THE BOOK--Playing The Percentages In Baseball

I don’t get it.

Why is the leadoff walk more horrendous with a more than 1 run lead? If anything, the bigger lead gives you a bigger margin for error, hence the walk is not as bad (the WPA added with the walk is not as big).

The reason why the walk is worse in the more-than-one-run-lead scenario is the same reason defensive indifference happens. You just need baserunners until its the tying run; it doesn’t really matter how far anybody before him is advanced.
That being said, I’m not sure I agree with Tango, at least based solely on this argument.
More later

If we’re nitpicking the announcer for saying “There is NOTHING more frustrating for a manager than walking the first batter with a one-run lead in the 9th” then sure, I get it. There are other events in baseball that should be quantitatively more frustrating. But that is extremely frustrating, and I’m guessing that announcer said about 100 dumber things just that game than that sentence.

I think this makes perfect sense. With a late one-run lead, the thinking is pitchers have to be a little bit careful, because a home run ties the game. But with a larger lead, the thinking is that you want the pitcher to challenge the hitters. I don’t know how many times I’ve had to watch the Tigers’ pitching staff walk Nick Punto with a big lead over the past couple years, and it makes me want to kick the TV in, much more so than if, say, Jose Valverde walks Mauer/Morneau in the 9th with a small lead(which is scary, but not necessarily frustrating).

I fail to understand the “balance theory.”

I get that:

A. 1-run lead: leadoff HR >> BB
B. >1-run lead: leadoff BB = HR (almost)

But A doesn’t logically follow from B--or even depend on B in any way.

and

C. 1-run lead: manager upset with leadoff walk
D. >1-run lead: manager REALLY upset with leadoff walk.

C and D mean that manager is relatively less upset with a leadoff walk with a 1-run lead than he would be with a >1-run lead.  But it does not logically follow that the leadoff walk with a 1-run lead is better or worse than other outcomes.

MGL, why are you limiting your universe to “leads”? What about tie games and games you’re losing? It *could* be, that allowing leadoff walks is bad for all leads, but not tie games or games you trail, for example.

And by “bad”, I mean “relatively worse”—we’re not talking in absolutes here.

Also, aren’t there two things at play here. One, the relative values of the events and two, the magnitude of those events.

For example, events might have the same relative weights, but but be twice (or half) as important as “usual” because of the leverage of the situation. This is a worse spot for a walk (or any negative event) but not relative to a home run (and you could argue it’s a BETTER time for a walk relative to a HR b/c the absolute difference is larger).

I think this thread is a little confused, and I think it’s because “The Balance Theory” wasn’t actually clearly stated as a theory. I understand the example, but I don’t think i know how to apply it to other situations, because I don’t know exactly what it is...MGL?

The balance theory is this:

If you know the value of something overall and that something is X is one situation, then it must be 1-x in all other situations.  I don’t necessarily mean that quantitatively.  X could be “good,” in which case, 1-x would be “bad.”

Here is another example:  You often hear announcers say, “Team X doesn’t want to play team B, toward the end of the season, when team B is out of a pennant race, because they have nothing to lose and are dangerous.”

According to the “balance theory,” that would have to mean that teams that were IN a pennant race would play worse than average.

I don’t know how to respond to some of the above comments. I didn’t think (and still don’t) there was any controversy in this matter.  Post #4 above hits the nail on the head.  With a one-run lead (or tied or losing), you don’t “mind” a lead-off walk.  It is a lot better than giving up an extra base hit.  It is, by far and away, the best negative event that a pitch can allow.  The manager would obviously not be pleased that his pitcher did not register a first batter out, but he should be pleased that his pitcher pitched to the batter carefully, especially if it was a batter who was reasonably capable of an extra base hit.

On the other hand, if a team had more than a 1-run lead, the last thing in the world the pitcher should do is give up the walk.  That should drive a manager crazy.  A lead-off walk with a 1 run lead (or tie game) should NOT drive a manager crazy in any way shape or form, other than the obvious fact that it is a base runner and not an out.

The “balance theory” is an excellent way to figure out whether a lead-off walk in the 9th with a 1-run lead is ESPECIALLY bad (relative to a walk, when you don’t know the score).  It is not so obvious to a person who is not sabermetrically or statistically inclined about baseball.  However, the relative value or “drive a manager crazy factor” of a lead-off walk with a 2 or more run lead in the 9th is obvious to most people.  That automatically tells you the value with a 1 run lead.

If the value of a lead-off walk in the 9th, not knowing the score, is X, then if the value of the walk (to the batting team) with a 2 run lead is X+something, which it is, then the value of the walk with a 1 run lead, must be X-something.

If the value of a lead-off walk in the 9th, not knowing the score, is X, then if the value of the walk (to the batting team) with a 2 run lead is X+something, which it is, then the value of the walk with a 1 run lead, must be X-something.

I’m not following. Isn’t the value of a lead-off walk in the 9nth dependent on the score? Or, is this a completely non-quantitative post and are you simply describing what goes on in the mind of an average fan/announcer, and what their logic is?

I still don’t understand what we’re comparing a walk to. You say a walk in a >1 run lead is the worst thing. Isn’t allowing a home run or extra base hit worse than that? You walk a guy, he’s only on first base, there’s a chance you’ll get him out before he scores. He hits a home run, the run has definitely scored.

I feel like you’re trying to implement a false choice. “If it’s this level of badness here, it can’t be as bad in this other situation.” I think it very well can be equally bad in all cases (not saying it necessarily is the case here).

"Isn’t the value of a lead-off walk in the 9nth dependent on the score?”

Yes of course.  But if you don’t know the score, then it still has a value (in win expectancy).  And that value can be called X (an actual number).  And with a 2 run or more lead, if the value is then X plus Y, for the batting team, then it must be X minus Y with a 1 run lead or less.

Again, in “words”, a lead-off walk with a 1 run lead (or tied) in the 9th is not particularly bad.  How do we know that?  Because a lead-off walk in the 9th with more than a 1-run lead in the 9th is horrible.  The balance theory.

Because a lead-off walk in the 9th with more than a 1-run lead in the 9th is horrible.

But why? Why is the balance theory correct? If we’re evaluating the human psyche that may be correct, but if we’re properly analyzing the situation I fail to see why it is correct, given what win expectancy tells us.

The balance theory is correct because the value of anything in situation X plus the value of anything in situation Y must be equal to the value of that same thing in situations X+Y.

If you break ANY situation up into 2 components only, X and Y, and you define the entire (unbroken) situation as neutral (that is your comparison point - in this case, a walk in the 9th inning, not knowing the score), then if X is good (for one team or the other), Y must be bad (for that same team).  And if X is bad, Y must be good.  That is irrefutable.  That is the balance theory.

Here is another example:  You will often hear an announcer say that so and so would never attempt a steal of second with a great batter at the plate because the pitcher would then IBB the batter.  Now, that may change the break even point for how often the steal would be successful, but surely if the pitching team offered the runner second base he should always accept the offer. How do we know that?  Because if that were not the case (if the runner should decline the offer), then it would have to be correct for the pitching team to walk the batter with the runner on first.  We know that is virtually never correct.

So

1. Announcers say leadoff BB with a 1 run
lead is bad.

2.  The theory says a leadoff BB with a hypothetical 2 run lead is worse.

Theory’s Conclusion.  Leadoff walk with 1 run lead is “not bad”, or at least, “not particularly bad” because a BB is worse in a situation that does not exist (2 run lead) at the time the BB is issued.

???

Ok so I think you are saying that the “balance theory” is that if a particular situation is better than the average than all other situations must be worse than the average.

This is correct if there are only two alternatives but if there are three or more alternatives then it is not necessarly correct.

While a walk with a 2 run lead may be worse than with a one run lead is the same true for very large leads? For example is a leadoff walk in the 9th with a 10 run lead worse than a leadoff walk with a 1 run lead?

Or to put it in announcer speak “..and so the leadoff batter is walked here in the bottom of the 9th with the home team leading by 10 runs, coming up next a brand new sitcom!!” or in other words the announcers wouldn’t comment on the perils of a leadoff walk in an extreme low leverage scenario.

James

MGL, your second explanation of the balance theory makes sense, but I’m not convinced that it is applicable to the situation you described in the original post.  The balance theory, as described in the most recent comment, appears to be talking about a “zero-sum game” situation, whereby if one team benefits from an event then, by definition, the opposing team is hurt by the event.  That makes logical sense. 

The situation you brought up in the original post seems more like a comparison.  I agree that the walk to a batter with more than a one run lead is clearly worse than a walk to a batter with a one run lead.  And I agree that the walk to the batter with a one run lead is not a terrible thing.  I just don’t believe that the fact that the second situation is worse than the first proves that the first is not bad.  It simply proves that it’s not AS bad.

In fact, if you were trying to apply the balance theory to the situation in the original post, you would end up with the conclusion that the walk to the leadoff batter with a one run lead is a great thing, because it would have to balance how terrible the walk to the batter in the second situation is.

Mark, you said this:

The situation you brought up in the original post seems more like a comparison.  I agree that the walk to a batter with more than a one run lead is clearly worse than a walk to a batter with a one run lead.  And I agree that the walk to the batter with a one run lead is not a terrible thing.  I just don’t believe that the fact that the second situation is worse than the first proves that the first is not bad.  It simply proves that it’s not AS bad.

I previously said this:

Now, obviously a walk is not a good thing in that situation, as opposed to an out or even a generic PA. But, the question is whether a walk in that situation is particularly bad.

The manager would obviously not be pleased that his pitcher did not register a first batter out, but he should be pleased that his pitcher pitched to the batter carefully, especially if it was a batter who was reasonably capable of an extra base hit.

The “balance theory” is an excellent way to figure out whether a lead-off walk in the 9th with a 1-run lead is ESPECIALLY bad (relative to a walk, when you don’t know the score).

I still can’t figure out what MGL means here, perhaps because of undefined terms like “particularly” or “ESPECIALLY.” The balance theory could tell you, I suppose, that a walk with a 1-run lead in the 9th is less bad than the average value of all 9th-inning leadoff walks while leading, relative to other possible outcomes of the PA.  If that is all that MGL means, fine. 

But it doesn’t tell you that a leadoff walk in that situation is better or worse than the average value of all walks.  In fact, it’s fairly obvious that a lead-off walk there is worse than walks in most other situations and also worse than most other possible outcomes of the PA.

The balance theory could tell you, I suppose, that a walk with a 1-run lead in the 9th is less bad than the average value of all 9th-inning leadoff walks while leading, relative to other possible outcomes of the PA.  If that is all that MGL means, fine.

Yes.

Here is another example.  I was listening to a game on the radio today.  The leadoff batter hit a soft liner into medium RF. The announcer thought that it was going to be an easy out.  The RF’er let it drop in front of him.

The announcer said something like, “Well, maybe he (the RF’er) figured that with no outs, he didn’t want to allow an extra base hit (in case he dove or tried to make a shoestring catch and it got past him).  He decided to play it conservatively.”

Makes sense, right? Not necessarily. How do we know that with NO outs, it is correct to play it conservatively?  Now, obviously there is a certain break even point for every situation (how certain you have to be of making the catch versus the chances of an extra base hit, if you go for it), but you can easily figure out whether no outs is a good time to be conservative, as opposed to one or two outs, by using the “balance theory.”

With 2 outs (and no one on base), would you rather be conservative or try and make the catch while significantly risking the extra base hit? 

That is easy to answer (just like the question about the walk with the multi-run lead is easy to answer).

With 2 outs, you don’t mind the single, but you definitely mind the double or triple (or inside the park HR).

Therefore with 0 or 1 out, you do NOT want to be conservative.

Balance theory:  If X is not so easy to answer, but 1-X is easy to answer, then that gives you the value of X.  Again, “value” is not necessarily quantitative.

MGL,

I’ve never heard of the balance theory before, but if I’m understanding it correctly, then you can only compare the event of (a walk) to the event of (not a walk).  Once again, none of the people who posted on here seem to be questioning your conclusion that the walk with a one run lead is not as bad as a walk with a multiple run lead.  We are questioning your application of the balance theory.

MGL, you said this:

[Again, in “words”, a lead-off walk with a 1 run lead (or tied) in the 9th is not particularly bad. How do we know that? Because a lead-off walk in the 9th with more than a 1-run lead in the 9th is horrible. The balance theory.]

Just because the walk with a one run lead is not as bad as a walk with a multiple run lead does not mean that the walk with a one run lead is not, in your words, “particularly bad.” That’s tantamount to saying “100 degrees is horribly hot, it is less than 100 degrees, therefore it is not particularly hot.”

If you are trying to conclude that a walk with a one run lead is not as bad as a walk with a multiple run lead then you are correct.  If you want to use the balance theory to prove this by saying that the alternative to a walk with a multiple run lead is less bad than the alternative to a walk with a one run lead, then that is also correct, though I don’t believe you need the balance theory to convince anyone of your overall point that it is worse to walk a batter with a multiple run lead than a one run lead.

The example you mentioned about teams’ play during a pennant race is a perfect application of the balance theory.  If it is true that teams out of the race play better than average, then clearly this means that teams in the race would play worse than average. 

The example you just gave about the RF playing conservatively doesn’t seem to make sense either.  With that logic, if you don’t want to give up a home run with two outs, then you DO want to give up a home run with 0 or 1 outs.

"If you are trying to conclude that a walk with a one run lead is not as bad as a walk with a multiple run lead then you are correct.”

Yes, my only point.

It can be used for strategy and approach decisions by players (and managers), when the situation at hand does not lead to the decision being so obvious.

My example of the hit to RF is one that an OF can use to decide how aggressive to play.  He may not know what to do with no outs (or 1 out), but he certainly knows that to do with 2 outs (be conservative).  So he can simply do the opposite with less than 2 outs.

In the walk situation in the 9th, all pitchers know that it is a crime to walk the lead-off batter with a 2 or more run lead.  Surprisingly, many ballplayers think that it is also a crime to walk the lead-off batter with a 1 run lead, and on a 3-0 or 3-1 count, they might throw a cookie.  If they use the balance theory, they would know that it is correct to pitch carefully to the lead-off batter with a 1 run lead, and throw strikes with more than a 1-run lead.

It is not complicated and I am not sure why most of the above posters are making it out to be as such.

By the way, I just made the name and the concept up, so I would not get caught up in semantics.  It is simply a way to sometimes figure out correct approximate strategies when it is not so obvious and also to estimate the “outrage factor” by managers and fans, also when it is not so obvious (or conventional wisdom is wrong).

And by the way, outfielders should be playing slightly shallower and first basemen further from the lines with 0 outs as opposed to 2 outs.  Do you think all teams know this?

And by the way, outfielders should be playing slightly shallower and first basemen further from the lines with 0 outs as opposed to 2 outs.  Do you think all teams know this?

Since I was taught this at age 13 in Babe Ruth League, yes, I believe all professional teams know this.

“If you are trying to conclude that a walk with a one run lead is not as bad as a walk with a multiple run lead then you are correct.”

Yes, my only point.

Actually, I don’t think anyone has established that that point is correct.  The win expectancy for the batting team goes up more in absolute terms with a leadoff walk and a one run lead than with a greater than one run lead.  That is because a team is more likely to score one or more runs without a home run that with one.

I think a lot of the confusion is that MGL is making a smaller claim than what people think, and also that the balance theory may not be particularly helpful when addressing the announcer’s comment that opens the post.

MGL is asking: is a walk a particularly bad outcome of this at-bat?  He is not asking: is a walk worse here than in most other situations?  He is really comparing a walk to other possible outcomes of that particular at-bat, not to walks in other situations.

Or, that the fraction:

WPA (walk)
------------
WPA (avg PA)

will be less when leading off the 9th with a 1-run lead than when leading off the 9th with any other lead.

This is a little confusing, because in absolute terms,
WPA (walk with 1-run lead) > WPA (walk with >1 run lead)

It sounds really like the LI of a batted event by game state.  A walk or a HR with bases loaded down 1, with 2 outs in the bottom of the 9th are both equally bad (relative to each other), but are not equally bad (relative to a walk or HR in other game states, respectively).

Therefore, a walk is absolutely a horrible result and you should avoid a pitching philosophy that allows walks.  A HR is not that bad, and so, you don’t need to pitch in a way to avoid a HR at all costs.

Even though a walk and a HR are of the exact same value here!

So: don’t nibble on the edges, and don’t throw down the middle.  The LI of the walk here (relative to other walks) is going to be much higher than the LI of the HR (relative to other HR) is low, and so, it’s more important to not throw at the edges than it is to not throw down the middle.

MGL you said this,

[My example of the hit to RF is one that an OF can use to decide how aggressive to play.  He may not know what to do with no outs (or 1 out), but he certainly knows that to do with 2 outs (be conservative).  So he can simply do the opposite with less than 2 outs.]

Just because the RF knows what to do in one situation, does not mean that he can simply apply the opposite strategy in other situations.  The balance theory, in order for it to make any logical sense, can only be applied across a SINGLE situation.  If it is a below average strategy to dive for a ball in a specific situation, then, by definition, it is an above average strategy to not dive for a ball in that particular situation.  This can only be applied across a single situation, not multiple situations like 0, 1, AND 2 outs.

In any given situation an individual is faced with a certain spectrum of strategies and has to choose one.  I think the balance theory may be applied to the outfielder situation by reasoning that because it is not a good strategy to dive for the ball with two outs, it clearly must be a good strategy to not dive for the ball with two outs.

If it is not a good idea to dive for a ball with 2 outs, then it must be OK to do it with 0 or 1 out.  That is precisely the balance theory in action.

If you want to figure out what to do with 0 outs only, the answer is once again obvious. Clearly, the more outs there are, the less you want to dive for a ball.  So, diving with 0 outs is fine…