THE BOOK--Playing The Percentages In Baseball

May need to widen the net to all #9 batters faced, or all batters faced with OPS < .700 or something.  How many times do you think Maddux has fallen behind a pitcher 3-0 in his career?  I’m going to put the over/under at 30… and he’s a pitcher who’s pitched entirely in the NL and longer than nearly anybody in the last few decades.

Yes, I looked at this a year or two ago, figuring the same thing - that this would be the limit of a pitcher’s control.  I think I got something like 72% for the average pitcher, but I am not sure.  It might have been 80%, but I doubt it.

Of course, you would need to control for the pitcher if you wanted to find the average limit of control for all pitchers, since the pool of pitchers who are 3-0 on a pitcher will be the wild ones in the first place.

You also might want to limit it to no runners in scoring position as you will get a few times where a pitcher might not want to throw a cookie to certain good hitting pitchers, like with 2 outs, runner on second or third, in a tight game.

If you have enough data, it would be great to see the “limit of control” for each individual pitcher and then compare that to their overall walk rate to see what kind of correlation you get.

The difference between a pitcher’s “limit of control” and his overall walk rate might be the difference between how well he CAN control his pitches and how well he CHOOSES to control them.  There might also be differences for pitchers who can control their fastballs well, but not their other pitches.  In any case, you probably won’t get any decent sample sizes for individual pitchers unless they have been around for many years.

I’ll definitely take the under on Maddux.  About 12 years ago, when Maddux had already pitched almost 10 years in the majors, he walked a pitcher and the announcer remarked that that was the first time he has ever walked a pitcher.  I thought that was amazing.  But as I said (we posted at the same time), I agree that we are not going to get any meaningful sample sizes for individual pitchers.

If you start to include other situations, you are not going to get the “limit” of a pitcher’s control.  For example, with a 3-0 count and 0 outs and a big lead late in a game, all pitchers SHOULD be trying to throw a strike down the middle, but not all of them do (try), for some reason.  With a big lead, some pitchers try and get “cute” with batters even though they shouldn’t.

What you can do, is to compare the strike percentage with pitchers at the plate and no runners in scoring position with other situations.  If the strike percentages are the same, then you can use those other situations in order to increase the sample size for individual pitchers. 

Or if you find, for example, that all pitchers throw 3% fewer strikes in those “other” situations, you can include them in individual pitcher data and then make the adjustment to figure those individual pitchers’ “limit of control.”

For example, let’s say that all pitchers throw 75% strikes to pitchers on a 3-0 count with no runners in scoring position.  And let’s say that they throw 70% strikes to #9 and #8 hitters in similar situations. Now, let’s say that pitcher A throws 70% strikes with pitchers at the plate and 62% in those #8 and #9 batter situations.  Simply add 5% to the 62% and throw everything together for that pitcher to figure out his “limit of control.”

Of course, you still are going to get massive random fluctuation for individual pitchers.  Let’s say that pitcher A throws 73% strikes in 81 of those situations.  The best you can say is that his “limit of control” is 73% plus or minus 11% at 2 sigma, which doesn’t really tell you much since the SD of talent is probably going to be a lot less than that.  And actually, you would regress the 73% toward some mean (maybe the mean limit of talent for all pitchers who have the same BB rate as this pitcher).

From 2000-2007 I found 674 instances with a pitcher batting, no runners in scoring position, and a 3-0 count.

The 4th pitch was:

2 blank (runner getting picked off, caught stealing?)

3 swinging strikes (batting pitcher should be fined for ever swinging 3-0)

3 fouls

469 called strikes

196 balls

1 pitch sequence = “L” - anyone know what that is?

So all pitchers together throw 71% strikes, 29% balls.  I’ll try and group the pitchers by walk rate and see what changes.

Maddux was 2-2 in throwing strikes.

Wow, much worse than I thought.  This is fairly disgusting.  If you look at all 3-0 counts, I think you get the called ball 33-35% of the time (IIRC).  So, to get it 29% of the time in the most favorable situation for the pitcher is really extremely disappointing. 

They are throwing it down the middle in a situation where you expect a swing only 1% of the time (compared to the 8% or so for a league average hitter), and you still miss the middle of the plate by 9-12 inches?  On a (likely) fastball?  Ouch.

Again, I think you are going to have a population of pitchers that are wild in the first place.  I think.  “L” is a foul bunt, which is an odd thing unless the pitcher was sacrificing, I guess.

Just saw Ryan Howard hit an 0-2 pitch for a homerun - why would the pitcher give him a hittable pitch?  Is he wild in the zone?

Perhaps it would be instructive to look at the opposite event in this thread and see how many homeruns are given up on an 0-2 count and maybe some other condition (bases empty?).  Why would a pitcher through a hittable pitch 0-2?

I am sure some percent would want to strike the batter out, but you could control versus K/9 and probably the strikeout rate of the batter.  Howard does strike out a lot, but probably not on pitches down the middle as often.

Obviously a good percentage of bad 0-2 pitches are when the pitcher completely misses his target.

Also, whether and by how much you want to throw a pitch out of the zone depends on the batter and the game situation.

Finally, some pitchers don’t like to throw waste pitches for whatever reasons, like a Maddux.  Also, some pitchers “stuff” is more conducive to throwing a waste pitch than others.

Again, I really wish that pitch f/x included where the catcher was set up. That would be a gigantic addition to the data.  Obviously not much more work for the operators.

Isn’t part of the problem in this case sample bias?

Often, when a pitcher falls behind a bad hitter 3-0, he will be experiencing a small period of bad control. So, if we look only at what happens on the next pitch, we’re likely to really underestimate a pitcher’s ability to control his pitches under normal circumstances. We might be unfortunately including a number of cases where a pitcher has momentarily lost it.

This would sort of be like trying to tell how good a pool player someone was by asking them to make a very easy shot with only one ball (+ the cue on the table), but only ever measuring it after they had missed their last 3 shots. I realize that it’s hard to find other, better situations in baseball, but this one likely overestimates lack of control.

Dan, I doubt that there is a “hot hand” in pitcher control.  If there is, I am guessing that it is slight.

The case sample bias is probably more as I mentioned - that these 3-0 pitchers are more wild in general (career-wise) than the average pitcher.

This is a little different, but I once looked at pitcher K percentage after he just walked a batter on 4 pitches.  Conventional wisdom is that you take the first pitch when a pitcher has just thrown 4 straight balls.  I was thinking that that was the time NOT to take a pitch - that a pitcher was more likely to throw a strike/cookie on the first pitch after just walking the last batter on 4 pitches.  I was right.  He throws considerable more strikes after just throwing 4 straight balls than when not just throwing 4 straight balls.

In fact, in general, the more balls in a row a pitcher throws, the higher his K percentage on the next pitch.  That could simply be a function of the count of course, but I found that interesting.

Anyway, all that does not mean that there is NOT a “hot hand” effect, of course.

Dan, I doubt that there is a “hot hand” in pitcher control.  If there is, I am guessing that it is slight.

Really? I mean, it certainly seems subjectively to be the case that a pitcher often “loses it” or has a slight mechanical flaw or problem with a certain pitch that gets corrected by a pitching coach.

You might be 100% right. But I’m not sure the “hot hand” effect (at least, in the sense of the Gilovich study) is really anything like having good or bad control or any particular day. Would you agree that pitchers can either “have it” or “not have it” on any particular day? Or do you think this is it all just random variation on a pitch-by-pitch level?

This is a serious, not a rhetorical question, by the way. Having never pitched a major league game, I really have no idea.

In fact, in general, the more balls in a row a pitcher throws, the higher his K percentage on the next pitch.  That could simply be a function of the count of course, but I found that interesting.

I think we could make some pretty convincing arguments that this is, as you point out, really a function of count, nibbling, what hitters will swing at in different counts. For example, the only way to throw 3 straight balls and follow with a K is to have gotten a hitter 0-2 in the first place, etc.

"Would you agree that pitchers can either “have it” or “not have it” on any particular day?”

The research in The Book indicates that there is very very little to this.

Tango, would you say then that a manager who pulls a pitcher who is getting shelled is generally not really doing anything effective (in terms of winning a ballgame)?

The manager would be preventing the pitcher from working too much, and replacing him with a scrub pitcher who exists on the staff to mop up low leverage innings.

He’s saving his starter for another day when he has a better chance of contributing to victory.  Though maybe a manager doesn’t see it that way, just thinks his starter doesn’t have it, his actions usually coincide with the optimal approach anyway.

Right, what Rally said.

However, if you track pitcher usage in the 60s and today, you will note that managers of today will let the pitcher work through it, treating the results as random variation.  In the 60s, they would pull him very very quickly.

The result is that in the 60s, the pitchers would have lots of 70 and fewer pitches starts, but also tons of 130 and more pitches starts.  (Even Koufax.) Standard deviation is far wider in the 60s, even though the mean is the same.

Overall, the average number of pitches per start has not really changed, except for the enormous blip in the 70s, and the drop in the last 10 years.  The 60s, 80s, and 90s are fairly similar.

Doesn’t it seem very possible that there is indeed a “cold hand” phenomenon, but that it’s not very common/extreme/long-lasting, so it’s hard to see in large sets of data?

And that if such a phenomenon existed, it would be most likely to show up in extreme situations, such as Rally’s sample of pitchers who have gone to 3-0 counts on opposing pitchers?

It seems surprising that even a subset of pitchers with poor control can only throw the ball in the strike zone 71% of the time if that’s all they’re trying to accomplish.

Unless this sample of pitchers is made up almost entirely of really bad pitchers, I think what Tango/Rally have stumbled on is evidence that there is a “cold hand” phenomenon, even if that wasn’t the original intent.

I don’t think it is evidence of a cold hand.  I think it is evidence that it is not that easy for a major league pitcher to throw a strike when he wants to.

Let’s compare that to the first pitch of the AB against all poor hitting pitchers with no runners on base and 2 outs.  We have to assume that the pitcher is trying to throw a strike almost as much as on a 3-0 count.  I would guess 5% less.

If the first pitch strike percentage in that situation is more than 65%, then I would say that 71% is evidence of a cold hand.

As far as pulling pitchers who are getting shelled, I agree that even though getting shelled has little predictive value (for veteran pitchers at least - we found evidence that young pitchers who get shelled early tend to keep pitching poorly), pulling a starter when he is losing by quite a bit is no big deal for reasons that Rally mentions.

The BIG mistake that managers make ALL the time, which costs them lots of WE, is leaving in the mediocre to poor starters in the 6th and 7th innings (or later) when they are pitching well in a close game.  I see that ALL the time.  A poor starter, like Byrd last night, is horrible (substantially worse than replacement) after throwing 90 pitches and facing the order for the 4th time around.  Yet, if that mediocre to bad starter does not have a high pitch count and has not let up a lot of runs (even if he was “lucky” and got out of several jams), many managers invariably leave him in there UNTIL he gets shelled or puts himself in another jam, which happens quite often because he such a horrendous pitcher by that time.  You could put the absolute worst reliever on the planet in and they would be better than a mediocre to poor starter in the 6th or 7th inning.

I would love to confront a panel of major league managers and ask them, “OK, you have your #4 or #5 starter in the game and he has pitched great for 5 innings and his pitch count is only 85.  The game is close.  Do you leave him in there?”

I believe that the answer from 90% of these managers would be, “Of course. He is pitching great and his pitch count is not high.  Why would I take him out?”

Then I would put up on a 10-foot high screen the stats on these pitchers in the 6th inning and later of all those games when they were pitching great, and I would ask them, “So this is the kind of pitcher you want throwing the 6th and possibly 7th or later innings of a close game?”

Plan: You should scrap whatever lecture you had planned for Sunday and we should just continue this discussion. =)

By the way, what time in the class @ MIT? I think I’ll be able to make it, I’m in Boston for the weekend.

It’s 10 am, Dan. Will be happy to see you there.

How about we give a lecture on, “What managers SHOULD do, but don’t (and what they DO do but SHOULDN’T), but you were afraid to ask,” and invite all 30 managers?

This is weird, I was literally thinking about this yesterday in my car. I was at a game and wondered why balls and strikes aren’t shown more in stats, etc.  I’ve always felt (just on gut, no proof) strikes to ball ratios were great indicators of success and wondered why I hadn’t seen any major stuff in that.

Then that shifted to thinking about measuring control through 3-0/3-1 counts, but also recognized how hitter and situation plays a factor. Also cognizant of the idea that on 3-0 umps are known to “expand the zone” looking for strikes as well as just game strategy problems.

Nonetheless, it would be interesting to see and it was funny you brought it up so recently to when I was randomly thinking about it. Perhaps great minds work alike? Although the key difference between you and me is that you are actually qualified enough to research and make discoveries about your ideas

Also cognizant of the idea that on 3-0 umps are known to “expand the zone” looking for strikes as well as just game strategy problems.

That is conventional wisdom.  And one that I assumed was true.  But apparently it is not.  In a pitch f/x article some time ago, the author/researcher showed that umps are less inclined to call a strike on a borderline 3-0 pitch.  Now, there might be some selection bias with the umps.  I don’t know.  I can’t remember the exact methodology of the study.  Also, I think it is fair to say that there are some umps who will give an automatic strike on a 3-0 borderline pitch, but apparently, there are not many and there are at least as many who won’t call a borderline strike, presumably because the pitcher has not “earned” it.

Anyway, I have always thought that we might be able to do better in predicting a pitcher’s B and K rates by looking at their ball and strike totals.  For example, say you have two pitchers who have the same BB and K rates so that your BB and K rate projection for them is exactly the same.  And say that one of them has a higher ball to strike ratio. I would guess that his BB/K projection should be higher as well.

It is kind of like a pythagorean projection for a pitcher’s K/BB ratio, based on his ball to strike ratio.

I’d guess there’s selection bias stemming from the fact that umps with tighter strike zones will get fewer 3-0 counts than umps with wider ones.

MGL,

I like pitch f/x and certainly believe that ball tracking is the future of baseball analysis (particularly on defense) but in its current form I just cannot take s absolute fact. There can be interesting stuff found using pitch f/x, but I personally have seen plenty of problems with it that don’t allow me to trust it completely.  That being said, pitch f/x is a lot better tool than generalizations made by watching baseball. I can offer no proof against the 3-0 claim, I’m just not sold either way I guess.

On the strikes/balls issue, have you or tango ever done any research on the matter? If you had had thoughts about it before, it seems like you could crunch some numbers on the matter. I’m personally very envious of you guys and your ilk, you have the ability to sift through thousands of games of data to find answers in a *relatively* short time

20 years ago, Bill James did the ball/strike BB/K thing with two Jays pitchers (Stieb and ... I forget his name… very average pitcher).  He didn’t find what we expected.  Maybe someone can dig that up…

The pitchers were Stieb and Jimmy Key, and it was the 1986 Baseball Abstract [Blue Jays essay p.114].

The gist of it was that they had similar ball/strike ratios but Stieb got more called and swinging strikes and Key got more foul balls and balls put into play, and that dramatic differences in overall walks and strikeouts arose from apparently small differences in these rates.

“although ... Stieb walked men about 50% more often ... Key threw more balls as a percentage of pitches than did Stieb ... 37.1% to 36.8%...Although the difference in strikeouts is about 50%, the difference in strikes thrown is only 7%...Dave Stieb had 90% as many balls in play as Jimmy Key.” [By “strikes thrown” James meant called,swinging and fouled, separating strikes put into play into their own category.]

Interestingly, when intentional balls are removed, I get very similar percentages of balls at 3-0 count from 2000-2007, regardless of whether a runner is at first or not.

With a runner on 1st,1st+2nd or bases loaded, it’s 34.7% called ball (or hit by pitch), and 35.6% when 1st base is open. This is for all hitters, not just when pitchers are hitting.

Well the first thing that comes to mind when hearing about James study is sample size. Those findings might prove to be true, but I’d want more than just two players seasons used as sample size

James is notorious for making claims and gathering evidence from VERY small samples.  I am not implying that he does not understand the issues surrounding and regarding sample size.  He does.  It is just the “writer” in him that loves anecdotes and it permeates his research.  I think.

His “study” is only half completed.  You have to look at that for one time period and then again for another time period.  IOW, if Stieb and Key had similar ball and strike ratios but different BB/K ratios over some period of time, the hypothesis (my hypothesis, at least), like a team’s pythag record, would be that in another period of time their BB/K ratios would be closer, adjusting for regression to the mean.

That last part is important (adjusting to regression to the mean).  Say that the average K/BB ratio among major leaguers is 1.5.  Say that Stieb was 2-1 and Key was 1.5-1 in some time period.  No matter what, they will be closer in another time period, as Stieb will tend to regress towards the league average of 1.5/1 and Key will tend to remain the same (since he already was at league average).

Joe, is that 34.7% an average value for 1, 1 and 2, and bases loaded, or are all 3 the same?  How about you just tell us the ball 4 % for all base runner situations?  If you don’t mind, that is.

I suspect that it will be around the same for 1, 1 and 2, and 1 and 3.  Less for bases empty and bases loaded, and more for first base open.

Mickey, that was all 3 situations combined - guess I left out runners at 1st and 3rd - I can rerun for all base out scenarios tonight.

To digress a little ... The general criticism of James’ analytical style is fair, and the small sample size critique is perfectly fair; James didn’t prove anything. OTOH, James wasn’t “studying” this issue, just reporting something counter-intuitive. Also, I think James’ methods in those days (close analysis of limited data) generated a number of insights which have stood up pretty well. Historically, at this time [1985], STATS was years away from doing the kinds of data collection necessary to support a real study anyway. This was two years into project scoresheet, and although data had been collected, I think it was slow to be systematically processed. [Remember computers and data transfer methods and programming tools from those archaic times?] In terms of published data, there was just data collected for 5 or 6 individual teams for 1 or 2 or 3 years and published in individual newsletters by guys like Dewan and Don Zminda and Chuck Waseleski and David Driscoll (source of the Blue Jay data James analyzed). Let’s be kind to ‘80s era analysis when it comes to sample size issues.

I don’t know if there has been a followup study of the sort Alex mentioned. I take the main hypothesis to be extracted from James’ observation to be that overall ball-strike counts don’t tell much, that the ability to “miss bats” is the key to lengthening atbats long enough to get walks or strikeouts. Pizza Cutter made a similar point about going beyond simple “strike percentage” in his recent series on foul balls at the statistically speaking blog ...

Anyone have a link to the pitch f/x study MGL refers to?

I have not thought about it too much, but I agree that because pitching involves more than just the percentage of balls and strikes you throw, it would be imperative to consider each pitcher’s style of pitching and “how” he gets his balls and strikes.  For example, one pitcher with nasty stuff might get a lot of swinging strikes on pitches outside of the zone and another with mediocre stuff may actually have to throw pitches IN the zone to get many strikes.

However, I am fairly sure that we can do better at projecting pitchers’ BB and K rates by looking at individual pitches.  I am just not sure how.  Right now.

A simple ball/strike ratio would not be adequate, as strikes can include balls in play, fouls, called strikes and swinging strikes.  If you can’t get the latter 2 you’ll never get a strikeout (except on a foul bunt

If you took the percentage of balls and combined with the 4 types of strikes my guess is you could get a decent multiple regression equation to predict strikeouts and walks.

For me, I’m interested in more than it just being an indicator of K/BB ratio, but perhaps an indicator of season success and/or individual game success.

Rally/33: that was actually the basis for my discovery of the Extended Pitch Count Estimator (xPCE).  I simply did a Markov chain of balls, strike and in play expectations at each count to generate K, BB, and BIP.

From Retrosheet 2000-2007: all pitches on count 3-0, with intentional balls and “balls awarded- no pitch” [retro code V] omitted. My code for runners is left to right, so 100 means runner on 3rd only, 110 means runners on 3rd and 2nd only… Balls=code ‘B’(called balls) plus code ‘H’ (hit by pitch)
+---------+------+-------+---------+----------+
| runners | outs | balls | pitches | ball_pct |
+---------+------+-------+---------+----------+
| 0 | 0 | 4819 | 14488 | 0.3326 |
| 0 | 1 | 3698 | 10982 | 0.3367 |
| 0 | 2 | 3310 | 9440 | 0.3506 |
| 1 | 0 | 1211 | 3486 | 0.3474 |
| 1 | 1 | 1543 | 4436 | 0.3478 |
| 1 | 2 | 1579 | 4510 | 0.3501 |
| 10 | 0 | 495 | 1315 | 0.3764 |
| 10 | 1 | 1041 | 2591 | 0.4018 |
| 10 | 2 | 1319 | 3260 | 0.4046 |
| 11 | 0 | 290 | 902 | 0.3215 |
| 11 | 1 | 595 | 1739 | 0.3422 |
| 11 | 2 | 870 | 2440 | 0.3566 |
| 100 | 0 | 83 | 223 | 0.3722 |
| 100 | 1 | 360 | 869 | 0.4143 |
| 100 | 2 | 653 | 1509 | 0.4327 |
| 101 | 0 | 116 | 330 | 0.3515 |
| 101 | 1 | 294 | 749 | 0.3925 |
| 101 | 2 | 449 | 1195 | 0.3757 |
| 110 | 0 | 94 | 264 | 0.3561 |
| 110 | 1 | 237 | 554 | 0.4278 |
| 110 | 2 | 335 | 809 | 0.4141 |
| 111 | 0 | 76 | 223 | 0.3408 |
| 111 | 1 | 176 | 538 | 0.3271 |
| 111 | 2 | 276 | 783 | 0.3525 |
+---------+------+-------+---------+----------+

overall ball % at 3-0 count
with bases empty: 33.9%
with runners on and 1b occupied: 35.0%
with runners on and 1b open: 40.5%

Same chart as above, with opposing pitcher batting [I haven’t tried to exclude any position players who came to bat while serving as emergency pitchers.]

| runners | outs | balls | pitches | ball_pct
+---------+------+-------+---------+----------
| 0 | 0 | 73 | 251 | 0.2908
| 0 | 1 | 41 | 177 | 0.2316
| 0 | 2 | 49 | 153 | 0.3203
| 1 | 0 | 6 | 23 | 0.2609
| 1 | 1 | 12 | 41 | 0.2927
| 1 | 2 | 21 | 65 | 0.3231
| 10 | 0 | 6 | 12 | 0.5000
| 10 | 1 | 6 | 28 | 0.2143
| 10 | 2 | 12 | 40 | 0.3000
| 11 | 0 | 6 | 9 | 0.6667
| 11 | 1 | 7 | 20 | 0.3500
| 11 | 2 | 10 | 45 | 0.2222
| 100 | 0 | 0 | 2 | 0.0000
| 100 | 1 | 4 | 12 | 0.3333
| 100 | 2 | 3 | 14 | 0.2143
| 101 | 0 | 1 | 2 | 0.5000
| 101 | 1 | 1 | 8 | 0.1250
| 101 | 2 | 4 | 23 | 0.1739
| 110 | 0 | 2 | 2 | 1.0000
| 110 | 1 | 0 | 7 | 0.0000
| 110 | 2 | 4 | 13 | 0.3077
| 111 | 0 | 1 | 3 | 0.3333
| 111 | 1 | 1 | 13 | 0.0769
| 111 | 2 | 5 | 22 | 0.2273

ball% of about 28%, but only 985 cases across 8 years. [At a 2-0 count with opposing pitcher at bat, I get 27% balls in 3679 pitches.]

The idea that a pitcher at the plate is like a mannequin and that throwing a 3-0 strike to him is tantamount to shooting a free throw, that it is only necessary to aim for a waist high fastball down the middle of the plate, is likely to be an exaggeration. The average pitcher may be able to hit well enough that game theory has to apply even here.

I’m in shock.  Joe, are you saying that the % of balls thrown on a 3-0 count is the SAME as overall, when the pitcher is at bat?

That is completely ridiculous (not for you to show, but for pitchers to throw).

According to our expectations, and quantified here:
http://tangotiger.net/halejon/allcounts.html

On a 3-0 count, pitches are thrown down the middle (or at least in the meat of the strike zone), unlike all the other counts.

What your data is suggesting is that the mound-pitchers don’t treat the plate-pitchers any different on any count!  That they are not trying to pitch around them, and are basically throwing at them 28% balls regardless of count.  (Understanding that we’ve only seen the 28% for overall and 3-0, but since 3-0 is the extreme count, it seems reasonable to think this is the case for all counts.)

Tango,

The other percentage I gave wasn’t for all counts. For pitchers at the plate I just gave the percentage of balls specifically at a 2-0 count as a comparison point because the 3-0 count was such a small sample. Here is the ball% for all counts for pitchers batting (2000-2007):

count| balls | pitches | ball_pct
0-0 | 14821 | 48563 | 0.3052
0-1 | 7882 | 25609 | 0.3078
0-2 | 5473 | 15265 | 0.3585
1-0 | 3688 | 14805 | 0.2491
1-1 | 3904 | 16179 | 0.2413
1-2 | 4919 | 17196 | 0.2861
2-0 | 989 | 3679 | 0.2688
2-1 | 1169 | 6157 | 0.1899
2-2 | 2337 | 10588 | 0.2207
3-0 | 275 | 985 | 0.2792
3-1 | 438 | 1876 | 0.2335
3-2 | 847 | 4773 | 0.1775

but this probably needs to be broken down further by sacrifice/non-sacrifice situation, since in those cases the pitcher-thrower IS trying to locate a difficult-to-bunt pitch. [for example the ball percentage goes up at a 1-0 count to a 2-0 count! That sounds like a severe selective sampling problem of some sort, because other things being equal, we’d expect the pitcher to throw more strikes when behind 2-0, as indeed we see when all batters are considered (ball rate drops from 35% at 1-0 to 32% at 2-0).

here’s a chart for all batters 2000-2007
count|balls | pitches | ball_pct
0-0| 619075 | 1496626 | 0.4136
0-1| 294512 | 689660 | 0.4270
0-2| 147786 | 319712 | 0.4622
1-0| 216150 | 616530 | 0.3506
1-1| 208284 | 577994 | 0.3604
1-2| 184262 | 490114 | 0.3760
2-0| 68646 | 214471 | 0.3201
2-1| 92710 | 311501 | 0.2976
2-2| 126770 | 421600 | 0.3007
3-0| 23919 | 67635 | 0.3536
3-1| 38285 | 133004 | 0.2878
3-2| 57379 | 257539 | 0.2228

There’s an interesting pattern here. For zero ball and 1 ball counts, the ball percentage to a pitcher batting is consistently about 10 points lower than to a regular batter, but only the 2-1 count is in that range. The other two ball and three ball counts show some convergence in the likelihood of throwing a ball.

Hmmm… the 3-2 count is obviously batters swinging at anything close, which is why the called ball% is so low.

How about just looking at called pitches, and excluding all swinging pitches?

pitchers 2000-2007

count |balls |called_str |ball_pct |called_str_pct
-------+-------+----------------+----------+---------------
0-0 | 14821 | 13664 | 0.3052 | 0.2814
0-1 | 7882 | 3757 | 0.3078 | 0.1467
0-2 | 5473 | 1294 | 0.3585 | 0.0848
1-0 | 3688 | 4206 | 0.2491 | 0.2841
1-1 | 3904 | 2437 | 0.2413 | 0.1506
1-2 | 4919 | 1659 | 0.2861 | 0.0965
2-0 | 989 | 1726 | 0.2688 | 0.4691
2-1 | 1169 | 811 | 0.1899 | 0.1317
2-2 | 2337 | 1072 | 0.2207 | 0.1012
3-0 | 275 | 699 | 0.2792 | 0.7096
3-1 | 438 | 763 | 0.2335 | 0.4067
3-2 | 847 | 396 | 0.1775 | 0.0830

The next comparison table is a little different than the ones I posted before; to make a more straightforward comparision, this shows results for non-pitchers only as opposed to overall results (ie both pitchers and non-pitchers taken together, which is what I had been showing. As before, “pitcher” is defined by the retrosheet event file code of defensive_position=1 for the batter - so I am not doing anything to handle at bats by position players as emergency pitchers, or pitchers who appear as pinch hitters. ]

count | balls | called_str| ball_pct | called_str_pct
-------+--------+----------------+----------+---------------
0-0 | 604254 | 432526 | 0.4173 | 0.2987
0-1 | 286630 | 72956 | 0.4316 | 0.1099
0-2 | 142313 | 12080 | 0.4674 | 0.0397
1-0 | 212462 | 137785 | 0.3531 | 0.2290
1-1 | 204380 | 62490 | 0.3638 | 0.1112
1-2 | 179343 | 20444 | 0.3792 | 0.0432
2-0 | 67657 | 56765 | 0.3210 | 0.2693
2-1 | 91541 | 33630 | 0.2998 | 0.1101
2-2 | 124433 | 19034 | 0.3027 | 0.0463
3-0 | 23644 | 37620 | 0.3547 | 0.5644
3-1 | 37847 | 20209 | 0.2886 | 0.1541
3-2 | 56532 | 10776 | 0.2237 | 0.0426

Pitchers take strike 3 about twice as often at any 2 strike count - they are more willing than position players to risk a strikeout to get a walk.

"The idea that a pitcher at the plate is like a mannequin and that throwing a 3-0 strike to him is tantamount to shooting a free throw, that it is only necessary to aim for a waist high fastball down the middle of the plate, is likely to be an exaggeration.”

Actually, free throw shooting is a good analogy. Last year the NBA shot free throws at a 75% rate, not too much different than the 71% strikes I found to pitchers with a 3-0 count.

Whether a pitcher, as an elite athlete, presents a threat when throwing the ball right down the middle, keep in mind that a pitcher will only swing 3-0 about 1% of the time.  For all intents and purposes, he is a cardboard cutout up there.

I was going to say the same thing as Rally.  There is no “game theory” for 3-0 counts with a pitcher at the plate.  Even if they knew that they were getting a fastball right down the middle, 95% of pitchers (maybe more) would still not swing.  The “reason” the ball % is so high (28% or so) is that pitchers simply cannot throw more strikes than that no matter what.

And even if you are concerned about some game theory element, such as the pitcher having a brain cramp and forgetting who is at the plate or that he (the pitcher on the mound) is just so used to NOT grooving all 3-0 pitches (which is possible), a 3-0 count with no one on base, especially with 0 outs, should take care of that.  Of course, your sample size is going to be small so the results are going to have a large variance, I think.

I agree.  Virtually no pitcher will swing at a 3-0 count (and the data bears that out).  The run value of the 3-0 count for the average hitter is around +.20 runs.  I will guess that for a pitcher it is +.15 runs.  A called ball puts him at +.32 runs (a walk), and a called strike puts him at 3-1, which I will guess is around +.08 runs for him.

A called ball adds +.17 runs, while the called strike removes .07 runs.  It is a high leverage pitch here.  And what happens if the pitcher puts it in play on a 3-0 count?  I will guess the pitcher is a league average hitter at that count?  It’s simply ridiculous for a mound-pitcher to not try to throw the pitch down the middle here.

My guess is that they ARE trying to throw it down the middle, and they are simply not able to hit their target.  Mound-pitchers seem to have very little control.

As to the applicability of game theory in the pitcher vs pitcher as batter matchup, consider this chart for pitchers’ hitting at each count (again, 2000-2007):

count|BA|SLG|AB
0-2|.060|.071|7329
1-2|.071|.085|9022
2-2|.099|.126|5767
3-2|.148|.208|2597
0-1|.212|.262|3739
1-1|.230|.291|3103
2-1|.230|.297|1529
0-0|.230|.307|5886
1-0|.262|.351|2329
2-0|.276|.422|351
3-1|.324|.510|241
0-0|.000|.000|2

Pitchers’ hitting follows the same progression as hitters’ hitting; when they are ahead in the count they hit for a higher average and more power. The results at 2-0 and 3-1 suggest to me that the pitchers who get into a 3-0 count are not so inept at hitting with the count in their favor that you can predictably throw them a waist high fastball down the middle of the plate. [Obviously we are not talking about big samples here; OTOH, the sample at 1-0 is 2329 AB; since we can reasonably expect significantly stronger performance than .262/.351 at 2-0 and 3-1 counts, without taking them too literally, I think the results are credible enough to establish my point.]

As to the theory that pitchers can only throw in the strike zone a maximum of roughly 72%, even if they are grooving the pitch, I think the data for pitchers and regular hitters at the 3-2 count [from post 41] is troublesome for that theory. Both pitchers and regular hitters offer at the 3-2 pitch about 74-75% of the time, with fairly similar rates of taken balls. Granted, both hitters and pitchers “expand the zone” to avoid being called out on strikes, but the overall strike percentages are 78% for regular hitters and 82% for pitchers as batters. Here pitchers are also trying to throw strikes, but at least to regular hitters they will still be varying their pitch types and locations. So why is the gap in strike percentage between regular hitters and pitcher hitters so narrow here? If the 72% theory is true, far from expanding the strike zone, pitchers as hitters should be TAKING borderline pitches in the hopes of a walk; we should still see a ball rate of close to 28%.

Two things off the top of my head.  Yes, pitchers can hit when the count is in their favor, and with a 3-0 count and RUNNERS ON BASE or IN SCORING POSITION, the pitcher is NOT going to groove a pitch all the time.  Sorry about yelling, but I think that I made it clear that if you want to figure out the maximum control for pitchers, you need to look at 3-0 counts with no runners on base or certainly with no runners in scoring position, even better with 0 outs, and even better eliminating pitcher/batters like Zambrano and Owings (and Hampton, etc.).

With 0 outs and no runners on, I guarantee you that NO pitcher (other than the Zambranos and Owings) are EVER going to swing at a 3-0 pitch even if the pitcher told them that he is going to throw a fastball down the middle (which they know anyway).  So, there is no need for game theory in that situation.  None.

As far as 3-2 counts, pitchers will swing at lots of pitches out of the strike zone because they are pitchers and they have little strike zone recognition skills.  Obviously some pitchers have more than others.  So I don’t see your point about the 3-2 count.  Even if pitchers threw only 65% strikes at 3-2 counts to pitcher/batters, we have no idea how many balls they swing at.  It could be another 17% (which would give you the 82%), it could be 12%, or it could be 22%.  We have no idea. Yes, they SHOULD take more borderline pitches than a position player (probably a lot more), but their pitch recognition skills are so much worse than a regular batter, we have no idea how many borderline pitches they actually take.