THE BOOK--Playing The Percentages In Baseball

Here’s the starting point with RE:
http://tangotiger.net/RE9902.html

2b/3b, 1 out: 1.467 runs
3b, 2 outs, plus run scored: 1.387 runs
1b/3b, 2 outs, no run: .538 runs

From a WE perspective (HOME team perspective)
http://tangotiger.net/welist.html

top8th, tied, same numbers:
.321 wins
.251 wins
.493 wins

It seems from this that the batting team (VISITING team) gains .07 wins on the successful suicide and loses .17 wins on the unsuccessful one.

Of course, the DP is a killer.

Am I looking at something wrong?

The “unsuccessful” squeeze is generally when the batter misses the ball and the runner gets tagged out at home.  Rarely does the runner get thrown out at home on the bunt, since he is running as the pitcher starts his arm motion home.  So the “state” for the unsuccessful squeeze is 2 outs, runner on second and the batter still at the plate, usually with an extra strike from missing the bunt.  So the last number should be .525 (generally) which is a loss of .2 wins.  So, the break even point is maybe around 75 to 80%.  So maybe it is not such a bad play.  Then again, there is also the bunt pop out DP I guess, increasing the BE point.  We’d probably have to look at the actual results to see the exact distribution of possible outcomes.

I would think the BE point with a runner on 3rd is still a lot lower though.  (I don’t have the time to look at the numbers right now.) If it is, either managers are squeezing way too infrequently with a runner on 3rd or my original proposition is correct.

With such an extreme range of possibilities (batter still at the plate with extra strike, or reaching base, other runners advancing or not, DP), it would be more instructive if we break out the PBP database to see what actually does happen with bunts and runner on 3B by outs.

I suppose that in failed suicide squeezes and batter still at the plate, that the runner will be out on a CS (or safe on a SB)?

From 2004-2006 Retrosheet, there were 355 bunts with 3d base occupied.  236 of these were with men on 1st and 3d and were not sucide squeeze bunts but were bunts to avoid a double play with pitcher or poor hitter batting.  So lets eliminate those. Of the 119 remaining bunts 18 plays resulted in the runner remaining at third base and so were either not suicide squeeze bunts or the runner missed the sign.  Of the remaining 101 bunts, 86 resulted in the runner on third scoring, including 36 times where there was no out recorded on the play.  There were 10 double plays with an out at home and 5 FC with an out at home.  As for MGL’s assertion that most of the unsuccessful plays were missed signs or missed bunts resulting in an out at home, there were only 15 cases were the runner was moving on the pitch and out at home.  Whether all these were missed suicide squeeze attempts or some were straight steals is open to speculation.  Hopes this helps with your analysis.  The 36 times where no out was recorded should be a big factor that was not included in your initial posts.

Peter, good job.  A couple of questions:
1. I’m ok with removing the pitcher (whether or not it was an intended squeeze play), since he brings a much different WE matrix with him, but why would you remove the “poor hitter” from the equation?  Even a poor hitter will have a (true) OBP of .280, which is far higher than your typical pitcher.  In any case, if you can present the “poor hitter” (and pitcher too) breakdowns separately, that’d be good to see too.

2. Does this include where the batter was still at the plate?  Therefore, the play would be recorded as SB/CS (I guess)?  If so, how many times did this happen?  If not, then what is the SB/CS numbers in these cases?

Tango - I wasn’t removing those bunts because they were a pitcher or poor hitter bunting, but because in the vast majority of the 1st and 3d plays the runner on third wasn’t moving with the pitch.  So the result of a “successful” sacrifice was second and third and an additional out, with only occasionally the runner on third scoring.

Without checking the chart, bunting to move the runner to 2nd without sending the runner from 3rd sounds like a horrible play, but you are right to remove them because its irrelevant to the suicide squeeze.  In a suicide squeeze he either scores, or is put out somehow - unless he gets in a rundown and the defense screws up and allows him to safely get back to 3rd.

Are the bunts that just try and move the trail runner coming with 1 out or none?

Assuming top of the 8th, tied, 1 out, 1b/3b (WE home team of .349), and using Peter’s numbers:

n: event
36: runner on 3b scores, no outs (which I assume means batter reaches safely, and is not a SB by the runner on 3B)… WE of .210

50: runner on 3b scores, one out made (which I’ll assume is 25 times the runner on 1b and 25 times the batter) ... WE of .259 or .273… average of .266

10: runner on 3b out, plus a 2nd out (doesn’t matter which, since it’s the end of the inning) ... WE of .604

5: runner on 3b out, batter safe ... WE of .513

That gives us a weighted WE of .292 for the home team (fielding team).  They started off at .349, which means the batting team improved by a whopping .057 wins.

The Leverage Index of a squeeze play is 3.6, compared to LI of swinging away of 3.8. 

So, a great hitter (+.010 wins) would affect the game at this point by +.038 wins.  Here we see it’s +.057 wins, which is enormous.

I’m guessing that Peter didn’t report the SB/CS numbers, which would bring down the overall number.

I guess I have not communicated clearly.  I eliminated all cases of runners on first and third since most were not suicide squeeze bunt. The remaining 119 bunts were distributed as below:

runners on----Outs----Bunts
3d-------------0--------2
3d-------------1-------79
2nd+3d---------0-------5
2nd+3d---------1------18
loaded---------1-------15

I then subtracted the 18 bunts where the runner on third remained on third base assuming that these were also not suicide squeeze plays, leaving 101 bunts.  The distribution of results of these 101 bunts were:

runner on third scores, batter out---50
runner on third scores, no out-------36
runner on third out, batter safe------5
runner on third out, batter out------10

In addition, there were 15 occasions were there was a man on third, but not first and third; 0 or 1 out, and the runner on third was moving with the pitch and was out at home.  On two of these occasions the batter swung at the pitch, so obviously were not suicide squeezes, leaving 13 plays that might fit MGL’s classification as missed squeezes. Five were actual missed bunt attempts and 5 more were pitchouts and therefore almost certainly squeeze bunts.  The other 3 were called balls and strikes, so were either missed signs or straight steals.  Hope this is clearer.

Peter, how many of the bunts on which the runner on third scored without an out being recorded ended the game, i.e. how many of these plays were executed in the bottom of the ninth or in the bottom of an extra inning of a tied game? On a play like that, the batter will be credited with having reached first base safely on a fielder’s choice (or maybe a basehit), although the defense never has a chance (or the desire) to put him out because the game ends as soon as the runner from third touches home plate. These cases should not be considered when trying to analyse the situation described above (top of the eigth inning of a tied game).

RGN - Good point.  Two of the 36 ended the game.  Both batters were credited with singles.  They should still be credited with a successful sacrifice squeeze for the analysis above, of course, but not one where the batter is safe.

In the sac bunt chapter in The Book, I mentioned that one of the worst plays a manager can do, which is done all the time, sometimes by a poor hitting position player, but mostly by a pitcher, is the straight sacrifice with runners on 1st and 3rd and 0 or one out.  BTW, Peter, how many of the presumed squeeze attempts were with 0 outs?  I don’t think they should ever be attempted with 0 outs.

My original point is not whether a squeeze is a good play or not.  I’m sure that it is when it is executed (on rare occasions). It is whether it is a good play with any other runner configuration other than with a single runner on third only.  So the above numbers from Peter would have to be tweaked a little and then applied to situations with runners on 2 and 3 or bases loaded.

MGL - Post 9 gives each of the Base-Out situations for the attempted squeeze plays.  It looks like managers agree with you that it should predominately be a 1 out play. 

I too was surprised at the large number of bunts with men on first and third where the runner on third didn’t advance.  My first impression was that it made no sense at all.  After thinking about it some more, I am not so sure.  If you have a batter that has a very low probability of getting a hit or a sac fly and a very high probability of hitting a ground ball double play a bunt attempt might be the most you can expect to gain in that situation.  If it is the pitcher bunting and he successfully sacrifices, you are left with the leadoff hitter batting with men on second and third.  If you are not ready to pinch hit for your pitcher, it might make sense.  It least it deserves a full blown analysis rather than conjecture or a quick dismissal.

Peter, as I said in my last post, I DID a full blown analysis in The Book.  IIRC, I did not specifically look at a player with a “low probability of a sac fly and high GDP rate (contrary to popular belief, pitchers do NOT ground into a lot of DP’s with a runner on first)”, but the cost of the sacrifice in that situation was so high, that I doubt that even a significant change in the GDP rate or sac fly rate will affect it enough to turn it into a correct play.

I have to check the book, but I think it is the 1 out 1st and 3rd situation which is really terrible to do a regular sac bunt.  The 1 out might not be so bad.  This makes a lot more sense, intuitively.  And BTW, the average result when a pitcher bunts is a lot worse than when a position player bunts (again, see The Book), which is one reason why pitchers bunt too much despite obvious poor results when hitting away.  Pitchers do not nearly the ROE and singles when sac bunting that position players do, there are lots more K’s when they continue bunting with 2 strikes, etc.

Without knowing if the runner was going and it is a true squeeze, it is hard to tease out the numbers from the Retrosheet data.  If the runner from 3rs does not score or get thrown out at home, you don’t know whether it was a bunt for hit (or regular sac with a runner on 1st and 3rd), or a squeeze where the runner missed the sign.  If the runner gets thrown out at home, you don’t know whether it was a squeeze where the bunt was right out in front of the plate or it was a safety squeeze or bunt for a hit.  And if it was a CS or SB of home, we don’t know whether it was a bunsted squeeze or a straight steal of home.  Etc.  I think all we can do is approximate the distribution of results when a squeeze is executed.

For the years 2004 and 2006 Retrosheet tells you if the runner was moving on the pitch.  There were no SB’s of home when the runner was moving on the pitch with less than 2 outs.  Post number 9 gives the number of CS (15)for the suicide squeeze attempts (non first snd third). That number should be increased by 7 or 8 to approximate the missing 2005 data.  For first and third situations, on only 10 of the 236 bunts was a runner moving with the pitch and we don’t know from the Retrosheet data if it was the runner on third or first so that is why I threw out all the first and third data from the suicide squeeze analysis.

I checked The Book about the sac bunt with runners on 1 and 3 and a pitcher at the plate.  Is is never correct to sac bunt with 1 out.  The RE and WE penalty is too strong, sometimes up to .3 or .4 runs, regardless of the GDP or sac fly rates of the batter.  With 0 out, The Book’s recommendation is for the better hitting pitchers to swing away and the poorer hitting ones to bunt (adjusted for the pitcher of course).  The sac fly and GDP rates and the batter/pitcher combo can and should obviously be considered with 0 outs.

Anyway, here are the percetages I used for the various outcomes of a suicide squeeze according to Peter’s numbers.  I am a little suspicious of the numbers, not having anything to do with Peter of course, only because it is difficult to figure out what is going on exactly.  The runner scoring and the batter safe percentage (30.4) seems high, but who knows.  If you looked at the number of singles and ROE for a regular sac bunt by a non-pitcher, you would be surprised also (10-20%).

Anyway, here is what I used:

44.6% runner scores, batter out
30.4% everyone safe runner scores
4.5% runner out at home, everyone else safe
8.9% runner at 3rd and batter out (DP)
11.6% runner at third out, batter still at the plate

With 1 out, the WE for the home team in the top of the 8th inning in a tie game is:

runner on 3rd: .371
runners on 2nd and 3rd: .321
bases loaded: .313

After a squeeze, according to the above distribution of results, these numbers are:

.347
.302
.288

So it appears to be correct to squeeze (at least in the situations that a squeeze actually occurred) in all 3 baserunner configurations.

With 0 outs, here are the numbers:

Average WE:

.297
.229
.208

After a squeeze:

.321
.238
.212

So a squeeze does not appear to be warranted with 0 outs, although interestingly runners on 2 and 3 or bases loaded is better than with a single runner on 3 with none out.  Also, with 0 out, the defense is definitely not expecting a squeeze, so maybe the results are a little more favorable (less pitchouts and fewer throws home as the corners are probably playing back).

Anyway, given the right circumstances, which are probably a close game, a good bunter and weak hitter at the plate, a control pitcher, and maybe an opposing manager who does not pitch out often in potential squeeze situations (and maybe a hitter’s count to also avoid the pitchout), it appears that the squeeze may be an excellent play.  I also think that it makes sense that managers would squeeze too infrequently especially when the game is on the line (when the squeeze is probably worth the most), since managers do not like to end a game and lose (a busted squeeze) on a strategy that appears to “come from them” (like a steal with 2 outs down by 1 in the 9th inning).  That is one of the reasons (perhaps the main reason) why managers bunt too often late in close games.  If the bunt is not successful, it is the batter’s fault.  If it is successful, the manager looks smart for calling for the bunt.  If a manager calls a squeeze down a run in the 9th and it is not successful, he is going to be second guessed. If he doesn’t squeeze and the batter fails to get the runner in from 3rd, the batter gets blamed.  We all tend to do things that make us look the least bad (or wrong), even when they are not the “optimum” things to do, in terms of what we really want or need to accomplish.

MGL - Re Post #13 Whether pitchers ground into more double plays than the average hitter depends upon your point of view.  They do not have more DPs/PA or DPs/Out but they have significantly more DPs/hit ball.  Non Pitchers are 26%, Pitchers are 36%. 

Your analysis in the book is flawed because it didn’t take into account the severe selection bias of the pitchers that were asked to bunt with men on third.  They are MUCH worse hitters than those that are allowed to hit away in that situation.  K rate is around .47 instead of .33, BA is around .070 instead of .161, GB rate is .42 instead of .37.  Bunting these pitchers with runners on 1st and 3d is actually a very positive strategy for both 0 and 1 outs.  With their high GB rate they would hit into DPs in about 17% of there PAs.  This falls to about 3.5% when bunting.  The direct scoring rate falls from about 17% to 13.5% and the on base rate falls from .070 to .052, but this is more than made up by the bunt moving the runner from 1st to 2nd 84% of the time.

I am not advocating that managers should bunt pitchers more often with runners on 1st and 3d.  I do think that the evidence shows that they are currently chosing which pitchers to bunt effectively.

My analysis in the book?  Did you read the book?  Do you actually think that I would not know that the pitchers who bunt are bad hitters and the ones who don’t are good hitters?  I specifically talked about that in the book.  And I don’t look at what actually happens, in terms of RE or WE, when a pitcher/batter hits away or bunts in order to determine which is correct.  Of course there is a “selection bias” for all bunts and non-bunts, for both pitchers and non-pitchers!  I look at what happens when a pitcher bunts, in terms of the distribution of results, advancing runner, not advancing runner, DP, etc., and then compare that to what various levels of hitters, including their DP rates, would do if they hit away.  For that, I use a Markov simulator.  And again, it ain’t even close (with 1 out).  (And yes, I know that the DP rate for pitchers per GB or batted ball is higher.  The DP rate per PA is around the same.  Most people think it is a lot higher.  But thank you for pointing that out.)

The RE after a sac bunt by a typical bunting pitcher with runners on 1 and 3 and 1 out is around .731.  If a hitter with around a .070 BA, .47 K rate (per PA), and .42 GB rate (and .02 walk rate) hits away, the RE is around .870.  Again, it ain’t even close.  Where do you get your numbers from to suggest that bunting is “actually a positive strategy with 1 out?” Please give me YOUR RE or WE for bunting and for hitting away, for a bad hitting pitcher.

Didn’t mean to be rude, Peter.  Just curious as to your numbers (RE or WE) for bunting versus non-bunting a pitcher (bad hitting one or whatever) with runners on 1 and 3 with 1 out.  If my numbers are wrong, I’ll take a look at them of course.  My numbers seem to indicate that it is not even close, regardless of how bad the pitcher is at hitting, or his GDP or sac fly (basically the fly ball rate, adjusted for the fact that pitchers don’t hit them very deep on the average) rate, or K rate.

From 2004-2006 pitchers bunted with men on first and third and 1 out 112 times.  This is the actual distribution of the resulting Base out states.

-End----Count----Runs----RE-end--Total RE+R
---0--------5------1----------0-------1
-202-------16-----16------0.351------21.616
-231--------1------1------1.462-------2.462
-232-------70------0------0.616------43.12
1031--------1------1------1.207-------2.207
1032-------15------0------0.526-------7.89
1201--------2------2------0.965-------3.93
1202--------2------0------0.460-------0.92
Totals----112-------------------------83.145

AVG. RE---0.742

Pretty close to the .731 that you had.

This is the batting line for the pitchers that bunted if they were to hit away base with the constraints that I gave in post #18.  These numbers are based on what the pichers who bunt in base out state 1031 actually do when they hit away in base out 1032.

PA--AB--K--BB-1B-2B-GB-GIDP-GB,hit-PU-FB-FB,hit
112-110-51--2--6--2-46---19-----5---3--6----1
LD--LD,hit
4-----2

Although it may not seem so, this is actually a pretty generous batting line for these pitchers.

This is the distribution of resulting Base-Out states for the above batting line.

-end----count---runs----RE-----Total_RE+runs
---0-------19------0-----0-------------0
-202--------8------8--0.351-----------10.808
-232--------4------0--0.616------------2.464
1032-------57------0--0.526-----------29.982
1201--------6------6--0.965-----------11.79
1202--------4------0--0.460------------1.84
1002-------10-----10--0.242-----------12.42
-201--------2------4--0.722------------5.444
1231--------2------0--1.633------------3.266
Totals----112-----28-------------------78.014

AVG. RE hitting away 0.697

Closer than your two RE’s but conclusively supporting bunting those pitchers.

I’m getting a much higher RE with my Markov sim.  I’ll have to check it out.

One quibble which will change the RE when hitting away:  You would certainly have to change some of those 1032 GB and GDP (and PU) to singles as the first and third basemen are going to be right on top of the pitcher when he swings away (plus I would say that the pitcher/batter is going to get more high fastballs).  Of course once you start not bunting all the time, the defense is going to play back more.  I would say 3-4 extra singles.  One way to estimate this is to look at the difference between the 1031 and 1032 line for pitchers who don’t bunt.

Anyway, I’ll check on my Markov sim.  I must have a bug or something.

BTW, I am pretty confident with my .731 as that is based on ALL pitcher bunts (a much larger sample size).  Plus it is sometimes hard to discern when a player is bunting from the Retrosheet data.  I think I did a pretty good job of that.  OTOH, with runners on 1 and 3 and 1 out, maybe the defense does not play as far in as they would with a runner on 1 only, as they are not as sure that the pitcher is going to bunt, especially with 1 out (as opposed to 0).  So the RE COULD be higher, in the range of your .742.

Wow, I did have a bug in my Markov sim!  It was crediting a run on a GB DP (with 1 out)!  Anyway, I still get an RE of .768 for that stat line (using around the same RE table).

I see you assumed that all singles advanced the runner only 1 base and all doubles advanced the runner 2 bases.  Is that right?  Did you assume any sac flies?  I even had the runner not scoring on some ground balls, like a comebacker, and certainly with the infield charging if a ground ball were hit to the first or third basemen, the runner on third would probably either be thrown out at home or not attempt to score.

Anyway, I think it IS close with the poorer hitting pitchers.  I would probably have to ammend the recommendations to bunt half the time with the poorer hitting pitchers, less with the better hitting pitchers.  You still want to mix up your strategy to keep the defense honest and to increase your RE when hitting away (with the defense playing up).

In The Book, I must have also screwed up my numbers (RE when hitting away) for runner on 1st only and a pitcher at bat, since I used the same Markov sim. I’ll have to check.

Thanks for the corrections, Peter!  Now I see why you might think that I did not take into consideration that the bunting pitchers would be poor hitters, as my RE numbers when swinging away would not have made any sense (and would have looked like much better hitting pitchers).

I think you would be surprised at how many extra hits a pitcher will get when hitting away in that situation by virtue of the defense being out of position and the pitcher throwing more hittable pitches.  As I said, take a look at the hitting line of those pitchers who DID NOT bunt with 1031 versus what they did at 1032.

In The Book, I must have also screwed up my numbers (RE when hitting away) for runner on 1st only and a pitcher at bat, since I used the same Markov sim.

With ONE OUT that is.  With zero outs, the sim is fine.

I did assume 3 sac flies which was probably too many, but 2 probably would have been too few.  Illustrates the problem of using whole numbers for the theoretical values when the numbers are so small.  For some reason I did only advance the runner 1 base on the six singles, but I did have both runners on first scoring on the doubles. The singles are obviously incorrect.  Changing to two bases for 2 singles increases the RE to .701. 

I hadn’t considered a bump effect for additional hits past the charging 1st and third baseman when bad hitters change strategy and hit away.  It is certainly a possibility.  After thinking about it some and running some numbers I think the effect would be smaller than 3 or 4 additional singles; more like 1 or 2.  My reasoning is this: the 1st and third baseman would be pulled in to double play depth in all 1st and third situations with less than two out so the batters would already be enjoying a better chance at hitting the ball by them.  Plus the 1st baseman would be holding the runner also increasing the batters chance of getting a hit.  Pitchers already hit away about 40% of the time with runners on 1st and third and one out so the corner fielders are unlikely to be charging with the pitch; they are probably waiting for the batter to show bunt.  Running some numbers on other pitcher sacrifice situations show a bump of only about .010 in BA above the pitcher’s normal average.  Even doubling that to cover the added surprise factor of having a poorer hitter hit away would only add 2 singles in the 112 PAs of the sample.

We could tweak these numbers to death.  For an academic it might be a Phd thesis.  I am satisfied that it is about a break even proposition and that managers should employ each strategy about 50% of the time based on game theory and intangibles that are almost impossible to quantify (perceptions of batters bunting ability, fielders ability to field bunts, runner on thirds intelligence, etc.).  From the numbers it appears that this is very close to what managers are already doing.

I am reasonably satisified that it is around break even for the poorest (maybe not THE poorest) batters.  They are the ones who should be bunting about half the time.  You looked at the pitchers who bunted 100% of the time.  I think they are bunting too much.  Clearly batters, and especially pitchers, in general bunt too much when the defense is really charging hard, as well as too much by poor and slow batters.  Actually the better batters probably don’t bunt enough.  In any case, I am glad you caught my bug in my Markov sim and I don’t think we have any disagreements.  As I explain in The Book, even if managers bunt the correct % of time, on the average, they still can be (and are) making many mistakes on individual bunts and non-bunts.  Read the sac bunt chapter again and I think it will be obvious that managers bunt pitchers too much in general, as well as slow and poor bunters, they bunt too much late in close games, taking away any possible surprise element, which is critical for just about any bunt situation (other than poor hitting pitchers with 0 outs), and probably don’t bunt enough with good bunters and fast runners who are otherwise very good hitters (their bunt attempt WE or RE is very high when the defense is not expecting a bunt).

Wow, I just realized I spelled squeeze wrong in the title to this thread.  A bad omen.

I have no idea whether the batters that bunted were the poorest hitters or some mix of poor hitters and good hitters.  The only thing that I am really confident of is that the actual outcome of the mix of bunting and hitting away that the managers actually used produced an RE of .877.  If the managers had hit away in all 195 1031 base out situations and the pitchers had hit at the rates that they usually hit at, the RE would only have been .831.  Since they increased their total projected runs by 9 over the 195 PAs I can only conclude that they chose their bunts wisely.  Or were lucky.  Of course, to put the whole discussion in perspective, that is 9 extra runs over 90 team seasons, or an extra .1 run per team per year.

Amend that to 48 team seasons and .2 runs per team per year.  I forgot that we were talking about pitchers batting.

Again, just because in the aggregate they gained, does NOT mean that they chose their bunts wisely, although, yes, wiser than not bunting everyone.  There may have been, and I’m sure there were, many instances where pitchers should not have bunted but did and should have bunted but did not, mostly the former.  I have seen many times (well, maybe at least once) Jason Marquis, for example, an excellent hitter, bunt with 1031.  You are giving managers WAY too much credit.  I agree and in fact I mention in The Book, that in the aggregate managers bunt about as often as they should, but that also includes many errors, some egregious and others subtle.  That includes pitchers and non-pitchers alike.

As I emphasize in the book, the KEY to bunting or not is three-fold.  One, is that when it is at all close, you MUST randomly mix up your strategy.  Some managers intuitively know that and others are slaves to what they SHOULD do (the conventional BOOK) or what they have their mind set to do.  Two, is the bunting proficiency and speed of the batter/bunter.  I believe that the poor bunter and/or slow runner should almost never bunt, even if he is a poor hitter.  I have numbers in The Bok to back that up.  And three is anticipating or seeing where the defense is playing.  For example, when the defense is breathing down the batter’s neck on pitch one, especially with a runner on second (where the SS may be covering third for the “wheel play"), it is almost always correct to switch to hitting away (and trying to hit the ball to the left side of the IF) or letting the batter have the option (an “option play” like in football) after he sees the defensive alignment, at least until the defense wises up.  NO managers understand this three-fold prinicple even though on the average and in the aggregate, they bunt about as often as they should.