THE BOOK--Playing The Percentages In Baseball

Which leads to the next question:

No swing: 50% chance of bases loaded, 1 out; 50% chance of 1st and 2nd, 2 out.

Original run expectancy: 0.97
RE of bases loaded, 1 out: 1.65
RE of 1st and 2nd, 2 out: 0.47
Average: 1.06

source

All right, now what if you swing. Obviously if you are a very bad hitter you should not swing. What if you are Albert Pujols? When he swings at a pitch not in the zone, he makes contact 65% of the time. When he swings at a pitch in the zone, he makes contact 92% of the time. The average is 79%. (source) So if he swings at this pitch he will strike out 21% of the time. In that case the linear weight would be -0.53. (source; from the above we would expect -0.50, so -0.53 is close enough)

If he makes contact, it might be a foul ball, non-foul out, which puts us right back where we started. If it is a BIP, let’s be generous and give him his overall BIP numbers. (Generous because this pitch is worse than the average pitch he swings at.)

single: 21% ... linear weight = +0.88
double: 8% ... LW = +1.54
triple: 0% (rounded down) ... LW = +1.90
HR: 8% ... LW = +2.39
ROE: 1% ... LW = +0.99
BIP out: 62% ... LW = -0.60

source for percentages
source for LW values

The weighted average LW = +0.14. So we have

Strikeout: 21%, LW = -0.53
Foul: X%, LW = 0
BIP: (79-X)%, LW = +0.14

Even if X=0, the overall LW is right around zero. For realistic values of X, the overall LW is negative. Compare to +0.09 if he does not swing.

Therefore, even Pujols should not swing. Neither should anybody else. Once you throw in game theory, it may make sense for the hitter to swing some of the time, but in a single situation the answer is no.

I am in something of a math mode, so I am going to approach this as a math problem.

The run value of a walk in this state is 0.72.  So, taking the pitch, if you estimate 50% chance of a walk, that is 0.36 runs.  The run value of a K is -0.53, at 50% is -0.265

So, taking the pitch has an overall benefit of 0.105 runs.

Now the swinging has many different outcomes of course.  Most players do not swing and miss very often.  I think like 10%. So we’ll give the K -0.05 runs. So if you have a 90% chance of making contact, to come out ahead (of the 0.105), you need to average 0.122 runs when you do in order for swinging to be an effective strategy.  Ignoring foul balls, let’s assume you get a hit 30% of the time.  70% outs is (-0.59*0.7) -0.413 so you need to get 0.535 runs out of 30% hits.  That would mean averaging 1.78 runs on your hits.

Even a double in this situation is only worth 1.57 runs, so you would basically need every hit to be an XBH for it to be worth it for you to swing, and on a marginal pitch i don’t think that’s going to happen.

Most of my estimates are going to be off for certain batters, but I don’t think it will change much.

So I’m going to say “take” is the correct strategy and hope I’m not laughed off the blog. . .

MGL - And you might want to stipulate that the “you” that is the batter is an average hitter because if you don’t, and I am reading the question correctly, than you will get a whole range of answers that could be correct.

My answer is that you don’t swing.  I’ll give my reasons later so as not to influence others.

I think MGL means his answer to question #1 is B—take less often—not A.

For Q#2, I think you have to take if your chance of a BB is 50% (OBP = .500).  There’s no way the run value of a swing on that pitch is anywhere near that high.

I agree with Guy. A.500 OBA with an average 1 base of runner advancement is a pretty good known outcome to settle for. However, in real MLB ball I suspect we’d see a lot more swings than takes because the typical batter has a ‘fear’ of being called out on strikes.

Q2: don’t swing.  Looking at the RE tables the average RE after taking the pitch (1.1) is higher than the RE before the pitch (1.0), so it has to be the right option.  The RE before the pitch includes the value of all outcomes, including taking the pitch.  If the RE of taking the pitch > RE of (taking + swinging) then taking is the right answer.

I am assuming that the RE before the 3-2 pitch is close to the same as the RE before the 1st pitch.  I have no idea if this is correct.

If this logic is OK then there’s are interesting results if you look at different out states.  For 0 and 1 outs (and men on 1b and 2b) you should not swing at the 50/50 3-2 pitch, but if there are 2 outs you should swing.

In how many situations are you presented with an opportunity to reach base 50% of the time? So, typically the answer would be ‘take the pitch.’

Of course, if the hitter is Yogi Berra (notorious bad ball hitter), there are 2 outs, and the pitcher is on-deck, then the answer is ‘swing away.’

Lastly, if the hitter is Luke Appling then the answer is, “Foul the damned thing off.”

The wOBA on a called ball (that leads to the walk) is 0.720 (by definition).

So, if you simply take all the way, you get 50% the called ball and 50% called strike.  That gives you a wOBA of .360.

If you swing all the way, on a pitch that is on the margins, you are guaranteed to have a below-average wOBA.  Call it whatever you want.  But it will be way lower than .330.

GIVEN that the pitch is on the margins, and you KNOW that it will be on the margins, it would be incredibly foolish to swing at such a pitch.  Not to mention I didn’t even factor in the DP.

***

I don’t understand the reason for the question.  Once you know a pitch is on the margins, and it’s a hitter’s count, is it ever correct to swing at such a pitch?  I’d say it’s impossible. 

BUT, it depends on the ability of the batter to know that the pitch will end up at the margins to begin with.

I would have preferred the question being runner on 3B, 1 out.  That would be more challenging.

"I don’t understand the reason for the question.  Once you know a pitch is on the margins, and it’s a hitter’s count, is it ever correct to swing at such a pitch?  I’d say it’s impossible. “

Conventional wisdom states that with 2 strikes, you have to swing at anything close.

I think you have to swing because your being paid to drive in runs not draw walks with runners in scoring position or strike out looking.  And if it’s your contract year, it’s a no brainer that you swing because your agent told you that the more runs you drive in, the more money you will make.

Ryan, if that C"W" applies to a 3-2 count as well, that’s not wisdom.

Xei: yes, fans never want to see a called strike 3, with runners on base.  That Carlos Beltran PA (last at bat against Cards in playoffs) is the perfect example.

Of course it goes without saying that I am looking for the correct answer from the standpoint of optimizing (maximizing) your team’s chances of winning the game (I suppose for some questions there might be long term considerations as well).

This was an easy question after the last one.  The reason I presented it was what Ryan JL said.  One of the things I am trying to do, in case you haven’t noticed yet, is to point out the plethora of “conventional wisdoms” in baseball that are clearly wrong, such that the next time you hear from someone that “So-and-so manager, ex-player/commentator or player, knows things that you don’t know,” or that, “You’ve never played the game,” you can roll your eyes and say, “OK.”

When this “game” is over, it will also be a valuable resource for teams to vastly improve their WE by following these guidelines.

Yes, CW says to swing at anything close with 2 strikes, when in fact, on a 3-2 count, it is not even close (whether to swing or not at a marginal pitch).  If you asked the same question to any player, manager, or commentator, they would quickly answer, “Of course you swing!  There are 2 strikes!  You can’t get rung up with the bat on your shoulder!”

One of the pitch f/x guys recently wrote about how often batters swing at pitches out of the strike zone with 3-2 counts, or something like that.  It was pitifully high, as you might expect.

So, so far we have batters taking pitches WAY too often after a string of balls, and batters swinging WAY too often on 3-2 counts.

And yes, I meant “B” take less often, for the last question.

I said I would make this one easy, which it is - for the smart people who read this blog that is!

So we’ll change it to 3 different, separate ones:

1) How about with the 2-2 count?  Swing or no swing?  And what is the BE point for how likely it is that the pitch is a strike, so that swing or no swing has the same RE/WE?

2) Tango’s example of 1 out and a runner on third and a 3-2 count.  Swing or no swing with a 50/50 pitch?  What is the BE point?

3) In the current situation, runners on 1 and 2 and a 3-2 count, what is the BE point (how often must the pitch be a strike for an average batter to swing)?

Assume an average batter at the plate and on deck.

Tango’s example of 1 out and a runner on third and a 3-2 count.  Swing or no swing with a 50/50 pitch?  What is the BE point?

(mostly) Table 50 of the book, 1 out, runner on 3B:

-0.58 runs: K (or out with runner still on base)
+0.13 runs: SF (or out with runner scoring)
+0.30 runs: walk
+0.72 runs: hit

Now, THIS is more like it.  If you take all the way, the K is -.58, and the walk is +.30.  Seeing that it’s 50/50, then if you take, you will be -.14 runs.  That is obscenely poor.  That’s what your average pitcher hits.

A strategy of take-all-the-way on a pitch that is borderline 50/50 means that you will be -.14 runs. 

On the other hand, what if you swing on a borderline pitch:
- 25% miss the pitch, K
- 20% swing-and-hit
- 25% swing-and-out-runner-scores
- 30% swing-and-out-runner-stays

.25*(-.58)
+.20*(+.72)
+.25*(+.13)
+.30*(-.58)
= -0.14

Hahaha!  It’s the same thing?  Whether you swing or take, if the pitcher throws a borderline 50/50 pitch, you get the same results!

So, if you are a FB hitter: swing.  If you are a GB hitter: take.

The lesson here is for the pitcher: on a 3-2 count, throw a borderline pitch.  It’s worth -.14 runs (good for pitcher, bad for hitter).  That is an amazing discovery that you can find a strategy that effective on a hitter’s count!

Someone double-check my numbers, please, because this seems remarkable to me.

Tango, does your .72 for “hit” include all types of hits?  I.e., does that value for hit account for the fact that some H will be HR and some will be 1B?  I assume it does.

Under your math, only 45% of non-K outs score the runner from third.  That seems low to me.  I don’t know what the actual average is for all balls in play, but I don’t think I would make an adjustment to outs, as you did for H, for hitting borderline pitches, on the grounds that extra shallow fly balls that don’t score runs are cancelled out by extra weak grounders that would score the run.

Hiz/16: correct on the .72 (all hits, from +.6 for a single to 1.33 for a HR).  Check out Table 50 in The Book (via Look Inside at Amazon).

45%: yes.  That was an educated guess.  Interesting thought on your last paragraph.

MGLs situaion 3, break even point for runners 1st and 2nd, 1 out, 3 and 2 count is about 60.8% strike, 39.2% ball.  Analysis to be given later.

MGLs situation 2, man on 3d, 1 out, 3 and 2 count. You swing with a 50-50 pitch.  I’ll have to work on the break even later , but is a pretty wide margin.

I’d think whether to swing or not depends on the type of hitter you are. Some hitters have the ability to simply foul off that close pitch. If I’m that type of hitter, I’m fouling off the borderline one and hoping the next one is either definitely a strike or definitely a ball.

If I’m the type of hitter who doesn’t have that sort of bat skill, I’m taking. No point in swinging at something I can’t really hit anyway.

By the way, I *love* the idea that the 3-2 count with runner on 3B and less than 2 outs is (seemingly) a pitcher’s count, and not a hitter’s count.

This will now haunt me, as I’ve spent alot of time working on my 12 pitch-count model on the basis of how much each count is a hitter’s or pitcher’s count.  I may have to include some of the base/out states now (if not game states).

If Jonathan Hale is out there, I’d love to see his charts broken down by (some) base/out states (at each count), to see which stands out:
http://tangotiger.net/halejon/allcounts.html

Don’t forget the run expectancies that the trailing runner and yourself might also score if you get an extra base hit (or a home run).

Hmmm…

Tango says that the 3-2, runner on third, 50/50 pitch, and 1 out is break even and Peter says it is easily a swing.

JD, sure all of these answers depends on your tendencies as a hitter.  For now, we are assuming an average hitter (and everything else average as well).

Rick, not sure what you mean…

It seems some people are basing their assumptions of a run scoring just on the lead runner scoring, neglecting there’s a second runner on base who can score and the batter himself that can score. I realize run expectancy factors in the trailing runner and batter to an extent, but some are phrasing their answer on just the lead runner scoring.

Run expectancy handles the trailing runners and future batters to a perfect extent, not to “some” extent.  I’m not sure who it is that is not considering everything, but I can assure you that I’m not one of them!

A 50-50 pitch is a good pitch. Of course the pitcher will get good results when he throws a fastball right on the corner.

MGLs situation 2 analysis.  With a man on third and 1 out I have the RE at .98. Taking when it is a ball walsks the batter puttin men on first and third with one out and the RE at 1.20 and the RVA at .22.  Taking a strike leaves the runner on third with 2 out and an RE of .39 and an RVA of
(-.59).  That makes the average RVA of taking a 50-50 pitch -.185 per PA.  RE’s are from my empirical table 2005-2008.

When a batter swings at a 3 and 2 pitch with a man on third and 1 out he either struck out or put the ball in play 616 times out of 1048 2005-2008.  His average RVA for these 616 PAs was (-.11) runs per PA.  However, the batter also hit foul balls at a rate of 32.8% of all swings or an additional 369 fouls with an RVA of 0.  So the average RVA per swing was -.07. 

So IF the pitch distribution from the empirical data was close to the hypothetical 50-50 distribution then swinging is the better strategy because losing .07 runs by swinging is better than losing .185 runs by taking.  But that is a big if that we can’t know for sure without researching Pitch f/x data.  The split of 389 walks to 43 strikeouts on called strikes would seem to indicate that the pitcher is pitching much closer to the edge of the strike zone than 50-50. But the batter is swinging at 69.5 % of the pitches so he either is swinging at a fairly large number of balls that are out of the strike zone or the pitcher is pitching much closer to the center of the strike zone than 50-50.  Interestingly, the actual empirical distribution results in an almost exact break even of -.01 runs per PA.

MGLs situation 3.  People seemed to come to the right conclusion, take the 50-50 pitch while still making a number of mistakes or omissions in their analysis.  dcj started OK figuring the correct RE values for taking a strike or taking a ball.  But then he averaged those values instead of taking the run value added to the starting run value for the 1201 base out state of .97.  My RE values (based on empirical data 2005-2008) were slightly different from Tango’s values that dcj used but the RVAs are quite close.  I have a gain of .69 runs if he walks and a loss of (-.49) runs if he strikes out and leaves the runners on first and second.  However, a 3 and 2 count with men on 1st and 2nd is a very popular situation for having the runners in motion on the pitch (21% of the time.) When the batter takes a strike with the runners going in this situation a runner is theown out 54% of the time.  38% of the time both runners advanced and 8% of the time runners were lefton 1st and 3d with 2 outs.  This lowers the RVA for taking a strike to -.53 runs per PA.  Still, the average value for taking is +.07 runs per PA. 

The actual average empirical value 2005-2008 when a batter swung at the pitch and either struck out or put the ball in play with a baseout state of 1201 and a 3-2 count was -.05 runs per PA.  Solving for the break even point results in 60.7% strikes and 39.3% balls, again, IF the empirical distribution is already close to 50-50.

Great analysis Peter!  I would have thought off the top of my head that the average pitch that a batter swings at with a 3-2 count is better than a 50-50 pitch, but as you indicate, probably not.  Which makes sense as batters swing at lots of really bad pitches at that count, making up for the ones clearly in the strike zone.

Next question:

It is the bottom of the 9th inning, you are the road team and you are nursing a one-run lead.  Your closer comes in to pitch.  There are no outs and no one on base (the first batter of the inning is up).

Do your outfielders and first and third basemen play:

A) At their normal (average) positions on the field, given the batter and pitcher tendencies of course (and other environmental factors).

B) The outfielders move up and the first and third baseman play closer towards second.

C) The outfielders play deeper and the first and third basemen play closer to the lines.

D) Some other configuration.

Same question with a 2-run lead.

With a one run lead, I will play “no doubles” with the outfield a little deeper and 3b/1b playing the lines. If the leadoff batter gets a double, the tying run is immediately in scoring position, and a second batter getting a single can tie the game. I am increasing the probability of a single, but it would take three sibgles to tie the game.

With a two run lead I play normal, the offense’s best bet is for a two-run homer to tie, so I want to minimize all hits.

Brian, can you back up your first paragraph with some numbers, if you have the time that is…

Peter: thanks, that was the hole in my analysis, that I did not include foul strikes.  That has a huge effect.

The K run value I have almost identical to yours, but my walk run value is way different.  In The Book, I had it as +.30 runs.  You said .22 runs.  Let me see if I look at the RE chart:
http://www.tangotiger.net/RE9902.html

Hmmmm.. that says +.26 runs.  So, the Markov chart says .30, my empirical 99-02 chart says .26, and you say .22.

I’ll have to research some more, since this has a huge effect of course.

Regardless though, fouling off the pitch allows the count to stay at 3-2, and forcing the pitcher to throw again, and this time, he won’t necessarily throw a 50/50 pitch again.  So, yes, Peter is correct: swing.

MGL - I hoped you would get more interest in this question as it is not trivial.  Maybe you should hold it over until Monday and then publish in its own daily thread again.  Maybe all the saberists are out watching baseball this weekend.  This is a great series.  Could you guys advertise its existence to some of the other numbers oriented websites to try and get the maximum number of participants?

Thanks, Peter, yes, I think this is a good series and it has gotten a lot of attention and drawn a lot of people out of the woodwork.  I am also pleasantly surprised at how informed and talented our readership is in terms of doing these kinds of analyses.

Tango and some of the others who have blogs can probably advertise it some.  Plus, Tango can separate the threads if he doesn’t mind. I can’t really do that, I don’t think.

Things are really slow on the weekends on this blog, so I’ll leave the last question up until the end of Monday.  I agree that it is a good one.  As I said, one of the reasons I started it was to point out how many things teams get wrong.  So far we have two things that teams completely butcher - swinging too often at 3-2 counts without the runner on third situation, and taking too many first pitches after a string of balls.  There are many, many more things that teams completely butcher.  One of them is fielder positioning.  For example, you will often hear TV commentators discussing whether to have the first and third basemen guard the lines.  They will talk about how one manager likes to do it and another one does not - as if it were a matter of taste!  Of course, either it is correct or not given the game situation (or about the same).  One of my many (many) pet peeves is when people offer their “opinions” about something that is either clearly right or wrong, as if it were a matter of opinion.  If I had anything to do with a team anymore and I had free reign with that team, I would tell the manager when and when not he should guard against the extra base hit.  And it would not be based on my “opinion” of course.  It would be based on which of several alternatives gives us the best chance of winning the game.  And there is NO one that can determine that in their head, other than the obvious ones.

(As I have said many times, one of the hallmarks of stupidity and a lack of success in one’s endeavors is not ignorance - it is NOT knowing what it is that you don’t know.  If you made a list of the things that managers think they know but clearly don’t, you could fill up a book.)

Seems like we are still not getting any interest in MGL’s new question of the day (Post #30).  Is there still a plan to make it a separate thread?  I have a methodology for answering the question but I am not sure that I have an answer in which I have much confidence.

I’m surprised that no one has made any comments about the type of pitch.  If the batter has enough time to decide that a pitch has a 50/50 chance of being a ball, he probably also has identified the type of pitch on the way, and he knows whether he’s a good fastball or curveball hitter. 

I.e., could/should the REs calculated above for “swing” be adjusted based on type of pitch?

Jim Tracy, MLB manager:

HOUSTON — Less than a week into Jim Tracy’s tenure as Rockies manager, one of his major pet peeves has emerged.

He despises the “backward K.”

In other words, nothing ticks him off more than when hitters strike out looking. He made that abundantly clear Tuesday night when the Rockies watched strike three go by on six of their 12 strikeouts in a 3-2, 11-inning loss to the Astros.

He hammered the point home again before Wednesday night’s game against the Astros, saying the Rockies have to become more aggressive at the plate in order to turn their season around.

“I keep trying to send them the message that if you are standing there with the bat on your shoulder and the ball is passing through the hitting area and you don’t do anything, you know what chance you have? None. Zero,” he said.

Tracy was particularly concerned with caught-looking strikeouts on Tuesday night by Clint Barmes in the ninth and Seth Smith in the 10th.

Strikeouts have been problematic for the Rockies all season. They entered Wed- nesday’s play averaging 7.43 strikeouts per game, fifth most in the National League.

The sure sign of an ignorant and poor manager is someone who generalizes concepts like Tracy is doing ("don’t get called out on strikes").  As we know, if you DON’T get called out on strikes some percentage of the time at the various counts and in the various situations, you are doing something wrong.  It is because of managers like Tracy that batters swing too often at 3-2 counts.

Other stupid generalizations are, “Don’t let so-sand-so beat you,” and my favorite (as in it is REALLY stupid and makes no sense), “Don’t get beat with something other than your best pitch,” which can ONLY mean one thing, which is that in a high leverage situation ONLY throw your best pitch, which is of course stupid if the batter knows that is exactly what you are going to throw.

If I were a pitcher and my manager told me that, I would ask him, “So skipper, in a tight situation, you want me to never throw any pitch but my X (whatever my best pitch is)?” He would say, I assume, “No, I didn’t say that.” Then I would say, “Well, if you never want me to get beat with anything other than my best pitch, how can I throw anything else when I might get beat on that pitch?”

The next day I get traded…