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Runs, RBI and Home Runs

June 16, 2019

Runs, RBI and Home Runs


          As a bird of whackground, word of background, there used to be a stat called Runs Produced, which was Runs + RBI – HR.   No one pays any attention to this stat anymore; it was kind of amateur sabermetrics from the paleolithic era, but for some reason the discussion about this essentially obsolete stat has come back to the surface.  I always argued, because I always believed, that it made no sense to subtract home runs from the stat, if you wanted to accurately evaluate hitters.   Suppose that you have two teams of players.   One team has scored 800 runs, driven in 750 runs, but has hit 200 home runs; the other team has scored 800 runs, driven in 750 runs, but has hit only 100 home runs.   Is one of them better than the other?   The unnatural removal of the home run, I always thought, was an expression of bias against power hitters, derived from the prehistoric preference for batting average.  

          Apparently not.   Tom Tango has taken time to try to tease through the test of whether Runs + RBI – HR or just Runs + RBI, leave the home runs alone, was actually the better formula to evaluate a hitter.  He concluded that Runs + RBI – HR was in fact the better formula.  I know this because he told me so, private and public exchanges, but I didn’t go to his blog and check out his research because I didn’t want his way of thinking about the issue to bias my own way of thinking through the problem.   If I was to try to figure out which was the better formula, how would I go about it?

          I decided to approach it in this way.   There must be SOME way to translate the "runs produced" by this formula into runs created, right?   How do we do this?

          I actually tested three formulas:

A.    Runs + RBI – Home Runs

B.     Runs + RBI

C.    Runs + RBI + Home Runs


I took all players who had 500 plate appearances in a season from 1980 to 2018, which is a total of 5,346 players, or about the average number of fans at a Baltimore Orioles game.   For each of those players, I estimated his Runs Created by a good and careful method, and also figured his Runs Produced by formulas A, B, and C.  

The 5,346 players in the study created an average of 83 runs—83.0919, if you really must know.

By formula A, the players had "produced" an average of 136.0322 runs.   The ratio of Runs Produced to Actual Runs Created, then, is 1 to .610 825. 

Suppose, then, that we estimated each player’s Runs Created by the formula (Runs + RBI – HR) * .610 825.    By this formula, the #1 offensive season of that era was by Manny Ramirez in 1999, when Manny scored 131 runs and drove in 165 runs with only 44 measly home runs.  That’s 252 runs produced (131 + 165 -44), which, multiplied by .610 825, suggests that he created 153.9 runs. 

In reality, he created only 139.1 runs, probably, an error of 14.9 runs, the way it rounds off.  Suppose that we figure the error for each of the 5,346 players in the study.   Then we repeat the process with Runs Produced formula B, and formula C.   I’d share the numbers with you, but that doesn’t matter; the only thing that matters is the conclusion. 

When I ran that study with Formula C, Runs plus RBI PLUS home runs, the gross error for the 5,346 players was 50,256 runs, or 9.40 Runs Per Player.  

When I ran the study with Formula B, Runs plus RBI, leaving the home runs alone, the gross error was 44,118 runs, or 8.25 Runs Per Player. 

When I ran the study with Formula C, Runs plus RBI MINUS home runs, the gross error was 43,884 runs, or 8.21 Runs Per Player.

          Conclusion?   Runs plus RBI minus Home Runs is in fact the most accurate of the three formulas, or, perhaps better stated, is the least inaccurate. 

          It should be noted, because it will later become relevant, that the difference between the accuracy of Formula A and the accuracy of Formula B is very, very small—an average error of 8.21 runs as opposed to 8.25. 

          What is very apparent from this data is that there would be a more accurate version of the formula, if we cared to pursue it, which would be something like (Runs + RBI - .55 * home runs) or maybe

(Runs + RBI - .62 * home runs) or something like that.   It is intuitively obvious, to me, that the graph charting the error in the formula has reached bottom and headed back up somewhere between (Runs + RBI - .000 * Home Runs) and (Runs + RBI – 1.000 Home Runs), somewhere probably in the range of .600.   But since no one would or should use that formula if I figured out what the optimal point was, I’m going to let that pass.

          But there is one more question to be answered here.   What if the number of outs is different?  In other words, we take the players who created 100 runs by this estimate, and the players who created 100 runs by that estimate.   If may be that estimate "A" is better than estimate "B"; it not only may be true, it is true, we’ve established that.   But what if the "A" players create their runs while making more outs? 

          I sorted players by runs created, estimated by Formulas A, B and Formula C, and then looked at the number of OUTS used by:

1)    The top 500 players,

2)    The top 1000 players,

3)    The bottom 1000 players, and

4)    The bottom 500 runs. 


And, sure enough, it does turn out that the players who are credited with creating more runs by Formula A are also making more outs.   The top 500 players in Runs Produced, by Formula A, made an average of 434.3 outs, while the top 500 players  in Runs Produced, by Formula B made an average of 432.0 outs. 

There are two questions here:

(q1) Which formula is most accurate in estimating the number of runs created by the player? And

(q2) Which group of players, identified by which formula, is actually the most effective at creating runs, per out used?


Formula A, while it is the most accurate in estimating runs created, is BY FAR the least accurate formula of the three at identifying the most effective offensive players.  It achieves "accuracy" at the expense of ignoring the number of outs made. 

The 500 players identified by formula A (as producing the most runs) created an average of 7.31 runs per 27 outs.   But the 500 players identified by Formula B as producing the most runs created an average of 7.53 runs per 27 outs (actually 7.53496), while those identified by Formula C as producing the most runs also created an average of 7.53 runs per 27 outs (actually 7.528.)   This is a relatively huge difference—much, much larger than the difference noted by the other approach. 

The 500 LEAST effective hitters, as identified by Formula A, created an average of 3.83 runs per 27 outs, while the 500 least effective hitters, as identified by Formula B, created an average of only 3.79 runs per 27 outs. 


So I have to say, bottom line, that I have reached a different conclusion in regard to this issue that Tango reached, repeating that I have not read his study, and don’t know how it was done or why he reached that conclusion.   The better formula is NOT Runs + RBI – Home Runs; it is simply Runs + RBI.  


COMMENTS (27 Comments, most recent shown first)

Bill: I think there will be a problematic and unintended takeaway from this article if that estimate of a more accurate version of the formula is let just stand without some comment from you.

I can imagine that maybe the reason you haven't commented on that (nor on anything) is that you don't regard this Runs Produced thing as being worth any further close attention, which is certainly what I think. (As you said: "if we cared to pursue it" -- and there isn't much reason to.)

But the thing is, you did state a range for what would be the most accurate version of the formula, and it did happen to be closer to the formula which, later in the article, you wound up concluding is worse, once you took further considerations into account.

I think that as it stands, a major takeaway from this article, probably the main one, would be that your view of the best formula is one that's closer to the "subtracting" version than the "non-subtracting" one, because it's the only kind of better version that appears here -- even though ultimately you wound up concluding the opposite.
5:08 AM Jun 24th
I know this once-hot topic is down to embers, but I want to address an essential point that Maris has raised, mostly to the sound of crickets, probably because it is a qualitative point that defies quantification:
BTW, I say an additional big factor is to take big account of how the thing was seen at the time, which it doesn't seem anybody else is considering important.

Like any historical artifact, "Runs Produced" is better understood within its own time context than through current values and priorities. I alluded to this when I wrote earlier about the modest ambitions for "Runs Produced" when it was devised. There were two statistics at the time for measuring parts of a player's direct contribution to putting a run on the scoreboard: Runs and RBIs. The point of "Runs Produced" was merely to improve on each of the two by combining them both into a total contribution. The formula subtracted home runs to avoid double-counting runs that were scored and batted in by the same player.

Ignoring this original purpose — how the thing was seen at the time — can lead to two kinds of misconception. One, a misguided aspiration, results from the other, a misunderstood terminology. I think Bill avoided both pitfalls in his methodology, but the discussion has wandered in a different direction.

1. To explain the aspirational issue: There's a reason no one designed a 2019 fuel-efficient automobile by adding to the compact chassis of a 1959 Studebaker Lark. It's not that such an endeavor would be impossible. It's just that 60 years of technology has enabled people to design 50 mpg cars, while revising the '59 Lark would limit them to maybe 35. Trying to convert "Runs Produced" into "Runs Created" or wOBA is a fun exercise if we accept a maximum accuracy of, say, 70 percent; I took a shot at it myself. But we don't try to pinpoint the Winter Solstice by making adjustments to Stonehenge. We use a calendar.

2. Current sabermetric usage gives us two easy ways to misinterpret the meaning of "Runs Produced." . . .
. . . . The term itself sounds a lot like "Runs Created," and understandably so, because "produced" and "created" are in fact synonymous outside the terminology of baseball lingo. But Robert Creamer did not call his new stat "Runs Produced" because he had prescient knowledge that a similar term 25 years later would estimate the near-entirety of a player's offensive value. He called it "Runs Produced" because "Total Direct Contributions To Runs Scored" would have made an awkward acronym.
. . . . Even the word "Runs" means something now that it did not mean in the 1950s. Besides its timeless meaning of "points scored," "Runs" is also a common shorthand for "Run-Equivalent Value." The concept of expressing total offensive value in a single number did not exist when "Runs Produced" was introduced. Not only that, but there's also no evidence that anybody working in the public domain even thought such a number would be a handy thing to have, or even might exist, let alone whether it could be calculated or how to do it.

If I went back to 1960 and told 100 baseball fans I could accurately translate the sum of a player's hits, walks, extra bases and whatnot into the number of runs they were worth, I think I would have gotten just two reactions:
Nah! No way! That's impossible! How?
(Best as I remember, people were using the idiom "No way!" in 1960.)

On the other hand, if Creamer were reanimated today with an appreciation for sabermetrics, it's hard to imagine he'd think it's a good idea to try to approximate Runs Created by primarily using stats that are team-dependent. And then he would remind us that "team-dependent" is another concept that no one considered in the 1950s.
4:42 PM Jun 21st
What, then, is the relationship between Runs Produced and Runs Actually Scored? Because it would always vary, thus being kind of unreliable, no?
6:44 AM Jun 20th
In between, in some-or-other proportions which we could say is a big part of the argument on either side.

(Right, folks?)

Most of the rest of the argument is what exactly is the best way to conceptualize and measure those things.

BTW, I say an additional big factor is to take big account of how the thing was seen at the time, which it doesn't seem anybody else is considering important.
8:40 PM Jun 19th
I lied...

Maybe I’m not clear on this point: Are we dealing with ACTUAL runs, or inventing a stat to show a different value, like points to show the KIND of a hitter this cat is?
8:08 PM Jun 19th
Doing my best to try to relate that to what we're looking at here, I guess it's an argument against not subtracting HR's. (Because if we don't, then the guy gets credit for 2 Runs Produced.)

And it's a decent argument.
But there are decent arguments on the other side.

To see that opposite argument, you have to somewhat relinquish your view of this thing as concretely meaning just "runs," and see it somewhat as an evaluative thing about what the guy did.

He didn't need any help to achieve that run. It didn't depend on any teammate doing anything.
Arguably that's something, isn't it?
(Answer: Yes.) :-)

And in fact, if you only want to do Runs Produced the other way -- i.e. with the subtraction of HR's -- it means that a batter who did less, in terms of his offense element, might get more credit: a guy who gets a single when a runner happens to be on 2nd or 3rd base and so he gets an RBI, then scores because of what the guys behind him happen to do, would get "2," while your leadoff HR guy just gets 1. In fact, a guy who doesn't get a hit (or walk) at all can wind up with 2x the Runs Produced of your leadoff guy: someone who reaches on a error and gets an RBI, then later scores. And arguably, these things aren't fair or accurate for the leadoff HR guy.

I'm not saying this is the only way to see it and that it means you can't argue for the "subtracting" method.
I'm just saying this is an answer to what you asked.
1:01 PM Jun 19th
Final comment for me: I have yet to attend a game where the visiting team’s lead-off hitter comes up in the first inning, no one else having come up, hits a solo home run, making the score 2-0. Maybe I haven’t seen enough.
11:33 AM Jun 19th
I've embedded a question for Bill in here that don't think even Maris can answer for him, despite his typically fair-minded skill at divining the intent of others. (I would expect him to push back against even an accurate third-party paraphraser, though, on grounds that his own words can create ample trouble for himself without the help of anyome else.... D'oh! Now I'm the one presuming to speak for him.)

My impression is that "Runs Produced" was the first attempt to create an off-the-rack statistic that would represent a player's total value. Robert Creamer introduced it in Sports Illustrated in 1956, when SI was in its second year. I know Branch Rickey valued OBP before then, for example, but was anything in public use before 1956?

"Runs Produced" had no ambitions as lofty as "Runs Created." I don't think anybody even thought in terms of measuring total offensive value with a single metric back then, perhaps excepting a few astute front offices. Pete Palmer was in high school and I doubt if Bill had yet learned multiplication tables. For that same reason, there was no attempt to determine its validity in measuring offensive production. It merely aspired to improve upon both Runs and RBIs as stand-alone stats.

I was 4 years old during the '56 season, two years younger than Bill almost to the day. (My first awareness of major-league baseball was in 1958, California's first year with NL teams, and I had no clue until the '59 World Series that New York had ever had more than one team.) I first read or heard about Runs Produced eight or nine years later, described as a brand-new stat even in the mid-60s. I was 12 or 13, an APBA-playing, baseball lover who was still pretty sure that girls weren't worth the trouble. It was one of those learning experiences that left an indelible impression, like "I before E," so I still remember my two reactions.

I'll share them by way of asking Bill: Did you have any similar moments, either of Aha! or of rudimentary creativity, before or during high school?

1. Wow! You mean you can DO that? You can make up your own stat? You don't have to settle for the ones from Street and Smith's yearbooks and baseball cards? Well, I know from playing APBA that batting average isn't all it's cracked up to be. Maybe I can prove what I've been saying about Ron Fairly, Joe Adcock and Ron Hansen being better than their .260-.270 averages.
.... Playing APBA taught a kid to appreciate the value of walks, so the first new stat I devised was something I called "Wave," for Walks Plus Average: (H+BB) / (PA+BB). I first calculated it for my APBA league on my Dad's slide rule, and later used it for our next season's player draft.

2. Cool as it was to see the measurement of something previously unmeasured, there were two things I didn't like about Runs Produced. . . .
. . . It assigned different values to runs by crediting two Runs Produced for most but not all runs. If Frank Robinson hit a home run with Vada Pinson on base, then Pinson's run generated 2 Runs Produced and Robinson's generated only 1. If nothing else, that made it useless as a team stat, and I also thought home runs were important enough not to be subtracted.
. . . It credited equal value to Runs and RBIs, when everybody knew back then that an RBI was worth way more than Run. :--) I also had a quarrel with RBIs, though, because they treated a groundout with a man on third as equal to a double that scored a man from first. So I devised BDI, for Bases Driven In, which credited 1 for the former and 3 for the latter, and turned out to be wildly misleading.​
5:52 AM Jun 19th
Since Bill hasn't started replying yet, I'll be his spokesman.
(Yeah right.) :-) :-)

Thoughtclaw, I think we can safely say he wasn't insulted by it. It's a good guess that he pretty matter-of-factly just wanted to indicate that he has never used that thing and that it's never been thought of as "runs created." He comes across misunderstandings of his work and of sabermetric stuff all the time, and I doubt it fazes him. And in fact I'd guess it's far less annoying to him than stuff like what people like me say -- like when somebody who knows almost nothing says "I'll be his spokesman." :-)
12:01 AM Jun 19th
For what it's worth (which is very little, in the grand scheme of things), I believe I prompted the "Hey Bill" discussion with a half-cocked question about the "runs produced" formula, which I mistakenly thought Bill was using when he mentioned "runs created" in a previous article. Upon further reflection, I realize that he would never use such a primitive statistic to make a point; perhaps he found my presumption insulting. I wouldn't blame him. I did reply with a message about how I had confused the two statistics, half-hoping Bill would post my message with a simple "thanks" or something, just to save face. But I suspected he wouldn't, since it doesn't really add anything to the discussion, and he didn't.

But the question I actually asked was whether he felt home runs should in fact be subtracted, as I feel it makes sense to give a hitter credit BOTH for scoring the run and driving it in. Bill chose to excise this portion of my missive, as of course he has a perfect right to do. It's his site, not mine. But it seems to have prompted a discussion about the validity of this subtraction, which in turn led to a study by the man himself, and I find that enormously gratifying, even though it started with a gaffe on my part.
9:33 PM Jun 18th
...but you said EVERY run is counted twice. And I know RBIs are sometimes counted on unearned runs. Don’t be condescending, please. And you answered my question, so thanks!
1:01 PM Jun 18th

Runs that are made without an RBI being credited get counted only once in runs produced, obviously. (The formula is Runs + RBI = Runs Produced, or in its other version, Runs + RBI - HR = RP) Whether the run is earned or not is irrelevant. (There is often an RBI credited when an unearned run is scored.)

12:07 PM Jun 18th
Bill: Question about that estimate you give, about halfway down in the article, that a more accurate version of the formula "if we cared to pursue it" (which I know you don't, and neither do I, for the same reasons as you) would involve subtracting about 0.6 x number of HR's....

I gather that in view of what you conclude later in the article (after taking more into account), if you had written that paragraph at that later point, the decimal estimate would have been a little less than 0.5, rather than more. Is that right?

(When I was looking at results from the two formulas and felt I was seeing that the 'non-subtracting' formula's results was somewhat better, I figured that the ideal subtraction would therefore be a little closer to the non-subtracting, i.e. something less than 0.5 rather than more. So, I'm figuring that the reason you were surmising a higher figure was just that you were talking about it before you got to the step where "Formula B" took over.)

I realize that this hardly matters, but I'm asking just because you did give a figure, and I suspect it's different than the figure you would have given if you'd talked about it closer to the end of the article.
5:48 AM Jun 18th
P.S. .....A word or two (actually I'm afraid, more than 2) about why I think Bill's method, in the last part of this, implicitly addresses what I said at the bottom there, although I'm sure he didn't intend to address it and I suspect he'll furrow his brow at this, at least at first blush.

What I said:
"What you arrive at by adding the consideration of outs-made.....I wonder if that implicitly involves and brings in that principle that I stated, that the non-HR hitter (or lesser HR hitter) 'needs more help' to wind up with the same number of Runs Produced.
I think it does."

Bill mentions, as a key thing in his analysis, that the group of players who are credited as creating at least 100 Runs by "Formula A" (the 'subtracting HR's" formula) made more outs than the group so credited by Formula B (non-subtracting).

He didn't address WHY that group might have made more outs.
I'm going to, and it's why I think his analysis implicitly involves the thing I talked about, or at least overlaps a lot with it.


Unless it's that those players played more than the players credited with creating at least 100 runs by Formula B, I would think it has to mean this (and that this is the more likely thing):
They tended to be on better teams or at least in better lineups, which would mean they batted more times, because in a better lineup you come to bat more times per game (somewhat balanced by having fewer 9th innings), which gives more "mass" to their offense, increases their opportunity to "produce" runs, despite their making more outs, which this also gives them more of a chance to do.
(I ought to emphasize: The differences are small. Bill's data show just a slight difference in "outs made" between the groups, and so the differences I'm talking about are likewise small. I'm saying just that there are tendencies in the noted directions, and that they make a difference -- not that the differences are large.)

So, that's about what Bill said (my take on it.)

And, the way I had seen it was: The 'lesser-home-run' players who had good numbers of Runs Produced needed and got more help to produce that number of runs.
They had to, because they didn't drive themselves in as much.
Looked at another way: It's very possible for a high-HR hitter to be among the leaders in Runs Produced by "Formula A" despite being in a bad lineup (although of course harder than in a good lineup); I think it's almost impossible for a low-HR hitter to be among the leaders if he's in a bad lineup, because he's not going to be driving himself in very much and he won't have that many men on base to drive in, plus the guys behind him won't be driving him in that much.

Cliff's Notes: Since "Formula A" includes a higher proportion of lower-HR players than "Formula B," and since lower-HR players (I'm saying) need more to be in a good lineup to get good numbers of Runs Produced, they tend to come to bat more, which helps them further to get more Runs Produced but also causes them to make more outs.


I should note, nothing in this post is about one formula being better or worse than the other. (Bill did find that the Formula A group was less good -- that the higher number of outs-made outweighed the extra 'runs created' -- but what I'm talking about here doesn't involve that.)
I'm just pointing out why I think what I said down there, i.e. that Bill's inclusion of "outs made" in his analysis is related to what I said about lower-HR players "needing and getting more help" to get good numbers of Runs Produced.
2:41 AM Jun 18th
I'd like to buy that piano necktie.

9:49 PM Jun 17th
...and if every run is counted twice, what happens to an unearned run that doesn’t come with an RBI? Do we make one up, just to keep things even? I gotta know!
8:23 PM Jun 17th
Okay, now you’re talking POINTS. Is it POINTS or RUNS? I’m not averse to finding out I’m so wrong and then learning something. If it’s points, okay. Just don’t call them “runs.” I’m confused enough by my telephone and television.
6:59 PM Jun 17th

In the runs produced world, every run is counted twice - once by the player scoring it, once by the player driving it in.
In runs produced terms, four runs get players eight points (one for each run, one for each RBI).... UNLESS a home is involved. Then's it's only seven points (one for each run, one for each rbi, then minus one for the home run).

This is the flaw in the Runs + RBI - HR system - it does not treat all runs equally

5:39 PM Jun 17th
Seriously, in what universe is a grand slam equal to five runs? Apparently, here. It’s a good thing I love Bill James so much. I’d have to go, otherwise.
3:54 PM Jun 17th
Minus home runs is logical. You get an RBI and a run when you hit a solo shot. Does that mean two runs were scored? NO! I thought we were dealing with actual runs scored here. I feel like I’m taking crazy pills! I invented the piano necktie! I invented it!
3:47 PM Jun 17th
I wouldn't guess that they were thinking that deeply.
I think it's more likely that somebody there (not that I know where; don't know if it originated at Sports Illustrated) .....somebody there just wanted to do something DIFFERENT, something that seemed a little creative and which put together the existing common stats in some different way. Merely doing "runs plus RBI's" wouldn't have been such a thing, but hey, runs plus RBI's minus HR's, we've invented something.....

But really, I have to say, it wasn't bad, for its time. In fact, given what else was available, it was even interesting, at least to me. I mean look -- I read it; I went looking for it when I came upon issues of Sports Illustrated, and really it's just about the only thing I remember from the magazine after all these years, except for how they always had articles about stuff I couldn't care less about like fishing and high school swimming. As I've mentioned, I didn't regard the rankings on "Runs Produced" as very well indicative, but they were something, and they were interesting -- for that time.
1:27 PM Jun 17th
The 'minus home runs' formulas always just seemed to be trying to make the guys who didn't hit home runs, look better.

'Anyone can drive in and score runs with a home run. It's those guys that do it WITHOUT hitting home runs that are the best hitters!' Seemed to be the what people were going for. Althought they would dress it up fancier than that.

1:16 PM Jun 17th
3for3: Why?
11:33 AM Jun 17th
Bill made the assumption that all 5,346 people who attend Orioles games are fans. This is generous, I think. Many of them are not fans at all, but rubberneckers, storm chasers, tabloid journalists, bloggers, whatever you want to call them - the crowd of people who congregate around any disaster.
10:55 AM Jun 17th
A better example might give the no power guy 110 runs and 50 RBI..
8:46 AM Jun 17th
......Actually, that one example that I gave seems pretty telling, in itself.
Please folks, just take a look. This is an Emperor's Clothes thing.

Player A: 40 HR, 100 R, 100 RBI
Player B: 0 HR, 80 R, 80 RBI

Going by the "subtracting" formula, they both have 160 Runs Produced.
I don't think anybody here, anybody at all, would say that the seasons are comparable on any meaningful concept "runs produced," other than the limited concrete thing of runs-participated-in -- and, as I said below, the home run guy participated in those runs to a greater extent (far greater, in this example) than the non-HR guy.
The HR season was far greater, by any measure.

Granted, this is an extreme example. Extreme examples don't necessarily tell the story, but then again, extreme examples are often used in basic mathematics to help see what's the story.

Again, I'm not saying that any of what I've said gives a definitive answer. I wouldn't say Bill's above work gives a definitive answer either, because any way that we look at it reflects our view of how it should be looked at, this weak primitive unsophisticated thing of "Runs Produced" that may never have been thought through in any depth in the first place. How should we look at it, to see which version is better? One person's notion of that isn't necessarily better than another's, and they may give different answers.

The only problem with what Tom did is how strongly he characterized his finding -- that he thought the issue is clear and that his conclusion is definitive. The issue isn't clear, and other conclusions are possible.
4:40 AM Jun 17th
Since that brief discussion of this on Hey Bill, we've had a thread about this on Reader Posts, in which I've been essentially a minority of one (not unusual here) :-) in arguing, well, a couple of things.
The main one was that Tom's cited work reflects a particular view of the question that isn't the only possible one and which IMO isn't a great view, but forget the IMO part:
It's not the only view, other views may give a different answer, and therefore the question and answer aren't as simple (he uses that word) nor as clear (he also uses that one) as he states them to be.

My lesser point was that from the way I look at the question, which I'm trying to make as close as possible to my impression of how this 'metric' was conceived and how it was viewed in its time, the 'non-subtracting' formula (i.e. just R + RBI) gives more appropriate rankings (slightly) and therefore is "better," I qualified it by pointing out that they were close and that neither way is great or even particularly good, that the whole idea of the stat was primitive and very unsophisticated by our standards and that I thought it was a bit silly to be parsing it so finely, because no matter what we do with the home runs it's still not going to correlate real well with value.

I didn't get around to saying what hypothetical version of the formula would be 'best,' but in view of how close the results of the two methods were, I had the impression that it would be: subtracting about ½ of HR's, perhaps a little less than half.

I reached about the same conclusion that you're stating here, obviously not by anything like such a precise approach nor by consciously considering things like numbers of outs made, but I think that was probably implicit in how I was looking at it. As Tom pointed out (and our member Myersb just said on Hey Bill), the 'subtracting' metric (i,.e. with the subtraction of HR's) is "Runs Participated In." I said on Reader Posts that trying to look at it by precise value estimates of positive elements of offense is like using lipstick to judge the looks of a pig. If it's "Runs Participated In" and we're wondering which way of looking at it is better, how about we confine our view to those runs-participated-in. That's what they were looking at, at the time, and I doubt that they had any impression or illusion that it was anything like "value." It's runs-participated-in.

BUT -- here's the thing:
In the results that we get by the 'subtracting' formula, there's a different degree of participation in those runs according to how many HR's the guy hit. In that formula, a player who had 40 HR's, 100 R, and 100 RBI got credit for 160 Runs Produced.
So would a player who had no HR's, 80 R, and 80 RBI.
But the home run hitter had a higher degree of participation in those 160 runs in which he participated. The non-HR hitter needed and got more help to get that same number of Runs Produced.

You said basically that same thing in your article in the 1987 Abstract. (I assume it was in that article; it's the one referenced by Tom.) The way you put it was that the home run "unifies" the two needed acts for scoring a run.

That was the intuitive thing that led me to feel HR hitters were unduly downgraded by subtracting HR's. But there was also a pragmatic thing: It simply always looked to me like even though the lists of leaders in Runs Produced were dominated by power hitters, the players with higher numbers of HR's tended to show less well than where they seemed to belong.

What you arrive at by adding the consideration of outs-made.....I wonder if that implicitly involves and brings in that principle that I stated, that the non-HR hitter (or lesser HR hitter) 'needs more help' to wind up with the same number of Runs Produced.
I think it does.
2:44 AM Jun 17th
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