THE BOOK--Playing The Percentages In Baseball

I think I’m gonna like these. 

A) more often.  Do I put my reasoning or just the answer?

A)more often

I think that in nearly any situation, you have to force the pitcher to throw a strike because he obviously is having some control problems. Going up there with the mindset of absolutely no swings until after taking a strike takes away all possibility of helping the pitcher out by mistakenly swinging at a ball, and possibly getting the pitcher back on track.

C. The same. That is assuming that your assessment of the pitcher’s true talent walk rate hasn’t changed.

My reasoning is that you shouldn’t really expect the pitchers true talent level to change in the middle of the game, but given the fact that he has pitched bad the last 2 hitters, their is the slight possibility that he is worse this game than in others.  Doing a Bayeisan style equation would lead you to swing slightly less often than you normally would. 

Then again, that is the mathematical angle.  Going by some logic (which isn’t neccesarily backed up by anything), if he has struggled to throw strikes, he would be more inclined to give the next hitter a pizza pie over the middle just to get ahead.  In that case, it would pay to swing.

If you’re on the Giants, it’s (b) and you ground into a double play.

(Serious answer may come later).

The same.

Sure, it might be right to take if he has no idea where the ball is going, but he also might be so desperate for a strike the he tosses a meatball down the middle.  Overthinking separates the body from the mind.  Just do what you’d normally do.

Nick, yes reasoning is required!  It is like in school when you don’t show your work in some classes, you get no credit…

I gave my reason… eventually.  Speaking of no credit in school, I recently failed a science test despite getting all of the answers right, because I didn’t show my work.  I should really be more thorough.

The same. A pitchers tendency to throw balls and strikes, whether a long term projection or a recent short term series of pitches, has no bearing on my hitting approach.  I am judging the first pitch on (a) whether I believe I can hit it for a base hit, and (b) whether I believe I will see a better pitch to hit later in the count if I don’t swing at this one.

There are 2 competing points of view: 1) take until strike one, just in case the pitcher really is having a short-term control problem, and 2) get ready to cream a likely get-me-over fat pitch.

Since they both make some sense, I’ll split the difference and say C) the same. That my ‘logical’ analysis of the situation.

From a ‘practical’ perspective, though, it’s my observation that batters who look to swing are sort of overanxious and swing at pitcher’s strikes too often. Therefore, it may be better for ‘most’ hitters to take a strike. OTOH, maybe I’m simply having selective memory about this…

So I’ll stick with C) the same

Most of the time, I’m slightly more likely to swing. I’m a “take the first pitch” kind of guy, normally. In this scenario, though, I sit on a fastball over the heart of the plate. If it’s anything other than that, I’m taking.

I have to complain about the question a bit, though. There’s not really enough data to be sure what’s going on here. If I’m 2007 Mike Lowell with two outs, I’m assuming the guy lost David Ortiz and decided to pitch around Manny to get to me. That means there’s no reason to believe the guy has really lost the plate. So in this case, I use my normal approach.

On the other hand, if it’s 2008 and Dontrelle Willis is the pitcher, you’d better believe I’m making him throw a strike before I even consider swinging.

I guess my point is that you don’t change your approach the same way in every scenario, making your “given the score, runners, inning, outs, etc.” caveat moot.

(c) the same

A 7 pitch sample is too small to judge the pitcher on.  It’s not even his entire sample from the game, which itself is pretty small.  You also have the information that the opposing manager has left the pitcher in.  So your best guess is that the pitcher is going to be his normal self.

I’ll say “take more often”...because what I do (or would do if I could play, which I can’t) is pick one specific location and pitch type and zero in on it, with the exclusion of other potentially hittable pitches.  In this case, I’ll probably pick a fastball down the middle and take anything else.
-j

(c) the same

This strikes me as analogous to the “hitters on a hot streak” claim that was examined in THE BOOK.  Those 7 pitches shouldn’t override the expected strike% of the player based on the hundreds of previous pitches.  The likelihood is that that pitcher is going to regress towards his overall predicted rates.

C, past performance provides little indication of future results.  (See the stock market for a real life example.) This is similar to the flips of a true coin question, getting 7 tails in a row has no effect on what the next coin toss will be.  (Of course this assumes that the coin is actually true, and not weighted one way or the other.) In the case of a pitcher not finding the strike zone for 7 straight pitches one may consider option A.  But this is where game theory balances things out.  If the pitcher thinks you are going to go with option A they will be more likely to just throw a fastball down the middle and the batter is quickly behind in the count.  The batter and pitcher could continue with the “if I know that you know that I know ...” or the batter could forget what was thrown to the previous batters and proceed with their normal plate approach (the wisest choice).

(a) more often.  Because that’s what my manager probably wants, and I like my job.....

Excellent question and the answer for me depends.

If I think I am overmatched by the pitcher, a condition which typically would elevate my level of ‘guess hitting’ anyway, then the answer is B, less often. If I think I am overmatched by the pitcher, then I take the chance that the pitcher will pitch down to my level and groove a first pitch fastball. If I get anything but, I take it. But I’m sitting and hitting on that fastball right off the bat, so to speak.

If I am confident that I can handle the pitcher, then the answer is A. In such a situation, I am not afraid of deep counts and figure I have pretty good odds of working a walk or getting a hit in a deep count. No need to take the possibility of a walk off the table by hacking at the first pitch.

Of course, if there are 2 outs and an extremely weak hitter is following me in the order, then the answer is almost always going to be B, regardless of the quality of the pitcher.

Sorry for the copout, but I’m going to say need-more-information.  If the pitcher has just entered the game, walked the only 2 players he’s faced, and is missing by a lot, then I’m taking more.  In that situation, I think it’s more likely that his strike-throwing ability is reduced on this particular night.

If this is the pitcher’s 5th inning, he hasn’t walked anyone previously, and his 7 straight balls didn’t miss by much, then I probably am going to swing away, because I figure he’s going to try to groove one on the first pitch.

But generally I think I’m with jinaz.  I’m not going up there with a take-no-matter-what approach, but I’m going to be looking for a specific pitch, which I suspect will result in me taking slightly more than normal.

A, I’m taking. I have no idea why I’m even up to bat, as I couldn’t hit my way out of a paper bag. So if this pitcher is out-of-sync enough or crazy enough or dumb enough not to lay one down the middle against me (since I probably would either pop up or ground weakly to second), I’m better off hoping for that walk.

But if I’m a major league ball player who isn’t in the game solely because of defense or because I pitch (excluding Micah Owings), then I look for my pitch and swing if I get it and wait if I don’t.

I’d say C) Same

Although I’m tempted to say B.  You’d only swing if its a great pitch to hit and that’s a scenario where you might get one right off the bat, pun intended.

If these were normal hitters, I would approach the atbat the same as always.  Sometimes it just happens.

If the string of balls included walking the opposing pitcher on 4 straight, then I’m thinking this guy has some mechanical problems and can’t throw a strike now, so I’m taking.

Forgot my reasoning for my real answer.  Essentially what others have said, 7 pitches doesn’t seem enough to change my approach, given that little information.

I’m making assumptions here, but I’ll presume that when the first guy who walked was up, the pitcher had him in a 1-1 count, maybe 1-2. That is, a strike must have preceded the run of seven balls, otherwise you would have told us that the pitcher threw 8 balls in a row. Or maybe not, and I’m making spurious assumptions. But having a guy in a 1-1 count, then throwing three straight balls, then walking then next guy on four straight (heck, it could have been intentional) can happen randomly to a pitcher that isn’t experiencing control problems. While I can imagine many circumstances in which 7 straight balls wouldn’t be indicative of an underlying control problem, I can’t imagine when 7 straight balls would be (significantly) indicative of an underlying control problem. So the answer should be c.

Of course, the question is the frequency with which I’m “taking the first pitch”, not “how should I theoretically alter my approach?”, so if “I” am an average major-league hitter (and not actually myself, which would render the strategic point moot), “I” may very well change my approach, because the game is played by human beings (or at least so I’m told). I don’t have access to the data so I don’t know, but I would guess that hitters are more likely to take in that spot, be that the theoretically sound choice or not.

I’ll give the answer later on today, at least MY answer that is.

No other information is really required and “depends” is not really an acceptable answer.  The question is, “Would you take more or less often, or the same, as compared to if the same pitcher had NOT just thrown 7 straight balls or something similar.  I did not specifically say so, but it is the first pitch of your AB.  I think everyone is assuming that anyway.

Here is a hint, although it is not really a hint - it is simply another way of couching the question (and, again, pretty much what everyone is thinking anyway):

Is a pitcher more or less likely, or the same, to throw a strike on the next pitch after a long string of balls, than if he had NOT just thrown a long string of balls?  That is the ONLY question you are answering.  And we are obviously talking about a “typical,” unknown pitcher.

Your answer should have nothing to do with how “anxious” you are or anything like that.  If you, say, normally swing at the first pitch 30% of the time, and you think that the pitcher is LESS likely to throw a strike in that situation than he would in a “normal” situation, then your answer should be (a).  If you think he is exactly AS likely to throw a strike, then your answer should be (c) which seems to be the predominant answer so far.  If you think he is MORE likely to throw a strike, then your answer should be (b).

One more thing:  Assume there is no game theory element to this, which there might be.  IOW, assume that the pitcher thinks that you are a typical batter in this situation - that you are going to do whatever the typical batter does after a long string of balls, or what a batter like YOU typically does after a long string of balls.  I say that because let’s say that your answer is, “I am NEVER going to swing at that pitch.” Well, if the pitcher knows that, he is supposed to throw a pitch right down the middle.  And of course if YOU know that, you would not take 100% of the time or even close.  If you don’t follow that last paragraph, don’t worry about it - just ignore it.  The 4th paragraph is the most important one.

I think who is hitting after me is important in this question.  If I’m batting right before the pitcher or a weak hitter/groundball hitter and there are one or two outs, I’m more likely to swing away and go for a crooked number, knowing that with the weak hitter coming up next, the chances of a double play are more likely. If there are no outs, I’d probably take the first pitch more often in hopes of a walk.  If I’m further up in the order, I’m also more likely to take the first pitch.

There are (apparantly) two runners on base now, which means a lot of force opportunities.  Putting the ball in play is more likely to result in outs in that situation.  It is also more likely to result in runs, since there are runners in scoring position.  I would say the expected run value of getting on base in that situation would be slightly greater than the expected run loss of causing an out or outs. 

Without knowing more details, my approach would be to try moreso to get on base....which would mean I’d be more likely to take pitches.  But the reasoning has nothing to do with the last 7 pitches, it has to do with the game state.  That’s my WAG.

My answer stands....depends on the quality of the pitcher relative to my abilities. If it is Tim Lincecum, I gotta jump on the grooved pitch. If it is Zach Duke, I’ll be able to handle something later in the count.

I think you would also have to factor in the game situation (sometimes a walk is not as good as a hit) and the quality of the batter on deck with respect to the game situation.

I’m looking forward to the MGL answer though.

Brain, Craig, and Rick, maybe my last post, #24, was not there when you made your last posts, but EVERYTHING is the same but one variable:  Whether the pitcher has just thrown a long string of balls or not.  So there is NO, “depends on the situation!”

For example, Craig, the question is if there are 2 runners on base and the pitcher DID just throw a long string of balls are you going to take the first pitch of your AB less, more, or the same, as compared to if there are 2 runners on base and the pitcher did NOT just throw a long string of balls.

Rick, same thing.  Whoever is hitting after you is irrelevant.  Assume the same player is hitting after you whether the pitcher just threw a long string of balls or not.  And assume that it is an average hitter.

Brian, same thing.  The pitcher is the same whether he threw a long string of balls or not.  And assume an average pitcher.  If you (or anyone else) wants to assume that it is a slightly wild pitcher in general (which it is, given that he just threw a bunch of balls in a row), that is fine. It does not change the answer.

Again, the only question you are answering is whether the pitcher is more, less, or the same, likely to throw a strike on that first pitch after a string of balls than if he had not just thrown a string of balls.  And of course we can look up the answer to that question in a database, right?

Also, I disagree that…

“Are you taking the first pitch (a) more often, (b) less often, or (c) the same, as compared to what you would normally do given the score, runners, inning, outs, etc.?”

is the same question as…

“Is a pitcher more or less likely, or the same, to throw a strike on the next pitch after a long string of balls, than if he had NOT just thrown a long string of balls?”

Just because I’m not taking, doesn’t mean I’m definitely swinging.

C) The same

The purpose of a plate appearance is not to generate a walk.  A walk is certainly one of the good outcomes, but of all good outcomes, it is the least desirable.  Even if we assume that a pitcher’s last 7 pitches are predictive of his next pitch (unlikely), as a hitter your approach should not change.  You should be sitting on a particular pitch that you have a good probability of driving.  If you get that pitch, you should make an attempt (e.g. swing).  If you don’t, you shouldn’t.  This approach should generate the highest likelihood of generating the best result from your PA.  The pitcher’s last 7 pitches should not effect that calculus.

Ok...assuming an average pitcher and assume I am an average hitter (assumptions not given in original question)…

Then I am more likely to take. A. If not for strategic reasons, then because I’ll get grief from my manager if I make an out on the first pitch while the pitcher is struggling with control.

Does anyone know that the average strike/ball ratio is for MLB pitchers? 60%/40% seems about right to me.

A pitcher with true 60% strike talent would throw seven consecutive balls .16% (.40^7) of the time or roughly 1-in-600. For starter, that’s about 1 every 6 starts. It could just be dumb luck, but it could also be a short-term control problem.

More qualitatively, note that after walking the first batter, the pitcher couldn’t even throw a get-me-over strike on the 3-0 count on the 2nd hitter.

I would assume it’s a short-term control problem, and I would swing less often

"Then I am more likely to take. A. If not for strategic reasons, then because I’ll get grief from my manager if I make an out on the first pitch while the pitcher is struggling with control.”

Well, I am the manager, so you are only going to get grief if you do the wrong thing, in terms of our win expectancy.  Plus the second part of the quote above assumes something that is not necessarily true - which is that the pitcher IS struggling with his control.  He has already struggled (at least he has missed 7 pitches in a row - what you want to call it is up to you), but what he has done in the past has nothing to do with you - other than whether he is more or less likely to throw a strike to you on that first pitch.

It is a given that if you normally swing at that first pitch 30% of the time, given the pitcher, the outs, the runners, etc., that if the pitcher is now (as compared to if he had not just thrown 7 balls) less likely to throw a strike, then you would swing less than 30% of the time, if he is more likely to throw a strike, then you would swing more than 30% of the time, and he is no more or less likely to throw a strike than if he had NOT just thrown 7 balls in a row, then you would swing 30% of the time, as always (given the pitcher, score, runners, inning, etc.).

A test of proportions indicates with a p value of 0.008 (<<0.05) that the new sample of 7 straight balls is unlikely to come from the same overall population of the pitcher’s history of 50% balls and 50% strikes (you have to go down to about 35% balls before it becomes insignificant at the 5% level).  This indicates that the pitcher is either operating under a new process or that there is a special cause at work.  If the pitcher continues with the same approach, experience suggests that the wildness will continue.

The correct strategy from this point depends on whether the pitcher will change his approach (game theory, perhaps) as well as the hitter’s ability (perhaps ignoring his ability to draw a walk).  A good hitter will be able to feast on the meatball often enough that the increased chance of a walk will not be enough to merit an automatic take (thus should take less often and should sit on the meatball), whereas a poor hitter won’t have a big enough jump in BPS (batting plus slugging) so he should take more often.

My initial inclination is to take the pitch, but given that MGL posed the question, I have to do a little Bayesian updating and change my mind.  The drum roll here makes it seem unlikely that the answer is, “Yup, manager is right on this one-- you should take the pitch.” But now I have set myself up to look foolish if it is.

Anyway, I disagree with the premise that the hitter decides in advance whether to swing or not swing.  The hitter’s decision should be which pitches and locations to swing at.  The hitter gets a noisy signal of the pitch and location by the time he has to choose whether to swing, and given that signal, he makes a decision. 

A guy at BtB wrote an article a couple months ago (http://www.beyondtheboxscore.com/2009/3/30/814883/bases-loaded-2-outs-full-c) which I made a very long comment on illustrating this point.  He posed the question of what should a batter and pitcher do when its full count, bases loaded, and two out.  He said given the percentage of times that the batter makes contact with pitches in and out of the strike zone, given the run value of making contact when you do, then the batter should swing a large percentage of the time and in equilibrium, the pitcher should throw a ball a large percentage of the time.  I explained in the comment that modeling the hitter as an agent who makes a decision to swing or not swing without having a signal of the pitch type and location first will almost always get you funny results like this.  The hitter decides on what to do based on his signal of the pitch type and location.

Coming back to this topic, I suspect that if the pitcher throws a ball more often, that doesn’t mean he’s less likely to throw one right down the middle of the plate.  If he’s been aiming for the corner and missing because his release point is off or something, he’s probably more likely to miss 9 inches off the plate as he is 9 inches towards the heart of the plate.  Batting average on contact might be quite different for hitters who swing first pitch in this situation versus hitters who swing first pitch in this situation in general.  That seems like it would really affect the decision.

(thinking my post has either been held [though I have no idea why it would be] or eaten… hopefully it doesn’t show up magically after I’ve re-submitted)

Since there’s nothing riding on it (and I have no credibility to lose at this point), I’ll go the other way and say B.  The argument would be that, to some extent, the pitcher is thinking he has to throw a strike, both for his own psyche and to not get pulled.  If the pitcher is thinking he has to throw a strike, it would be reasonable to approach the AB not like it’s a 0-0 count, but like a 3-0 count.  I don’t think I need to go look for the exact numbers to say that the batter’s success on BIP on 3-0 is as good as it will ever get.  So if I’m stepping in, I’m looking to swing, especially if we’re talking at the MLB level where presumably I’d have enough recognition skills to not swing on an obvious ball.

I go with b, less often.  You have to assume that a pitcher who’s thrown 7 balls in a row is more likely to groove a pitch down the middle of the plate, and therefore that the pitch is more likely to be an easy one to drive and get a hit on.  Also, you have at least two guys on base.  With runners on, a hit grows relatively more valuable than a walk, because of runner advancement.

I am going with (B) more likely to swing at the first pitch because first off you get paid to drive in runs not take a walk.  Chances are you are Dominican and you are of the mindset that “you can’t ‘walk’ off of the island”.  I would be more likely to swing at the first pitch… plus, chances are the pitcher is going to try to groove a strike one pitch.

Wow, some of you guys are making this question way more complicated than it is!  But it is nice that we have such deep thinking on this blog!  A high quality readership!

I’ll rephrase the question and you can forget about everything else.

“Is a pitcher more or less likely to throw a strike after 7 balls in a row than if he had not just thrown a long string of balls in a row?”

Also, as you can already see with this one, most of my questions will be ones that you hear discussed or mentioned all the time during TV and radio broadcasts.  In this situation, the prevailing “wisdom” is that you don’t dare swing at the first pitch and if you do, you will face the wrath of the manager (and the TV commentator).

Anyway, this is my last post for this question until I present my answer…

I hate to make this more complicated, but your post just made me think of something.  A lot of the time, a guy that gets four straight balls in a row was pitched around on purpose and the pitcher may want to challenge the next hitter.  So it might be that he’s more likely to throw a strike to the next batter for the same reason that he is less likely to throw a strike to the previous batter.

MGL/39- The answer is still yes, even if it’s only be the slimmest of margins.

Boy, there are a lot of Matts coming around here…

c) The same.

A pitcher should be approaching each batter in a different manner that is designed to induce that batter to get out in some manner. So what if he just threw 7 straight balls? They were to different batters, and therefore thrown to try and take advantage of those batter’s weaknesses. As the current batter, I would expect the pitcher to still try to make his pitches in a way that is trying to get me out. Since that doesn’t depend on the situation, I approach him the same.

To answer the revised question...I would guess that the pitcher is much more likely to throw a first pitch strike. Not only is the pitcher assuming you may be taking, but he is taking stuff off and aiming for the middle of the plate. A major league pitcher should be able to throw a garden variety 88 mph four-seamer somewhere in the zone.

I thought I’d do a quick DB analysis of this.  Going back to Retrosheet, I came up with 53 instances of this happening in 2008 (relatively small sample size).  I may have missed a few based on my query, because it wasn’t clear if we should count the situation where there were pick-off moves, wild pitches (which broke up events, etc.)

Anyways, of the 53 times the 7 straight balls (3 straight on two batters ago, then 4 straight balls AND it has been the same pitcher), the first pitch of the next batter went like this:

11 batter swings at first pitch (put in play, fouled, swinging strike,etc.)
22 called first strikes
20 balls

which is a 62% first pitch strike rate, however, if we look at the ratio of balls to strike when the batter DOESN’T swing it’s 52% called a ball.

Normally, first pitch strikes are about 60% (I calculated 59.3%).  The big differnce here is that the ratio when the batter doesn’t swing is 56.1% ball, a little worse than normal

Small problem we have is the characterization of those first pitches when the batter swung.

In the end, with the small sample size, and if our NULL hypothesis is that we needed to see a big enough difference from the overall, I would say (c) this shouldn’t change.  There isn’t enough evidence that the percentage that the next pitch is more likely a strike or ball changes compared to a standard situation.

I still think it matters whether the pitcher is just missing the corners or whether he’s bounced 7 straight fastballs in the dirt. 

Anyways, since MGL asked the question, I’m going to go against my first instinct and guess that the pitcher is just as likely to throw a strike. 

But is there a possible selection bias here?  I guess that the opposing managers will have removed pitchers who have thrown 7 balls in a row and are obviously being bothered by something that particular game (i.e., it’s damp and he can’t grip the ball, or he has a minor injury that’s hindering him somehow him) or maybe even just have a history of wildness.  So does that means that pitchers still in the game after 7 balls in a row will be more likely to throw strikes than average?  It’s either a low-leverage situation or the opposing manager has some reason to be confident in leaving the guy out there.

So I will guess: more likely to throw a strike on the next pitch.

I’ll rephrase the question and you can forget about everything else.

“Is a pitcher more or less likely to throw a strike after 7 balls in a row than if he had not just thrown a long string of balls in a row?”

Wait, are we talking about all strings of 7 balls in a row now, or just the conditions (2 walks, new batter) in the original question? Because I would expect a higher percentage of strikes if the analysis includes cases where the count is 3-0 after those 7 balls than if it doesn’t.

First, I want to reiterate MGL’s position regarding the game state: presuming the game game state you want, would your approach differ had the preceding 7 pitches all been called strikes as opposed to 7 called balls as opposed to a mix-and-match?  So, the inning, score, base, out, batter on deck, etc, is part of the “all other things equal” provision.

Also, MGL noted it’s a “typical” pitcher.

***

Now, my decision would be based on how many inches off the plate the called balls are.  If all the called balls are just inches off the plate, I don’t change my approach. 

If all the called balls are at least one foot off the plate, that’s something different.  My approach would be to consider the “apparently wild” pitcher to actually have me on a 1-0 count.  That is, I shrink my strike zone.  Therefore, I would have to take a bit more than I normally would.

This would be nothing more than a Bayesian process.  Since pitchers do not miss home plate by at least one foot 7 straight times, I have to presume that his talent level, at that moment in time, is at least a smidge worse than usual.

***

Going back to the “all other things equal”, it would have to matter if it’s late in the game.  Since we reasonably suspect that pitchers are humans who tire, if it was 7 straight pitches thrown in the 8th inning, and the pitcher has 130 pitches on him already, I’m thinking, as the hitter, that he’s hit a wall.

So, I think that while the “all other things equal” saves MGL on his question, you can’t presume that his fatigue-level would be considered the same if he had 7 straight called balls as opposed to 7 straight called strikes, after 130 pitches.

Tim/44

The thing is that you’re not adjusting for the quality of pitcher.  I would think that a pitcher that has just thrown 7 balls in a row is more likely to be Daniel Cabrera than Roy Halladay, so for that reason alone I would expect more balls.  Looking it that way, the fact that we have around the same strike-rate as normal (or a bit higher) suggests to me that you would be more likely to get a strike from these pitchers than normal.  But I dopn’t know if 53 (really 42 since I’m tempted to throw the swinging strikes out) is a large enough sample.

A

Unless I’m a perennial all-star, I don’t take the risk of getting my manager mad at me and affecting my playing time by swinging at the first pitch after 7 straight balls.

Besides, maybe this particular pitcher, whose common cause variation in control (i.e. his long-term performance) allows for an occasional 7-ball streak, has encountered some circumstance that triggers special cause variation (i.e. deviation from his long-term performance caused by a non-recurring, specific incident).  I think we all agree that special cause variation exists, although it may often be hard to distinguish beneath the usual layer of common cause variation.  Doesn’t mean it isn’t there…

Anyway, the cost of waiting for him to throw one strike is very low, so I’m in favor of doing it, albeit while maintaining the visual premise that I am ready and willing to swing…

Ryan/48

I did a quick check on this, and put in the pitchers who were on the list of 53 (which included Kazmir, Oswalt, Kuo as well as people like Tejeda, Gobble, etc.).  Anyways, this set of pitchers has a slightly worse first pitch strike rate (but not that much, 58.3% as compared to 59.3%).

I still say it’s (c).  Not enough evidence one way or the other to suggest that the first pitch on the at-bat after the 4-pitch walk is going to any more likely be a ball or strike than what would happen in the normal situation with this set of pitchers.

A) I swing slightly less often.

My reasoning is that the 7 straight balls is an indication that the pitcher has become tired. 
The pitcher is probably slightly less likely than normal to be able to throw a strike, and thus the chance I will swing is slightly less.

(As others have said, if my manager wishes me to take the pitch, because of the string of balls, then that overrides everything else and I take it)

Here are the assumptions I’m making from ‘all things being equal’

The pitcher was trying to throw strikes on at least 3 of the pitches to the batter before me.

The batter before him was not intentionally nor obviously semi-intentionally walked.

The correct call was and will be made on all pitches.

The pitcher is a robo-pitcher who feels no fatigue nor is subject to possible unknown unannounced injury such that if he can pitch at all he pitches at his historical level of ability regardless of environment or condition.

Robo-pitcher has no batter to batter memory, he will pitch to me the same in this situation no matter how the game got into this situation.

My normal swing at first pitch odds with this robo-pitcher are > 0 and < 1.

The batters ahead of me have league average plate discipline.

With all that I say C the same.

I dont think its reasonable to assume the pitcher is Robo pitcher and doesnt fatigue. 

I think that sometimes, this type of performance (7 balls in a row), indicates the pitcher is having some sort of problem, which will continue into the next pitch.  It doesnt always mean that ,but I think it does mean that at least sometimes.  If there is an X% chance that the pitcher is having a serious problem, and 100-X% chance that he is fine and it was just random that he threw 7 balls in a row, then I am at least going to swing a little bit less, due to that
g;e chance that he is having a serious problem, or is fatigued, or injured, or whatever.

As outlined in recent comments, it depends. 

Two examples. First. A starter in a 0-0 game with 60 pitches gives up a leadoff triple in the 7th inning and then walks the next two hitters (who are above average contact hitters) to bring me up.  He has walked nobody else in the game.  I draw the inference that these are semi-intentional walks, and I do not change my approach at all, as the 7 consecutive balls are not indicative at all of any change in the likelihood of the pitcher throwing me a first pitch strike.

Second.  The opposing starter leads off the game with a 5 pitch walk, and with the leadoff hitter on first, throws 4 pitches to the second hitter, the last two of which are quite far out of the strike zone.  I infer that the starter lacks his usual control and would be more inclined to take the first pitch than otherwise.

In spite of the rephrasings, I see that there have been two possible ways to interpret the problem:
1) do I change my approach? No. I still swing at fat pitches and take tough pitches.
2) Do I actually in practice swing more or less often, regardless of my intended approach? That is a practical question dependent on whether the pitcher, on average, in practice, actually delivers me a fat pitch more or less often. From 2000-2008, the stated scenario only occurred a bit over 500 times. Based on that sample, batters who swung at the first pitch were more slightly more successful than those who took. But I have not examined any adjustments for batter or pitcher quality, platoon advantage and so on.

MGL #39

Referencing your question:

“Is a pitcher more or less likely to throw a strike after 7 balls in a row than if he had not just thrown a long string of balls in a row?”

Does YOUR answer to this question change if I change the number of balls from 7 to a larger number, like say 9?  What about 11?  15?

If your answer does change, when and why?  If it doesn’t change, why doesn’t it?

I assumed the following:
1) the pitcher has thrown 7 or more balls in a row
2) within the same inning
3) excluding situations that included an intentional walk to one of the previous two batters

I found 501 such situations from 2007 through yesterday.  The batter took the pitch 234 times, garnering 123 balls and 111 called strikes.  He swung at the pitch 267 times.  So the pitcher threw about 75% first strikes to a batter in this situations, which is well above average.

However, the batter’s outcome was slightly better if he took the pitch anyway, although I’m not sure the difference is significant.  I found an eventual wOBA of .353 for the at bats where the batter took the first pitch and an eventual wOBA of .350 for the at bats where he swung at the first pitch.

That’s so close that I’d say the answer is C or that it needs more research.

Actually, now that I think about it a little more, I’ll change my answer to B since the linear weights that I used to calculate wOBA were for an average base-out state.  In this case we know we have at least two runners on base, so the base hits which are more prevalent in the swing-at-first-pitch scenario are even more valuable than usual as compared to the walks which are more prevalent in the take-first-pitch scenario.

Mike is that only when the “next” pitch is the first pitch of an AB?  That is the only situation I am talking about.  I am not talking about, for example, when the count is 3-0. Also, looking at performance (like wOBA) when taking or not taking is not going to get you anywhere.  For one thing, the pools of hitters are different.

Yes, it is only on the first pitch of an AB. 

Good point about the pools of hitters being different.  I think that had been mentioned before in this thread, but I neglected to consider it.

Again, the question is not complicated.  To the person who keeps saying, “It depends on the pitcher,” it does NOT depend on the pitcher. If it is Daniel Cabrera, then the question is, “If Daniel Cabrera just threw 7 balls in a row, what would you do on the next pitch, the first pitch of your AB, as compared to if Daniel Cabrera just threw 7 strikes in a row (or something else other than a strong of balls)?”

If the pitcher is Roy Halliday, then the question is the same - just substitute Halliday for Cabrera.

As I said, forget about everything to do with what you would or would not do.  The only question is whether an average pitcher throws more or fewer strikes after he just threw a bunch of balls in a row, all things being equal.  That is the “new” question.  Most of you are skirting around that question for some reason.  The answer is either yes, no, around the same, or I don’t know.  I concede that it is not easy to tell without pitch f/x data, because batters swing or don’t swing differently depending on what recently happened and when a batter swings, we don’t know what percentage of those swings were strikes or balls.

"To the person who keeps saying, “It depends on the pitcher,” it does NOT depend on the pitcher.”

If you’re referring to me, I only said it once, and I meant it with regards to Tim’s analysis, not to the question. 

With Tim’s mini-study, it does matter, as he was comparing the tendencies of a pool of pitchers that had just thrown 7-straight balls, with the regular tendencies of all MLB pitchers, instead of the “regular” tendencies of that same pool vs. the tendencies of the pool after it had thrown 7 straight balls. 

If you’re not referring to me, then nevermind.  But give us the answer already!

I’m going to go with “I don’t know”, and have “about the same” be a close second. I’ve seen a fair amount of games where a pitcher has thrown a string of balls, and I can’t say definitively that the “next” pitch would be a strike or not.  Who knows when the streak ends?

With every response, I grow more convinced that there is something fundamentally wrong with this question.  Many more interesting questions have come up, and it seems to me like the simplified version might just not be very meaningful.  I agree with the comment about “how many is enough consecutive balls?”

I know personally I wouldn’t swing after 30, but after 100 I might just to save the poor pitcher from further embarrassment and injury.  These are silly scenarios, yes, but the point is, there are many other factors which influence my swing/not swing decision far, far more than number of balls counted in a row.  MGL, I hope your answer makes me feel better about wasting so much time pondering this today during work

I did not realize that this was going to be such a “mind bender.” I’ll make sure the next one is simpler and less controversial. The “answer” will be posted later tonight.

The answer to the “new” question is that the pitcher throws more strikes than usual.  The numbers are given in my post #57.  All MLB pitchers throw about 74% first-pitch strikes (including pitches swung at as strikes). 

These pitchers in question are not the same as all pitchers.  Since they have thrown 7 straight balls, their typical first-strike percentage is probably less than the MLB average of 74%.  So the fact that they throw 75% first-pitch strikes means they are throwing more first-pitch strikes than usual.

Bahh.  The question changed. 

The new question, which can be rephrased to say “does 7 consecutive balls have a predictive value on the next pitch?” is empirically answerable.  Sadly, I lack the ability to answer it, but I can tell you what I would do.

I would start by looking at the 1st pitch strike% following two consecutive walks in which the most recent walk for 4 consecutive balls (or possibly 3 consecutive).  I find it impossible to believe that there is anything magical about 7 consecutive balls, so limiting data acquisition to that situation alone is more likely to produce noise than truth.

The problem with the 1st pitch strike% is batters swinging.  Preferably we would eliminate that consideration.  The best way to answer this would be pitchf/x.  So, I would look at the ball location as the ball crossed the plate without regard to weather a batter swung at the pitch or not.

I would then compare that result with the result from the same analysis for all first pitches.

My guess is there will be no predictive value in the string of balls, so I’ll stick with C.

----"I did not realize that this was going to be such a mind-bender.”

Well, the way the question was initially posed clearly (IMO) left all of the ‘extraneous’ considerations as fair game. And actually, the more expansive interpretations of the original question have produced the most interesting responses....

My guess is that there WILL be some predictive power in the string of balls.  (However I worry that the effect is small enough that it wont be statistically significant).

How can something be predictive and not statistically significant?

It would be cool to have the pitch f/x on these situations to answer the underlying game theory question.  How likely is it that the pitcher who has thrown 7 consecutive balls will throw a first pitch fastball right down Broadway?

(Another Matt)

My question is: Should the batter ever change his approach? It seems to me that the batter has three modes he can be in:

1. Take (don’t swing at anything - 3-0 counts, I guess, although I find this practice dubious, except for the most inept hitters)
2. Protect the plate (two strikes)
3. Swing at pitches you can drive (good location and not fooled) - otherwise don’t swing (all other counts)

It seems to be pretty independent of the tendencies of the pitcher.

The answer to the “new” question is that the pitcher throws more strikes than usual.  The numbers are given in my post #57.  All MLB pitchers throw about 74% first-pitch strikes (including pitches swung at as strikes).

These pitchers in question are not the same as all pitchers.  Since they have thrown 7 straight balls, their typical first-strike percentage is probably less than the MLB average of 74%.  So the fact that they throw 75% first-pitch strikes means they are throwing more first-pitch strikes than usual.

Absolutely 100% correct!  Pitchers who just threw a bunch of balls in a row are worse pitchers, walk-wise, than the average pool of pitchers.  In fact, pitchers that throw 5 or more balls in a row to the last 2 batters throw 1.4% fewer first pitch strikes than the average pitcher. So according to Mike’s numbers, you would expect 72.6% rather than the MLB average of 74% (I don’t know where he gets those numbers, BTW - they are WAY too high - the number is 61.9%).

But, whether Mike’s numbers are correct or not, the basic premise that he expounds is 100% correct.  The more a pitcher has missed the strike zone, the more he throws a strike on the next pitch - the exact opposite of what players and managers assume.

Now whether he does that because he knows the batter is not swinging very often or because he is frustrated at throwing balls, we don’t know. Probably some combination.  But the bottom line is that pitchers throw MORE strikes after a string of balls and NOT fewer strikes as some people might expect.

How often you swing at the first pitch of an AB, given the pitcher and game situation (and anything else you can think of), is dependent on one thing and one thing only – that is the frequency with which the pitcher throws a first pitch strike. If the pitcher tells you, “I am going to throw a first pitch strike 35% of the time, and you would swing x percentage of the time, given the game situation, then if we roll the clock backwards, and he tells you that he is going to throw a first pitch strike 36% of the time, then you should swing X+ percentage of the time. If he says 34%, then you would swing X- percent of the time.

Some people are having a hard time understanding that concept, but it is 100% correct.

So the answer is A.

Interestingly (or sadly, actually), batters swing way too infrequently as pitchers keep throw balls. When the last sequence of pitches is either a strike or less than 4 balls, the batter swings around 32.5% of the time.  When the last sequence is 5 or more balls in a row, the batter only swings around 26.3% of the time.  That is ridiculous of course. Completely the wrong strategy.

Which leads to the next question:

Runners on first and second and 1 out and you are the batter. The count is 3-2.  The pitch is on the way and it is marginal.  You estimate 50% ball and 50% strike.  Swing or no swing?  It might depend on the inning and score (and other variables), but we’ll assume that we don’t know anything else.

I guess (a). The pitcher is having control problems. The first pitch is more likely to be a fastball but less likely to be in the strike zone. The latter consideration outweighs the former.

All this is off the top of my head.

What surprises me about #57 is that batters in this situation swung at the first pitch more than half the time. (Am I reading the data right?) Yet, the conventional wisdom is “make him throw a strike.” So either we have the conventional wisdom wrong, or players don’t follow it!

Cross-posted with #73.

So the answer is A.

Based on what you wrote, you mean C?

How often you swing at the first pitch of an AB, given the pitcher and game situation (and anything else you can think of), is dependent on one thing and one thing only – that is the frequency with which the pitcher throws a first pitch strike.

I disagree. What if the pitcher is going to throw you a high fastball, and you are a good high fastball hitter?

When the last sequence is 5 or more balls in a row, the batter only swings around 26.3% of the time.

Unless I am misreading #57, Mike has this as over 50%. There must be some issue here, probably with my reading comprehension skills.

MGL, where I got my numbers for the first pitch strikes overall was from Baseball-Reference, but I realize now that I misinterpreted what I saw there.

When I run a query against my Gameday database, I show a 60.8% first-pitch strike percentage for all MLB pitchers 2007-2009, versus 59.5% first-pitch strike percentage overall in 2007-2009 for the pitchers who at some point threw 7+ balls in a row.

Mike/76- So doesn’t that mean that MGL’s answer is wrong, or is it too small of a sample size?

Nick, no, it is consistent with what MGL wrote. The pitchers throw fewer strikes overall, but in situations where they have just thrown many balls in a row, they throw more strikes.

I just posted a long analysis of the second question that got marked as spam. Short version: do not swing.

No, pitchers who threw 7 or more balls in a row immediately prior to the beginning of an at bat (excluding IBB) threw a first-pitch strike to the next batter 72.6% of the time in 2007-2009.  These same pitchers normally threw 59.5% first-pitch strikes (weighted by how many times they appeared in the 7+ balls in a row sample).  MLB average is 60.8% first pitch strikes. 

So these pitchers are below-average first-pitch strike throwers, but when they missed the zone for the previous 7+ pitches, they started the next batter out with a strike at a much higher than average rate.

Mike, I don’t think that 72.6% is correct either.  Remember when we had a thread about how often a pitcher can throw a strike if that’s all he was trying to do?  For example, with a 3-0 count with the pitcher batting?  It was like 65% or something like that.

In any case, pitchers throw strikes more often after a ball or a string of balls than after a strike.  As I said previously, that might only be because of how infrequently batters swing at those pitches.  If the pitcher knew that you knew that batters generally swing way too infrequently in those spots and knew that you would act differently, he might give you fewer strikes than otherwise. But that was not part of the question.

dcj, all things being equal means all things being equal means all things being equal means…

About the same. I will be willing to swing if the pitch looks like a fastball near the middle of the plate, but I’m not going after a borderline pitch (which I probably wouldn’t do with less than two strikes anyway).

At age 16, I was pitching in a spring training game for our summer league (up to age 20). A couple batter sin, I stop following through correctly, and everything is going up high and inside to a righty batter. I walk three straight to load the bases. I know what I am doing wrong, and tell myself to just trhow a f**ing strike. The first pitch to the next batter lands about 380 feet away in left center for a grand slam. At least I did strike out 5 of the next 6 batters.

I am confused, what is the answer?  I can’t tell what is MGL’s post and what is he quoting from other peoples previous posts.  If the next pitch is more likely to be a srike, then why is it correct to swing less frequently?  Not only did the question or questions confuse most people, but now the answer is confusing.  Can we get a post that is dedicated to just the final answer

ie (A) because blah blah blah

I’m sorry, I thought this was a probability or strategy debate not a mindreading test.  We’re not allowed to assume the skills of the batter after us nor know how many outs or any other conditions etc there are… yet we’re first asked whether we should take more often/swing more often/act the same, then instead, asked whether the pitcher is more likely to throw a strike. We aren’t even allowed to assume that the pitcher was a penny.

Yet the entire rationale for MGL’s answer is that MLB pitchers throw a first strike pitch 35% of the time.  Well, nowhere in the question are we told the pitcher was a MLB pitcher either. We weren’t even able to make assumptions of the quality of the pitcher.

In addition, we needed to guess that the pitcher was not a penny where the chance of an event is not affected by the previous event, but yet the belief that the law of averages would return a MLB pitcher to that 35% threshhold. 

Either way, it seems the answer provided is weak at best, and minimal usefulness if it is true because it requires precise conditions like an inhuman human pitcher throwing to a batter with no other context to the “baseball” situation.

Mike - I got very different numbers than you did.  I queried on previous batter “BBBB” and batter before that “*BBB” for 2005-2008 and got 282 instances.  First pitch after that was 112 B, 96 C, 21 F , 3 L, 1 M, 17 S, 1 T , and 31 X.  That has the pitcher throwing strikes 60.3 % of the time (assuming all swings are at strikes) and the batter swinging or bunting at 26.2 % of the pitches.  I can’t believe your number that has the batter swinging at the first pitch more than half the time in that situation.

So I’ll stick with my answer C.  I don’t expect the pitcher to pitch differently than usual and I go to the plate ready to swing at a pitch that I think I can hit well and take if I don’t see it.

Mike - Did you filter out situations where the pitcher was replaced after either the first or second batter walked?

MGL - You better repost your new question somewhere else or people are going to have a hard time finding it.

MGL:  If you can add updates to your original posts, on each question of the day I think you should add a line when you post your answer saying “MGL’s answer is posted at #xx”.  That way people can find your answer without searching through the whole thread.

I have spring training games as part of my Gameday database, and there was something weird about the data in the 2009 spring training games.  If I exclude them, I get 84 balls, 93 called strikes, 22 foul balls, 13 swings and misses, and 21 balls in play.  That means the batter was taking 76% of the time, and the pitcher threw a strike 64% of the time.  That seems more in line with the data that others have found from Retrosheet.  I will have to investigate why the data from 2009 ST in my database is screwy.

Btw, I agree with Guy’s answer and reasoning for Question 2.

Replies to MGL’s second question should go here:

http://www.insidethebook.com/ee/index.php/site/comments/question_of_the_day_05_29/

MGL/73 has his answer.

His answer is basically that the pitcher is more likely to throw a strike than a ball (following a string of balls), so the batter should swing more often.

I prefer my answer that the batter should treat the first pitch in the at bat as if the pitcher is already at 1-0.  At 0-0, the batter swings 30% of the time (with a wOBA of .327 if he swings).  At 1-0, he will swing 42% of the time (with a wOBA of .352 if he swings).

However, at 0-1, he will ALSO swing alot (45% of the time), but with a wOBA of .276 if he swings.

Clearly, the batter is swinging the same amount of time on 0-1 or 1-0, except the pitcher is throwing it way more down the middle at 1-0, and more at the edges at 0-1.

So, to simply say he should “swing more often” doesn’t help enough.  I think it would help the batter more to know that he should approach the at bat as if it’s 1-0, because with that comes the information that he should shrink his strike zone, and only go after his pitch.

Heck, even at 2-0, he will swing 42% of the time.  But again, his swing wOBA is way higher at that count than at 1-0.

It seems to me that the batter should be thinking about more than just the first pitch. A batter might be thinking that the pitcher is struggling with his control, so the odds of drawing a walk are higher. Does anyone have the percentage of strikes thrown in the next 5 pitches after 7 straight balls? It seems possible that some of these pitchers are correctly guessing that the next batter won’t swing at the first pitch and are able to get one over, but when they go back to worrying more about location, they continue to struggle.

That’s a fair point.

So, all we want to know is what happens in the PA following two PAs that ended with 7 balls in a row.

Tango/#91, the problem (or complicating factor, if you want to be more optimistic) with that is that you are dealing with two different pools of hitters and pitchers when you split the following PA by take/swing, as was pointed out to me by MGL in #59 (and implied by Matt S./#35).

Mike: which is why you can compare to the overall stats of those particular hitters.

(c) First pitch I’m always sitting on a very narrow part of my zone.  If I get the pitch I want, I’ll swing.  If not, I’ll take.  If I go up 1-0, I simply repeat the same approach until I get my pitch or he puts in a spot where I need to expand.

The fact that he’s thrown 7 balls in a row simply justifies this approach even more so.

That said, I would argue with the people who are insisting that a pitcher’s true talent doesn’t change throughout the course of a game.  I would guess that a pitcher’s ability to command his pitches does vary based on a set of conditions including, but not limited to, his emotional state and level of fatigue.

If it is not the case that his command has changed relative to his average level of command, than there’s really no reason to change my approach.  And if his command has changed, then even if I think he’s going to try to groove one, it could end up being on the black.  I just don’t see a reason to switch my approach.

Tango, you don’t shrink your strike zone and treat it as a 1-0 pitch because the reason you shrink your strike zone in a hitters count, in addition to the fact that the pitcher is more likely to throw a strike down the middle (any time a pitcher is more likely to throw a strike, he is automatically more likely to throw one down the middle), is that you don’t mind getting a called strike because you have strikes “to spare.”

You treat the situation as if the pitcher simply is a pitcher with a little more control then he normally has, which is THE WHOLE POINT of the exercise yet lots of people seem to be missing that as evidenced by their posts in which they still insist that we have a “wild pitcher.”

For the 100th time, after a string of balls, we have a pitcher who is LESS wild than he normally is, not MORE wild.  How do I know that?  Because I looked at the data.  The reason for that, presumably, is that he simply tries to throw more strikes because, one, he knows batters don’t swing as much as they normally do on the first pitch of an AB, and/or two, he is frustrated and is really trying to throw a strike.

Again, I don’t know what to say other than this is WAY less complicated than every single person who has posted on this thread has made it out to be. 

At the risk of repeating myself 5 or 6 times, we simply have a pitcher who is going to throw a first pitch strike more often than he normally does (with runners on base, as there will be after 7 straight balls) as opposed to LESS often which is the conventional wisdom.

How often you swing at any pitch from any pitcher is a function of how often he throws strikes, period, all other things being equal.  I’ll repeat this next statement one more time and then I am officially declaring this question closed.

“If you normally swing 28% of the time on the first pitch of an AB against a particular pitcher in a given situation (some people are also having a hard time even understanding what “swinging 28% of the time” means - it simply means that you add up all the times you swing for whatever reasons and divide that by the number of pitches!), and then you roll time backwards and the pitcher says to you, “Hey buddy, this time, I am going to try and throw more strikes” (for whatever reasons) and you respond correctly, at the end of 1000 of those AB’s, you will have swung more than 28% of the time.  And vice versa if he tells you that he will be throwing fewer strikes.

So the answer is 100% B, that you should take less often (swing more often).  At one point I accidentally said A, I think.

And it makes absolutely no difference who the pitcher is, the next batter, the level of play, etc.  That is because the question (and answer) is, “As compared to the exact same situation but the pitcher has NOT thrown a bunch of balls in a row.” Of course I don’t KNOW that high school pitchers throw MORE first pitch strikes after a string of balls than after some other pitch sequence.  If high school pitchers continue to be wild, as opposed to major league pitchers, who do NOT continue to be wild (they may still be “wild,” but even a wild pitcher can throw more strikes if he wants to!), then of course the answer would be A, “Take more often.”

A pitcher who is down 1-0 is more likely to throw a strike than a pitcher who is up 0-1 isn’t he?

MGL - I am not sure that I understand the numbers that you presented in Post# 74.  What I think you said was that the average major league 1st pitch strike percentage is 61.9%, that the pool of pitcher’s who threw 5 or more balls in a row had a usual 1st pitch strike percentage 1.4% lower than average.  Would that make their average 1st pitch strike percentage 60.5%?  Because as I stated in Post #84 I calculated that the pitcher’s first pitch after the 7 ball, 2 walk scenario described in your problem was a maximum of 60.3% strikes.  You claimed in your Post# 74 that a pitcher throws more 1st pich strikes than his usual after 7 balls, but I can’t seem to find where you actually state what the pitcher’s first pitch strike percentage actually was and why it might be different than the 60.3% that I found.

Peter, 7 balls in a row is too small a sample for your 60.3% or whatever it is to have much certainty.  The better thing to do is to look at a curve of 3 balls in a row, 4, 5, etc., and then to smooth that curve out.  That will give you a more accurate and reliable number for 7 balls in a row.  Also, I think that an umpire is less likely to call a borderline pitch a strike after a string of balls, so that means the pitcher is actually throwing more strikes than the numbers suggest.  I am not suggesting that the pitcher throws a lot more strikes than he normally does after a string of balls.  It is a little bit.  But, it is almost surely not FEWER strikes as everyone seems to think.

Tango, yes he is, but that is not the only reason for “shrinking the strike zone” as a hitter.  In fact, your don’t really shrink the strike zone as a hitter when the pitcher has a higher chance of throwing a strike.  You swing more often, but you don’t really shrink your zone.  You shrink your zone because, as I said, you can afford a called strike.  For example, if you have 2 strikes, let’s say even 0-2, and the pitcher told you he was going to throw a strike (as much as he can).  You would swing a lot but you would NOT shrink your zone.  IOW, you would not intentionally not swing at a pitch on the corner that you were pretty sure was going to be a strike.  That is the definition of shrinking the zone.

You said that the batter should treat the first pitch of an AB where the pitcher is going to throw more strikes than he usually does on the first pitch as a 1-0 count.  That is simply not true for the reasons I stated.  You cannot afford a called strike at 0-0 as much as you can with a 1-0 count.  You simply treat the AB as a regular one, assuming a pitcher who has a little more control than the pitcher on the mound normally has.

Peter, 7 balls in a row is too small a sample for your 60.3% or whatever it is to have much certainty.  The better thing to do is to look at a curve of 3 balls in a row, 4, 5, etc., and then to smooth that curve out.  That will give you a more accurate and reliable number for 7 balls in a row.

MGL -Now I am really confused. Have you done research on this or haven’t you?  If you have done research then why don’t you show it to us and where it shows that a pitcher is going to throw more strikes than he usually does? How do you know that the 282 pitches that I used in my empirical sample is not a large enough sample to be reliable?  How do you know that it is less reliable than extrapolating from a curve based on shorter strings of balls as you suggest?

So the big takeaway from this is that a pitcher who has thrown many balls in a row is MORE likely to follow this with a strike, not less likely, because he is trying to throw strikes.

Alex: I have no doubt this is true following 1-0, 2-0, and 3-0 as well.

I have to believe that the more called balls are thrown, the more likely the pitcher is going to throw “easier” pitches so that he can get pitches over the plate and the more likely the batter is going to shrink his strike zone (and not chase the borderline pitches).

So, I think this extends to 4-0, 5-0, 6-0, 7-0, 8-0, 9-0, 10-0, etc, etc.  I think MGL disagrees with my reasoning.

Tango - A couple of points about your Post #101.  A pitcher, may and I emphasize may, throw “easier” pitches intending to make it more likely that his pitch goes over the strike zone rather than pitch to the corners after a series of pitches outside the strike zone, but that is no guarantee that the pitcher will actually throw the ball where he intends and actually throw a strike more often than he usually does.  A pitcher rarely intends to throw a pitch outside the strike zone; he either wants it to be just barely in the strike zone or appear that it is going to be in the strike zone in order to induce the batter to swing.  That the pitcher has failed in a succession of pitches to accomplish this is an indication that his ability to control his pitches is below his normal ability.  This would be particularly evident in the described scenario on his seventh pitched ball when he failed to throw a strike on a 3-0 count after just having walked the previous batter, resulting in having at least 2 runners on base with at least 1 runner in scoring position.  Surely, his motivation for throwing that pitch in the strike zone was at least as great as on the eighth pitch (the one we were asked to evaluate), but he still failed to throw a strike.  Now, on the eighth pitch he is faced with the following problem; psychologically he probably needs to throw a strike to get some confirmation that he still can, but he is facing a new batter in an unfavorable baseout situation that he also badly needs to get out.  He has been left in the game by his manager even after his poor performance which indicates to me that either the manager has confidence in his ability to get this batter out, or that the game is out of reach and the manager wants to see if he has the ability to work himself out of the jamb he has created.  So opposing his right brain psychological need to throw a strike is left brain logical thought to approach this new batter as he normally would to best get him out.  I have no idea what wins out in the pitcher’s mind, I only know that in the 282 times that this situation occurred over the last 4 years the pitcher threw at most 60.3% strikes which is statistically insignificantly different to what a pitcher normally throws on a first pitch.

I have no idea what wins out in the pitcher’s mind, I only know that in the 282 times that this situation occurred over the last 4 years the pitcher threw at most 60.3% strikes which is statistically insignificantly different to what a pitcher normally throws on a first pitch.

Can you give us the line (PA, BB, H, HR, K, wOBA) for these matchups on these 282 occasions?

If I counted correctly 42 batters atruck out and 22 walked.  The other information would be harder to find out as I used excel and didn’t export the entire event line to Excel from Access.  I could get if it is important to you but not right away.  Some of the posters had theorized that the pitcher was tired.  I can tell you that the median number of pitches that the pitcher had thrown previous to the seven balls was 23 so he shouldn’t have been tired.

42K, 22BB on 282 PA.  That’s .15K, .08BB per PA.  That sounds like it’s a tick below league average in both cases (.17, .09 IIRC).  So, 77% contacted PA, as opposed to the average, which is probably around 74%.  That difference is around 1 SD.

The K/BB ratio is pretty much right on league average.  It sure looks like the results look indifferent regardless of how many consecutive balls are called.

Probably even closer to average than that as I didn’t take out the 4 or 5 times that the pitcher was removed in the middle of the PA after pitching a couple more balls.

Here is the 05-08 data from retrosheet:

First column is the sequence of balls in a row in the previous pitch/pitches, with at least first and second base occupied.

Second column is how often that occurred, with at least first and second base occupied.

Third column is the overall first pitch ball percentage for that pool of pitchers with at least first and second base occupied.

Fourth column is the percentage of first pitch balls after that string of X number of balls, with at least first and second base occupied.

0 51124 .416 .418

I’ll explain each number before I go on.

0 means that the last pitch to the previous batter was not a ball.

51124 is how many times that occurred.

.416 is the first pitch ball frequency for this pool of pitchers with at least first and second occupied.

.418 is how often they threw a ball on the first pitch to a batter after the last pitch to the last batter was NOT a ball.  So, as you can see, after they just got done throwing a strike (or a batter swinging at a ball out of the zone of course), they throw MORE balls than they usually do on the first pitch to the next batter.  That alone tells us a lot!

Anyway here is the rest of the data:

1 10139 .420 .399 (the last pitch was a ball, which means that the last batter walked.  Apparently they really try and throw the next batter a strike!)

2 5522 .421 .389
3 3373 .421 .406
4 5503 .421 .395
5 409 .430 .418
6 191 .427 .366
7 118 .425 .398
8 171 .431 .386

As you can see, in ALL cases, the pool of pitchers are particularly wild pitchers AND they throw considerably more strikes than they normally do on the first pitch to a batter after a string of balls.  (I said before that they throw marginally more strikes, but I was wrong.)

And that is EXACTLY what I would have expected from watching 200-300 games a year for the last 20 years.  Pitchers that have thrown a bunch of balls in a row are usually frustrated, they are often one or two balls away from being taken out of the game by a pissed off manager, and they know that the batter is taking considerably more than he usually does in that situation (absent the prior string of balls). OF COURSE he is going to throw more strikes!  Easy for me to say after the fact, but before I did the research, it is indeed exactly what I would have expected.

Now, with pitchers who are 1-0, 2-0, and 3-0 on a batter, there is a completely different reason why they throw strikes, although SOME of the same reasons still apply.  And that is because they can NOT afford to throw any more balls, for risk of the walk, and they HAVE to throw more strikes, and it is correct to throw more strikes.

In the case of the pitcher who just threw a string of balls and is now facing the next batter, the batter, as we know, is making a huge mistake in taking too often.  The pitcher MAY be doing the correct thing by throwing more strikes given that the batter is taking so much. BUT, if the batter were taking as often as he would in a normal situation OR if the batter were actually swinging more given that the pitcher is throwing more strikes, then the pitcher is throwing WAY too many strikes.  The Nash equilibrium point in that situation, assuming that the pitcher has the same true talent control that he always has, is for him to pitch to the new batter as he normally would and for the batter to approach the first pitch as he normally would.  IOW, for both batter and pitcher to have no memory of the last sequence of pitches. The only consideration should be the normal ones - the score, inning, base runner(s), etc.  If the true talent control of the pitcher is a little different than normal - i.e., he is a little wilder, than the Nash equilibrium point would be for the pitcher to continue to throw FEWER strikes and for the batter to swing a little less often than he normally does against that pitcher and in that situation.  We see neither of these, which means that at least one of the participants is making a mistake.  As I said, I am positive that the batter is making huge mistake by not swinging so often.  Again, we would expect that judging by the answers to this question by smart folks and what you hear all the time from commentators on TV (chastising a player for swinging at a pitch after the pitcher has just walked a player or two), and just from human nature.  As I also said, I am not sure if the pitcher is making a mistake or not by throwing so many strikes.  Probably not how infrequently the batter swings.

For example, if we look at pitcher who throw a lot of first pitch strikes compared to pitchers who don’t, we see a big difference in how often batters swing at first pitches, as we would expect.  That would suggest that if a batter does not swing a lot at first pitches, that the pitcher SHOULD deliberately throw a lot of strikes.

BTW, for that same data I printed above, here is how often the batter swing at the first pitch, again with at least first and second base occupied:

0 .323
1 .326
2 .333
3 .321
4 .304
5 .269
6 .257
7 .305
8 .240

It looks like batters don’t seem to do anything differently unless and until the last batter gets walked on the last 4 pitches at least.  And if he gets walked on 4 straight pitches (5 or more balls in a row), there seems to be an unwritten rule that you don’t swing at the first pitch of your AB very often at all.  With 5 or more balls to the last batters, batters only swing at 26.6% of the first pitch.  Given that they normally swing about 32% of the time and that pitchers are throwing them MORE strikes than usual, that is ridiculous. Just another example of how conventional wisdom and tradition can hurt a team’s WE.

If someone wants to bite off a lot, I would love to know an estimate of how many wins this poor strategy by batters cost a team per season.  My guess would be on the order of only .1 or .2 wins, but it could be more.  A lot of assumptions and approximations would have to be made, but I think it can be done.

Just assume that batters take around 7 or 8% (at least 5%) more often after a string of 4 or more balls in a row, and assume that that extra 5% is incorrect, which it is.  Estimate how much that costs a batter and multiply that by how many times the average team faces a pitcher who just threw 5 or more balls in a row to the last batter.  According to my numbers, that is about 10 times per team per season (890 times total). 

If a .1 win per season cost is correct, that would imply that if a batter takes 7-8% more than he should for no good reason, that it costs him .1 runs in that AB.  I don’t know off the top of my head if that is reasonable.  It sounds a little high.

I think something is wrong with the list of first pitch balls after a sequence of balls. With 0 preceding balls, there are .002 more balls than expected on the next pitch, in 51,124 trials. that’s an estimated excess of 102 balls beyond expected. (allowing for rounding errors in the statement of the percentages, the difference could approach .003, and the maximum number of extra balls around 150. Repeating that process with each of the other rows, for 1 through 8 preceding balls, there are a total of 611 balls below expectation. If the baserunner + 1st pitch scenario was properly partitioned into sequence of preceding balls, these totals should approximately balance. [only cases with 9+ balls are left out; those aren’t going to have much iimpact.] Something is off ...
FWIW, when I had analyzed the original problem statement (1st pitch after two straight non-intentional walks and at least 7 balls in a row, I found a ball percentage of 43.1% for the period 2000-2008.

they throw considerably more strikes than they normally do on the first pitch to a batter after a string of balls

This statement is true, whether it’s the first pitch to the batter or the fourth pitch, as you agree to later.

Your theory is that even though
- when a batter has just seen 4 straight balls (to the previous batter), then he’s going to be a bit more patient
- when a batter has just seen 4 straight balls (2 to the previous batter, and 2 to get him to 2-0), then he’s going to be a bit more patient

That the reason he’s going to be more patient is because in the former situation, the batter thinks the pitcher is wild, while in the latter situation, the batter has the pitch count in his favor.

And you are also suggesting that the pitcher in the former situation just wants to get one over there for confidence reasons, while in the latter situation, he wants to get one over so he doesn’t fall behind to 3-0.

I can accept all these reasons.  The point though is how should a batter approach such situations?  I was suggesting shrinking the strike zone the more consecutive balls he’s seen, implying that his swing rate should increase in balls closer to the center, and reduce his swing rate on balls closer to the edges.

Are you suggesting that he should increase his swing rate, as long as the pitch is anywhere around the strike zone, because he will have taken a bit off, and therefore, becomes more hittable?

Joe, don’t forget that I am only looking at batters where there is at least first and second base occupied for all sequences.  Did you do that as well?  Also, when you say “than expected” are you adjusting for the fact that the pool of pitchers in each sequence is different (the more balls in a row, the more the pool of pitchers is generally wild).  Also, I did not mention this in my last post, but the frequency of pitches thrown out of the zone is NOT equal to the number of balls thrown.  It is equal to the number of balls thrown plus the number of balls (pitches out of the zone) swing at.  If the batter is not swinging at many pitches, as they don’t after 5 or more balls in a row, don’t forget that the the number of balls thrown (and not swing at) will go up even if the pitcher is not actually throwing more balls out of the zone.  In one of my earlier posts, I said that I actually take the number of balls and add 15% of the number of swings (estimating balls swung at).  Did you do this?  Even my chart above didn’t do that.

For example, let’s say a pitcher throws 40% first pitch balls after a strike to the last batter and the batter swings 32% of the time.  Now let’s say that the same pitcher throws 40.5% balls after a string of balls and that the batter only swings 25% of the time.  Well, the pitcher is actually throwing FEWER pitches out of the zone in the second situation even though he throws .5% more balls not swung at.  And all we are interested in from the standpoint of how often the batter swings is what percentage of pitches out of the zone the pitcher throws.

“Are you suggesting that he should increase his swing rate, as long as the pitch is anywhere around the strike zone, because he will have taken a bit off, and therefore, becomes more hittable?”

Tango, I don’t know HOW he should increase or decrease his swing rate.  At any given count, if a pitcher throws more strikes, the batter should swing more.  If he throws fewer strikes, the batter should swing less, given the same count and game situation of course. I think we agree on that.

4 balls in a row to the last batter is a completely different situation for the batter than 1 ball to the last batter and a 3-0 count to the current batter - obviously.  In the first instance, the batter should swing about normally, probably a little more, at least I am claiming that.  In the second instance (a 3-0 count to the batter after the last pitch to the last batter was also a ball), the batter should rarely swing. In the second instance when you rarely swing, you basically only swing at pitches right down the middle. In the first instance when you swing around normally, you try and only swing at strikes of course, but when you are swinging 30% of the time, you will end up swinging at lots of balls and strikes on the edges.  When you are swinging at a pitch 5 or 10% of the time, you will end up swinging mostly at balls near the middle of the zone, occasionally bat balls at the edges and out of the zone of course.

So again, X balls in a row to the last batter and the first pitch to you is a COMPLETELY different situation than if some of those X balls were throw to you, such that you have a 1-0, 2-0, or 3-0 count.  I don’t know what you are asking.  You originally said that you should treat the AB as if it were a 1-0 count, which is clearly wrong. If the pitcher throws 40% balls at a 1-0 count and he throws 40% balls on the first pitch of an AB, clearly you swing more often when it is the first pitch.  So you do NOT treat it as if the count were 1-0 even though the pitcher may throw the same percentage of balls and strikes after a 1-0 count as he would if the last pitch to the last batter was a ball.  Surely You’re not suggesting that a batter with a 3-0 count should swing as often as he should if the last batter just had 3 balls in a row, and it is the first pitch of the AB to the new batter?  How often you swing given the pitcher and the game situation (and all other relevant information) is determined by two things and two things only: The count, and how often the pitch is going to be a strike.

Now, IF a batter were to swing at the same percentage of pitches at a 1-0 count as the first pitch of the AB, and the only way that would be correct would be if the pitcher were going to throw a lot more strikes at the 1-0 count than at the 0-0 count, then I imagine that he would swing at the same pitches, location-wise, but I am not sure.  He still might tend to swing more at pitches in the middle of the plate with the 1-0 count as compared to the 0-0 count, even if he is going to swing the same percentage of time at each count. I am not sure about that.  But, as I said, that can only happen when the pitcher is going to throw a lot more strikes on the 1-0 count than on the 0-0 count.