By Bill James

April 8, 2020

OK, our task for today is relatively straightforward. At the end of the last round of this project, our average error was 123 runs per team, and our standard error was 155 runs per team. Since those numbers are much larger than the standard deviation of runs allowed, our method is at this point useless. It is a "prediction" of runs allowed which, at this point, is less accurate than just guessing that every team will allow the league average number or runs.

That was using the old process for establishing the zero point for each team’s Runs Prevented. In Monday’s article I introduced a new process for establishing the zero point. Using the new zero point process, the average error is 65 runs per team, and the standard error is 77 runs per team. Basically, we’ve cut the error in half by making this substitution.

It is, in a certain manner of speaking, a cheat. What I have in essence said is that, since I am unable to make my calculated values match my predicted values, I will change my prediction to better match my calculations. It is cheating, in a sense, and it isn’t, in a sense. It is still true here that I have a method of measuring runs saved which is derived from team numbers, and a method which is derived by an entirely different process and relies on completely different statistics, but which reaches essentially similar conclusions. The only change is that I had a theory about how to derive one of those two estimates that did not work, so I have had to discard that theory, and approach it a different way.

But we’re still 7% low, in a global sense. Our next task is to bring the sum- of-the-categories estimate up to the sum-of-the-teams estimate. We can do this, initially and temporarily, by simply increasing the value of each event by about 7%; it’s the new 7% solution.

We have placed an "initial value estimate" on each run-prevention event, right? We valued each strikeout at .30 runs prevented. But when we reach the point where we are now.. .well, not actually the point where we are now, but the point where we will be tomorrow. When we reach this stage, we can ask the data "Is our prediction more accurate, or less accurate, if we value the strikeout at .31 runs prevented?" And then we ask "Is our prediction more accurate, or less accurate, if we value the strikeout at .29 runs prevented?"

Unless the estimate of .30 runs prevented by a strikeout is precisely accurate, then our predictions HAVE to become more accurate either if we move the estimate down, or if we move it up. Three possibilities, right? Our estimate of the value of a strikeout has to be either:

a) Too low

b) Too high, or

c) Exactly right.

We test to see if it is too low; we test to see if it is too high. If it fails both tests, then we leave it where it is.

The process isn’t QUITE that simple, because we have to accommodate changes to the global balance at the same time we make changes to the category values. Still, that’s ESSENTIALLY what we do from now on; we look for ways to reduce the standard error by monkeying with the category values.

First, though, before we get to that, we’re about 7% too low overall. We can solve this, probably, by just moving everything up by about 7%. This, again, is what we could consider to be a Global Cheat. We’re not *actually* learning anything here; we’re just artificially making things match, because they don’t match and we want them to.

So then, we increase the values given:

For a strikeout, from .30 to .32,

For a walk or a Hit Batsman, from .32 to .34,

For a Home Run, from 1.40 to 1.50,

For a Wild Pitch, a Passed Ball or a Balk, from .16 to .17,

For a play not made in the field (DER), from .81 to .87,

For an error, from .60 to .64,

For a Double Play, from .62 to .66, and

For an estimated Run of Stolen Base Value, from 1.00 to 1.07.

Remember, I handled stolen bases a little bit different than I did everything else; I combined stolen bases and caught stealing in one category, which I called Stolen Base Value. Stolen Base Value is stated on a "runs" scale, so that each point is supposed to be a Run, hence the value of 1.00. However, this category is not immune to the rules of the process, which are: that maybe the values I chose are wrong, so we need to adjust them. I adjusted SBV up from 1.00 to 1.07, and we’ll see where it goes from there.

Anyway, these adjustments reduce the average error for the study from 65 runs to 49—actually, 48.704. Our average error now is less than 7%. Remember, we’d like to get it to 2%, probably won’t make that, but at 7%, it’s still not where we need it.

OK, that was easy, so we’re going to go one more step. The next thing we’re going to do is to automatically adjust the values so that we get the total we want. The total we have, with these values, is 1,725,202 runs. The total we want is 1,783,676. We’re still low by 3.389%, from now on we’re going to AUTOMATICALLY adjust every value by whatever percentage is necessary to make the total come out right.

Except that, for some reason, that makes the average error significantly worse, rather than slightly better, so I won’t do that right now. I’ve got the spreadsheet set up to do it, but I won’t do that until I figure out why it is backfiring on me. Anyway, thanks for reading.

Don’t get COVID-19, but also, if you hear of anyone within our community who does get it, let us know, please. Some of us ignorant peasants may want to pray for you. Thanks for reading.

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## COMMENTS (6 Comments, most recent shown first)

MarisFan61(In the current article "(Re-Establishing the Values"), Bill makes it explicit that it is so.

I suppose it's possible he made a point of expressing it explicitly there because of the question having been raised here.)

1:42 AM Apr 11thbjamesdavidt50

It is fun to listen to you work this out in front of us. My son takes a course called Financial Math, and he is very interested in your methods and reasoning and thinking out loud, as am I.

Thanks.

5:25 PM Apr 9thMarisFan61Kaiser: I think that

has to beso.3:56 PM Apr 9thKaiserD2Could some one please clarify something for me? Some of the events in Bill's list--a strikeout or a double play--do in fact prevent runs. Others--such as a home run--increase runs. But all of them are shown with positive values. Are we to assume that the run-prevention value of a strikeout refers to one more strikeout, while the value for a home run refers to one less? Thanks.

David K

1:02 PM Apr 9thdavidt50It is fun to listen to you work this out in front of us. My son takes a course called Financial Math, and he is very interested in your methods and reasoning and thinking out loud, as am I.

12:37 AM Apr 9thMarisFan61It's not a "cheat," it's

perfect! (In my little opinion.) :-)I'd be interested in whether anyone sees it any differently. I'm reasonably confident they won't.

If I understand right, what this is is the normal

optimalthing of keeping on checking on a developing method's relation to apparent reality and to common sense.The only difference from the usual is that Bill is thinking out loud the whole way and sharing the checking-outs and the adjustments.

2:24 PM Apr 8th