# Thread: New Special Batting Stats on BBRef

1. 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%.

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

3. 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?

4. 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.

5. 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?

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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.

6. 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.

7. 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

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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.

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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.

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

9. 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.

10. 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.

That makes me rethink my criticism of James' ultra-low .200 W% margin (he doesn't know that's what it is...but that's what it is...a .200 W% roughly)...and wonder if all sabermetricians everywhere including myself have been overvaluing great players and undervaluing bad ones.

12. Matt, do you have a counting stat measure of how many runs each player is worth -- something like runs-above-"replacement"?

13. Originally Posted by SABR Matt
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.
While we can fairly argue that a .200/.230 player (in a 5.0 RPG environment) is the point at which a player must reach to provide positive value, such a player, all the way up to a, say, .310/.360 level, will still get paid the league minimum. Even though there is a world of difference between .200/.230 and .310/.360, the sheer abundance of players between those levels allows team to pay such player the league mininum (or not at all, by simply placing them on waivers).

The concept of "replacement level" aligns itself more toward the salary/supply side, which is why I use a team replacement level of .300. Matt's use of the "margin level" aligns itself more toward the idea of not unleveraging the performance of the rest of the team. Imagine if Michael Jordan played with 4 of us. He'd be triple-teamed, and the other two guys would cover 4 of us. I doubt Jordan would score 30 points, since we couldn't provide even the minimum level of competence that would allow Jordan to leverage his skills.

14. Originally Posted by skyking162
Matt, do you have a counting stat measure of how many runs each player is worth -- something like runs-above-"replacement"?
Yes. I track Marginal Runs. As a rule that is what I use to find wins created but I can express it as marginal runs too.

15. Originally Posted by Tango Tiger
While we can fairly argue that a .200/.230 player (in a 5.0 RPG environment) is the point at which a player must reach to provide positive value, such a player, all the way up to a, say, .310/.360 level, will still get paid the league minimum. Even though there is a world of difference between .200/.230 and .310/.360, the sheer abundance of players between those levels allows team to pay such player the league mininum (or not at all, by simply placing them on waivers).

The concept of "replacement level" aligns itself more toward the salary/supply side, which is why I use a team replacement level of .300. Matt's use of the "margin level" aligns itself more toward the idea of not unleveraging the performance of the rest of the team. Imagine if Michael Jordan played with 4 of us. He'd be triple-teamed, and the other two guys would cover 4 of us. I doubt Jordan would score 30 points, since we couldn't provide even the minimum level of competence that would allow Jordan to leverage his skills.
Hey Tom...I noticed just now that the true player margin as you derived it above (1/3) is interesting. Using the pythagorean equation, I can figure out what that represents in terms of W%. Let's assume a 5 PRG environment. That makes the X term 10^0.285 or 1.928 and the PythagenPat W% of the margin would be (1/3)^X or 0.120. Which is pretty close to the team winning margin I found before (of 0.100).

16. Originally Posted by SABR Matt
Yes. I track Marginal Runs. As a rule that is what I use to find wins created but I can express it as marginal runs too.
Can you discuss why, if you're the GM of a team, you'd rather use your Marginal Runs than the usual Replacement Runs? (Same calculation, different baselines.) Your lower baseline shifts some value from players with high quality to high playing time -- is this helpful? How does a lower baseline affect your rate stats?

17. Matt, that 1/3 level is for offense only. So, that gives you around the .100 or whatever offensive winning%, and presumably you'd have a similar .100 level on the defensive side. And if you have both, you'd be close to the .000 level.

However, I wouldn't want to proclaim this the level right now. This was just an off-the-cuff look at it. And, in the my Markov, I treated everyone on the team as an average .326 batter, instead of 8 .341 and 1 .206. If I were to run those numbers through a sim or Markov, I'm not sure it would necessarily come out the same.

18. Using the replacement level would tell you something about how you can expect the minor league shmoe would cost you compared to your current option, but I'm not convinced this is really the best way to team build. Sabermetricians have made a big deal about the replacement level player being immediately obtainable by anyone at any time, but GMs really can't take ANY production for granted because it's not really true that you can always get those replacement level players, even if they can be bought for the league minimum. I think it is important to know how much each player is actually contributing to the winning of ballgames in order to better understand how the choices you make as a GM actually combine to make wins in the standings.

Besides which, a lower replacement level rewards players who stick around longer and have therefore established lower levels of risk (it may be true that the average 26th roster spot can produce at the replacement level, but I think you will find more variability in performance among players of the same replacement level talent...some will completely fold and some will not when exposed to the major leagues...the ones who stick have proven they won't fold). I guess when you're deciding how much to pay a free agent, you should use a high replacement level but when you're trying to figure out what your team needs to win, you should use a marginal analysis.

19. Originally Posted by Tango Tiger
Matt, that 1/3 level is for offense only. So, that gives you around the .100 or whatever offensive winning%, and presumably you'd have a similar .100 level on the defensive side. And if you have both, you'd be close to the .000 level.

However, I wouldn't want to proclaim this the level right now. This was just an off-the-cuff look at it. And, in the my Markov, I treated everyone on the team as an average .326 batter, instead of 8 .341 and 1 .206. If I were to run those numbers through a sim or Markov, I'm not sure it would necessarily come out the same.
Fair enough, Tom. If you ran a series of Markov simulations where instead of averaging out the bad player you keep 8 average players and add a progressively worse 9th player until you reached the level where the 9th player had zero value, you could probably learn more about what the real margin is.

20. It might be very close to the pitcher level. I don't have The Book handy (either Tables 61 or 63), but I did run a Markov on a real NL team with the pitcher and without, and for some reason, I have the numbers 4.6 and 5.2 in my head.

5.2 / 9 * 8 happens to equal 4.6. If the numbers in the previous paragraph are correct, then the "zero margin" level could very well be what the pitcher provides, which has a certain real-life appeal.

21. That would make sense, Tom. If the math really does come out to the zero margin being that low, I will have to make significant changes to my methods ITF. I believe in using a zero margin to evaluate players (and compare them to each other), so my analysis is going to have to rely on whatever the data leads me to as to what the zero margin is.

22. 5.25 runs per game, without the pitcher. 8/9 of that is 4.67.

With the pitcher, it's 4.60 runs. So, the pitcher does depress the 8 batters negatively. The zero-margin will be somewhat higher than that.

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