Mitchel,

Thanks so much for all the great info. I find myself nodding a lot and saying YES! WELL PUT! when reading your answers.

I had trouble coming up with a good question because I already seem to know everything.

I am more from a probability background than a pure stats background, so in 1995 when I got my hands on the Baseball Workshop play by play database for an entire season (purchased for $100 on a floppy from... um... the Baseball Workshop guy whose name escapes me) the first thing I did with it was basically (re)invent Win Shares and do some graphs of Win Probability for Cardinals games... names like Jordan Gilkey and Lankford were dancing in Excel graphs... I showed it to some of my fantasy baseball cohorts and their eyes glazed over, they chuckled and said what will that guy think of next. The spreadsheet was huge and computers were slow and I shelved it. I did tell them "In ten years everyone will evaluate games like this" ... I'm somewhat surprised that it is coming true.

After I "invented" win probabilities I later found out I had reinvented the wheel, I saw something similar in "The Hidden Game of Football" and later read someone had done something like it in the 60s, by hand! This is not surprising, it is a very logical way to think about the game to anyone with a creative mind and background in probability. This leads me to question 1....

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What is the sound of one hand clapping?

oops, that's not it... wrong note card... ah, here it is, question 1:

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What is the earliest known "invention" of a probabalistic approach such as Win Probabilities (or even Run Shares) in the analysis of baseball?

Second subject, remember those Sagarin rating things in the USA Today where he would run some simulations of how many runs "a team of 9 Barry Bonds" would score -- perhaps those are still published, I'm not sure. Didn't anyone ever tell that guy about Markov chains? Rhetorical question, I'm sure he's a smart dude doing his best.

Anyway, this is similar to a RC/27 type of evaluation, except for someone like Bonds, as valuable as he is, this is way overinflated because he is drawing lots of walks and then driving himself in with his HRs... the walks increase the value of the HRs and vice versa.... you alluded to this when talking about considering this effect when evaluating pitchers and teams, and how it did not apply to batters (since they do not, in fact, play on a team with 8 clones.... I just shuddered thinking of 8 clones of Barry Bonds... but I digress)

One way I like to evaluate a player is (R+RBI)/2 per Outs. Very simple but effective. True Run Shares or RC would be better but, simplicity is nice too.

However, in some respects this type of calculation (regardless of your "R" metric used) has a very subtle catch that is similar to the Sagarin flaw.

Consider Case 1:

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HR Out Out Out

Case 2:

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2B 1B Out Out Out

Let's assume both created the same number of Runs by whatever metric we are using. Both made 3 outs. Equivalent? Not really.

One of them did it in 4 plate appearance, one did it in 5. In a team context, if this is "above average" performance, and it is, then the player who did this in 4 Plate appearances will "repeat" his performance more often than the other player. Not obvious? Bear with me.

So I came up with the following.

I like to use 4.5 runs per game as a constant "baseline" for an "average" team because it changes every year anyway and it is a nice "1 run every 2 innnings"

Let's think about how many plate apperances our average team has. If we assume an average OBP of 1/3 which is fair,then our Out% is 2/3. you are either getting on base or making an out. okay.

so for our baseline player, Outs/PA = 2/3

at 1 run per 6 outs, this equates to = Runs/PA = (2/3)*(1/6)= 1/9

Now the simple part.

How does our example player factor into a team of 8 of these guys?

well he has 1 PA for each 8 PA of his teammates, so we just do a weighted sum at a ratio of 8:1 and THEN and only THEN do we divide

Runs/PA by the Outs/PA to get our final Runs/Out number for the combination.

So for example 1:

Runs / PA = 8*(1/9) + 1 run / 4 PA = 8/9 + 1/4 = 41/36

Outs / PA = 8*(2/3) + 3 outs / 4 PA = 16/3 + 3/4 = 73/12

Runs/Outs = (41/36)*(12/73) = (41/3)/73 = 0.187

Runs/27 = 5.05 RPG

Compared to 4.5 RPG this is +0.55

For example 2:

8/9 + 1/5 = 49/45

16/3 + 3/5 = 89/15

Runs/Outs = (49/45)*(15/89) = (49/3)/89 = 0.1835

Runs/27 = 4.96 RPG

Compared to 4.5 RPG this is +0.46

So in summary, I think it is very important to look NOT just at RC/27 or any similar (Productivity per out) for a player, but to put that in a team context you must put it it terms of

RC/PA and Outs/PA

and only after factoring that into a team context can you take a true measure of RC/Outs for the combination of that player in a lineup.

Which brings me to question 2:

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What is your destiny?

Oops, wrong card again....

question 2:

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Has anyone else realized this or am I reinventing the wheel again?

Your post is a good one and made me laugh (not nearly as much as Seinfeld tonight though - he was hilarious).

Player win averages were computed by the Mills brothers of course (not the musical group - at least I dont think) in 1970 or so.

RC is a stupid stat, as you say, because it captures an interactive affect among a hitter's own stats, which is not what happens in real life of course.

I don't know of what use how many runs a team of 8 or 9 Bonds' or Neifi Perez' would score, other than it tells you that one player is really good and one player is really bad.

Before you invent a wheel, do plenty of research to see if it has already been invented. If it has, spend your time on improving it (and make sure yourimprovements have not already been invented as well), or move on to something else.

A corrolary to that: Before you embark on any project, spend lots of time learning all you can about it.