# Thread: New Special Batting Stats on BBRef

1. Let me think about that...it's hard to approximate for a hypothetical when your metric is a top-down metric, but I can get a rough figure for the marginal RC I would award that batter.

2. Ok. Give me the marginal RC for that batter and for the average batter on that team. Plus give me whatever win value you come up with for that batter, and the average batter on that team.

3. How many PA does your new batter get? .323/.400/.484 can't be turned into RC without a PT estimate (RC = TIMES ON BASE * OBP roughly...we need the times on base).

Obviously PCA's RC are linear weights based but I don't have any of that information so I'm winging it here. I'm not comfortable giving a RC value for a player when I don't have how many singles, walks, homers, GIDP, K etc he produced.

4. He gets one-ninth of his team's PA.

His profile is 41 pa, 36.3 ab, 11.7 H, 2.3 2b, 0 3b, 1.2 hr, 4.7 bb, 0 hbp, 8.2 so

The average player is 41 pa, 37 ab, 10 H, 2 2b, 0 3b, 1 hr, 4 bb, 0 hbp, 7 so

Scale that up however you need to get to 162 GP. If it makes it easier, presume no outs on base and no GIDP or SB.

5. 41 PA * 162 G = 6642 team PA / 9 = 738 PA

738 / 41 = 18, so multiply everything in your profile by 18

442 Outs, 145 1B, 41 2B, 5 3B, 20 HR, 85 BB, 148 K

Remember this is just a rough estimate using rough LW...PCA is a lot more reliant on very specific league and team level information.

I don't use average-centric metrics. I don't consider that a good place to start when analyzing a player...I use replacement level metrics which means I use LWRC not LW.

442 * -0.10 +
145 * +0.47 +
041 * +0.80 +
005 * +1.08 +
020 * +1.40 +
085 * +0.33 +
148 * -0.03 = 113.8 LWRC for the good batter

The average batter's line is:

486 * -0.10 +
126 * +0.47 +
036 * +0.80 +
000 * +1.08 +
018 * +1.40 +
072 * +0.33 +
126 * -0.03 = 84.6 LWRC for the average batter

The margin being .250 for individual batting, the level of the margin exists at:

(0.25 / 0.75) ^ (1 / X) * (84.6 RC / 486 Outs)

X = (2 * RS/G/Side) ^ 0.285 = 9.92 ^ 0.285 = 1.923

The margin occurs at 0.0983 LWRC / Out

The average player's margin occurs at 47.77 RC giving him 36.83 Marginal Runs

The good player has fewer Outs so we find that he would (marginally) be expected to produce 43.45 runs. He actually produced 113.8 runs, which gives him 70.35 marginal runs.

ON AVERAGE (this is NOT how PCA works...I don't want that to be misunderstood....PCA is a top down model so the success of each player's team would be considered), 8.3 Marginal Runs = 1 W (I looked it up in the PCA database), so the first player is worth roughly 4.4 wins and the second player is worth roughly 8.5 wins.

6. The difference between the two (8.5 wins and 4.4 wins) is 4.1 using your process.

In my post 36, I said .024 wins difference per game, times 162 games is 3.9 wins.

It sounds like we're talking about the same thing, but using a different dialect.

7. Originally Posted by SABR Matt
What the heck is a marginal win?

There's no such thing as a marginal win. The marginal for team performance (in the sense of wins and losses) is ZERO wins. Wins are explained by marginal runs...marginal wins? That's just fiction.
If there are marginal runs, there are marginal wins. A replacement-level team still wins some games -- that's the margin for wins, not zero. By signing players better than replacement-level, teams score more runs and win more games. The ratio of these additional runs to additional wins is what we're after, right?

8. There's never been in the history of major league baseball a team which had all replacement level players. And if there were such a team, I believe they would win zero or near zero games.

9. Originally Posted by Tango Tiger
The difference between the two (8.5 wins and 4.4 wins) is 4.1 using your process.

In my post 36, I said .024 wins difference per game, times 162 games is 3.9 wins.

It sounds like we're talking about the same thing, but using a different dialect.
Evidently so. The scales might be ever so slightly different but it's encouraging that you got the same answer I did.

10. Originally Posted by SABR Matt
There's never been in the history of major league baseball a team which had all replacement level players. And if there were such a team, I believe they would win zero or near zero games.
Matt, in your analyses, can you give me a player name or player batting/pitching line you'd consider replacement level? Is your replacement level in the ballpark of something like BPro's VORP -- around 80% of league-average? (I realize you don't arrive at replacement via average, though.)

11. Actually, I do arrive at replacement level through league average. I use pythagoras to convert average into a margin at the .250 W% level. Which means when I say replacement level...I'm talking about 52-60% of league average...not 80%.

12. the closest team to a truly marginal roster was the 1899 Cleveland Spiders and even they had something like 116 marginal runs on offense.

13. Originally Posted by SABR Matt
Actually, I do arrive at replacement level through league average. I use pythagoras to convert average into a margin at the .250 W% level. Which means when I say replacement level...I'm talking about 52-60% of league average...not 80%.
Is that a .250 team winning percentage? If so, doesn't that mean a team of replacement players would win 25% of their games? Otherwise, I'm not following.

Would a theoretical team of replacement-level hitters score 52% of average team runs, or is there a non-linear effect in your model? How many runs would a staff of replacement-level pitchers give up? What does Pythag say about how many wins that replacement-level team would have?

14. no...a .250 margin refers to a single player's (or a team offense or team defense's) W% compared to average (think in terms of Offensive W%). A mrginal team would have a .250 OW% and a .250 DW% and according to the Tango Distribution they'd win about 9-10% of their games...so I guess if you want to call that the win margin, you can...I don't think in terms of marginal wins because they're negligible on the scale that teams normally win games.

15. Ok, even with a replacement level so low, that's not a negligible number of wins. 10% of 162 is 16. That's one-third of a really bad team's wins and one-sixth of a 100-win team's.

If you subtract out 16 wins for 30 teams, how does your runs-per-win conversion change?

*************

Matt, have you discussed how you arrive at replacement level in any threads here? I'm sure it's not a simple answer, so if you could point me in the right direction, I'll read up on it. Thanks.

16. I don't really consider it "replacement level"...that's a concept made popular by VORP as you know but I don't think that is mathematically relevant. When trying to explain how teams win games, you need to find the level at which players stop aiding the creation of wins. The popular (and much higherly) .380 type replacement level you see used by VORP and BPro has nothing to do with when players stop creating wins...it has to do with when players stop creating value above what a AAA guy would create...which is not helpful when explaining how a team got 90 wins.

I arrived at the .250 replacement level for team offense and team defense through simple linear deduction and linear correlation. I know the linear assumption starts to break when you get to the extremes, but the logic went:

"I notice that OW% + DW% - 0.500 = W% -> I run a correlation which confirms this is true with at most a 2% error -> given that relationship and assuming the margin for offense is the same as the margin for defense, the .500 W% must be split in half, yielding OMargin + DMargin = .500, OMargin = DMargin = .250"

That works extremely well for major league teams in the real world, but the Tango distribution says a marginal team would win 10% of the time not 0%...so I guess if you subtracted out 16 wins for each team, you would get a different rate than 8.3...hmm...

I believe I understand this point now. take out 10% of the wins and you get something more like 8.3 runs per 0.9 wins or 9.3 marginal runs per marginal win.

17. I use the following as the replacement levels:
nonpitcher: .380
starter: .380
reliever .470

All this will give you a team replacement level of .300

***

If you are looking for a face of a replacement-level player, it's Willie Bloomquist, likely the worst under-30 player with at least 500 career PA. If he wasn't from the Seattle area, I don't think he'd be on the roster of the other 29 teams. To his credit, he's having a great (for him) year this year.

***

If you want to use a .250 level for a player as the replacement-level, that would include everyone on the 40-man roster and then some. The typical way to think of replacement level is "who's the freely-available guy that I can put on my roster for the minimum salary?".

Rather than "replacement level", I prefer the more generic "baseline level". This allows me, Patriot, Matt, and Clay to choose whatever level we want, without necessarily being tied-down by someone else's definition of the word.

18. Note: I just saw Matt's post. I'll add to it in a sec.

19. That's why I don't like the word replacement level. I call it the margin because that's what it is...the level at which production stops having any positive value. A replacement level player has some ability to create wins. A marginal player does NOT.

20. Originally Posted by Tango Tiger
It seems that there are two things being talked about. If someone creates say 0 runs and uses 500 outs, he in fact has created "negative" runs.

We can for example have 9 average players, who have an average OBP and SLG of .341/.405, creating 4.96 runs per game:
http://www.tangotiger.net/markov.html

So, per game, each player created almost 0.55 runs. (So, for 162 games, each player will have created 89 runs.)

If we have 8 such players, and another one who is .000/.000, the team OBP/SLG will close to .300/.360 (set "AB" in the above link to 42). This team will score 3.75 runs per game. Since we know that our 8 average guys average 0.55 runs per game, we'd expect that these 8 guys plus a zero to score 0.55*8+0=4.40 runs per game. They created only 3.75, meaning the sum of the parts is greater than the whole. The reason is that this zero player managed to unleverage a substantial portion of his teammates' performance.

This team (8 average guys plus a zero) actually scored almost 200 runs less than a team of 9 average guys. Since the average guy created 89 runs, we would have expected only 89 fewer runs scored (and created). This zero guy managed to "uncreate" 100 additional runs by being a black hole.

I suspect that Matt's "marginalization" approach, as Bill James, tries to correct somewhat extreme cases (not extreme like this one), to the point where he can make a claim like 8 runs = 1 win.

Since Matt agrees with the example I originally set forth, our difference in explanation of 8 or 10 is simply one of context of explanation.
Let me modify this example, to go with Matt's idea about "zero margin" level. As I noted, the .341/.405 team creates 4.96 runs per game, or 0.55 runs per player. And, if I had 8 such player, plus a guy who makes an out every PA, this team will NOT score 0.55*8 runs (4.4 runs per game), but substantially less.

The question therefore is what level of performance do we need from our 9th player, such that a team with 8 average players will score 4.4 runs? That is, since we "know" that each of our 8 average players are worth 0.55 runs each, then what performance level do we need from our 9th guy to get a team run scoring level of 0.55*8+0=4.4?

A team level of .326/.385 would fit the bill. Since our 8 guys are .341 OBP players, then our 9th player must have a .206 OBP level (and .234 SLG).

That is, while a team of .206/.234 players would in fact score 1.6 runs per game (according to my Markov calculator), adding such a player to an otherwise average team will allow that team to score as if this player received no credit (since we "know" each average player is creating 0.55 runs per game, and we "know" this team of 8 average and 1 terrible player scores 4.4 runs per game).

This is, I believe, basically what Matt is talking about. It is, I'm sure, what Bill James is really talking about.

This level is about one-third the level of the average player, which is somewhat lower than the one-half level that James posits.

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