Uribe comes out with such a good score and in fact any batter sitting that far out in the tails of the distribution is probably going to be overestimated.  However, I do think that any player who achieves that kind of batting eye rating would still have an above average score if they shifted their selectivity – which is actually the point here.

  9. Guy said...

    1) It may be a fine model of perceptual abilities for some purposes.  But you want us to believe it’s a good model for understanding how well hitters are distinguishing between balls and strikes, so you need to demonstrate that. Not for my satisfaction, but for anyone you want to read your stuff or use your metric.  It’s not like no one has ever looked at this issue before.  You need to show your metric have some value-added, not just appeal to authority by telling us it’s used in other fields.  The fact that Uribe and Scutaro are exactly equal in this “skill” gives us good reason to be skeptical, given that Uribe has a 3.42 K/BB ratio compared to Scutaro’s 1.27.  Why should we believe that they have an equal ability to distinguish balls from strikes?

    2) I understand exactly what you’re doing.  But at this point in the distributions, a 12-point gain in swinging at strikes is equal in value to a 36-point gain in taking balls.  And given the frequency with which hitters actually swing at strikes and balls, I think you will find this disparity holds in most cases.  Why don’t you see if batting eye correlates at the hitter level with overall swing%?  I think you will find that hitters who swing more often tend to have better “eyes.”  More generally, you need to explain why using these distributional functions is better than a more simple metric, such as percentage of correct choices made. 

    3)  I’m sure the metric correlates with something. But the question is whether it is a SKILL in baseball.  Do high batting eye hitters strike out less?  Walk more?  Hit for higher average?  Is there any evidence at all that it matters?

  10. MGL said...

    A little confusing, as you can tell from the comments, but great, great stuff!  I look forward to more work in this area.  Especially with regard to individual batters (and pitchers). This is the type of stuff that teams need to be doing in order to identify which batters (and pitchers) seem to be acting optimally, and which ones are not.

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