THE BOOK--Playing The Percentages In Baseball

Tango, when you say a (replacement) reliever is a .470 pitcher or that Rivera is a .700 pitcher, what exactly does that mean?  And what is a replacemtn starter in those terms?

A replacement pitcher, pitching only as a starter, is a .380 pitcher.  That same pitcher, pitching only as a reliever, is a .470 pitcher.

A .380 pitcher is one who allows about 28% more runs than the league average.

A .470 pitcher is one who allows about 7% more runs than the league average.

As for closers, using the GuyM method, you do the following:
a: wins above pitcher replacement (.470)
b: wins above closer replacement (.570)

If you have a closer with a win% of .670, then his “a” wins is +.200.  This provides no extra value for his closing.

However, if his LI is 2.00, then he gets a bonus of 1.00 for every win above the .570 line (+.100 x 1.00).  If his LI was 1.80, you give him an extra +.100 x 0.80.

This way, you can give Mo the extra leverage impact of his performance, but only if it exceeds the “typical” performance expected.  The theory is that the leverage will happen, regardless of who is in the bullpen.  The reliever doesn’t control how the game unfolds when he is finally brought in.  But, if he exceeds the performance expected, it is that extra performance that is leveraged.

We discussed this last year, and I think it’s an ingenious way to use leverage, without crediting all the leverage to the pitcher.

My replacement level is -18 per 150 or -20 per 162 games.  I am pretty certain that that is about right. 

You can’t just make up replacement level.  Since the whole (only) point of replacement level is to compare a player to what a team can have if it got the best player available (on the average) for .5 mil or so, replacement level HAS to be exactly what some pool of min salary players are projected.  I am pretty sure that you can get scrub players for the major league minimum who are 20 runs below average at their position.  It probably varies by position, but I am talking about all positions combined.  As I keep saying, all someone has to do is look at all the min salary (.5 mil or less) FA from the last few years, and add up their collective runs below average.

As far as a replacement level team being .300, I don’t even know what that means.  Is that including pitchers? You can’t lump pitchers and position players together.  A replacement pitcher may be 1 win or 3 wins below average and a replacement position player may be the same or different.  It just depends on the distribution of talent at each position which is NOT going to be the same or even similar.

So let’s stop talking about replacement level until we can at least agree on a level that approximates real life (What is the average level below average of freely available talent)!!

Let’s talk about average and just say that an average starting pitcher gets 10 mil and an average starting position player gets 8 mil (FA of course), or whatever it is.

Tango, if a 5/4/3/2 gets Lowell to +5 runs, then with aging, that is zero, no?  And what about regression?  I am also regressing Lowell to a 31 year old player of his height and weight, whatever that is.

Tango, can you put this thread at the top?

And, ALA just traded Cabrera for Garland.  I have Garland as around .2 runs better than an average starter.  That is around 2.5 WAR.  I have Cabrera as around league average for SS, or 2 WAR.  They are both signed through 08 only and Garland makes a little more money I think.  This is the true definition of a trade.  You give me something worth $1 and I’ll give you something worth $1.  Actually in the case of both of these players, they are “worth” nothing.  When a team has a player whose salary is what he is worth on the FA market, that player should have no value to the team and the team has no equity in the player. It is like owning a house where the balance on the mortgage is equal to the value of the house. Of course, you may be able to sucker (and probably can) another team into giving you something with equity (like a prospect or an underpaid pre-FA player) for that player you “own” with no equity.  Or that player may have some “extrinsic” value even though he is getting paid what he would be worth on an open FA market, simply because a team or two may want a player like that but none are available on the FA market.  Again, supply and demand influences the baseball market over and above instrinsic value.

MGL, it doesn’t matter what replacement level you use.  All I’m asking for is what is the total number of wins above replacement for the league.

In my case, I have exactly 972 wins above replacement total (or 32.4 per team).

Since the average team has a payroll of around 85MM, and since the minimum payroll is 380,000$ x 30 players or so per team, that’s 11MM that is the minimum.  The total salary above minimum is 74MM per team.

Therefore, for me, the $ per win is 2.28MM per win.  The free agent cost is roughly double this rate, at 4.4MM.

So, my question to you is: how many wins above replacement is all your MLB players?  It is purely on that basis that you can tell me if Lowell is over or underpaid.

I estimate, based on what you’ve been saying, is that your total wins above replacement is 729 wins (24.3 per team).  Since you’ve got 74MM to allocate, it costs 3.0 MM per mglWin.  A free agent dollar is therefore close to double that, or almost 6MM.

O.K., got it. I think. Well, MY replacement for position players is exactly 19.44 runs below average per 162 games.  I am not sure what that means in terms of wins per team.  Isn’t that 8 times that number for an NL team and 9 times that number for an AL team?  That is 15.6 wins per team for an NL team and 15.9 wins for an AL team, using 10 runs per win for the NL and 11 for the AL.  So we’ll call that 16 wins.  I don’t know where you get 24.3 wins from.  Does that include pitchers?  If it does…

My pitchers are a separate issue.  As they should be.  As I said, you cannot lump pitchers in with position players (you really shouldn’t lump relievers in with starters or first basemen with SS).  Anyway, my average pitchers are around a run per game better than replacement in the NL, and 1.25 runs in the AL, which is another 16 wins for the NL and 18 wins for the AL.  Call that 17 wins.  That is now a total of 33 wins.

If that is what you mean, then my players, pitchers and non-pitchers, are 33 wins above MY replacement and not 24.3, suggesting 4.5 mm per marginal win, same as you, although, as I said, you cannot combine pitchers and non-pitchers, as they are two different entities.

You have to look at how much of that 74mm is allocated to pitching and how much to non-pitchers and then use your average=x above replacement for pitchers and non-pitchers separately. In my case, it is 17 and 16, pretty close to one another.  In your case, maybe different, I don’t know.  Is the 74mm split up evenly between pitchers and non-pitchers?  If it is a little more for pitchers, then that is what it is supposed to be according to my replacement levels.

Why did you think that I was 24.3 when I have said multiple times that my replacement non-pitchers are 20 runs below average and that my replacement pitchers are 1 to 1.2 runs worse than average, or am I doing something wrong in my math or my conception (multiplying that 20 times 8 in the NL and 9 in the AL, for position players at least)?

I think you had said 0.75 for your starters.  But, even so, even if your replacement starters are one run below the average starter, you can’t possibly have your replacement relievers also one run below your average reliever.  Is that what you are implying?

I think you need to expand your description on your starter/reliever levels.  To allocate 50% of your payroll on pitching, when you’ve been saying how the replacement level is alot closer to average than most of us follow is inconsistent.

The % salary allocation for pitching is around 42% in reality, which is what my replacement levels imply.

A win above replacement pitching and nonpitching is worth the same to me.  I don’t see any reason for it not to be.

The definitive study I’ve seen on replacement level is Nate Silver’s Freely Available Talent investigation, located at http://www.baseballprospectus.com/article.php?articleid=4891.  It’s got plenty of good stuff in it--most notably, that SS replacement level is faar lower than any other position because it’s the only spot where replacement players are meaningfully below-average fielders, and conversely that 1B replacement level is higher than expected because it’s the only spot where replacement players are meaningfully above-average fielders.  Also, it finds that replacement DH’s are basically league average hitters. 

When comparing to league (rather than to positional) average offense you always have to remember to subtract 0.6 wins per 162 games from replacement level for AL players to account for the effect of the DH. 

My own investigation finds that the very large gap between SS and C rep level that Nate sees over the whole 1985-2005 period has almost entirely evaporated, with SS now about 2.6 wins per 162 below league average (counting pitcher hitting) and C around 2.4.  In 1980 it was 3.6 for SS and 1.6 for C--a very big difference.  Also, I find that 2B, 3B, and CF rep level all run about even in the modern game, while 2B was considerably lower than 3B and CF until about 1985.  I’d be happy to share all my data on this, and fascinated to hear any of your thoughts on what might account for these substantial shifts.

If you’re trying to make cross-era comparisons, you also have to take into account changes in the standard deviation of player performance over time.  Hitters are now bunched more tightly together than ever before, while pitchers are more spread out than ever before.

"My pitchers are a separate issue.  As they should be.  As I said, you cannot lump pitchers in with position players (you really shouldn’t lump relievers in with starters or first basemen with SS).”

How fine a distinction are we making here? It’s true that there is some value in differentiating between players based on position. But in reality most ballplayers have a range; a replacement left-fielder is probably also a replacement first baseman, and a replacement shortstop is probably also a replacement second or third baseman, maybe even a replacement center fielder. The same holds true with pitching as well, to the extent that a replacement starter is also a replacement reliever.

So let’s say that over the course of a season we have a replacement SS/2B that plays 80 innings at second and 20 innings at shortstop; he’s an adequate defensive shortstop but the team doesn’t need him there as often. Do we measure his value simply against other second basemen? He’s clearly more valuable than some players who can only play second base, at least in a replacement context. But the innings he played at second didn’t provide his team as much value as they would have had he been playing shortstop (ignoring the opportunity cost of not playing their regular shortstop).

Clear distinctions between positions for replacement players doesn’t conform to the reality of the situation; in order to stick around as long as they have and to stay with teams, many replacement players can and do play multiple positions.

Maybe this is just a diversion and doesn’t really impact replacement level as it affects player valuation; it’s just something that came to me.

MGL, 19.44 runs per 162 games is 0.12 runs per game.  A team scoring 4.61 and allowing 4.73 according to PythagenPat will win .488 games, or -.012 wins). i.e., the RPW conversion is exactly 10.00 at this level.  (I chose the numbers on purpose).

There are 8.65 nonpitchers per team (it’s 9.0 in the AL, and 8.35 in the NL, because of PH).  So, -.012 wins per game times 162 games times 8.65 nonpitchers is 16.8 wins above replacement for the average team of nonpitchers.

***

MGL, if we look at posts 11 (me) and 12 (you) here:
http://www.insidethebook.com/ee/index.php/site/comments/replacement_pitchers/#11

I state that the average starter in 2007 allowed an RA of 4.99.  You state that the scrap heap level is 5.74.

The average reliever in 2007 had an RA of 4.55.  Now, if the scrap heap pitcher, as a starter, you’d expect an RA of 5.74, clearly he’ll perform better in a reliever role (as would most anyone).  I’d call for an RA of say 4.74.  But, maybe you’d want something a bit higher.  I don’t know.  But, it’s certainly not going to be 5.30 (4.55 + 0.75 = 5.30), as that would imply the the actual average reliever in 2007 was = actual average starter in 2007.

So, if I accept that your average starter is +0.75 runs per 9IP above the scrap heap line, then your average reliever is probably, what, +0.30 runs per 9IP above the scrap heap line?  With 65% of pitchers as starters, that gives us that the average MLB pitcher, under these assumptions, as being +.6 runs per 9IP above scrap heap (.06 wins).  For an average team of pitchers over 162 games, that’s 9.7 wins.

And 16.8 nonpitcher wins plus 9.7 pitcher wins is 26.5 mglWins above scrap heap.  This is roughly how I ended up with the 24.3 that I mentioned.

***

So, given that the average MLB starter posted a 4.99 RA and given that the average MLB reliever posted a 4.55 RA, can you tell me how would a scrap heap pitcher perform, as both a starter and reliever?  (I’m talking about the same pitcher in two roles.) What numbers are you using?

By the way:
“And 16.8 nonpitcher wins plus 9.7 pitcher wins is 26.5 mglWins above scrap heap. “

implies 37% of the marginal wins (and dollars) go to the pitchers, which is below what actually happens, and below what I call for (43%).  However, since you believe that pitchers are overvalued to begin with, this 37% is consistent with your basic position.

Lot’s of good stuff here!  Dan, I have to re-read the article you refer to and digest your excellent post.

BTW, when I made my comment about lots of near average 2B, I meant as opposed to all of them being either crappy or great.  Obviously the total has to equal an average 2B, but the variance within the population at a particular position can change.

Tango, I have to redo my thinking about replacement pitchers.  I think there is a conundrum with starters and relievers and I am not sure what the answer is.  Since we claim that the typical difference between a pitcher as a starter and reliever is around .9 runs, either a replacement starter must be A LOT worse than an average starter OR a replacement reliever has to be close to an average reliever. 

I have to think about this some more. I think it is close to the latter.  Because relievers are worse pitchers than starters, there are more of them.  Even though a team carries more relievers than starters (at least 1-5 starters), there are still many more relievers available, I think, within a narrow range of ability. IOW, I think the range of ability for relievers is much more narrow, which makes replacement level indeed much closer to average. 

I am not sure of this and have to think it through a bit.

Given what DR says, I think this kind of blows our whole notion of replacement level out of the water though.  I mean if a SS replacement player is truly a win worse than another position’s replacement player, then we CAN’T use a one-size fits all replacement level for all positions.  After all, replacement level is supposed to define a player’s $ value, is it not?

I think we need to get back to average and simply use the average salary for each position as our baseline.  If what Dan and Nate say are true, then the average SS should get paid a lot more than the average player at other positions.

Colin also makes a good point about replacement players being replacement for multiple positions.

This is a naive question relative to the rest of the thread. Concerning the magnitude of the effect, is this about right for pitchers?

park: .1 runs/game
league: .25 runs/game
rotation/bullpen: .9 runs/game

Forgive me--I’m new to this debate--but why would you *ever* use a “one-size fits all replacement level for all positions?” That seems totally batty to me.  Why would you assume that the standard deviation of talent (which is what determines the average-to-replacement gap) would be the same at all positions?  It’s not just that there’s no empirical grounding for the assumption, it’s that it’s completely illogical.

Think about it.  At SS, you have the simply superlative athletes who can hit AND play SS, whether it’s the Ripken/Trammell/Yount triumvirate of the 80s or the ARod/Nomar/Jeter/Tejada quartet of the 90s.  Then you have a lot of guys who can’t hit their weight AND hurt you in the field--think Neifi Pérez.  You’re talking maybe 75 runs on offense and 40 on defense from top to bottom.  By contrast, at DH, you have no defensive value for players to distinguish themselves from each other, and only about 50 runs on offense from top to bottom (replacement = league average, and the best are the league’s premier hitters).  Clearly, the gap between the best and worst SS is far greater than the gap between the best and worst DH.  Thus, the gap between average and replacement will be a different size as well.  How could it be any other way?

In short, yes, a league average SS is of course worth more than a league average player at any other position (not counting P), because the opportunity cost in wins of employing replacement level talent at SS is substantially greater than the cost of employing it elsewhere.

This is true today, but was even truer in the 1970s, when half the shortstops in the league were Neifi Pérezes (check out Rob Picciolo!) AND when overall standard deviations were so low that a 150 OPS+ made you a contender to lead the league (who knew Reggie Jackson was the AL leader during his Baltimore year!).  This is why I think David Concepción and Dagoberto Campaneris, brilliant fielders and baserunners who blew their positional contemporaries out of the water at the plate, should be in the Hall of Fame.  You couldn’t win a World Series without them from 1972 to 1976.

MGL: you will find it’s the “latter” in your two scenarios.  Relievers are a dime-a-dozen.  My position is that the replacement level pitcher is a .380 pitcher as a starter, and .470 as a reliever.  Roughly speaking, if the average team scores 4.7 runs per game, then a replacement pitcher will give up:
5 runs / 9ip as a reliever
6 runs / 9ip as a starter

This is about as simple a rule of thumb as I can make it.

***

As for replacement-level…

I start with the following:
+1.0 C
+0.5 SS/CF
+0.0 2B/3B
-0.5 LF/RF
-1.0 1B
-1.5 DH

If the average SS is a -0.5 wins as an offensive player, and since he’s average for his position fielding-wise (by definition, and this applies for all positions), then adding in the 0.5 adjustment would make the average SS = average MLB player.  If the average SS is a bit worse hitter than -0.5, he’s below average.

What you will find is that the average 2B is a below average MLB player.  The average CF is an above average MLB player.  And, everyone out there knows this to be true.  We fawn over all the CF, and we barely register anything when any 2B is available.  And teams pay to this as well.  This is the reality.

I would never start with the premise that the average player at each position is equal to those of other positions.  Doing this means that in the late 40s, early 50s, when the average CF actually outhit the average 1B, would have implied that overall (hitting+fielding) that the average CF = average 1B.  This is clearly an impossibility since the average CF would have to be a better fielder than the average 1B.  And we established they are also better hitters.  Ergo, they can’t possibly be equals.

This is the reality you have to model.

Tom,

I strongly disagree with using a player’s standing relative to positional average as a baseline and then adding on a flat positional adjustment factor and flat replacement level to that, because the standard deviation of performance is not the same across positions.  Again, the gap between the worst and best SS is far, far larger than the gap between the worst and best DH, and anchoring to average will lead you to overrate DH and underrate SS.  To be honest, I really don’t think positional averages tell you *anything*--they are just too susceptible to fluctuations in the distribution of talent at a given position in a given year.

The correct approach in my mind--and the one I take in my WARP system--is to calculate replacement level for each position, summing offense and defense, relative to overall league average.  Nate Silver’s numbers for the 1985-2005 period, calculated by looking at the average performance of players over age 27 making less than twice the league minimum salary, have these at (measured in wins per 162 games in a DH league):

SS -3.6
C -2.7
2B -2.2
CF -2.0
3B -2.0
LF/RF -1.6
1B -0.8
DH 0

By using my method of using the worst regulars in each league to track changes in replacement level over time, I get these numbers for the modern game (again, in a DH league):

SS -3.2
C -3.0
3B -2.4
2B -2.3
CF -2.1
LF/RF -1.5
1B -0.9
DH 0

To calculate value above replacement, you simply multiply these numbers by the player’s fraction of the season played (G/162), and add that to his offensive wins above overall league average and defensive wins above positional average.  This prevents your numbers from being muddied by star gluts or droughts--the fact that ARod, Jeter, Nomar, and Tejada were all playing in 1999 would cause an average-based system to be unimpressed by Tony Batista’s year, whereas I give it a very impressive 5 WARP. 

I have this data--adjusted for the standard deviation of position player performance in each league-season--for all position player seasons above 50 PA since 1893 if anyone is interested.

Dan: I don’t think you are really following how I’m doing it.  What I’m doing is taking this:
+1.0 C
+0.5 SS/CF
+0.0 2B/3B
-0.5 LF/RF
-1.0 1B
-1.5 DH

And adding 2.0 to each one, giving me this:
+3.0 C
+2.5 SS/CF
+2.0 2B/3B
+1.5 LF/RF
+1.0 1B
+0.5 DH (normally, this is zero, but DH get overly punished because they hit worse as DH, as noted in The Book)

Compare that to what you listed (if you reverse the sign):
SS -3.2
C -3.0
3B -2.4
2B -2.3
CF -2.1
LF/RF -1.5
1B -0.9
DH 0

That’s a fairly similar system don’t you think?  There’s a 0.7 win gap with the SS, 0.5 for DH (for good reason cited above), 0.4 win gap with 3B, CF, 0.3 win gap with 2B, and the rest are a dead-on match.

I’m willing to accept that the 2B/SS/3B should all get an extra 0.1 or 0.2 in my system, and the OF should drop by 0.1 or 0.2 as well, which would make our systems that much closer.

In short, we are agreeing!

It may be that both approaches get us to a similar point, but I would still argue for conceptual supremacy--just like the BaseRuns vs. linear run estimators issue.  As the standard deviation of performance at a position changes, so does the relationship between replacement level and average for that position.  If your positional adjustment factor is flexible enough to capture that, then yes, it will always come out to the same.  But I’d prefer to just always compare players to replacements at their position, and leave average calculations which can muddy the waters out of it altogether.

The 0.4 win gap at 3B may very well be a sample size blip with my worst-regulars average approach--your 2.0 figure for 3B is exactly the same as the 1985-2005 average.  I certainly wouldn’t lose any sleep over that one.

But I DEFINITELY think you are substantially underrating shortstops, for the critical reason that replacement SS are well below-average fielders, which is not true of any other position, per Silver’s research.  That’s a sizable and meaningful difference.  I haven’t run ‘07 numbers yet but I bet I will agree with Rollins’ MVP award, and you might not.

Replacement SS are not well below-average fielders, as per my research.  As for Rollins, I guess you missed my other thread from a few minutes ago!

I repeat: I think you are arguing with the wrong guy, since we are mostly in agreement!

If you look at the main blog entry here:
http://www.insidethebook.com/ee/index.php/site/comments/replacement_level_fielding1/

As well as MGL’s post at post 37, you will see that the starter/bench relationship in terms of fielding is the same across the board.  I based it on A and PO, and MGL based it on UZR.

And, those two posts convincingly argue that the fielding level of starters and the bench are virtually the same, for all positions.

I’ll go ahead and hit a few points here, a la Tango.

******

That Nate Silver post about FAT probably exemplifies the best and worst of BP in a nutshell. The plus side is that they have some very bright people and a great wealth of resources.

And yet Silver, on a lark, is able to find some interesting—and perhaps foundational—flaws with their “crown jewel” stats, VORP and WARP. Dozens of others have picked apart the MLV and Davenport Translation families of stats and found them wanting in a variety of areas.

I understand their desire to “black box” and proprietize this sort of stuff; the profit motive exists all over the place. It just frustrates me that they have absolutely no shame about the fact that Silver (their OWN GUY) routinely calls out areas where their metrics are lacking (by inventing things like FAT and SuperVORP), and they do nothing about it.

******

I’m left wondering what the talent distribution is for fielding for regulars compared to replacement players. Maybe they both average out to about the same, but my hunch is that the talent is more evenly distributed among MLB regulars than it is among replacements.

I have no data at hand to back this up, and am not exactly sure how to go about getting it, but it seems to me that replacement players are generally ones that didn’t make the jumps to the bigs for three reasons: 1) inability to hit well enough for their position; 2) inability to field their position at the major-league level; 3) organizational incompetance.

When an organization scrapes up, say, a replacement shortstop, they can go with a guy that plays the position well but is only going to see the right side of the Mendoza Line in their baseball card collection, or someone who hits pretty well but plays the position like a battleship. (Battleships field like Derek Jeter, for those curious.) If you average them together, they’re league-average defenders in aggregate. But I don’t know if that means that the replacement level for shortstop is an average defender.

I could be wrong, and am willing to be shown so. I’m also willing to do some grunt work, if anybody has ideas on testing this.

******

The larger problem with replacement level, in my opinion, is that it seems (to me) to presume a more-liquid market for baseball players than really exists; 40-man and 25-man roster spots are very valuable and involve very real opportunity costs, which (in my mind) further increases the value of replacement players who can handle positions like shortstop, center field, and 2B/3B; their additional flexibility in backing up multiple positions creates more value for their club by freeing up roster spots for other players.

In the larger view, the sorts of valuations that sparked this conversation really should be compared to actual replacements, not theoretical replacement: the appropriate comparisons for the Garland-Cabrerra swap from the White Sox point of view are probably Danks/Gonzales/etc. and Uribe plus whatever else they have available to play second base. I understand that such comparisons get very unwieldly very fast, because they involve a lot of chaining (Player X moves to Position A, freeing up Player Y to Position B, etc. ...) and such models are impractical to build without some subjective human judgement.

But—at least in some applications, like deciding who “won” a trade, or if a free-agent signing is worthwhile for a club—I think such models capture something that a straight theoretical replacement model lacks.

You can’t use bench player fielding to assess replacement defense!!  There are, roughly speaking, two types of bench players--pinch hitters and defensive replacements.  Pinch hitters field rarely, and defensive replacements hit rarely.  So one would expect bench fielders to be substantially *above* average; I’m surprised they’re not.

The only way to measure replacement fielding is to look at actual replacement players (as measured by their economic availability, not their role--the worst handful of starters at any given position tend to be replacement level).  This is what Nate Silver did when he found that they average 5.5 runs below average per 162 games at shortstop, 2.5 runs above average per 162 games at 1B, and roughly league average at all other positions.  Check out his study.

Also, I am pretty sure that Nate’s MORP is calculated using the WARP on the PECOTA cards (which uses a real replacement level), not the WARP on the DT cards (which uses an asinine replacement level).

First off, don’t talk about “replacement fielding”.  There’s no such thing.  It’s “replacement players” and “fielding level of replacement players”.

Secondly, he uses “freely available talent”, which is not what I’m talking about, though it is close.  I’m talking about “bench players”, and “rest of players”.  If you are not in the top 50 in playing time at your position, you are in the “rest” group. 

It doesn’t matter how much those “rest” guys are making or how old they are: they can be had for nothing.  It could be a guy who is being paid millions, but a team will trade him to you, and they’ll take an overpaid player back.  That is, he’s in foreclosure, and a team will take a foreclosed player back.

Age cutoffs and salary cutoffs biases studies.

Btw, I did something similar with pitchers, elsewhere in this blog.  I looked for pitchers making peanuts, and being over a certain age (past peak).  Their ERA was right around league average, maybe a smidge worse.  The dataset is biased, when you do it like this.

What about September callups?  What about guys who were injured?  There are all sorts of reasons guys don’t accumulate playing time…

Dan:  What matters is using the same pool of players to measure both fielding and offense, and I think we all agree on that.  You and Tango are only disagreeing by half a win on replacement SSs, and given the reliability of BPro defensive stats, that doesn’t seem like much of disagreement. 

Nate even speculates that the reason his replacement SSs underperform on defense is age, i.e. defensive ability at SS declines rapidly with age and his pool of FATs are age 27+.  But of course there are younger FATS, on the bench in MLB or in the minors—we just can’t identify them.  They are players you could trade for w/o giving up anything of real value.  So it’s quite possible that if we knew who all those younger FATs were and included them in Nate’s pool, the SS defensive performance would increase a bit.

* *

I don’t understand your point about SD of performance by position.  Why does that matter?  The value of a good SS is the difference between his performance and that of a replacement SS.  Period.  Why should I care about the variance of performance at that position?

Fair enough.

I took MGL’s UZR 03-mid07, and totalled the games and runs for each SS.  That gives us 203 players who played SS.  The top 30 SS in playing time had a UZR of +2.0 per 150G.  The next 30 were -1.3. 

Everyone else was -8.5 (11% of SS games).

If I look at CF:
top 30: +1.8
next 30: -1.9
rest: -8.1 (19% of all games)

Looks remarkably like SS to me.

Here’s the same thing for the other positions:
1B: +1.3, -0.9, -4.0
2B: +2.6, -0.4, -6.1
SS: +2.0, -1.3, -8.5
3B: +1.2, -2.2, -3.4
LF: +0.0, +5.6, -1.5
CF: +1.8, -1.9, -8.1
RF: +1.6, -1.8, -3.1

A remarkably stable pattern across all positions except LF.  I wouldn’t be surprised is the LF is the NL’s DH, the guy who simply can’t field, and his backups are guys who can.  And maybe CF move there as well.

The data shows that the argument for SS is the same as the argument for CF.

The SD matters for systems that compare players to positional average, which I mistakenly thought Tango was doing.  A position where the SD is high has a bigger wuns gap between positional average and replacement than a position where the SD is low.

Silver’s article is still saying that the gap between SS and 2B/3B is 0.8 or 0.9 wins.  I can’t see how anyone can argue for anything more than 0.5 wins.  Silver is also saying that the gap between CF and the corners is 0.6 wins, whereas I have it around 0.9 wins.

Perhaps over the last 20 years (the years of his study), all this is true.  This is decidedly untrue over the last 4 to 6 years.

The three IF positions has a 0.8 win advantage over the three OF positions according to Silver.  I have it as only 0.2 advantage.  In this case, I am willing to concede that the gap may be higher, perhaps even as high as Nate is saying, since this is around the gap between their offense.  And IF/OF inter-class are nowhere near as movable parts as the intra-class.

It is *definitely* true that SS replacement level has risen since the 1980s, at least if you measure it using my approach of tracking the worst regulars...I have SS rep level increasing by a full 1.1 wins from 1985 to the present, which is e-normous.  I posted my numbers for the modern game above, which do differ significantly from Silver’s 1985-2005 averages.

Ouch, I’ve been quoting your numbers, but attributing Nate.  I definitely disagree with your benchmarks (insofar that we can disagree by 0.3 wins).  And it looks like we’ll have to agree to disagree.

The data in post 28 is very interesting.  I always thought of 1B as the end of the defensive spectrum, where you put a guy whose bat is so good he has to play despite his defensive shortcomings.  But this data shows, at least in today’s game, that LF is where they try to hide these players. 

Does the pattern differ between the leagues? Do AL teams, with DH at their disposal, have better LFs?

Note that as we lower our sample size, we allow individual players to influence the results more (like Everett and Jeter).  We’re talking about a 60-run swing here, which would be a 4 run gap.  I strong urge you not to pay too close attention to league differences.  For this reason, I’m presenting rounded numbers only

In the AL, top 14, next 14, rest:
1B: +0, -1, -5
2B: -1, +1, -6
SS: -2, -3, -6
3B: -2, -5, -9
LF: -2, +6, -1
CF: +9, +5, -3
RF: +1, +3, -2

NL (16):
1B: +2, -1, -2
2B: +3, +1, -2
SS: +7, -1, -6
3B: +4, +2, +1
LF: -0, +6, -0
CF: -3, -2, -11
RF: +3, -8, -3

Overall, NL is +0.5, AL is -0.5.  NL has the better fielders, barely.

But there’s a clear difference between IF/OF in the two leagues.  The NL has the better infielders, and the AL has the better outfielders.  Each are +2/-2.

The popular theory among Hall of Merit voters at Baseball Think Factory is that the steep drop in SS hitting from about 1970-85 is due to the advent and then decline of artificial turf.

Heh, I saw the heading for this thread: “There are a few replacement-level posts in one of the other threads.  They have all been moved to this thread.  Please make those type of posts here.” And I thought it was a droll way of saying that there had been some posts that added no value to the discussion, so they were being quarantined here, making an example out of them.  I figured these were the kind of posts that anyone could write, so I’d add something. =)

Just wanted to say that I’ve found this thread to be very helpful in trying to wrap my head around these issues.  So thanks everybody. -j

Well, after re-reading Silver’s article and a little of Dan’s posts (I have not re-read all of the posts in this thread), I am pretty convinced that using a one-sized fits all replacement level for all positions (let alone for pitchers) is not the thing to do.  Nates article suggests that there is a gigantic difference among the different positions as far as the difference between average and replacement (FAT).  And his methodology makes sense.  I have been barking for a while now to simply look at players who make a small amount of money and are FA or close to it.  That is essentially what Nate did.  I am not sure why he did not just add up their total stats exactly weighted by PA though.  Instead he treated everyone as a max of 130 PA.  I am not sure that is even close to being correct and may depress the replacement level of some or all positions.

Anyway, if Nate and Dan’s ideas are correct, which they probably are IMO, then we have to completely redo our $ values for all of these players.  We will find that SS and catchers are worth a lot more than we thought, 1B, DH, and crners are worth a lot less when we think.

Bottom line is that I think we need to discard this replacement level altogether and use average as our baseline.  Of course if we do, we still need to figure out how much average players at each position should make and THAT will depend on what replacement level is at that position relative to average, unless we want to simply use how much the average player actually gets paid at each position.  If we do, I think we will find that it is not nearly efficient relative to a replacement player.  According to Nate’s numbres, an average SS or catcher should get like 12-15 mil per season, while an average first baseman or DH should get like 5 mil per season.  If anything, it is the opposite, as players with big garbage numbres, the 1B, DH, and corners, tend to be overrated because teams do NOT understand the whole replacement level thing nor do they understand the positional adjustment thing.

MGL:  according to Nate’s #s, the avg. SS and avg. 1B should be paid about the same.  The replacement SS is 2.8 wins worse (-3.6, compared to -0.8 at 1B), but the average SS is also about 2.5 wins worse as a hitter.  So it balances out.

Why not try to incorporate position flexibility into the repl framework? I mean, if a repl level player wants to stay in the Show, he better be able to play more than 1 position. As a first-order approximation, how about 1 run for each position a guy can (and does) play? So W Bloomquist, Tango’s poster boy for replacement, would get an extra 7 runs, moving him from -25 to -18. That helps explain why he has a steady job every year. That, and that he carries Ichiro’s bags off the plane.

For some reason, I thought that Nate’s/DR’s numbers were runs below average for that position.

Given that they are not, I think everyone’s numbers are pretty much in agreement AND there IS a roughly one-size fits all replacement level below average for that position.

If I look at average offense at each position in MGL offensive lwts per 162 over the last 4 years, I get:

C -15.3
1B +12
2B -6.5
3B +2.2
SS -10.9
LF +5.5
CF -3.3
RF +4.4
DH +5.5

If we use a flat -19.5 per 162 games for replacement, we get:

C -33.7
1B -7.5
2B -26
3B -17.4
SS -30.5
LF -14
CF -22.7
RF -15
DH -13.9

That is roughly the same as Tango and Dan and even Nate.  DH is screwed up for various reasons, one of them being the DH penalty, another being that the level of the average DH is too low because teams are throwing non-DH players into the DH role all the time.

Another way, BTW, to get a replacement level is to take someone’s projections and from that list, take the best 60 players at catcher, and the best 40 or so at the other positions.  The next few players on your list are replacement level at each position.  You also might need to do some “mixing and matching” at the OF positions and some of the IF ones because some CF can be (and should be) corner OF’s and vice versa, some SS could/should be SS and vice versa, etc.  Anyway, that should give you the “in-practice” replacement level for that year.  If you do that for several years, you should get a pretty good idea of average replacement level for a certain group of years.

My big problem with that list is that I have the replacement level the same for 2B and 3B, while you have it as a 9 run gap.

The SS to 2B/3B is a 8.8 run gap, whereas I have a 5 run gap.  I can kinda live with that.

The CF to corner is an 8.2 run gap, which is ok.

Your IF (2B,SS,3B) to OF gap is 7.4 runs, while mine is 3.3 runs.  I think mine is a bit low, and yours may be the correct one.

The DH of course has its own issues, as we all know.

Really, your list is fine, except for the 2B/3B.  I think it’s simply the case that over these last 4 years, the quality of 3B has much outstripped those of 2B.  Fielding-wise, they are virtually the same.  Hitting-wise, it’s no comparison.

***

MGL, can you answer this question:
Given that the MLB average runs scored per 9 IP is 4.7, how many runs will a replacement-level pitcher give up:
a) as a reliever?
b) as a starter?

My answers are 5 and 6.  What are yours?

I really don’t know other than a guess based on my projections.  And since relievers are both long and short and there are swingmen, etc., I don’t think you can use a 1 run gap.  I think the gap has to be smaller.

I don’t think I am much different from you.  I have said things like .75 in the past, but that is wrong.  Probably 5.9 and 5.2.  But I am really not sure.  I am pretty sure that as a starter, it is 5.7 to 5.9, and I lean towards the latter.  I am not so sure of the reliever and it depends on what kind of reliever, although obviously the question can be for all relievers combined (the average of short and long relievers, swingmen, etc.).

Again, all I need to do is to look at my projections and take the best 180 as starters and the best 180 as relievers and the next few are replacement.

One of the problems is that we are not sure what happens when a pitcher starts and when he relieves and that we know that it depends on his role as a starter (full-time, swing-man, etc.) or reliever (short, long, occasional, etc.).

As far as 2B and 3B, are you saying that when players switch from 2B to 3B or vice versa, they stay the same in UZR?  Why do you think that 3B has such a large advantage in hitting if they are SOMEWHAT interchangeable on defense?  Maybe simply because for 3B you need to be bigger with a stronger arm which probably correlates with better hitting, more power.

I went through my projection database and tried to reserve the 180 best starters and relievers and then look at the rest.  It ain’t that easy to do.  First of all I am not even looking at players in the minors who have never pitched in the majors.  I am quite sure that there are lots of those whom I have projected better than some of the worst ones that have pitched in the majors.  Plus I have three classes of pitchers on my projection list.  One, mainly starters (75% or more IP are starts), two mainly relievers (no more than 25% IP are starts), and, three, neutral, all the rest.

If I take the 180 best starters, I am left with pitchers who project anywhere from 1 run to 1.4 runs worse than average per 9.  While that suggests that Tango’s 6 RA per 9 (in a 4.7 RA environment may be right), there are tons of pitchers in the minors who project better and tons of pitchers that I have classified as relievers or neutral pitchers who would project better than that as starters.

If I do the same thing with relievers only (not neutral pitchers), and I get past the best 180, there are a ton left who project at around .2 runs worse than average in RA per 9.

So, even though as I said, it is hard for me to do what I thought might work, that is, reserve the best 180 starters and best 180 relievers, and then look at the projections for the next few players (I don’t know how many deep to go either - IOW, is a replacement player the best single freely availbale player or the next 30 freely available players averaged out?), it definitely looks like:

A replacement pitcher as a starter is somewhere in the 1 run above average range and that the replacement pitcher as a reliever is only in the .2 above average range.  I have no problem with Tango’s 1.3 and .3, although I think it is closer to 1 and .2 and that the reason the gap is not 1 run is that relievers are short and long relievers and pitchers as long relievers probably do not pitch much better than as starters.  The gap that we talk about between starters and relievers is really between starters and short relievers.

Let me try and do the same thing (get past the best 40 players at each position - 60 for catcher - and look at the next few) with some position players and see what I get.  I am actually going to extend each position to 60 players on my list for various reasons, and then average the next 10 players.

For RF, it is -8.5, as compared to an average ML hitter, and an average RF’er in defense.  IOW, these are offense, baserunning, and defense, where the defense is compared to the average player at that position and the offense and baserunning is as compared to the average ML player.

For CF, it is -18.

LF, -17

SS, -19

3B, -16

2B, -18

1B, -7

C, -24

I am not sure what to make of these numbers other than I don’t think they are very helpful or accurate.  For one thing, for players on my list with very little major league experience, it is assumed that their UZR (defense) is around zero.  That might not be the case and that might be one reason why they have little major league experience.  IOW, I may have a decent hitting SS with little ML playing experience as well-above replacement including being an average defender, but the reason they are not playing despite being decent hitters for a SS is that they are not good defenders.  IOW, I am regressing the defense of players who hit decent but who hardly play toward zero (so if they have hardly any ML time, they get a UZR of zero) whereas maybe they should be regressed toward something like -5 (and assigned a UZR of -5 if they have little or no ML playing time).

Since I have such a good number for SS after the first 55-60 or so, which is quite a bit different than Nate and DR get, and what we would expect, let me at least list my best SS who are supposedly above -19, which is only around 9 runs worse than an average SS:

Reyes, Jose
Rollins, Jimmy
Tulowitzki, Troy
Guillen, Carlos
Everett, Adam
Jeter, Derek
Furcal, Rafael
Tejada, Miguel
Renteria, Edgar
Counsell, Craig
Greene, Khalil
Izturis, Maicer
Ramirez, Hanley
Wilson, Jack
Bartlett, Jason
Escobar, Yunel
Reese, Pokey
Tracy, Andy
Cabrera, Orlando
Eckstein, David
Vizquel, Omar
Theriot, Ryan
Upton, B.J.
Young, Mike
Castro, Ramon
Peralta, Jhonny
Uribe, Juan
Hardy, J.J.
Betancourt, Yuniesky
Hall, Bill
Hernandez, Jose
Cruz, Deivi
Flores, Jose
Young, Ernie
Almonte, Ed
Almonte, Erick
Brazell, Craig
Crosby, Bobby
DeCaster, Yurendell
Gomez, Chris
Gonzalez, Alex
McDougall, Marshall
Balentien, Wladimir
Hu, Chinh-Lung
Redman, Prentice
Self, Todd
Barmes, Clint
Izturis, Cesar
Gonzalez, Juan
Kiger, Mark
Torres, Andres
Bruntlett, Eric
Cannizaro, Andy
Lugo, Julio
Escalona, Felix
Perez, Neifi
Swann, Pedro
Morse, Mike

Here then are the replacement SS, or the next 10 or so best:

These guys, the supposed replacement SS, are only around 20 runs worse than the major league average in hitting and baserunning and UZR (with no positional adjustment).  That means that they are only around 10 runs worse than an average SS since I have an average SS being 10 runs below average in hitting and baserunning over the last 4 years.

Scutaro, Marcos
Basak, Chris
Cedeno, Ronny
Drew, Stephen
Jennings, Robin
Klassen, Danny
Merloni, Lou
Ransom, Cody
Salazar, Oscar
Zobrist, Ben
Clayton, Royce

I never heard of half of these guys in both lists, so who knows?  I sure don’t.

As we know, the “replacement” SS would also be a replacement (or better) 2B or 3B.  It’s one big reason I don’t like this approach, as it treats each position separately.

If you want to be fair, you start with SS, take say one-third of the 61-90 players, and count them as SS, take another third and count them as 2B/3B (with the appropriate positional adjustment), and take the last third and count them as OF.

You follow a similar process for the other positions, but this time include 1B as their destination.

***

As far as 2B and 3B, are you saying that when players switch from 2B to 3B or vice versa, they stay the same in UZR?  Why do you think that 3B has such a large advantage in hitting if they are SOMEWHAT interchangeable on defense?  Maybe simply because for 3B you need to be bigger with a stronger arm which probably correlates with better hitting, more power.

Yes, if you look at the UZR of SS-2B, SS-3B, and 2B-3B, you will see that the SS-xx implies about an even shift in UZR, and 2B-3B implies a bit better for 2B. 

While 2B/3B are somewhat interchangeable, this will only happen with “spare parts”, like Nick Punto.  For established players, like Beltre, Rolen, Zimmerman, Crede, Chavez, the manager won’t mess with a good thing. 

Just as having Barry Bonds in LF will mess up any hitting “average” for that position (I mean, the guy was like two Mannys out there in his heydey), the presence of such gold glove candidates at 3B will mess up any average.  We shouldn’t expect that a short-term average to balance itself out over 4 years.  We are simply in the presence of the best fielding 3B of our generation.

Hard to believe Stephen Drew can not be one of the top 60 SS today.  He must have some really bad MLEs and UZR to pull down a current (short) career of OBP/SLG above MLB SS.  Fans like his fielding.  Likely a perfect example of a guy who will find *some* home somewhere in baseball, if he can’t cut it at SS.  I.e., he’s part of the replacement pool for all non-C positions.

***

Ok, with a replacement level of 1.00 and 0.20 for pitchers, worse than overall league average, and 19.44 per 162 for hitters, we have what we need to figure out an mglWin.

65% of 1.00 and 35% of 0.20 (those are the proportions of innings) gives us 0.72 runs worse than replacement per game.

Total above-replacement runs for nonpitchers per team:
19.44 * 8.65 = 168 runs

(8.65 is the number of nonpitchers fulltime, including DH, PH)

Total above-replacement runs for pitchers per team:
0.72 * 162 = 117 runs

The proportion gives us 41% for pitching, which is pretty much what pitchers actually make, and very close to my proportion of 43%.

The total runs is 285 runs, which let’s say is 28.5 marginal wins.  I use 32.4 marginal wins per team.

Therefore, each mglWin costs 14% more (since there are fewer wins to go around, but the same number of dollars).

If my free agent win is 4.4, mgl’s is probably 5.0MM per win.

I hope someone responds to my post #40. IIRC, W Bloomquist is as avg overall defender. But he is not ‘really’ that, because of position flexibility. Since position flexibility is an important quality for marginal players to possess, it should be incorporated somehow.

I’m not sure how much position flexibility should be worth. 

As I’ve shown in the past, moving guys to secondary positions within their position class (SS/2B/3B, or LF/CF/RF) might cost you 3 or 4 runs.  And if you move from one class to another, the penalty would be higher, say 7 or 8 runs.  How long it takes to “catch up” so that the lack of experience is no longer an issue, I haven’t studied yet.

As for WFB, it’s possible that if he were to always play one position (say a neutral one, whichever one you think that is, 2B, 3B, CF), then he’d be an average defender, and have 0 runs. 

But, because he doesn’t have that single position, maybe he’s really a -2 there.  So, if he were to play every single position, he’d average a -2 overall.  This would compare to someone who’d be say 0 at a primary position, and -3 at his secondary position and -7 at his tertiary position, and if he spends 50% of his time at the primary, 30% at the secondary, and 20% at the tertiary, he’s -2.3 runs.

It’s possible that the position flexibility’s con is that the player doesn’t develop as fully as others at one position.

***

I would also say that the reason WFB plays so many positions is because he’s not good to begin with.  The way he’s surviving is by doing what he is doing.  If John MacDonald was a bit worse fielder, he’d end up having WFB career pattern, playing every position on the field.

So, if we want to give a “bonus” for playing multiple positions, I’d give it on a sliding scale to every righthanded thrower in baseball, starting at say +2 runs bonus at the bottomest level, and sliding it up to say 0 runs bonus at the league average player.

I think the aggregate value for pitchers and position players implied by these replacement levels is interesting.  If we take Dan/Nate’s numbers for position players, the average team of position players is about +17 WAR. 

If we take Tango’s pitcher numbers (1.3 R/G for starters, .3 R/G for relievers), then a staff of average pitchers produces 16 WAR.  Essentially, that’s equal value on both sides.  If we give the average DH a little credit, pitchers’ share of the value pie falls to the 45-47% range. 

That’s somewhat different from the distribution of payroll (I think Tango has reported that about 42% goes to pitchers), and vastly different from the 35/65 (pitcher/non-pitcher) Win Shares allocation.  I think the breakdown implied by these replacement levels is correct, with the lower salaries for pitchers explained by the much higher variance in performance (less reliable = lower pay).

I’m not sure I’d want to mix-and-match.  I determined my numbers by figuring the talent distribution among pitchers and nonpitchers.  That is, 1 SD = 2.0 wins per 162 g for nonpitchers, and 1 SD = 1.5 wins per 162 IP for pitchers.

(I don’t remember exactly what it is, but something like that.)

I set the replacement level SD such that my team of players is .300, which implies the .380 for nonpitchers and .410 for pitchers that I’ve been using.

I would not take the Nate/Dan numbers for nonpitchers and attach my pitcher numbers to them.

I know we think that baseball pays a discount for the variability in pitching, but they also pay a premium for the perceived “durability” of pitching, to the point that it basically cancels out.  Baseball GMs pay without considering variability in performance or injuries.

I agree that mixing-and-matching isn’t quite right.  But I think that if Nate ever did a FAT analysis for pitchers (if you’re reading, Nate, please tackle that), he’d likely find something close to your values.  (Woolner’s prior work actually set the replacement level a bit lower). 

I think the SD approach is a legitimate approach, but only if you find the average SD within a position for non-pitchers. That is, you need to find the SD for Cs, SSs, etc., and find the average of those.  Otherwise, you are overestimating the variance among position players, because some of that variance comes from mixing weak-hitting Cs and SSs with 1B/OFs.  And if you do that, I think you may find that the SD for position players isn’t much bigger than that of pitchers.

Ah, but don’t forget, there is the positional adjustment.  It’s offense, fielding, plus positional adjustment.

You see, if I have a fielder as -5 at SS, then I have him as +5 in the corner OF.  But, overall, he gets zero for position+fielding.

That’s why I have no problem lumping all nonpitchers together in one huge pool, and taking the standard deviation of their overall runs or wins per 162 G.

***

As for low-paid, old pitchers, I did that study a few months ago here.  It’s that study that made me realize how the approach was not good: it’s strife with sampling issues.  I’ll see if I can find it.

See post 10:
http://www.insidethebook.com/ee/index.php/site/comments/the_replacement_pitchers/#10

And post 18 of that same link.

In short, the cheap over the hill pitchers performed just as well as the league overall.

MGL, in your list some of those guys are not shortstops.  Ernie Young, Craig Brazell, Wladimir Balentien are 1B or OF.  Some others - Deivi Cruz, Pokey Reese, I think are retired.

"Ah, but don’t forget, there is the positional adjustment.  It’s offense, fielding, plus positional adjustment.”

I don’t think Dan/Nate’s numbers need any additional positional adjustment.  They reflect the combined hitting/fielding gap between replacements and league-average players.  If their figures are right, then a team of average position players is about 17 wins above replacement.  So that’s the total value of all position players.

I was responding to the mixing positions leading to overestimating variances.  It doesn’t overestimate anything.  It exactly estimates it, if you go to the Tango school of Players Drawn from Moveable Pools.

So, Tango, did we finally conclude then that MGL uses a higher $/win value than you do and therefore his valuation of players needs to be interpretted as so?

Yes, it was in one of the other threads. MGL has some 10-15% or so fewer WAR than I do, meaning that you need to use a higher $/win to compensate (since we obviously use the same $).

Since I use 4.4MM$/tangoWin, you need to use 5.0MM$/mglWin.

Gary Huckaby has an article today in BPro about replacement level:

http://www.baseballprospectus.com/article.php?articleid=6999

In it, he basically argues that Jack Cust represents replacement level for left field types.  Which is another way of looking at things, I guess: not the average bench, but the best FAT player available.  I may be wrong, but I’m guessing that typically results in a very high replacement level on the unskilled part of the defensive spectrum, and a low one on the skilled end.

I may be dense, but I don’t really understand Huckabay’s point. Just because the GMs undervalued Cust, because of his strikeouts and lack of defensive value, doesn’t mean that he is ‘really’ a replacement player.

I just don’t get his point.

As I think of it, replacement level production (offense + defense) is the upper end of production that one could reasonably expect to get from a player acquired from the population of freely available talent.  Therefore, given that it’s a description of a population (or, perhaps, a subset of a population), it seems rather silly to me to set the baseline to the production of a single player on a single team.

Another point, of course, is that even if you’re going to define replacement level with a single player, you have to consider both his offense and defense for your baseline to be even remotely relevant.  Cust’s actual value was lower than what Huckabay indicated because Cust was a below-average defender.  I have him at -7 runs or so...not a huge difference, but a difference.
-j

Tango, referring to your post in #58, everything in the other thread makes sense, but I was wondering what mgl’s replacement level (which is as he says -18 per 150, -20 per 160) would have to be to become more in line with your $4.4 mil/win? Or if that didn’t make sense, I am basically asking what your replacement level value in runs is per 150? 160?  It’s obviously less than minus 18, so I’m assuming like minus 15-16 runs (around 12% less than mgl’s value).

My replacement level is 2.25 wins per 162 G for nonpitchers, .380 for starters and .470 for relievers.

Since I have more wins above replacement, each tangoWin costs less than an mglWin.

That’s right.  Okay, so the 2.25 wins per 162 is around 25 runs, as compared to mgl’s 20 runs per 162 (1.8 wins, using 11 runs/wins).  This makes mgl’s $/win $2.50 million, as opposed to your $2.28 million.  I think I got that part…

What does your .380 and .470 win % translate into in runs/wins for pitchers?  I know your overall numbers translate into a .300 win % for a replacement level team (48.6 wins, or 49 wins).

In 2007, the average starter was a .485 pitcher or so, and the average reliever was a .530 pitcher.  The average pitcher gets around 66% of the innings.  You can work it out from there.

I don’t know why you said your replacement level for nonpitchers is minus 2.25 wins when I’m pretty sure your replacement level of .380 for nonpitchers is -19.44 runs below average per 162 (.500-.380*162), or minus 1.76 wins.  That is in line with your salary scale (where a league average player should receive a 1-year, $8 million contract).

As far as the pitchers go, I think I must have messed up in my calculations or the replacement level for starters is lower than .110.  Before I calculated the pitcher runs/wins below replacement, I took your info that a replacement pitcher pitching only as a starter is a .380 pitcher and that same pitcher, pitching as a reliever, is a .470 pitcher.  In 2007, I used the average starter as a .490 pitcher and the average reliever as a .530 pitcher.  So, the average starting pitcher is +.110 runs per 9 IP.  Assuming 180 IP per starter, the average starter is +1.8 wins per 180 IP.  The average reliever is +.060 runs per 9 IP, and assuming 70 IP per reliever, that’s +0.38 wins per 70 IP.  Combined, replacement level for pitchers is -23.98 runs below average, or minus 2.18 wins.  Even if you don’t combine starters and relievers, minus 1.8 wins for starters is more than nonpitchers, which doesn’t make sense.  If nonpitchers are are minus 19.44 runs below average I would have thought that starting pitchers would be around 14 runs, not 19.8 runs.  As a note, in these calculations I used 11 runs/win, not 10.

Take a look at my calculations because I don’t think the runs/wins for pitchers is correct but I can’t figure out what’s wrong in the methodology.

Each nonpitcher is a .486 player (-.014 wins per game).  There are 8.65 full-time nonpitchers per team (includes PH and DH where appropriate).  .014*8.65 = .12 wins per game.  (Or 19.44 WAR per season.)

So, .014 x 162 = 2.268 wins as the repl level per nonpitcher per 162 G.

***

You said: “In 2007, I used the average starter as a .490 pitcher and the average reliever as a .530 pitcher.  “

That however will not give you an average of .500.

Presuming .485 starters, .530 relievers, and 66.7% IP to starters (which will give you exactly .500), and you have a repl level of .380 for starters and .470 for relievers, then:

(.485-.380)*162*.667= 11.34 WAR (starters)
(.530-.470)*162*.333= 3.24 WAR (relievers)

Total WAR:
19.44 - nonpitchers
11.34 - starters
3.24 - relievers

34.0 - total WAR per team

57% of salary should go to nonpitchers
33% of salary should go to starters
10% of salary should go to relievers

***

The starter/relief split implies about 78% of the salaries (and value) should go to starters.  Perhaps because of leverage following talent, that relievers should be bumped up following the GuyM method.  It’s possible that the starter share will go all the way down to 70%.

Alright, now I got everything.  I know you guys have talked about the “GuyM” method before, but I haven’t seen the posts.  I think is has something to do with LI and closers and not just multiplying a closer’s LI by his marginal win value to determine his dollar value.

The GuyM method:

Figure your relief pitcher’s win%, and his Leverage Index (LI).

Figure the “replacement level closer’s” win%.  I use .570.  You can make it the average of the top 60 relievers, or make it the 30th/31st best reliever.  .570 is a reasonable line.

Presume the replacement level for a pitcher as a reliever is .470.

(win%-.570)*LI
plus
(.570-.470)

The theory is that the closer is not responsible for the LI=2.  That every team has a reliever at the .570 level that they can put into that role.  So, he shouldn’t get credit for that.  But, if you have a guy like Mo, with his .670 win% (or whatever), then he should get credit for being above the replacement-closer level, and get to apply his LI to his performance above that level.

I think it’s a genius application that satisfies both sides of the LI argument.

It has a “chaining” aspect to it, but is much easier to explain and implement.