# The Adam Dunn debate: Defining plate discipline

May 24, 2007 15 Comments

A small brag, if I the reader will humor me. A study of mine on strikeouts and walks has been published in *By The Numbers*, which is the official newsletter of SABR‘s Statistics and Analysis Committee. The study (which you can find in this PDF file published under my… umm… real name… shhhhh) is entitled “Is Walk the Opposite of Strikeout” and I argue that the answer is no. Walk and strikeout are actually more alike than similar and that the opposite of these two is “ball in play.”

My starting point is the Adam Dunn debate as to whether he is a “disciplined” hitter. Dunn is the paragon of the “three true outcomes” hitter. He’s hit at least 40 HR in the last three years, while averaging something like 170 strikeouts and 110 walks. In 2006, he had one of those three outcomes in more than half of his plate appearances. Because of the large number of walks that he draws, Dunn has been referred to as a very disciplined hitter by some (probably all those who just finished *Moneyball*), while others have called him undisciplined, for the obvious reason that he’s been flirting with 200 strikeouts over the past few years. Who’s right? Well, a lot comes down to how you define plate discipline.

The most common measure of plate discipline that I’d found is some sort of ratio between strikeouts and walks, usually K/BB. The problem, which I point out in my article is that there is more than one way to avoid striking out. A walk certainly is one, but is it necessary that players with low walk totals are undisciplined. Is it not equally disciplined to take a big fat hanging curve ball and place it in the left field stands?

To that end, I developed two new metrics based on signal detection theory while taking advantage of the pitch-by-pitch data in the Retrosheet data files. The article in *By The Numbers* goes into greater detail on how the metrics are calculated, but the basic idea behind signal detection theory is this: A batter must see whether or not the pitch is hittable (i.e., in the strike zone… more on the obvious objection to this in a minute) and then decide whether or not he should swing. He might swing at it and miss, or he might not swing and have it be a called strike. Either way he’s made a mistake and will have a strike called against him. However, from a signal detection theory standpoint, the type of mistakes he makes are telling. In fact, through looking at the two types of mistakes, plus the times that he actually hits the ball or takes a called ball, signal detection theory can generate two measures. One looks at how likely a batter is to swing, the other at how good a batter is at reading the strike zone and making good decisions. He may be good at reading the strike zone, just too anxious (or too passive) with his swings. Or, he may simply be guessing in the strike zone.

It turns out that the two measures actually correlate differently to walk and strike out rate. How good a hitter is at reading the strike zone was very correlated with his strikeout rate, but not walk rate. How likely he was to swing was more correlated with his walk rate, but not strikeout rate. Players who swung less walked more. Looks like walks and strikeouts are manifestations of two different skills.

There are a few problems. One is that players do swing at pitches in the strike zone and miss them. The other is that they will sometimes golf a hit off of their shoetops. Retrosheet data (which is free!) doesn’t give pitch locations. Eventually, I’ll learn how to mine the data from MLB’s Enhanced GameDay to my advantage on this one. But, for now, I think it’s an enhancement over the simple K/BB metric we have now.

In any case, take a look at the article, and discuss. I’d like to refine this a bit and it’s always better to have a little bit of collaboration.

And for what it’s worth, Adam Dunn finished #401 last year among all hitters with at least 100 PA. Out of 431. Perhaps you can tell which side of the debate I’m on.

PC — I’m keen to hear your thoughts about the reliabilty of the stepwise regression. Given all the issues of the technique I tend to look at all results with a heavy dose of salt …keen to hear your thoughts

By the way, enjoyed the article — an interesting way to think about plate discipline. I need to digest what you said before coming back with specific thoughts

Excellent work. True or false:

David Eckstein is a more disciplined hitter than Troy Glaus.

Back in the good ol days when they were Angels, though Glaus took far more walks my answer was Eck. The walks were a product of pitchers less willing to challenge Troy.

Last year, among qualifiying hitters (100 PA or more), Eckstein finished #125 in the league in sensitivity, while Glaus checked in at #358. Glaus had a response bias rating of .892, and Eckstein had a rating of .841, which means they should both be swinging more. If you like, Sean, give me some years and I can check your hunch against the evidence…

John, I’m a fan of stepwise in situations like this. My research question was something like “Which of you is the best predictor, seeing that you all correlate pretty well with each other and my dependent variable, and are you all one big redundant variable or are you actually six or seven semi-orthogonal ones?” I’m familiar (although not deeply) with some of the technical critiques of the stepwise algorithims and some of the parameter estimates that they yield, so I would put some salt in reading my (or any stepwise) R-squared values and coefficients. I’m much more interested in the empirically best order in which to block my variables.

Pizza,

Really nice work–there is no more controversial player among us Reds fans than Adam Dunn. Watching him play with some frequency, he does seem to make the mistake of taking a lot of pitches for strikes. I’d be interested in seeing his actual sensitivity and response bias values.

Regarding stepwise regression…my understanding is that the key issue of concern with the stepwise regression has to do with the sequence with which variables are added or removed from the regression equation.

Have you tried an all-possible subsets approach instead? Are there alternative models that are extremely close to the model chosen by the stepwise regression algorithm? If the stepwise’s “favorite” model is heads and tails better than the competing models with respect to adjusted R^2 and such, then there’s no issue. But if there are models that are extremely close in adjusted R^2 that contain different sets of variables, it might be worth reevaluating the tables on pages 7 & 8.

SAS does the all-possible subsets approach automatically in proc glm, though 7 variables is do-able by hand too.

-justin

JinAZ

I understand why PC used stepwise but my understanding is that the issues are more intractible than you state. Simply put, for many stepwise cases it can be shown that another approach gives a drastically different answer. I believe the subset approach, although better, is flawed

I’m not a huge fan ….

I’d be interested to hear why you find the subset approach flawed. It might result in an unclear “answer” if there are multiple models that are close to being equivalent in quality, but that doesn’t mean it’s not giving you the best view of your data.

I agree that stepwise (and especially forward and backward) selection is dangerous to use for datasets with a lot of correlated variables. But if the all possible subsets approach finds that one model is much better than the others, and this corresponds to what the stepwise algorithm comes up with, there wouldn’t be a problem for this analysis. -j

JinAz, a couple things. Dunn’s 2006 sensitivity rating was .48, which put him at #404 in MLB (I think I said 401 earlier… he just got worse). His response rate was .918. He doesn’t walk because he has a good eye, but because he’s reluctant to swing. Now, when he does swing and make contact, it’s a sight to behold.

I actually don’t have the capability of doing all possible subsets (short of doing it by hand). If anyone else would like to give it a whirl, I’m happy to share this (or any) of my data sets. I actually did run a few extra models (at Phil Birnbaum’s request) on that data set, but none overtook the stepwise model.

Thanks to both of you–I’ll have to look into the literature a bit more on the variable selection algorithms, as those concerns you mention are all new to me. We use all possible subset selection a lot in my day job (biologist). -j

JinAZ

Stepwise methods have more issues than just what order you select the variables. In particular:

– R sq is usually overestimated

– there is a lot more ambiguity over the interpretation of p-values

– F test and Chi square tests have the wrong distribution

– it can often given biased regression coefficients that much be shrunk

– and, ironically, it doesn’t work that well when variable correlate with each other!

Variable selection doesn’t necessarily come into it. The all subset approach wouldn’t correct for any of this.

JinAZ

Here is a link worth reading:

http://www.biostat.wustl.edu/archives/html/s-news/2000-11/msg00184.html

There are also papers out there too.

John

pc,

would you please run the numbers for morgan ensberg? he is as controversial in houston as dunn is in cincy.

thanks,

lisa

Ensberg’s a lot like Dunn, actually. Sensitivity rating is .65 (#356 in the league in 2006) and criterion was .863. He takes too many pitches and isn’t a very sensitive hitter. I should put these into spreadsheet form and post them for folks.

Hopefully this works: All 2006 hitters with more than 100 PA in 2006.

http://spreadsheets.google.com/pub?key=p7lF8U3MSyYPhcvrcQuz3ZA

Players who debuted in 2006 (or perhaps 2005) don’t have their name given on the sheet, but are listed under their Retrosheet and possibly their Lahman ID.

Ok, I’m a year late, but I’ll comment. The “obvious objection” should be that certain strikes with fewer than 2 strikes should be taken since they aren’t as hittable. Conventional wisdom would say that with 2 strikes, selectivity and bias would go up while BABIP or BPS (batting plus slugging) would go down. Apparently Dunn does not change his approach with 2 strikes. It would be interesting to see whether his selectivity and bias change.