THE BOOK--Playing The Percentages In Baseball

tango: would you value bloomquist at +.75 for position because he can play shortstop, or at less because he won’t (because he’s not good enough to) play shortstop regularly, or more because he offers the versatility of moving easily between positions? basically, i’m asking if there should be a premium for so-called super-subs or how you would otherwise place a value on that talent.

Again, don’t get hung up on Willie himself.  As I said:

...some composite who is average in all tools respect (speed, strength, agility, etc), and who is equally experienced at all positions

I said more:

Jeff: no, I do NOT adjust by position.

If Willie Bloomquist is -2 wins per 700 PA as a hitter, I don’t care what position he plays.

If he is -0.75 wins as a fielder, relative to the average SS, I then give him +0.75 wins because the average SS is that much better than an average overall fielder (Hubie Raines, Willie Mora, or whatever composite you want to come up with).

If he is +1.25 wins as a 1B relative to the average 1B, that’s no great feat.  I give a -1.25 adjustment to that.

In the end, the fielding + position_adjustment is really what his fielding is, relative to the composite average Hubie Raines.

While we have a composite average hitter (that’s the league average on 189,000 PA), we don’t have such an animal on the fielding side.  So, I have to “make one up”. 

what i’m asking is if there should be a premium (and how much) for a guy, bloomquist or otherwise, who is average in all those tools and equally experienced at all those positions. we say he’s an average fielder, so wherever he plays, his defense and the positional value cancel out (or whatever - maybe he’s better than average, so wherever he plays he comes out a bit plus defensively), but i’m wondering if you think there should be a premium beyond his fielding+position for that versatility. i don’t know how to quantify it, but it seems like it does have real value (e.g. being able to carry an extra pitcher or an extra pinch hitter who should never field because you have a guy who can fill in wherever you need him). i guess that question’s not terribly useful or relevant at the moment, but if this flexibility has real value teams could/should start developing players for this role (giving good fielding minor leaguers who can’t hit experience at every position so that they can become utility men, the same way some underachieving starting pitchers are turned into relievers in the minors). or maybe i’m over-/under-thinking it.

Man, there’s a lot of wasted HTML in that thread.  Let’s sum this up for people who don’t want to spend an hour thumbing through semantics.

Chris Dial doesn’t care about ability, only value.  This is dumb, but this is Chris’ only care. 

The rest of us care about ability and value.  Therefore, we recognize that position adjustments are a better way to do things.

You may be willing to acceed to Chris Dial’s definition of value, David, but I’m not. Because it’s also VORP’s definition of value and PCA’s definition of value and so on and so forth and it’s wrong, wrong, wrong. There can be periods of time - maybe even years, maybe longer than years - that for whatever reason the sum of all players position can be more or less valuable than the sum of all players at another position. Especially when you split up by league!

This isn’t about ability versus value, it’s about how you define value.

I was trying to be brief.  Don’t worry, you and I are in agreement.  Chris’ picture of value is way too narrowly defined.

Chris may be trying to frame it as an ability/value debate, but I don’t accept his framework.  I don’t particularly care about ability either (looking backward, that is).  While I did not read the entire thread, the gist of it seems to be that Dial is defining value as “contribution compared to that of your peer”, which I am fine with, except that he is narrowly defining “peer” as “the guy who plays the same fielding position for the opponent”.

As a general comment on this issue, I think the proponents of DPAs should be taking more care to explain that the results of a DPA-based analysis are not radically different from those of an OPA-based analysis.  It seems to be causing some confusion, like Rob Neyer asking (and yes, I realize it may be for exposition’s sake) “Have we been underrating shortstops all these years?” Certainly the DPA changes thing at 2B, CF, and 3B, but the results are not a radical departure from OPA.  It’s like changing from RC to BsR.  It is a big step up theoretically, and it changes some results, but no one is going to go from being seen as a superstar to being seen as a scrub.

You’re correct, Patriot - except that the most popular OPA metrics, and its strongest advocates, also seem to base everything off one-year baselines, sometimes even relative to league, thus compounding the error. You can design an OPA metric that, say, properly values a center fielder versus a left fielder in the 1999 AL, but it’s probably not going to be Dial’s OPD or VORP.

Agreed, Colin.

Even as an OPA user, I only use long-term averages, and Pete Palmer does the same.  If you switch from Dial or VORP’s one-year to a DPA, then I agree that it is in fact a great leap forward.  Switching to long-term OPA would be a step or two forward.  But that is all a long-winded way of concurring with your post.

I’ve read a little of the “Dial versus David and Tango” debate on Primer.  Some of the argument is semantics (e.g., what do we mean by “value?"), but some of it is not.

This is where Dial’s argument really breaks down:

Let’s say that the average offense at SS and 2B are the same for one year or even for 10 years.  So a player who plays SS and hits X has exactly the same value as a player who plays 2B and plays 2B, according to Dial and his followers.

But I can easily prove that that is not correct, assuming that we know that SS is the more difficult position AND that a SS can play 2B and be better than he is at SS and that a 2B can play SS and be worse (relative to the other players at that position).

We start out, according to Dial, with the presumption or conclusion that both players have equal value.  So why don’t I just move my SS to 2B. Now he is no longer an average defensive player.  He gains 5 runs or so on defense and all of a sudden he is worth 5 more runs.

A player’s value cannot change by moving positions when he is average at the original position!  If it does, which is the case in this instant, than there is something wrong with the methodology for calculating value.

The reason that this happens is that either there are two many or two few players at one or more positions in any one year OR teams have players at the wrong position.  Usually both of those things are present at any one time.  But they should not change a player’s value, unless you want to define “value” to include where teams put players (given that that placement is inefficient) and how many players we have at each position in any given year.

I don’t think that is a good definition of value, but if that is Dial’s then so be it and he is right in defending his methodology for computing it.

A player’s value should be independent of where he is placed, either by virtue of team suboptimal decision-making (about where to place players), or by virtue of where other players are placed.  A player’s value should be based on him being placed in an optimal defensive position.

Using fixed positional adjustments takes care of this automatically.  And they SHOULD be fixed to the extent that the relative difficulty among positions stays fixed.

I am starting to get a little swayed by the “use offensive differences to establish positional adjustments,” although I am pretty sure you have to go with replacement levels and not league averages.  And I am not sure how to handle the issue of year to year replacement level fluctuation (which should be smaller than fluctuations in average offensive performance - thankfully).

Here is the argument:

Let’s say that each position were independent of one another, such that you could not take a LF and move him to 1B and expect him to be better (on the average of course), or a SS to 2B and expect him to be better. 

If that were the case, then you would have to treat each position independently and compare a player at any position to a replacement player at that position in order to establish his value, right?

Assuming you (Tango, David, Colin etc.) agree with that, you might say, “O.K., in your hypothetical example, no one position is easier or harder than another, so we HAVE to treat them independently (or perhaps treat them independently) so there are no intrinsic positional adjustments anyway.

But, what if there are easier and harder positions.  How would we know that if I just said that it were not true that if we moved a player from one position to another, that he would get better or worse?  Remember I said that in my hypothetical sport, if we move a player to another position, he ALWAYS gets worse.  In other words, each position is unique and requires a different set of skills.  But one could still be more difficult than another.  How do we define “difficulty” then, if by moving from a more to a less difficult position, I am saying that a player will still get worse?  Simple.  There are a larger pool of players at one positions because the skill set for that position is more common.  That does not mean that a player with a less common skill set can play a position with a more common skill set any better, at least in my hypothetical world.  It is like the LH and RH thing.  There are many more RH players so that even if CF and SS were equally “difficult” there would be a larger pool of players for CF than for SS, and presumably the CF would hit better, even though both pools are equally talented on defense.

So now we have more or less difficult positions, as defined by the size of the pool of players with each skill set, with the less difficult positions having a better average offense because the pool of players with that skill set is larger.

But we don’t have the Tango construct where the small pool can play a large pool’s position and play it better.  So we have no instrinsic positional adjustments.  What do we do to establish value and be able to compare players across positions?

All we can do is to use replacement offensive level (and defensive level) at each position independently.  That is ALL we can do.  That is the Dial method.

So let me summarize.

If we know that any one position can play any other position and do it better or worse (in fact, there really are no “separate positions” - there really is only one pool of defenders as Tango likes to say), then we can establish intrinsic positional adjustments based on the differences between playing one position and another.  This is what Tango is doing.  No problem with that.  He does it correctly although he certainly does not have enough data to establish the exact adjustments AND he has lots of selective sampling issues with the data he does have.

If we know that positions are completely independent - basically everyone who plays another position, whether we consider it harder or easier (based on the size of the pool of players who can play that position), will do worse than his “own” position, then we have NO intrinsic positional adjustments and all we can do to compare players across positions is to try and estimate the level of the replacement player at each position.

I don’t think too many people are going to disagree with the above 2 constructs.

So what do we have in reality in MLB?  I think it is clear that we have a combination of the two.  As Tango has admitted, we know that catchers don’t automatically (on the average) play all other positions much better than they do at catcher, even though we give the catcher a giant positional adjustment.  We give the catcher giant positional adjustment because there are only a few players, relative to the other positions, that can play catcher, and thus the average offense is low (not to mention the fact that the defensive skills related to a position are also related to offense - for example, if we had lots of players who could play catchers, they would probably all be slow and somewhat fat and thus be worse offensively right off the bat).

So since MLB is clearly a combination of the two hypothetical constructs, the positional adjustments must also be based on a combination of the two methods - one being an instrinsic adjustment based on how an “average” player would do if he played each position, and two, the differences in offense between a replacement player at each position.

I have gone back and forth on this issue, but I am fairly confident that I now have it nailed.

Until I change my mind again of course…

MGL, I believe the root of the positional adjustments can best be explained by the different offensive levels. Most of the people at ESPN who were new to the conversation seemed to have a really hard time grasping the concept the way it’s been described by Tango and Eric as adjusting the player’s defensive value. Your comments at Neyer’s blog about how to measure the the offensive differences are certainly valid, but these differences are the starting point.

I do believe that what we are trying to measure is replacement value, and therefore replacement level certainly is part of the equation.

An economic theory of my own, which I’ve used for many years, is that there are two main things that determine your fair market value as an employee (regardless of whether you are a janitor or shortstop)
1. How much revenue do you generate for your employer?
2. How hard are you to replace?

I also get your point a ss being able to play 2b better than a 2b play play ss, which then should make the ss more valuable, everything else being equal.

Flexibilty gives the team more options to put together the highest value 25 man roster. For example, if the Red Sox sign Tex, he has to replace someone. They can trade Lowell, and move Youk to 3b. Youk might not be as good defensively at 3b, but him at 3rd and Tex at 1b has more total value than Lowell at 3b and Youk at 1b. BUT, it couldn’t happen if Youk couldn’t play 3b - they’d have to look for another scenario, which may be of lesser value.

And here’s more of what I wrote (I’ll comment on your posts above a bit later):

==========================================
Blackadder/127: ditto.

***

In the 2008 NL, the average batting line at each position:

SS - .276/.334/.404
2B - .271/.338/.408

Chris/128:

It’s very easy to see how SS one year could hit higher than 2B, right?  So, while there is no extreme situation as I presented in high school, you will get some imbalance, certainly if you only look at it on the basis of single-leagues, single-years.  What happens in an 8-team league where you happen to have great concentration of talent at one position?  You get a less extreme scenario of the high school issue.

In any case, as Chris noted, our positions now are quite crystallized, and it’s up to the reader to establish his questions, his needs, and then find the metric and process that answers to that.

***

A fielding position requires a set of skills.

If 2B and SS was as distinct as QB and K, then yes.  I can definitely see the argument if you want to compare C to CF.  Indeed, if one wanted to treat C, IF, OF, 1B/DH as 4 separate position classes, and then ensure that the adding up to zero is at those 4 groups, then I would not be opposed to it necessarily.  I wouldn’t be totally in favor of it, but I’d have less opposition to it than saying that LF and RF are two distinct positions, when clearly no one in MLB behaves as if there are. 

Heck, there is less movement in the NHL between LW and RW than there is between LF and RF, and no one thinks of ensuring that LW = RW.  And certainly, no one compares centers to centers.

***

Ivan/130:

Can we use Tango’s system to estimate that if Escobar was +5 at SS, then he’d likely be +10 at 2B?

The average player who is a +5 at SS would be a +10 at 2B.  That’s presuming there is no “familiarity factor” to account for.  Players are humans, and the positions have enough distinction that there is value in experience. 

At the same time, a +10 2B should be a +5 at SS… with enough experience.  A +5 at SS, with no experience at 2B, might be +5 at 2B.  Similarly, a +10 at 2B, with no experience at SS, might be 0 at SS.  Averaging it out, and you get the 5 run conversion value.

Regardless though, the comparison point is not “how would they do if...”, but exactly the question I was asking “How does this player compare to Willie Bloomquist?” (understanding of course that I’m not talking about Willie specifically, but a composite who is average in all toolsy and experience matters).

***

but I am supposed to think that David Wright moving to 2B would have the same defensive impact as Carlos Beltran moving to 2B

That wasn’t the question I was asking.  Again, I’m comparing players to a common baseline: Wins Over Willie (WoW for short).

***

Colin brings up two good more examples (which, by the way, are very easy to find):

1999 AL - hand to God, the average LFer was out-OPS’ed by the average CFer.

CF - .275/.346/.430
LF - .272/.339/.432

...

Or let’s go back to, say, the 2008 NL. The average shortstop hit about like the average second baseman. Meanwhile, over in the AL, the average shortstop hit worse than the average catcher. We know Dial’s OPD seperates the leagues - does it really make any sense to say that the average AL SS was equal to the average NL SS? Or should we think that for some reason, all of the best shortstops ended up in the NL this year, and it’s biasing our results?

Chris’ system, as we are both asserting, is based on treating each position as something fixed, like QB, DT, and K, rather than as “roles” like a batting order.  You either buy his premise, or you don’t.

And Chris noted: “If everyone is special, then no one is.”. He means it to say “everyone is special… at that position, in that league… then no one is”.  I think this obviously makes the cross-position comparison very difficult, and makes the cross-league comparison just as difficult.  If for example in an 8-team league, Willie, Mickey and The Duke were all in the same league, while the other league had 8 rather typical centerfielders, the other 5 guys in the 8-team league would take a huge hit.

***

The disagreements with Chris really is based on accepting his premise of “positional (and league) counterparts” or not.  You have to decide if you want to do this.  If you do, then you follow Chris lead.  If you don’t, then you have to look elsewhere (and the solution to that is not necessarily my proposal).

Quick question that I don’t think I’ve seen addressed directly:  why is there a penalty LF/RF, 1B, DH?  Why not start DH at 0, and move up accordingly as you move through the defensive spectrum.  (Is it a penalty because you’re talking about replacement value?) Couldn’t you rescale the positional adjustment it so you weren’t adding the 2 wins or so when you were trying to figure out a player’s total value?  I think we understand that Manny should be penalized for being a butcher in LF.  It’s not as clear to me why Ortiz should be penalized for not playing the field, as it were.  Or, if you decide to penalize your DH since he can’t do half his job, as it were, why are you penalising your 1B since you need someone to field the position?

Hope this all makes sense.

Thanks.

Here’s what I’m going to do after the Steelers are done with the Titans -

We want to know what’s the current value of the market at each position, but smooth it enough to avoid being skewed by a few players.

1. Calculate the wOBA for all position players from 1954-2008
2. For each position, each year, compare to all the players in the league that year to get a +/- runs per 600 pa.
3. Smooth the yearly totals with a Marcel weighting, each previous season 0.7.

I’ll probably put it up at StatSpeak in order to meet my weekly quota.

Jurgen: It’s all same-same. You can add your positional and rep-level bonuses together first, or you can add your position and rep-level bonus to the player’s offensive stats and get something that looks like VORP, or you can add your position bonus to fielding numbers and end up with defense relative to league-average and then add offense and rep-level. They’re all the same ingredients going into the same stew-pot.

MGL/12 aligns itself well with what I said here:

If 2B and SS was as distinct as QB and K, then yes.  I can definitely see the argument if you want to compare C to CF.  Indeed, if one wanted to treat C, IF, OF, 1B/DH as 4 separate position classes, and then ensure that the adding up to zero is at those 4 groups, then I would not be opposed to it necessarily.  I wouldn’t be totally in favor of it, but I’d have less opposition to it than saying that LF and RF are two distinct positions, when clearly no one in MLB behaves as if there are.

Heck, there is less movement in the NHL between LW and RW than there is between LF and RF, and no one thinks of ensuring that LW = RW.  And certainly, no one compares centers to centers.

Forcing a zero at C, IF, OF, 1B/DH is a position I can accept, to some extent.  (To the extent that C don’t move to IF/OF/1B, and to the extent that IF don’t move to OF, and to the extent no one moves to 1B.)

So, you can see why I have SOME relunctance.  Not a whole lot, but some.

HOWEVER, there is simply no way you can take a one-year, one-league offensive performance totals to do that.  Things jump up and down far too much, and you have Barry Bonds or other talent concentration issues.  This I can go for alot more:

http://www.insidethebook.com/ee/index.php/site/comments/offense_by_position_groups_by_decade/

But even then, you have issues…

Thanks for responding, Colin.

I wonder if this is part of the problem of people “getting” it.  Personally, it’s what I tend to get hung up on:  I get that SS is more valuable than 1B, and a +10 SS is different than a +10 1B, but why penalize someone for playing 1B if everyone needs a first baseman--especially if you’re going to add back 2 wins (almost the same as the DH “penalty") to calculate out their total value regardless? 

I’m just sure the scaling is intuitive, and leads to confusion (for me) down the road.  (Or maybe it’s just me.  I also don’t like the scaling of wOBA, and still prefer using .300 like EqA and GPA.)

Whoops.

That should read:

“I’m just not sure the scaling is intuitive, and leads to confusion (for me) down the road.”

As I said in 12, forcing any one position or group of positions to zero is NOT the correct way of doing it no matter what.  Finding out what replacement level is in each of those categories is the way to do it.  Now, if replacement level varies a little from year to year, then it gets a little tricky.  And replacement level does vary a little, just not as much as average, I don’t think.

I think we should be resigned to the fact that there is no clear-cut answer and no exact “number” (to do the adjustment), no matter what method we use.

The thing is Tango, if we say that LF/RF are interchangeable, and maybe even 1B/DH, and 2B/SS/3B, then the difference in replacement level between positions within each category should really approximately equal your fixed adjustments, if MLB is utilizing players even close to optimally or correctly.  And if they are a little different, it does not mean that one method is better than the other, since both “camps” admit that their numbers are estimates anyway.

So, bottom line, I would say that using fixed adjustments, like Tango’s, is fine, if that floats your boat, and using some kind of offensive differences (replacement is best, but I can live with average, since it is hard to define and figure replacement), as long as they are somewhat long-term averages, is fine as well.  6 of one…

I think the DPA (Tango) is the more correct way to do it. But I also think the OPA (Dial) is a good approximation or shortcut.

We have seen the examples where the OPA produces ‘unusual’ results, such as CF/RF in the 50s, Giles/Bonds, etc. But what about the DPA? Will this method also produce cases of seemingly absurd results or ratings? And if so, how would we be able to identify them, and see where the approach should not be used?

I’m trying to follow the entire conversation and failing, but I have one simple question (actually, an assumption) that has probably been answered somewhere.

Up to now, I have considered this entire process a way of “fixing” the new fielding metrics that compare players to average fielders at their positions.  I guess there are two ways of thinking about this fix:

- Each position has more or less inherent fielding worth in total
- The range of replacement fielders at each position differs

Am I right about this adjustment being a “fix” to “plus/minus” fielding systems?  And do you guys think of one or the other bullet points as the best description of what the adjustment is addressing?

"1. How much revenue do you generate for your employer?
2. How hard are you to replace?”

The second question is the bane of the Sabermetrician.  How much money would I have saved for the Astros in the 2006-07 offseason?

At least 30 million over several years, the difference between what they paid for Carlos Lee and the price of another available player, who just happens to be better than Lee, JD Drew.

But I also would have been very easy to replace.

But I also think the OPA (Dial) is a good approximation or shortcut.

We have seen the examples where the OPA produces ‘unusual’ results, such as CF/RF in the 50s, Giles/Bonds, etc. But what about the DPA? Will this method also produce cases of seemingly absurd results or ratings?

Using just 14 teams from one-season to do this, as Chris does, is not good.  I think Chris showed that last year, the 2B/3B were even in hitting in one league, and differed by 7 runs in the other league (or something like that).  There are just way too many of these that you will find.

So, I cannot at all get behind the half-league seasonal numbers, I won’t get behind single-seasonal numbers.  I might be able to get behind 3-5 year numbers, but not really.  At 10 years, I start to accept it, but not totally.  At 20 years is where my threshhold to resist starts to diminish.

But, Tango, the point of my post was to ask where does the DPA method break down. By identifying examples where it seems to give silly or absurd results, we can perhaps extrapolate the rate of breakdown from the average to the absurd. Maybe, because of the possible disconnect rate in comparing avg values to individuals, the DPA is accurate overall, but very unreliable for individuals. That is something I’d want to know.

As I said several times already, since the correct method seems to be a combination of long term offensive adjustments (which assume that all positions are independent) and fixed positional adjustments (which assume that all positions are interchangeable), there is no need to argue which approach is right, as there is no one right approach.

Certainly a long-term offensive approach tweaked by some notion of fixed adjustments is the best way to arrive at the correct answer.

Long term offense alone would actually be fine but for several things:  One, how long is long? Two, team inefficiencies (putting players in the wrong positions) will screw up those numbers.  Three, changes in the relative value of positions.  An example of the last one is:

If it is true that artificial turn changed the relative values, and we want to make adjustments now, where there are no longer too may artificial turf fields (especially the fast ones), we don’t want to use long-term offensive numbers (which include periods of time when there was a lot of turf) and we also don’t want to use short-term ones, since we know that there is too much fluctuation in them from year to year.  So we want to use some kind of hybrid method.

Some things just don’t have a “clean” methodology and there is not much you can do about it.

There is also an elephant in the room which no one is talking about in this thread.  If we really are trying to get at the value of a player as compared to any other player, and we all agree that ultimately the value of a player is based upon the value of a replacement player at the same position or at all positions combined, what about the fact that it might be true that replacement level is different, relative to average, at each position. Didn’t some researchers find, or at least posit, that that is true?

If that is true, not only do we have to use positional adjustments, but we also have to use a unique replacement level (rather than, say, 2 wins) for each position, depending on a player’s primary position.  Even though a SS CAN play other positions, if there happens to be a very low replacement level for SS, for whatever reasons (say, 2.5 wins below average), then an average SS is going to be worth more than an average 2B, or whatever.

I don’t think we’re ignoring any Babar here.

Since 3B hit better than 2B, and Tango uses the same position adjustment for each, then replacement level at those two positions is different, relative to average.

How about treating the catcher as a different position? Is that really too farfetched? I’m convinced that the difference between a replacement level catcher and average catcher is less than two wins. Two wins would put a replacement level catcher at about a .280 wOBA. That’s ridiculous. By the way, this all stems from my belief that Varitek just can’t be worth $10 million.

We know that catching and playing the field are not interchangeable in defensive ability, especially with a catcher moving down the spectrum. The scarcity of the position and difficulty of catching determined its market value, and therefore positional adjustment, moreso than at other positions where ability, defensive value, and offensive averages prove more important. It seems that the +12.5 value was determined by convenience rather than evidence.

jeremy, I agree.  Catcher is such a unique position that it begs for you to use replacement level to determine a catcher’s value, and not a fixed positional value.  Of course, once you determine that replacement level, it becomes sort of a fixed value anyway, unless long-term ("real") average versus replacement should change for some reason.

David: you could get silly results if there’s been a shift in talent that you are not capturing with a long-term outlook.

Let’s look at LF/RF, which we, I think, can agree that it takes pretty much the same skillset to play (with a couple of runs extra for exposing a weak arm at RF compared to LF).

The Fans’ Scouting Report, while usually a bit down on LF compared to RF, was totally down on LF compared to RF in 2008.  It’s possible that we witnessed a huge shift these last couple of years, such that teams are treating LF as the DH spot (especially in the NL).  By continuing to use an equal adjustment for LF and RF, we are implying that the two positions have equal fielding talent.  If you believe this to be untrue, then my adjustments are wrong.  While I usually accept a 2.5 run uncertainty level, it’s possible that the fielding gap between the two positions could even be 5 runs.

It seems that RF gets refreshed with young talent, while LF becomes the repository for aging OF.

That said, the number of silly results between using single-league single-year numbers far outstrips what I propose.  It’s possible that 20-year offensive numbers might be close to what I’m doing, but, like I said, then you miss any actual shift in talent that is happening within those 20 years.

jeremy: I don’t disagree that catcher should be treated as a position separate from non-catcher, much like a QB is distinct from WR, DT, or K.  Its sports equivalent is probably best captured by D/F in NHL.  While there are more catchers that end up playing 1B or OF at some point in their careers, this is not as true in hockey, though it happens sometimes.  You have a couple of players every year that move between F and D in the NHL.  Its rare enough that you can consider the positions separate like skater and goalie, but not so rare that you can totally keep them separate.

I think MGL provides a good overview of the respective merits of the two approaches.  And David S may be right that DPA is the “more correct” approach, at least for those positions which players can move in and out of.  Nonetheless, for most purposes a system that is heavily weighted toward offensive replacement is what you want.  It has two big advantages over Tango’s approach:
1) MUCH more robust data is available for assessing offensive performance of repl players at each position.  Small sample sizes and selective sampling problems are pretty serious problems for most if not all position comparisons on defense (not to mention the lower accuracy of defensive metrics). 
2) OPA tells us the actual cost to teams of purchasing defense at a position, in runs sacrificed at the plate.  And that cost is also the value of that defense.  We don’t need to separately assess the scarcity of a position’s defensive skills, because the cost paid in reduced offense reflects that scarcity.

The ONLY reason we ever need to consider DPA at all is because of the possibility that teams are not maximizing the allocation of players by position.  And while I generally tend to think that is less likely, and smaller in scale, than Tango does, I certainly don’t dismiss the possibility.  If it can be shown that most/many average-fielding 3Bmen could also be an average-fielding 2Bman, then we have a serious market failure.  It means that a lot of reserve and minor lg 3bman should be playing 2B in MLB.  I’m skeptical:  there are huge incentives at every stage of a player’s development—for the player, his agent, his coaches and managers, his franchise—to play him at the most defensive challenging position possible.  I suspect that if we could measure all the defensive value of 2Bmen (turning DPs, flyballs, tagging on SBAs), we would find that most 3Bmen couldn’t make the switch w/o a defensive decline.  But I have an open mind on this one.

Still, most of the time—at least in today’s game—we are going to be best served by using offensive replacement level to make position adjustments.  The superiority of the data alone argues strongly for that approach.

Seeing that MLB teams themselves pay less for 2B than 3B (and not because of the service years bias), there is an actual realization by the market that the average 2B is worth less than the average 3B. 

Teams seem to not care about this, and prefer to not be in positional equilibrium, as long as they are in financial equilibrium (dollars per win is constant for each position).

As I said, you can’t say “offensive adjustments” unless you tell me the number of years.  Chris Dial uses the smallest number possible (14 or 16 teams’ worth).  I prefer at least 20 years (some 500-600 teams).  And even at that, I would ONLY do it to separate C, IF, OF, 1B/DH.  I would NOT do it at a LF/CF/RF level.  No way.  I cannot have a case like in the 1950s where the hitting level of RF was lower than that of CF.  It was a blip that lasted several years.

***

More posts from me at Primer:

The defensive position adjustment really isn’t about an individual fielder’s ability to change positions. It’s about measuring the relative defensive talents among the positions.

Right.  As I keep saying, it’s Wins over Willie (WoW), or whatever composite player you want to come up with that is average in speed, strength, agility, etc, and has no experience leverage at any particular position.

***

I thought it was established that it was not linear, but rather exponential. It seems I have assumed more than the truth.

It is almost entirely linear.  Seeing that for the last 3 years in offseason signings, I’ve been able to link a free agent’s WAR to his actual salary on my blog, without bias to how high or low his WAR is, I challenge anyone to show me when a free agent’s salary is not linearly linked to his WAR.  These are minor exceptions, and not the rule.

(And don’t use WARP that has a too-low level of replacement level, which requires an exponential to undo the damage.  I.e., two wrongs makes a right.)

Despite’s Dan’s claim that Nate and I use the same WAR level, we do not.  As Sky showed citing his reference, Nate is using WARP.  And on my blog I showed how if you take Nate’s formula, and my formula, that we give out the same results for anyone at 1 or 1.5 WAR or above.  That is, for all players that have a chance to be a starter, Nate agrees that they are linearly linked all the way up to Pujols-level.  And for the guys who are bench players or worse, we have a slight disagreement.  While I would pay close to nothing for someone who us a -2.25 per 162G player, Nate would still pay him something.  Once Clay finally changes WARP, Nate’s going to have to change MORP, and guess what… it’s going to come out so close to linear, that to put a 1.05 or 1.1 exponent or something simply obscures that reality (especially since those guys will give a long-term discount to cancel that out!).  It’s linear, plain and simple.  Occam’s razor.

For arb-players, there’s an extra discount applied for long-term signings, over and beyond the fact that they are not free agents.

23/studes comes up with the right question:

“Am I right about this adjustment being a ‘fix’ to ‘plus/minus’ fielding systems?”

I wouldn’t use the word “fix”.

I would say that REGARDLESS of whether Moises Alou or Brian Giles plays LF or RF, their fielding value (runs saved above the average at his position, and the “raw” fielding difference between the average LF and average RF), should be close to the same whether they are LF or RF.

This is slightly less true between CF and corner OF.

This is a bit more than slightly less true between SS and 2B/3B.  (Jose Reyes at SS should have the same value if he’s at 2B or 3B… but not entirely… because at SS he gets more opps to display his fielding talents, he has more value there).

The 2B/3B is tougher.  So, instead of players actually moving, you have a constant player (Bloomquist, Figgins, Punto, Iwamura, etc) to compare against, to determine the baseline.

C can be considered its own position group, as the same for 1B/DH.

Tango:
I don’t think your points about differing mean levels of talent (e.g. 2B vs. 3B) is an argument against using replacement level offense to calculate PAs.

As for number of years, is there evidence of big anomalies at replacement level?  Did replacement level CFs outhit replacement LF/RFs in the 1950s?  If so, then I think you have a case.  But again, differences at the mean level aren’t an argument against a repl-level OPA approach.

I don’t even know what a “replacement level CF” is.

In hockey, would you have a “replacement level” left winger?  They are forwards.  Sorry, but this idea of calling someone a “replacement level CF” as something distinct from LF or RF isn’t reality.  Is Endy Chavez part of the LF, RF, or CF bench? 

If your premise starts with the idea that you have 8 positions distinct from each other, then I will have to disagree with even that.  If you can accept that we really have 4 position groups, then I can be on board with that discussion.

Tango:
Sorry, I’m not clear on your position.  You would consider using offense to set a general OF position value, compared to the other 3 groups, but then use defensive data to further adjust the value of CF vs. the corner positions?

That makes sense to me, when the quantity and quality of fielding data on positions switchers permits.  And that may well be the case in the OF.  I’m less confident about IF. 

But I don’t think it’s true that there’s no such thing as a replacement CF.  If you took all the non-starting OFs, I think you would find there is a large group who almost never play CF, and another group who play in CF with some frequency.  The former group are corner OFs, and I think we’d find they are offensively superior (in most years) to those who can play CF.  Don’t you agree?

You would consider using offense to set a general OF position value, compared to the other 3 groups, but then use defensive data to further adjust the value of CF vs. the corner positions?

Right.  That’s what the “offense position by decade” thread is about.

If you took all the non-starting OFs

Why would you take those guys out?  Don’t starting LF/RF play CF when the CF goes down?  Leaving those guys out, the starting 3, you will still find quite a bit of overlap in the bench players playing a corner OF and CF.

I think the point that teams actually pay 2Bs less than 3Bs is pretty important.  I’d like to a closer analysis (pro-rating arbitration salaries up to the free agent scale and ignoring pre-arb player), but it does show that MLB “knows” there’s more talent at 3B than 2B, and they don’t assume all positions have equal talent.  In fact, I’d love to see that same thing for all positions.

I would say it’s “somewhat” important, because of potential bias in evaluation of fielding.

If for example you find that CF are properly valued vis-a-vis LF/RF, then I think a comparison of 2B/3B/SS would be instructive.

I would not necessarily use the IF/OF valuation of MLB GMs to determine if they have that correct, though.

I know this is probably a beginner’s question for such an advanced discussion, but do all players get a position adjustment, no matter how well they perform offensively/defensively?

Jared--

Yes, they do.

Jared - basically, to know how replaceable a shortstop is, you want to compare a shortop’s offense to all the other shorstops, and his defense to all the other shortstops. There are some variations on the formula, which is why we have 45 posts and counting.

I have always assumed that teams pay the higher offensive positions more money than the lower ones, simply because they seem to value offense more than defense and more than defense implied by positional adjustments.  I have always said that corner outfielders and 1B get the most overpaid FA contracts (with no evidence). Maybe that is not true of catchers, SS, and CF, because of the old adage that “you need defense up the middle.” Anyone have average FA salaries or all salaries, adjusted for service time, for each position?

The 2007 Hardball Times Annual has that data, I believe.  Look for “Net Win Shares Value”.

In an older thread, MGL, I posted average FA and non-FA salary by position. I can’t remember which one ATM.

From this thread:

http://www.insidethebook.com/ee/index.php/site/comments/average_payroll_per_position/

POS FA salary players
2B F 1738118 640
P F 1769559 3895
LF F 1771917 536
C F 1966151 514
C T 2382242 591
CF F 2429511 877
RF F 2506405 427
2B T 2633676 826
1B F 3036402 1050
3B F 3361814 369
P T 3501708 4341
SS F 3566561 229
1B T 3748711 1257
SS T 3855324 263
CF T 3863925 651
LF T 4160572 569
3B T 4422071 213
RF T 4738349 416
DH F 5438879 199
DH T 6447661 348

And now, numbers for starters only:

POS FA salary players
2B F 2464515 340
C F 2631265 343
LF F 2766137 230
CF F 3490339 424
3B F 3504265 349
SS F 3580935 228
C T 3626764 304
RF F 3853779 213
SS T 3855324 263
2B T 4384358 328
3B T 4788818 193
1B F 4962055 403
LF T 6308026 220
DH F 6817210 103
CF T 6938114 245
RF T 7409503 183
1B T 8602027 286
DH T 8894423 150

Those are in 2007 “constant dollars,” indexed to baseball salary inflation. There’s a ton of other data in that thread as well.

I think the easiest way to put it is that defensive adjustments as a base make more sense because defense is more restrictive than offense.

To wit, premium defensive position players are often put at easier positions for their bat, yet we don’t often see it the other way around. Take Victor Martinez or Jorge Posada over the past two years, for instance—both moved from Catcher to 1B for their bats.

Offense is a fixed quantity. We can tell how many runs (give or take) a player will generate, and that is the same regardless of whether he’s behind the backstop in between at-bats, or sitting on the bench as the DH. While I’m sure an idiot sportswriter somewhere has said that player X plays better when he’s in the field as position Y, I don’t think there’s any support for that notion in a large enough sample size.

And therein lies the problem with using average offense at a position to determine defensive worth. A team could stick a high-offense player in a defensively challenging role (Derek Jeter?), and then to judge the quality of defense at that position because of those poor choices would simply compound the mistake.

It just makes more sense to compare defense by position as Tango does because it takes offense entirely out of the equation. It’s comparing apples to apples without being restricted to the whims of GMs and managers. Were Adam Dunn, Pat Burrell, Bobby Abreu and Manny Ramirez all to be hired as SS for NL teams this year, would the position suddenly become defensively easier?

Yes, we are aware of the drawbacks of using offense as the baseline for comparing players across positions.  We are also aware of the drawbacks of using fixed defensive adjustments which assumes that each position is exactly X (and Y, Z, etc.) harder or easier than any other position.  Two of the drawbacks are that we don’t know exactly what those numbers X, Y, Z, etc. are, and defensive positions are not exactly inter-changeable - i.e., we don’t know which ones are easier or harder than others to any degree of certainty.  These two drawbacks are related of course.

So, while you articulate one of the problems with using offense, there are problems on the other side of the coin as well.  Therefore, it is not clear, and it may never be, which one is better.  I say that it does not really matter and/or some combination is fine.  There simply is no precise, correct, or “right” answer, at least right now, so let’s not pretend that there is.

In any discussion or argument, just because one of two methods has some weaknesses, drawbacks, or what have you, certainly does not mean that the other method is correct, when that method has its own drawbacks and weaknesses as well.  That is the case here.

I’d have to disagree on this one. There are methods for comparing the same player at different positions, and while they aren’t perfect, are comparing a relatively known quality in condition A to a relatively known quality in condition B.

That makes it reasonable, in my mind (if not 100% accurate, which obviously defensive statistics aren’t close to yet) to draw a conclusion about the relationship between A and B especially as the sample size grows larger with every year of more comprehensive data.

While I agree that some conclusions can be drawn (particularly value-based conclusions) from offensive data and the pool of potential talent at a position, I think that, as has been pointed out in this thread, it is very easy to make gross errors because of poorly distributed samples of which there will be a lot.

Taking another sport into consideration, obviously the pool of Centers is going to be smaller than that of guards or forwards just because of body size. But I think it would be a gross mistake to say that the pool of people who can do it as a professional makes it the most difficult position. Obviously the value of the position increases because the supply is decreased, but that says little (nothing?) about the difficulty of the position.

For determining player value (which seems to be a key focus), I agree that offensive valuations could be just as helpful in the grand scheme of things so long as defensive capability is taken into account at some point down the line. But determining defensive ability at each position due to the potential talent pool strikes me as a bit off.

Ideally (and obviously this isn’t an ideal situation) we’d be able to bring up minor league players spending exactly half their time at each position and play exactly half their time in the majors at each to eliminate many of the problems. And ideally we’d get some players who can throw equally well with both arms so that we can test out some of the handedness comparisons.

But we can’t. So instead we have to deal with the information we have in order to determine what a position adjustment should be, and basing it off value rather than determining value from the positional adjustment strikes me as backwards.

If you’re a GM, the value matters. If you’re actually trying to determine defensive value/difficulty, then you have to look at defense itself.

Sal:  You’re underestimating the difficulties of making accurate defensive comparisons.  In the OF (CF vs the corners), we have pretty good data and I think most of us would be comfortable relying on a defensive adjustment.  But everywhere else, you face serious problems regarding sample size and selection bias.  Indeed, the variation in skills required is such that it may not even be meaningful to say one position is X runs more difficult to play.

On the other side, you’re underestimating the strength of the offensive approach.  It tells us EXACTLY what the price of defense is at each position, in offense gained or lost.  To obtain league-average defense at 2B, it costs 10 runs (or whatever).  That is the value of that defense in today’s game—it can’t have any more value than that if every team can acquire it at that price. 

Now, if baseball succeeds in pushing virtually every position player to play the most defensively valuable position he’s capable of playing, then offense gives us a perfect position adjustment.  But that may not be true.  Only then do we have any need at all to worry about the defensive data. 

And even if there are system-wide inefficiencies, the offensive adjustment arguably does measure player value well in today’s game, as it’s actually played.  Let’s say a couple of teams suddenly proved that MLB has been playing weaker hitters at C than they needed to—than many minor lg OFs and 1Bmen could play catcher well.  Soon other teams followed, and offensive performance at catcher rose to league average.  We would of course change our position adjustment going forward.  But should we go back and reduce our valuation of all catchers in the past by 20 runs per season?  I’m not sure we should.  In the game they played, league-average hitters at catcher was very valuable—they helped their teams win games against the oppoenents they faced (who were also playing weaker catchers than necessary).  So even if I concede that baseball may misallocate talent, if everyone does it I’m not sure it matters for our valuation of players.

I posted some tables at StatSoeak which use Marcel to track the positional wOBA over the years
http://statspeak.net/2008/12/batting-runs-above-position-1.html

So even if I concede that baseball may misallocate talent, if everyone does it I’m not sure it matters for our valuation of players.

You are still faced with the reality that MLB teams value 3B much more than they value 2B.

Now, you could argue that hitting is valued better than fielding is, but then, SS are also paid more than 2B.

So, this is similar (though not to the same degree) as to what you find in HS or College, or low A ball, and that is that SS and 3B are better overall players than 2B.

And, that while we HOPE that at the MLB level, there is enough equilibrium forces that would make 2B be a spot for quality players, the reality is that this is not the case.  At some point, we have to deal with reality, and not presume that every position must be equal, even at a long-term 10- or 20-yr period.

Brian’s post 54 keeps proving my point.  Look at how well the CF hitting was: better than RF!  And almost as good as 1B.

And not just for 1 year, but for a few years.

When you have Mays and Mantle et al all finding a home in CF, of course it’s going to make the offense at that position look great.  But this is completely and utterly irrelevant.  Just like in high school, your best hitter and best fielder will be at SS or 3B, you happen to have players who were stellar with the bat and the glove… where else to put them, but at CF?

You have to compare players to their pool of candidates.  This is true in baseball or in corporate America.  CF is not distinct from LF or RF as it is from Catcher.

I already showed in the other thread the enormous amount of time that CF play in the corners and vice-vera.  Model that reality.

It makes no sense at all for us to force in a model that makes things clean.  There won’t be a single GM that will listen to you try to explain that.  And he’d be right.  He’s going to ask: “Why are 2B paid 30% less than 3B”.  What will be our answer: “inefficiency in monetary valuation?”.  Why can’t he say: “Inefficiency in positioning allocation?”

The reality is that players are catchers, and if they can’t stick there, they find a home as infielders, outfielders or firstbasemen.  Players are infielders, and if they can’t stick there, they move to OF or 1B.  And players are outfielders, and if they can’t stick there, they move to 1B. Anyone else either plays 1B or DH. 

Are we going to ignore this reality?

Even if MLB was efficient, I’m not sure that we should necessarily expect equilibriums between all positions. Playing catcher leads to more injuries and a lot more wear and tear, so it’s rational for baseball decision makers to move their top offensive players away from the position.

I’m not sure if the data supports this, but there’s a lot of lip service paid to the idea that 2B is a dangerous position because they have to turn so many double plays. So, it makes sense that teams would choose to put their best players at other positions.

We should probably still expect something close to an equilibrium at the replacement level, but I don’t see why we should necessarily expect there to be an equal number of stars at each position, which will throw off the averages.

The reality is that players are catchers, and if they can’t stick there, they find a home as infielders, outfielders or firstbasemen.  Players are infielders, and if they can’t stick there, they move to OF or 1B.  And players are outfielders, and if they can’t stick there, they move to 1B. Anyone else either plays 1B or DH.

This is only the reality if a player can produce more offensively and defensively in total than other players already playing those positions, or can produce equally well for less money.  If not, the player is out of baseball, which is the more typical result.

Right, we need to compare to the replacement level.  But as I keep repeating, the replacement-level 2B and replacement-level SS come from the same pool of players. You simply cannot treat them as if they come from different pools.

No need to think that the gap between average and replacement is not only identical for each position, but that it’s identical every single year.  This is just a made-up idea to keep us from doing the hard work of modeling reality.

Peter/58: right, I agree with you.  The totality of his offense plus his defense is what counts.  Ozzie Smith, if he was pushed off SS/2B by better fielders (say Adam Everett and Pokey Reese in their primes), would have found a home in CF.  That’s only because the totality of his off+def would still be better than the Willie Bloomquist list.

As long as you can produce above the Willie line (or some composite player that looks alot like him) at one position, then you’re in the pool of MLB players.

Tango:
I don’t think anyone—anyone here, that is—is arguing that total value at each position must be identical.  But using replacement offensive production to estimate position value does not require one to assume that at all.  It only means that the difference between mean and replacement levels will differ by position, which is clearly often the case. 

You’re beating a dead straw man here (or something like that) ....

"But using replacement offensive production to estimate position value”

But again, are you presuming that LF is a “position” distinct from RF?

Unless the conversation occurs at “position pools”, I simply will continue to beat the horse beyond dead, until it’s disintegrated, if we continue to talk about “positions”.

No one talks about “replacement level” left wings and right wings in hockey, even though LW and RW move less between each other than LF and RF.  And they move even less between winger and center, and no one talks about “replacement level centers”.  They are all forwards.  The discussion has to start there.

Whoops...and I see my question about DPA and selective sampling, etc. was brought up in #33.

Okay, so I now get DPA and how that matches with a player’s offense and defensive runs above/below average to determine his dollar value. However, I am unsure of something on the offensive side.  Do we compare all players (whether they are OF, IF, C, etc.) to replacement level of 20 runs, -2 wins or is it better to break it into 4 position groups: 1) OF replacement level is used for all OF, C replacement level is used for all catchers, 3) 1B replacement level is used for all 1B, 4) SS/3B/2B replacement level is used for all SS/3B/2B.

This is the only part I’m confused about.  Thanks.

From what I’ve read in this thread it sounds like every position player is compared to (offensively) the same replacement level (which is what like - 2wins?).  Someone more qualified than myself may be able to answer that better though.

I should probably rename the metric from WAR to WOW (or WAW), as in Wins Over Willie.  This should make it crystal clear that we are comparing players to Willie Bloomquist.

Expanding on the concept of all players coming from the same pool, the fixing of positions tends to come rather late in player development—how many high school aces end up as position players, and vice versa? To suggest that we’re dealing with different pools of players for each position when the same pool of players is used for hitters and pitchers seems a bit off to me.