By Bill James

March 28, 2020

In order to figure the number of runs saved by each team’s pitcher’s strikeouts, we need to know four things:

How many batters the team’s pitchers faced,

How many they struck out,

How many of those strikeouts we should remove, as "background" or "zero competence level", and

The run-prevention value of each strikeout.

The first two of those we know now.

The fourth one we will not know for some time.

The purpose of this stage of the research is to generate some options for the third—the background level. The zero competence level. In order to generate those options, we need two additional pieces of information: the period norm for strikeouts per plate appearance, and the standard deviation of same, on the team level. I don’t know if that makes sense; it makes sense to me, which is all I can offer you at the moment.

So anyway, we need four pieces of information, then: the first two above, plus the period norm for strikeouts and the standard deviation of the same.

The 2018 Houston Astros hold the major league record for strikeouts in a season, with 1,687, out of 5,913 batters that they faced. Our question is, how many of those 1,687 strikeouts should we regard as merely background—batters who were going to strike out no matter what kind of a fool was on the mound. An average pitching staff in their era, given the same number of batters faced, would have struck out 1,216 batters.

But we are comparing them not to an average staff, nor to a replacement-level staff, but to a zero-value staff, which is a staff which would allow twice as many runs as the league average. That number (of background strikeouts) might be represented as 3 standard deviations below the norm (70), 4 standard deviations below the norm (60) or 5 standard deviations below the norm (50). The period norm for strikeouts is .205664 of plate appearances.

Doing the math, then, if we use 3 standard deviations below the norm as the background level, then 794 of the Astros’ strikeouts were background, and 893 were acts of run prevention. The average of strikeouts is .205664, and the standard deviation is .023830:

5913 * (.205664 – 3*.023830) = 794

1687-794 = 893

It’s actually 894 if you carry enough decimals; it’s a case in which 793.xxx rounded up and 893.xxx rounded up add up to 1687.xxx. Anyway, Ii we wind up using 4 standard deviations below the norm as the background level, then the 2018 Astros will be credited with 1,035 strikeouts above the cutoff level:

(5913 * (.20566 – 4*.023830) = 652

1687 – 652 = 1035

And if we use 5 standard deviations below the norm, we wind up with 1,175 "contributing" strikeouts:

(5913 * (.20566 – 5*.023830) = 512

1687 – 512 = 1175

At this point, we don’t know whether we are going to wind up using 3 standard deviations below the norm, 4 standard deviations below the norm, 5 standard deviations below the norm, or some other number entirely. We don’t know.

Also, at this point we don’t know what the value of a strikeout is, in this structure. One can estimate the value of a strikeout, using different approaches, at anywhere from .13 runs (negative .13 runs to the offense) up to .35 runs. We don’t know what the number is that will work in this structure. We’ll start with .30 runs as a test assumption, but. . . we don’t know.

We know, from the work we did yesterday, that the 2018 Astros saved 935 runs against a zero-value pitching-and-defense combination. That number is fixed; it will not be allowed to adjust as our analysis evolves. But how many of those 935 runs will we credit to the strikeouts?

At this point, we could reasonably get a number anywhere from 116 to 411. 116 is 894 * .13. 411 is 1175 * .35. That’s our operating range. We have to figure out what the number is in there that consistently gets the answer that we need to make this system work. The number that works logically HAS to be the "right" answer.

It’s just like a runs created method, only backwards. The values that work, in a runs created method, are the numbers that tell you how many runs the team will score. The values that work, in a runs saved against zero method, would be or will be the numbers that tell you how many runs the team will allow.

The 2018 Astros are the #1 team in "relevant strikeouts" whether you use 3 standard deviations below the norm, 4 standard deviations or 5. They’re #1 any way you look at it.

But as to who has the FEWEST relevant strikeouts, there you get a different answer with each test. The 2003 Detroit Tigers (43-119; Mike Maroth and Jeremy Bonderman). . .the 2003 Tigers struck out only 764 batters among 6,376 who teed off against them. If we use the 3 standard deviation standard, then the Tigers are credited with only 25 strikeouts, the lowest total of all time.

But if we use the 4 standard deviation cutoff, then the 2003 Tigers scoot all the way up to the 4^{th}-worst team ever, and the worst team ever would be the 1918 Philadelphia Athletics (52-76 in a war-shortened season.) The Athletics struck out only 276 batters among 4,834 that they faced, which would be 131 strikeouts above the level of 4 standard deviations below the norm.

And if we use the 5 standard deviation level, then we get a different answer again. Using the 5 standard deviation level, the worst team ever would be the 1925 Boston Red Sox (47-105). They struck out 310 of 6,025 opposing batters, which would be only 197 strikeouts better than five standard deviations below the norm.

We’re not arbitrarily ** choosing** the right values. We’re trying to

Thanks for reading.

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## COMMENTS (14 Comments, most recent shown first)

MarisFan61You have 10 little bottles of sanitizer, and can't get more. That's all there is.

Being perhaps quite fond of sanitizer, you want to use it for all kinds of stuff. Like, you want to use one of the entire bottles right now to clean your laptop, another half bottle to clean your phone.... and you're about to do it.

Your friend sees that, and bodily prevents you from it -- says hey, we've got a pandemic, you're going to need that.

He has saved a bottle and a half of sanitizer for you.

Later on, you feel like you need to use it for.....

well I didn't know what example I was going to do there, but just then, the mail came, so........you feel like you want to use 2 of the bottles to sanitize all your mail. Your mother sees that, grabs you bodily and asks if you're an idiot, tells you that you can maybe just put it aside for a few hours, she heard Dr. Fauci and she thinks he said something like that any virus on there would die.

Your mom has saved you 2 bottles.

We could go on further with this, and pretty soon, the total amount of "sanitizer saved" would be greater than the amount that you ever had.

In any kind of metric thing that you might want to do on it, you

couldn't(I don't think) have there be such a thing. But it helps to realize that in whatever model you develop that puts it in some meaningful operational terms, you're going against the usual sense of how to see the number of sanitizer bottles that each person saved you -- and it would help tremendously, in expressing the model, for this to be indicated.While both the usual-sense concept and the metric concept talk in terms of the same words, "sanitizer saved," they

aren't reallyabout the same thing;sort ofthey are, but largely they're not.5:00 PM Mar 30thMarisFan61I now get it -- totally -- with the extra help of MichaelPat's posts.

It might not seem like those were quantum leaps, but they put it in a way that the rest came together.

It's what I had suspected, and mentioned a couple of times: a disconnect (very divergent one) between the common concept of "runs saved," even in a large segment of those who are pretty good with sabermetrics (as we've been seeing here) and the

strictsabermetric concept of it.This will be discussed further on Reader Posts, in a new thread probably to be titled The "Runs Prevented" Confusion, Resolved.

At this point I really really won't say more :-) except for my next Comment, which will be sort of an allegory.

Not about Runs Prevented, mind you.

It will be about

sanitizer.Any resemblance to other issues, real or imagined, will be merely coincidental. :-)

Actually I think the 'allegory' (or whatever it should be called) will reflect very accurately on this whoop-de-doo.

4:41 PM Mar 30thChihuahua332Thank you Clay (I’m assuming that is your first name) and thank you Bill for affirming Clay’s original comment. I was dancing around the logic but wasn’t able to get my feet fully under me until I read your comment.

2:30 PM Mar 30thMichaelPatiF Offense = Defense, then Runs created = Run prevented

Not runs scored scored, but runs created (UNDER James' system). Runs prevented will be a new stat, like runs created.

11:05 AM Mar 30thMichaelPatWhen a player slugs a three run homer, we don't automatically assume that he will be credited with three runs created in the runs created system.

The same will be true in the runs prevented system (if it comes together).

The outfielder leaps at the wall and pulls back a three run homer. He won't be automatically be credited with three runs saved.

Runs prevented, like runs created, won't work that way.

10:03 AM Mar 30thMichaelPatMaris, what is defense if it isn't runs prevented?

You can say offense is singles, doubles, triples, stolen bases, sac flies, etc., etc. The sum total of course is runs scored.

You can say defense is fielders' range, errors, home runs robbed, effective pitching, etc. etc. James is looking for a stat like runs that would cover all of these things. Runs prevented is this stat.

The tricky part is that while runs are an actual thing that go up on the scoreboard, runs prevented is simply - at this point - a concept.

What information do we have that could help us define this concept? The idea that offense and defense are the same side of the coin, that they are equal (at the whole league level). Using that proposition is what gives you a runs prevented....

We say played X created Y number of runs int he runs created system. That system works because all of the players' runs created equal (or at least are very close to) the actual number of runs created in the whole league.

James wants to develop a similar number for defense.

10:00 AM Mar 30thMarisFan61I said I wasn't going to say more, and although I meant that as not saying more

to Bill, I now want to make it be nothing at all whatsoever, but just this final thing:OF COURSE about offense = defense (BTW, upon which Bill put an interesting footnote on Hey Bill, unrelated to what we're talking about here but a pretty big little thing, and very interesting).

Yes, offense = defense.

But what hasn't been explained or even addressed -- everybody saying it seems to think this next thing is axiomatic -- the leap that neither I nor many others get is, how that leads to anything about Runs PREVENTED.

I'm out.

7:57 PM Mar 29thMichaelPatOffense and defense (pitching and fielding) are equal.

How do we represent [measure] offense? Runs scored.

James wants to develop a system that represents defense in a way we can measure.

So if offense and defense are equal, we must represent defense as an equal number of runs prevented.

I think it really is that simple. It is an arbitrary figure in a way, but it is premised on the pretty strong principle that offense and defense in MLB are equal.

Of course, you could argue that offense and defense are not equal... but that is a different argument entirely. This work starts from the assumption that offense and defense are equal.

It could be, somewhere down the road, that we can never make an effective system based on that starting assumption. In that case, we will have to go back and re-examine the idea that defense and offense are the opposite sides of the same coin.

3:17 PM Mar 29thMarisFan61(Clay: Sorry -- the key point more so was the last sentence of Tenet 5: "So, we’ll start with a zero point determined by the lowest (most negative) standard deviation for the components of runs prevented."

If the whole thing is that this is being taken as an assumption for the model, that would appear to answer it.

12:20 AM Mar 29thclayyearsleyMy apologies. I see now this has been played out in Reader Posts ad nauseum.

12:15 AM Mar 29thMarisFan61Clay: Of course -- but you don't explain the thing that's the center of the confusion; you merely

state itas part of your path.Everything before and after it is clear, and never was any problem.

(Memory refresher: It's this, which you state in Tenet 4: " In order to make Tenet 1 true, we have to start with twice the number of runs scored."

That may be a clear step to you. It's not clear to many of us.

10:38 PM Mar 28thCharlesSaegerYeah, thanks for saying what I was trying to find a way to say since it's obvious to me. Especially tenet 1.

10:29 PM Mar 28thbjamesClay Yearsley for President.

9:40 PM Mar 28thclayyearsleyTo Maris, et al.

This is my understanding of what Bill is attempting to do. I may be totally off. BTW, when I say “we” and “our” below, I really mean “Bill”, of course. :)

Tenet 1: The essence of baseball is that the offense tries to score as many runs as possible, while the defense (including pitcher) tries to prevent run scoring.

These elements are equally balanced. Defense/pitching = offense.If you don’t buy that, then you’re not going to agree with this methodology. I would say that this is supposed to be true over a large sample, not at the individual game level. Surely, some games the offense plays a larger role in, while defense/pitching does the same in other games.Tenet 2: We already have a good idea of how to measure offensive contribution. We can use Runs Created, wOBA, or whatever you like.

Tenet 3: Because we can account for the offense, we’re going to do that in an additive manner, starting with zero. The sum of all teams’ offensive contributions (or each individual players’) is equal to the number of runs scored for the league as a whole.

Tenet 4: Defense/pitching contributions will be done in a subtractive manner. In order to make Tenet 1 true, we have to start with twice the number of runs scored. Then we subtract 1 from that total for each run prevented. Once we’ve done that, we’ll end up meeting in the middle.

Tenet 5: We can’t simply take a bunch of counting stats and use a single formula (or chain of 3, like the Runs Created ABC process) to derive runs prevented. So, we’ll start with a zero point determined by the lowest (most negative) standard deviation for the components of runs prevented.

Tenet 6: Somehow, those standard deviation measures will give us a way to place a value on each of the run prevention components. How? Beats me. That’s what Bill is working on. When he’s done, in theory, we’ll have a run prevention contribution for each team/player. The total of those will equal the runs scored for the league.

7:44 PM Mar 28th