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## Saturday, December 20, 2008

#### Rob Neyer: Explaining some new math

As you know, I’ve been wrestling with this notion of positional adjustments, which on Thursday led to the following e-mail exchange with FanGraphs’ Eric Seidman …

Eric: Rob, I thought I would try to see if I could clarify the adjustments for you. Basically, it is all due to defense. Tom Tango likes to refer to the adjustments as “Runs Over Willie” (in honor of Willie Bloomquist, who can play everywhere). Essentially, the idea is that if you took Willie Bloomquist and put him anywhere on the field, what would an average fielder produce, runs-wise, compared to his production?

So, if you put Willie at 1B, the average 1B would cost his team 12.5 runs more than Willie. If you put Willie at shortstop, the average SS would save 7.5 runs more than Willie.

It’s really just a quantifiable way of showing which positions are the toughest to play. Catcher gets +12.5 runs because not everyone can play there. Shortstop gets +7.5 runs because it is the toughest non-catching position. Then comes 2B/3B/CF, at +2.5 runs apiece. LF/RF are docked -7.5 runs, and 1B docked -12.5 runs. Using these adjustments allows us to compare Carl Crawford in LF to Chase Utley at 2B.

If Crawford is +15 runs via UZR and Utley is +19 runs, it really isn’t as close as it seems, given that LF are docked -7.5 runs and 2B gain +2.5 runs. Before even factoring in offensive contribution or adding two wins (20 runs) to be above replacement level, Utley would be a +21.5 run defender, Crawford a +7.5 run defender.

Hope that makes some more sense. It is a very confusing concept, but basically it just allows us to make cross-positional comparisons so someone like Crawford doesn’t have an overstated defensive value.

Me: Is this a new thing? I don’t recall seeing any discussion of positional adjustments before the last couple of weeks. I’m just wondering if everything we thought we knew about player valuations have been wrong. Is Dave Concepcion worth more than we thought? Tony Perez less?

Eric: I wouldn’t necessarily call it two weeks new, but definitely new in the last year or two, as far as I know. Granted, I didn’t really “come onto the scene” until May 2007, but I can recall as far back as June 2007 reading Tango’s positional adjustment work.

I don’t think it means that everything we have already done is wrong, per se, because defensive stats weren’t really ever taken into account outside of Fielding Percentage for the longest time.

Huh, I didn’t realize that positional adjustments is considered so ‘new’.

Tripon Posted: December 20, 2008 at 05:01 AM | 301 comment(s) Login to Bookmark
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201. Tango Posted: December 21, 2008 at 03:00 PM (#3035189)
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).
202. Foghorn Leghorn Posted: December 21, 2008 at 03:27 PM (#3035206)
This method of value only works if we assume that every player has only one position, or at least that each player is being used optimally - and even then, concepts like "average hitting at LF" or "average fielding at SS" seem to at least bend, if not break, during the peaks of Bonds' or Ozzie Smith's career.
Colin, you are asserting this, but I don't see any reason this is true.
203. Foghorn Leghorn Posted: December 21, 2008 at 03:35 PM (#3035209)
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.
I don't get the significance of this. There is no rule that dictates which position players must hit higher than others. And as you correctly note:"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."

Right, but what's your question? Is Willie Mays' 1954 batting season more valuable in the 1954 NL or in the 1954 AL? More valuable in 1954 or 1922? OPD claims Mays is much more valuable in the 54 AL or 1922. Because the baseline is much lower.
204. Foghorn Leghorn Posted: December 21, 2008 at 03:36 PM (#3035210)
That wasn't the question I was asking. Again, I'm comparing players to a common baseline: Wins Over Willie (WoW for short).
205. Foghorn Leghorn Posted: December 21, 2008 at 03:40 PM (#3035211)
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.
I disagree with this. I suspect that the ratio of innings for a RF or LF (compared to the other position) is extremely high, and that most players are treated like that. Sure, a younger player may start his career as a RF and move to LF as his skills decline, but AFAICT, few players play LF one day and RF the next. And "regulars" never do.
206. Foghorn Leghorn Posted: December 21, 2008 at 03:44 PM (#3035212)
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.
I'm not sure they are.

Chris: Compares players to other players at his position, both at bat and afield
Tango: Compares all hitters to each other, fielders to other players at his position, and adds an adjustment factor for positional differences based on the average performance over (about) five years.

Does that accurately describe your position?
207. Ivan Grushenko of Hong Kong Posted: December 21, 2008 at 03:54 PM (#3035213)
Sure, a younger player may start his career as a RF and move to LF as his skills decline, but AFAICT, few players play LF one day and RF the next. And "regulars" never do.

There are exceptions to this though. Nick Swisher comes to mind.
208. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 03:57 PM (#3035214)
Okay, once more into the breach, dear fellows.

When you're putting a baseball team together, you don't try to find the best shortstop, center fielder, etc. You try to find the best starting eight you can, and then slot them into positions as best you can.

If the Braves already have a shortstop, why were they intersted in Furcal? Because they think they can put Furcal at second and their current second baseman in left field. This isn't exactly an unusual idea - teams move players to different positions all the time.

The problem is that there is an underlying bias to the data - we know that teams put their better middle infield defenders at SS, and then the next best at 2B/3B. In years where SS also happen to be worse hitters at the same rate they're better fielders, then everything works out.

We have a common baseline for offensive performance, because everybody can be compared to the league average hitter. What we want to establish is a similar common baseline for defense.

I guess I presume too much in saying "What we want," because it's possible that some of you don't want that. But it's difficult to confidently make the cross-positional comparison when you're not trying to establish the relative value of each position compared to the league average.
209. Mefisto Posted: December 21, 2008 at 03:59 PM (#3035215)
Chris, suppose you're advising the Mets GM. He comes to you and says that the Braves have offered to trade their average OPD 2B for your average OPD SS. The two players are the same age and have identical OPD for their career. Do you advise him to make the trade?
210. Foghorn Leghorn Posted: December 21, 2008 at 04:18 PM (#3035220)
If the Braves already have a shortstop, why were they intersted in Furcal? Because they think they can put Furcal at second and their current second baseman in left field. This isn't exactly an unusual idea - teams move players to different positions all the time.
So they could trade Escobar for Jake Peavy.
teams move players to different positions all the time.
Not really.
211. Foghorn Leghorn Posted: December 21, 2008 at 04:20 PM (#3035221)
Chris, suppose you're advising the Mets GM. He comes to you and says that the Braves have offered to trade their average OPD 2B for your average OPD SS. The two players are the same age and have identical OPD for their career. Do you advise him to make the trade?
The other factors outside of that matter more. If asked which improves the team more, the answer is neither.
212. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 04:25 PM (#3035224)
Players who were qualified starters in 2008 who played multiple positions:

"playerID" "Num"
"derosma01" "6"
"teahema01" "6"
"lopezfe01" "6"
"scutama01" "6"
"damonjo01" "4"
"dejesda01" "4"
"swishni01" "4"
"winnra01" "4"
"ramiral03" "4"
"keppije01" "4"
"blakeca01" "4"
"martiru01" "3"
"figgich01" "3"
"guilljo01" "3"
"blancgr01" "3"
"fukudko01" "3"
"hamiljo03" "3"
"kubelja01" "3"
"mclouna01" "3"
"peraljh01" "3"
"hannaja01" "3"
"riosal01" "3"
"suzukic01" "3"
"atkinga01" "3"
"cabremi01" "3"
"lewisfr02" "3"
"morame01" "3"
"pujolal01" "3"
"rossco01" "3"
"longoev01" "3"
"youkike01" "3"
"ellsbja01" "3"
"hernara02" "3"
"lopezjo01" "3"
"schumsk01" "3"
"ludwiry01" "3"
"griffke02" "3"
"huffau01" "3"
"custja01" "3"
"ibanera01" "2"
"sizemgr01" "2"
"uptonbj01" "2"
"mauerjo01" "2"
"penaca01" "2"
"soriaal01" "2"
"utleych01" "2"
"delgaca01" "2"
"reynoma01" "2"
"jacksco01" "2"
"sotoge01" "2"
"victosh01" "2"
"garkory01" "2"
"abreubo01" "2"
"jacobmi02" "2"
"braunry02" "2"
"millake01" "2"
"giambja01" "2"
"anderga01" "2"
"jeterde01" "2"
"suzukku01" "2"
"leede02" "2"
"gilesbr02" "2"
"rodrial01" "2"
"dyeje01" "2"
"molinbe01" "2"
"glaustr01" "2"
"bartoda02" "2"
"wrighda03" "2"
"jonesch06" "2"
"morneju01" "2"
"rowanaa01" "2"
"kempma01" "2"
"teixema01" "2"
"gordoal01" "2"
"sanchfr01" "2"
"beltrca01" "2"
"cantujo01" "2"
"ordonma01" "2"
"ramirar01" "2"
"howarry01" "2"
"berkmla01" "2"
"youngmi02" "2"
"ethiean01" "2"
"ramirha01" "2"
"scottlu01" "2"
"fieldpr01" "2"
"guerrvl01" "2"
"ramirma02" "2"
"hunteto01" "2"
"konerpa01" "2"

Same list, excluding DH:

"playerID" "Num"
"lopezfe01" "6"
"derosma01" "6"
"teahema01" "5"
"scutama01" "5"
"swishni01" "4"
"ramiral03" "4"
"keppije01" "4"
"blakeca01" "4"
"winnra01" "3"
"atkinga01" "3"
"lewisfr02" "3"
"youkike01" "3"
"rossco01" "3"
"ellsbja01" "3"
"schumsk01" "3"
"ludwiry01" "3"
"damonjo01" "3"
"blancgr01" "3"
"dejesda01" "3"
"mclouna01" "3"
"hannaja01" "2"
"gilesbr02" "2"
"cabremi01" "2"
"glaustr01" "2"
"pujolal01" "2"
"bartoda02" "2"
"morame01" "2"
"longoev01" "2"
"hernara02" "2"
"kempma01" "2"
"cantujo01" "2"
"lopezjo01" "2"
"ethiean01" "2"
"griffke02" "2"
"huffau01" "2"
"custja01" "2"
"utleych01" "2"
"martiru01" "2"
"figgich01" "2"
"guilljo01" "2"
"soriaal01" "2"
"victosh01" "2"
"reynoma01" "2"
"fukudko01" "2"
"peraljh01" "2"
"hamiljo03" "2"
"riosal01" "2"
"jacksco01" "2"
"suzukic01" "2"
"kubelja01" "2"

So, even excluding DH, that's 53 out of 149 qualified starters who played more than one position in 2008. Is that so rare?
213. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 04:31 PM (#3035228)
Since I have a feeling someone will ask, we'll limit it to players who START at a position:

"playerID" "Num"
"scutama01" "5"
"lopezfe01" "4"
"teahema01" "4"
"derosma01" "4"
"keppije01" "4"
"swishni01" "4"
"ellsbja01" "3"
"dejesda01" "3"
"blancgr01" "3"
"schumsk01" "3"
"ramiral03" "3"
"mclouna01" "3"
"ludwiry01" "3"
"rossco01" "3"
"lewisfr02" "3"
"winnra01" "3"
"lopezjo01" "2"
"kempma01" "2"
"hernara02" "2"
"martiru01" "2"
"suzukic01" "2"
"figgich01" "2"
"riosal01" "2"
"custja01" "2"
"hannaja01" "2"
"cabremi01" "2"
"victosh01" "2"
"utleych01" "2"
"fukudko01" "2"
"jacksco01" "2"
"damonjo01" "2"
"glaustr01" "2"
"blakeca01" "2"
"cantujo01" "2"
"kubelja01" "2"
"hamiljo03" "2"
"ethiean01" "2"
"griffke02" "2"
"youkike01" "2"
"longoev01" "2"
"peraljh01" "2"
"huffau01" "2"
"guilljo01" "2"
"atkinga01" "2"

Drops all the way to 47, again excluding the DH.
214. Foghorn Leghorn Posted: December 21, 2008 at 04:48 PM (#3035234)
Yes, that's an absolutely awful way to look at it. I see Evan Longoria on this list: Longoria played 9 innings at SS and 1046 at 3B. That's not a team that thinks he can play anywhere.
215. CrosbyBird Posted: December 21, 2008 at 04:50 PM (#3035237)
The thing is, some of those guys look much more versatile than they really were. Over 80% of Scutaro's innings in the field were at SS/2B; he's really a middle infielder and secondary 3B with a few random starts at other positions. Utley played about 1/100th of his innings at 1B and all the rest at 2B; his 14 innings will do practically nothing to change the average quality of NL 1B.
216. Foghorn Leghorn Posted: December 21, 2008 at 04:51 PM (#3035239)
Chase Utley - 1396 IP at 2B, 14 at 1B. No, he's a utility guy, not a second baseman. It's completely unfair to consider him as a 2B - his baseline should encompass the 8 ABs he made as a 1B. Come on, Colin.
217. CrosbyBird Posted: December 21, 2008 at 04:56 PM (#3035240)
The other factors outside of that matter more. If asked which improves the team more, the answer is neither.

I would have thought the Mets getting an average OPD 2B would improve their team more than the Braves getting an average OPD SS would for two reasons:

1) The Mets already have a plus SS so the average SS is of little value to them.
2) The Mets have a minus 2B so the average 2B is an improvement.

There appear to be fewer league-average 2B available right now in the NL as compared to league-average SS. If this is true, then all other things being equal, wouldn't a league-average 2B be more valuable than a league-average SS because of positional scarcity?
218. Mefisto Posted: December 21, 2008 at 05:02 PM (#3035244)

No, the Braves end up improved. They now have a SS, you don't. The Braves' GM will have an easier time finding a new 2B than you will have finding a new SS.

This example would be even more extreme if I had made the trade involve a SS and a 1B. By your logic, the trade would improve neither team, but in fact it would improve the team which acquired the SS.

Now, I suppose you could say that I'm getting into "other factors" at this point. In one sense that's fair, in another it's not; regardless, I'll accept that for the moment. What I'm arguing is that our economic system here -- the system of trade and value -- should internalize all costs. You want to externalize a particular cost (the cost of finding a new SS). That's a bad way to design a system. A good system internalizes ALL the costs and benefits; only one that does so will run most efficiently.
219. Tango Posted: December 21, 2008 at 05:03 PM (#3035245)
Chris/206: pretty much (as long as you qualify this: average performance as average fielding performance, which I think is implied or understood by you, and maybe not by a few others).

***

I agree that I wouldn't go with Colin's list. I'd look at guys over more than just one year, and look at those who played more than just one game, to come up with a list that shows that players are somewhat fluid. Teams think nothing of moving a LF to RF or vice-versa when contemplating trades or bringing up players.

I'd also say that since experience matters, and you want to keep your regulars happy, you don't move those guys around unless necessary. Mike Cameron, when faced with Beltran. If Punto was an average hitter, there's no question he would have found a home at one position, and not keep bouncing around. If Orlando Hudson hit as well as Punto, he would have played all 3 infield positions each year.
220. Foghorn Leghorn Posted: December 21, 2008 at 05:08 PM (#3035246)
No, the Braves end up improved. They now have a SS, you don't. The Braves' GM will have an easier time finding a new 2B than you will have finding a new SS.

This example would be even more extreme if I had made the trade involve a SS and a 1B. By your logic, the trade would improve neither team, but in fact it would improve the team which acquired the SS.

Now, I suppose you could say that I'm getting into "other factors" at this point. In one sense that's fair, in another it's not; regardless, I'll accept that for the moment. What I'm arguing is that our economic system here -- the system of trade and value -- should internalize all costs. You want to externalize a particular cost (the cost of finding a new SS). That's a bad way to design a system. A good system internalizes ALL the costs and benefits; only one that does so will run most efficiently.
Those are all comepletly outside factors by what occurs on the field. Those aren't about performance. You are certainly encompassing that. I get an average 2B, I move Jose Reyes from 2B to SS. The Mets get the better end of the deal. There is no "ceteris parabis".
221. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 05:09 PM (#3035247)
The only point I was trying to make was that players do move around, and not just utilty guys.

The point is not that these guys are versatile - quite the opposite! David DeJesus isn't more "versatile" because he can go over to play LF - any CF can. Nobody cares that Utley can play 1B because anybody can play 1B. A SS playing 2B? So what, they're both middle infield positions, same-same.

That's the point. 2B/SS and LF/CF/RF are not "different positions" in the way that, say, QB and WR are, and it doesn't make sense to have a value system that treats them that way.
222. Tango Posted: December 21, 2008 at 05:09 PM (#3035248)

No, the Braves end up improved. They now have a SS, you don't. The Braves' GM will have an easier time finding a new 2B than you will have finding a new SS.

Right. See, the problem here is that Chris constructed his metric to answer a specific question. We'd LIKE to be able to maybe apply that metric to other questions. But, there's no way you can do that with his metric.

I keep bringing up Giles: in 2003 he was in the NL as a LF, and in 2004 he was in the NL as a RF.

Under Chris' scenario, Giles' peers includes Bonds in 2003 and did not include Bonds in 2004. So, even if Giles hit exactly the same in the two years and fielded exactly the same, then he would look very different, simply because Chris has chosen two different peer groups for him.

Fine, if that's what Chris is trying to answer. But in no way can you take those results and then try to analyze whether the Padres should have traded for Giles from the Pirates in 2003, thinking that they can increase his value by moving him to RF, so that he won't be compared to Bonds. That Bonds is a LF, or in the NL, or that he even exists at all in 2003/04, is irrelevant to the discussion of Giles, vis-a-vis the rest of the players in the outfield in MLB.
223. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 05:10 PM (#3035249)
Those are all comepletly outside factors by what occurs on the field. Those aren't about performance.

I think the word you're looking for here is "value."
224. Foghorn Leghorn Posted: December 21, 2008 at 05:12 PM (#3035250)
Teams think nothing of moving a LF to RF or vice-versa when contemplating trades or bringing up players.
I disagree. If this were true we'd see more of it. The RF's arm is a large factor here, as well as his ability to make plays. There's is considerably more damage on a misplay in RF than there is in LF, and I believe they are treated as such.

I'll suggest that every team considering Manny is considering him for LF at most. I don't think the Cubs are thinking "We could sign Manny for RF".
225. Foghorn Leghorn Posted: December 21, 2008 at 05:13 PM (#3035251)
I think the word you're looking for here is "value."
So you think someone other than Pujols was the MVP last year? What does teh "V" in that stand for, and how do "we" feel it should be applied?
226. Foghorn Leghorn Posted: December 21, 2008 at 05:16 PM (#3035254)
Right. See, the problem here is that Chris constructed his metric to answer a specific question. We'd LIKE to be able to maybe apply that metric to other questions. But, there's no way you can do that with his metric.
This isn't true. Please stop asserting it. Ask me a specific question, and I'll answer it with my method.

The same is true for Mefisto's question and your method. Say the Yankees wanted to trade for a 3B, and they got the Rangers SS. What would he do at 3B?

Is the 1954 Willie Mays more valuable in the 1954 NL or AL? Or does he have the same value (as your method would indicate)?
227. Foghorn Leghorn Posted: December 21, 2008 at 05:17 PM (#3035255)
Under Chris' scenario, Giles' peers includes Bonds in 2003 and did not include Bonds in 2004. So, even if Giles hit exactly the same in the two years and fielded exactly the same, then he would look very different, simply because Chris has chosen two different peer groups for him.
because his on-field performance value *would* be different. Heck, if he could move to CF, he'd be more valuable, even by your method, wouldn't he?
228. Foghorn Leghorn Posted: December 21, 2008 at 05:18 PM (#3035257)
But in no way can you take those results and then try to analyze whether the Padres should have traded for Giles from the Pirates in 2003, thinking that they can increase his value by moving him to RF, so that he won't be compared to Bonds. That Bonds is a LF, or in the NL, or that he even exists at all in 2003/04, is irrelevant to the discussion of Giles, vis-a-vis the rest of the players in the outfield in MLB.
I flat-out disagree. I can certainly analyze that, and I just did so regarding Daniel Murphy moving to 2B for the Mets. Your claim is untrue.
229. CrosbyBird Posted: December 21, 2008 at 05:20 PM (#3035258)
2B/SS and LF/CF/RF are not "different positions" in the way that, say, QB and WR are, and it doesn't make sense to have a value system that treats them that way.

That's a gross generalization. In reality, most 2B wouldn't be as good defensively at SS, and there's no guarantee that a SS will improve defensively by moving to 2B. They really are different positions, with different skillsets, and different physical and mental challenges.

I can buy LF/RF being a position called "corner OF," but that's pretty much it in terms of truly interchangeable positions (other than any position and DH). A player might well have the athletic ability to play a capable CF but not the field presence to be the leader in the OF.
230. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 05:30 PM (#3035261)
I disagree. If this were true we'd see more of it. The RF's arm is a large factor here, as well as his ability to make plays. There's is considerably more damage on a misplay in RF than there is in LF, and I believe they are treated as such.

But this is true whether or not the average LF or the average RF hits better that season.

Teams will take their two corner OFers and generally try to put the best arm and better fielder in RF. If this season those better fielders are also the better hitters among corner outfielders, a metric like OPD will underrate the RF and overrate the LF.
231. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 05:32 PM (#3035263)
In reality, most 2B wouldn't be as good defensively at SS.

And this is true even if 2B are also worse hitters than SS that season.
232. The District Attorney Posted: December 21, 2008 at 05:35 PM (#3035265)
Chris, you said the difference between batting order positions and fielding positions is that fielding positions require a set of skills and batting order positions do not. (Which obviously is not true in its most extreme form, but let's pass on that, as I do agree you could bat best-to-worst 1-9 and it wouldn't make all that much difference.)

Well, Chase Utley has the skills to play 1B. Whether he actually did so in '08 or not is a red herring IMO, and I wish people would get off that. He could have done it, and the Phils thus could have replaced Howard with a 2B. They could not have replaced Utley with a 1B.

I don't see how Utley's ability to play 1B is less relevant to the evaluation of Howard than Lance Berkman¹'s ability to play 1B.

To deny that is basically to deny the defensive spectrum as a concept. "But Alex Rodriguez was a better SS than 3B!" doesn't get you there.

No one can seriously think that playing 2B requires "second base skills" that only the guys who are currently regular 2B have. So, how does this make sense?

¹ recently converted from the OF...
233. Foghorn Leghorn Posted: December 21, 2008 at 05:39 PM (#3035266)
Well, Chase Utley has the skills to play 1B. Whether he actually did so in '08 or not is a red herring IMO, and I wish people would get off that. He could have done it, and the Phils thus could have replaced Howard with a 2B. They could not have replaced Utley with a 1B.

I don't see how Utley's ability to play 1B is less relevant to the evaluation of Howard than Lance Berkman¹'s ability to play 1B.

To deny that is basically to deny the defensive spectrum as a concept. "But Alex Rodriguez was a better SS than 3B!" doesn't get you there.

No one can seriously think that playing 2B requires "second base skills" that only the guys who are currently regular 2B have. So, how does this make sense?
I don't know where I am losing you, but none of that in anyway is involved in any of my claims. Yes, tehre is a defensive spectrum. You are only the position player of the position you play though. Chase Utley *DID NOT* play 1B. He's anot a 1B. He IS NOT in the pool for 1B replacement players. I don't think ANYONE includes him in their RL value. Does anyone?
234. Foghorn Leghorn Posted: December 21, 2008 at 05:41 PM (#3035268)
Teams will take their two corner OFers and generally try to put the best arm and better fielder in RF. If this season those better fielders are also the better hitters among corner outfielders, a metric like OPD will underrate the RF and overrate the LF.
Repeating a claim like that doesn't make it true. It does no such thing.

Is Willie Mays more valuable in teh 1954 NL or the 1954 AL? Or, as you would have me believe, the same value?
235. David Concepcion de la Desviacion Estandar (Dan R) Posted: December 21, 2008 at 05:41 PM (#3035269)
Is the 1954 Willie Mays more valuable in the 1954 NL or AL? Or does he have the same value (as your method would indicate)?

Of course he has the same value, so long as AL and NL teams have access to the same pool of replacement players...
236. Foghorn Leghorn Posted: December 21, 2008 at 05:41 PM (#3035270)
And this is true even if 2B are also worse hitters than SS that season.
And that doesn't matter. What matters is what he does on the field relative to what his opponents put on the field.
237. Foghorn Leghorn Posted: December 21, 2008 at 05:44 PM (#3035271)
Of course he has the same value, so long as AL and NL teams have access to the same pool of replacement players...
He has the same *raw* value, but his relative value is greater.
238. Erik, Pinch-Commenter Posted: December 21, 2008 at 05:51 PM (#3035277)
Whoa, wait a minute. This is making an enormous assumption that I don't necessarily buy. It could well be that there's something physiological that causes more or less variance in the defensive play at a single position, or that causes one position to be harder (this is basically true prima facie.) You're assuming that the entire equation is in the control of the GM and manager.

What I mean is that the total offense plus defense value over the history of the game at the professional level should be fairly similar at each position. Of course there is always the GM miscalculation factor, but over time this should even out. If a position is of little defensive value over time teams will adjust by adding more offense. If a position is of high defensive value teams adjust in the opposite direction. There is no reason to think that leftfielders on average, are lesser players than third basemen, or that first basemen are lesser players than shortstops or whatever. Each position simply represents a different balance of offensive value and defensive value.
239. The District Attorney Posted: December 21, 2008 at 05:53 PM (#3035280)
I don't know where I am losing you, but none of that in anyway is involved in any of my claims. Yes, tehre is a defensive spectrum. You are only the position player of the position you play though. Chase Utley *DID NOT* play 1B. He's anot a 1B. He IS NOT in the pool for 1B replacement players. I don't think ANYONE includes him in their RL value. Does anyone?
Well, what is the practical difference between increasing the level of the guys to whom Howard is being compared in order to reflect the fact that Utley and other 2B could have replaced him, and giving the 2B Utley an "after the fact" bonus relative to Howard for the same reason? (That's a legitimately-wanting-to-know question, not a gotcha question.)
240. Foghorn Leghorn Posted: December 21, 2008 at 05:55 PM (#3035282)
That's the point. 2B/SS and LF/CF/RF are not "different positions" in the way that, say, QB and WR are, and it doesn't make sense to have a value system that treats them that way.
Are QB and RB different positions? Aren't all these lines blurred at the "it happened once" level?
241. fret Posted: December 21, 2008 at 05:58 PM (#3035287)

Blackadder/197: Thanks for letting me know. In that case the gap between average production for 2B and 3B has more to do with a "star glut" at 3B, per Dimino, than anything else.

Jeff/198: I don't think you should know me. I'm a long-time lurker, posted occasionally in the past, these days more often. Twice I solved your diff-eq problems in the Lounge.

Well, no, not really. The reason you prefer the jump from 200 to 190 is that it's a harder jump to make. It's more of an outlier, it's more standard deviations away from the median, however you want to put it. If we assume a normal distribution of performance, 200 to 190 is a more valuable difference than 110 to 100. That's why teams pay more for it, which is reflected in \$/Wins Added, which is not the same causality model. Your progression is akin to paying for the cart with the horse.

I still hold to my previous position. Teams don't want standard deviations, they want wins. I'll expand on this later when I have more time.

I haven't seen this discussion, but on face, I'd have to agree with Tango, assuming the disagreement is whether higher \$/WA is equivalent to equal \$/WA for more years. For one, even if you purposefully machined the contract to do this, discount rates will vary in the real world, and you'd never hit it on the nose.

I wasn't clear. Tango says that the market is basically linear: a 4 WAR player gets paid twice as much as a 2 WAR player. I think that isn't true, and teams consider the 4 WAR player to be worth more than twice as much. The reason we can't get a handle on it is that we aren't good at comparing contracts of different length. I agree with what you said about discount rates etc.

Regardless, no offense intended in my second answer. You never know with unfamiliar handles around here how versed that person is in stats. Or anything, really. :) I'm certainly no maven, myself.

None taken, and I'm no maven either. Better with pure math than stats.
242. Gaelan Posted: December 21, 2008 at 06:01 PM (#3035291)
I've avoided posting in this thread since it has been remarkably polite and I'm incapable of politeness in the face of obstinance. So I'll just say that I think what Tango is doing is brilliant and I completely agree.
243. Foghorn Leghorn Posted: December 21, 2008 at 06:04 PM (#3035292)
Well, what is the practical difference between increasing the level of the guys to whom Howard is being compared in order to reflect the fact that Utley and other 2B could have replaced him, and giving the 2B Utley an "after the fact" bonus relative to Howard for the same reason? (That's a legitimately-wanting-to-know question, not a gotcha question.)
I might be getting you - there isn't anything wrong with an "after the fact" adjustment. That's just the math in a different order. But there's this static-ness that I disagree with. 1B in the AL in 2008 were terrible. It would be a big advantage to pick up a good hitting 1B in the AL. Here are park-adjusted runs created (XR) using 465 outs by position in 2008.
``` Pos    AL    NLC    71.8    73.11B    91.6    100.52B    85.5    81.23B    83.7    88.8SS    70.7    77.9LF    87.5    93.8CF    87.9    85.8RF    90.5    92.3  ```
In the AL, 2B out-produced 3B. That devalues a team's advantage. If I have a 2B that hits OPS+ 110, and then everyone goes out and gets one, so that everyone has a 110 OPS+ 2B, well, having a 110 OPS+ 2B isn't an advantage. Everyone has one. It's the new norm.
244. Mefisto Posted: December 21, 2008 at 06:04 PM (#3035293)
Those are all comepletly outside factors by what occurs on the field. Those aren't about performance. You are certainly encompassing that. I get an average 2B, I move Jose Reyes from 2B to SS. The Mets get the better end of the deal. There is no "ceteris parabis".

This is both right in the specific case and wrong in general.

What Tango's approach does is allow us to answer the question "on average, what is the cost of finding a replacement level defensive player at position X compared to the cost of finding one at position Y?". When I said the GM would have a harder time finding a replacement SS, that's what I meant. A good market system will be constructed to answer that question on average.

Now, market systems don't claim to be perfect, they claim to be efficient. That means there can be specific cases, such as having Jose Reyes at 2B, when a team is not average. A good GM will recognize those inefficiencies and exploit them. But most cases won't be clear cut like that -- my example was intended to be general, not to bring in the specific case of Reyes -- and a GM wants to know the average answer.
245. Foghorn Leghorn Posted: December 21, 2008 at 06:05 PM (#3035294)
I've avoided posting in this thread since it has been remarkably polite and I'm incapable of politeness in the face of obstinance. So I'll just say that I think what Tango is doing is brilliant and I completely agree.
Thank you.
246. Foghorn Leghorn Posted: December 21, 2008 at 06:07 PM (#3035296)
and a GM wants to know the average answer.
What does the average 2B hit (in Tango's system)? How does the GM know this?
247. Gaelan Posted: December 21, 2008 at 06:08 PM (#3035297)
Thank you.

In fairness I also think what you are doing is smart but I just can't buy into the fundamental premise that secondbaseman should be compared to secondbaseman on offense when no one hits as a secondbaseman.
248. Foghorn Leghorn Posted: December 21, 2008 at 06:11 PM (#3035301)
but I just can't buy into the fundamental premise that secondbaseman should be compared to secondbaseman on offense when no one hits as a secondbaseman.
That is essentially the core of the differences. I think they do hit as 2B. Because you have to play the field. You don't have 9 hitters and 9 fielders. Each hitter has to assume a defensive responsibility (leaving aside the traveshamockery that is the DH).

But I don't find that difference of opinion "obstinance".
249. Tango Posted: December 21, 2008 at 06:11 PM (#3035302)
But, there's no way you can do that with his metric.

When I said that, I meant in the context of trying to answer the trade question.

***

Chris' metric is designed to answer a specific question. Indeed, he asserts it most recently right here when discussing moving Mays between leagues:

He has the same *raw* value, but his relative value is greater.

So, Mays is less above average in the Willie/Mickey/Duke league than in a typical league of typical CF.

But, when constructing lists, it doesn't help to force the issue that the NL 2B = NL RF, each and every year. The baseline for each position is different.

This would be similar to plus/minus in hockey. All the players on the great team as pluses, while all the players, no matter how good, on the bad team are minuses or close to it. You can't then list the plus/minus figures in one list, because people will think this is an apples-to-apples comparison. But it's not.

If Chris agrees that Mays' "raw" value is the same regardless of the league, then it doesn't help to show he's +30 in the NL and +35 in the AL, or that he's +30 if he's CF and +33 if his equivalent is a RF.
250. Foghorn Leghorn Posted: December 21, 2008 at 06:16 PM (#3035304)
If Chris agrees that Mays' "raw" value is the same regardless of the league, then it doesn't help to show he's +30 in the NL and +35 in the AL, or that he's +30 if he's CF and +33 if his equivalent is a RF.
It doesn't help *what*? By "raw value", I mean the math that calculates how many runs he saved or generated. That number doesn't change.
251. Erik, Pinch-Commenter Posted: December 21, 2008 at 06:17 PM (#3035305)
Of course he has the same value, so long as AL and NL teams have access to the same pool of replacement players...

He has the same *raw* value, but his relative value is greater.

The player leads his team to the same number of wins within the season either way, AL or NL. Now his value as a commodity would reduced due to a glut of good players at the time but this is a factor that would affect all players in both leagues, not just one league vs the other. Still the player is creating the same number of REAL WINS in both environments. His value on the field is the same in both leagues, and his value in the market is the same to both leagues.
252. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 06:17 PM (#3035306)
In the AL, 2B out-produced 3B. That devalues a team's advantage. If I have a 2B that hits OPS+ 110, and then everyone goes out and gets one, so that everyone has a 110 OPS+ 2B, well, having a 110 OPS+ 2B isn't an advantage. Everyone has one. It's the new norm.

Yes, but (after the advent of free agency) everyone is pulling from the same pool of 2B - everyone has the same draft and the same free agent pool, and everyone can trade with each other. This is a matter of where you're choosing to draw the lines.
253. JoeD has the Imperial March Stuck in His Head Posted: December 21, 2008 at 06:26 PM (#3035312)
Well, no, not really. The reason you prefer the jump from 200 to 190 is that it's a harder jump to make. It's more of an outlier, it's more standard deviations away from the median, however you want to put it. If we assume a normal distribution of performance, 200 to 190 is a more valuable difference than 110 to 100. That's why teams pay more for it, which is reflected in \$/Wins Added, which is not the same causality model. Your progression is akin to paying for the cart with the horse.

I still hold to my previous position. Teams don't want standard deviations, they want wins. I'll expand on this later when I have more time.

For pitchers the opposite is definitely true.

100 ---> 110 is much, much more important than say 250 ---> 260.

League average 4.50 R/9 IP.

Pitcher A - Allows 100 runs in 240 IP = 120 RA+
Pitcher B - Allows 90 runs in 240 IP = 133 RA+
Pitcher C - Allows 80 runs in 240 IP = 150 RA+
Pitcher D - Allows 70 runs in 240 IP = 171 RA+
Pitcher E - Allows 60 runs in 240 IP = 200 RA+

Notice the gaps in ERA+ get bigger and bigger, but each pitcher saves just 10 runs more than the previous one.

I'm not sure if OPS+ works the same way, it's kind of a complicated calc that I'm having trouble wrapping my brain around right now. But if it does, 190 -> 200 provides less value than 100 -> 110.
254. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 06:30 PM (#3035313)
This just occured to me.

Because each team has to field a person at each position. There is no position of "hitter" (in the NL). For the Marlins to maximize their wins, they need to outperform their opponents at as many positions as possible. Dan Uggla then needs to outperform NL 2B. His teammate Hanley Ramirez needs to outperform NL SS. The Marlins do not compete with teh AL teams (directly), and only face themin the playoffs in a short series. So, that's why Uggla only needs to outperform NL 2B. Obviusly, the Marlins need the total offense plus defense (OPD) to surpass the other teams, and it doesn't matter if that is done by Uggla or some other combination, but to identify Uggla's value to the Marlins, his performance is weighed by how he did compared to the Marlins competitors, and how they did with their 2Bs.

Given this explanation, isn't the logical extension of this line of thiking to compare a player's performance to that of the opposing team's 2B/SS/etc., depending on where he played? If the Mets play the Phillies, and Reyes produces .5 more runs than Rollins in that game, does it matter - given the logic above - how well Tulo or Greene did that day?
255. Tango Posted: December 21, 2008 at 06:31 PM (#3035314)
Joe: you are the 1,003,343rd person to fall into the ERA+ trap. Please, Sean Forman, stop the insanity, and calculate ERA+ the correct way so that we don't have smart people like Joe making mistakes like this.

Joe: calculate it as 100/ERA+.
256. JoeD has the Imperial March Stuck in His Head Posted: December 21, 2008 at 06:34 PM (#3035315)
But Jeff wasn't calculating it the way when you just said to when he said 190 -> 200 is more valuable than 100 -> 110, was he?

I'm sure you're right, but can you explain a little further?
257. JoeD has the Imperial March Stuck in His Head Posted: December 21, 2008 at 06:37 PM (#3035319)
Joe: calculate it as 100/ERA+.

Pitcher A - Allows 100 runs in 240 IP = 120 RA+
Pitcher B - Allows 90 runs in 240 IP = 133 RA+
Pitcher C - Allows 80 runs in 240 IP = 150 RA+
Pitcher D - Allows 70 runs in 240 IP = 171 RA+
Pitcher E - Allows 60 runs in 240 IP = 200 RA+

So they become:

A = 100/120 = .83
B = 100/133 = .75
C = 100/150 = .67
D = 100/171 = .58
E = 100/200 = .50

So the differences are all the same, and lower is better. This is good and the numbers are directly comparable which is good.

I'm still not sure I see how this applies to Jeff's comment.
258. Rally Posted: December 21, 2008 at 06:42 PM (#3035321)
"Sure, a younger player may start his career as a RF and move to LF as his skills decline, but AFAICT, few players play LF one day and RF the next. And "regulars" never do."

That's not right. We can find many examples of regulars who moved between left and right, and even center. And I'm not talking about late career moves to an easier position, like Puckett and Murphy going to right.

Brian Giles played mostly left in Pittsburgh, he goes to San Diego towards the latter part of his career, and he's a rightfielder. Delmon Young moved to left when he went to Minnesota. Garret Anderson started in left, went to right for season, and played a few years in center before going back to left. Then he played another year in center and returned to left.

The players do this because of changing circumstances on their teams, either somebody gets hurt, free agents are signed, or trades change the composition of the roster.
259. JoeD has the Imperial March Stuck in His Head Posted: December 21, 2008 at 06:43 PM (#3035323)
Taking it one step further using pythaganpat:

Pitcher A = .583 WPCT
Pitcher B = .627 WPCT (+.44)
Pitcher C = .673 WPCT (+.46)
Pitcher D = .720 WPCT (+.47)
Pitcher E = .768 WPCT (+.48)

Each 10 runs provides slightly more WPct value, but that's just because the run environment is being lowered. For offense, I imagine the effect would be the opposite, each marginal run would provide slightly less win value that last, because the offensive environment (and pythaganpat exponent) are being increased.
260. JoeD has the Imperial March Stuck in His Head Posted: December 21, 2008 at 06:45 PM (#3035324)
"Sure, a younger player may start his career as a RF and move to LF as his skills decline, but AFAICT, few players play LF one day and RF the next. And "regulars" never do."

That's not right. We can find many examples of regulars who moved between left and right, and even center. And I'm not talking about late career moves to an easier position, like Puckett and Murphy going to right.

Brian Giles played mostly left in Pittsburgh, he goes to San Diego towards the latter part of his career, and he's a rightfielder. Delmon Young moved to left when he went to Minnesota. Garret Anderson started in left, went to right for season, and played a few years in center before going back to left. Then he played another year in center and returned to left.

The players do this because of changing circumstances on their teams, either somebody gets hurt, free agents are signed, or trades change the composition of the roster.

This isn't new, Babe Ruth played 1131 games in RF and 1057 in LF. Heck, he was split just about every season.

He and Bob Meusel were switched from game to game. Both split time every season from 1922 on.
261. Harold can be a fun sponge Posted: December 21, 2008 at 06:54 PM (#3035327)
Joe: you are the 1,003,343rd person to fall into the ERA+ trap. Please, Sean Forman, stop the insanity, and calculate ERA+ the correct way so that we don't have smart people like Joe making mistakes like this.

Agreed about ERA+. People assume it behaves like most stats, that it's denominated in innings. So they conclude that it can be averaged simply, that the 15-point differences between 100 vs. 115 and 150 vs. 165 denote the same differences in run, etc. I don't really blame people for this, but ERA+ (and RA+) don't work that way; they're "uspide down", denominated in ER (or R), rather than IP.
262. JoeD has the Imperial March Stuck in His Head Posted: December 21, 2008 at 07:11 PM (#3035334)
I would add I still don't see how I was making a mistake - I pointed out that 10 points of ERA+ aren't created equal, right?
263. Mefisto Posted: December 21, 2008 at 07:33 PM (#3035346)
What does the average 2B hit (in Tango's system)? How does the GM know this?

It doesn't matter. In Tango's system (he can correct me if I'm wrong), the GM would add up the offensive value and defensive value (including the relative positional value) of each player. That tells him that X, his 2B, is giving him more value than Y, his 1B, even though Y hits better. That's a handy thing to know because now he can dangle that 1B and his fancy hitting performance in front of Dumbass GM and get, say, a good CF (having, of course, compared that CF to his 1B).

Nobody wants to know how his 2B compares to other 2B, except in odd cases. What he wants to know is whether player X is better than player Y (a judgment which is complicated because there are so many variables).
264. Jeff K. Posted: December 21, 2008 at 07:45 PM (#3035350)
But Jeff wasn't calculating it the way when you just said to when he said 190 -> 200 is more valuable than 100 -> 110, was he?

Lots of catching up to do. Christ you people are busy. To start with this here, Jeff did not calculate it the way Tango said, because Jeff said OPS+, not ERA+.

Glad to see we're on the same page generally (shut up Harold, we just had this discussion.) So, you are also falling into the trap that others have been, mixing production and value. I said from the beginning that we were talking about 200 to 190 and 110 to 100 as being the same in production while not the same in value. You've proved to yourself that they're the same in production. The value comes not in Pythagenport, but intrinsically due to roster limits. We discuss this every offseason. Assuming that replacement level is freely available and that there is a non-zero chance of a guy being signed turning out above replacement level, one +30 guy is better and more valuable than three +10 guys. Because you have two roster spots that will at worst give you zero and may give you more than that.

I'm going to use this analogy and then probably watch it fail: just as someone like Saberhagen gets a bonus when considering "pennants added" because all else equal, concentrating value is likely to be beneficial, so too does concentrating value in one guy rather than three provide a bonus.
265. snapper (history's 42nd greatest monster) Posted: December 21, 2008 at 08:16 PM (#3035357)
Assuming that replacement level is freely available and that there is a non-zero chance of a guy being signed turning out above replacement level, one +30 guy is better and more valuable than three +10 guys.

But, that's only vs. replacement value, correct?

Vs. average, 3 +10 guys are worth a lot more than a +30 guy, or another way, 3 110 OPS+ hitters are worth more than 1 130 OPS+ hitter, b/c there's a ton of value in being average.
266. David Concepcion de la Desviacion Estandar (Dan R) Posted: December 21, 2008 at 08:48 PM (#3035366)
Jeff K., no, that's not right, because replacement level isn't a floor, it's an average of replacement players. Some replacement players will be better than the replacement player average (which we call replacement level), others will be below it. Below-replacement performances happen all the time--Nick Punto in 2007 or Cristián Guzman in 2005 leap to mind, not to mention the worst performances by true replacement players (e.g. Randall Simon hitting .188/.266/.266 in 214 PA as a first baseman in 2004, or Hideo Nomo tossing 101 innings of 60 ERA+ ball in 2005 after throwing 84 IP at a 50 ERA+ the year before). There is indeed a non-zero chance of a guy being signed turning out above replacement level, but there is just as high of a chance he will be below replacement level. For every 2007 Carlos Peña, there is a 2004 Randall Simon.
267.  Posted: December 21, 2008 at 08:49 PM (#3035367)
Nobody wants to know how his 2B compares to other 2B, except in odd cases. What he wants to know is whether player X is better than player Y (a judgment which is complicated because there are so many variables).

Right - with one of those variables being the ability to play a more demanding defensive position.

-- MWE
268. Chris Dial Posted: December 21, 2008 at 09:03 PM (#3035372)
Nobody wants to know how his 2B compares to other 2B, except in odd cases.
The odd case of every seasonal MVP vote. It's a VERY common discussion. I see it about every FA signing.

Every one that cites Chase Utley talks about how much he hits "for a second baseman". Everyone. His value is "as a second baseman".
269. Chris Dial Posted: December 21, 2008 at 09:10 PM (#3035375)
Brian Giles played mostly left in Pittsburgh, he goes to San Diego towards the latter part of his career, and he's a rightfielder. Delmon Young moved to left when he went to Minnesota. Garret Anderson started in left, went to right for season, and played a few years in center before going back to left. Then he played another year in center and returned to left.
They sometimes do play where their team needs them, but you cite rarities, not common occurrences. Yes, some versatile players do move, but most do not. For instance, the "go to" player for this is on the verge of retirement.

And even then, Giles is more valuable the further up he moves on the defensive spectrum. And that increase in value (which Tango adds statically after the fact, and I add in season dynamically) is evident in both systems. OPD measures based on that seasonal performance, while Tango's does not.
270. Chris Dial Posted: December 21, 2008 at 09:13 PM (#3035377)
Given this explanation, isn't the logical extension of this line of thiking to compare a player's performance to that of the opposing team's 2B/SS/etc., depending on where he played? If the Mets play the Phillies, and Reyes produces .5 more runs than Rollins in that game, does it matter - given the logic above - how well Tulo or Greene did that day?
Because the Mets compete with those teams for the playoffs.
271. Jeff K. Posted: December 21, 2008 at 09:15 PM (#3035378)
Vs. average, 3 +10 guys are worth a lot more than a +30 guy, or another way, 3 110 OPS+ hitters are worth more than 1 130 OPS+ hitter, b/c there's a ton of value in being average.

Good point, to be sure no one forgets that.

Jeff K., no, that's not right, because replacement level isn't a floor, it's an average of replacement players.

All true and perhaps I was a bit too strident and exact, but the case remains. The EV of starting a replacement player is 0, definitionally, almost. What's more, any extended performance below RL is the fault of the GM and manager. I would not have a problem throwing those out of the equation even if it meant the valuation wasn't perfect. I'd rather not, but I could see a reason to.

A +30 player is more valuable than 3 +10 players. Teams will pay for that concentration. They will pay more, marginally, for each additional win because each one makes other players capable of the same production (and hence competing for the same dollars, taking into account Colin's excellent points on the subject)less likely. The existence of a Guzman 2005 does mitigate the impact of my point a smidge, but that's all it is, a smidge. The effects of roster limits and the # of players who can be in the field/lineup simultaneously have a significant impact on the valuation of top-tier talent.
272. Chris Dial Posted: December 21, 2008 at 09:17 PM (#3035379)
MEfisto, I appreciate your hypothetical, but let's talk about application. Have you read my "Keystone Options" piece? In teh comments I use it to assess where Murphy will end up. I don't think it's necessarily accurate to say "Murphy is an Avg LF, so he's a -5 2B." The real possibility is he cannot play the position at all.
273. Jeff K. Posted: December 21, 2008 at 09:17 PM (#3035380)
His value is "as a second baseman".

I've skimmed a lot of this back and forth, so forgive me and ignore me if I'm interceding with redundant or useless points, but would it make the two sides come closer to agreement if you changed that to "His value is 'as a player capable of playing second base at or above replacement level, purely defensively speaking'"?
274. Mefisto Posted: December 21, 2008 at 09:18 PM (#3035382)
Right - with one of those variables being the ability to play a more demanding defensive position.

Exactly.

The odd case of every seasonal MVP vote.

You lost me here. MVP voting is, like historical comparisons, one of the places where Tango's approach is clearly more useful. MVP voters are trying to decide how valuable a player's offensive and defensive contributions are compared to players at different positions. The ability to play a more demanding position is a key factor, and Tango is telling us how much that's worth.
275. Mefisto Posted: December 21, 2008 at 09:22 PM (#3035383)
MEfisto, I appreciate your hypothetical, but let's talk about application. Have you read my "Keystone Options" piece? In teh comments I use it to assess where Murphy will end up. I don't think it's necessarily accurate to say "Murphy is an Avg LF, so he's a -5 2B." The real possibility is he cannot play the position at all.

However, the fact that Murphy can't play 2B isn't really relevant. Tango's not really saying he can or should. What he is telling us is how much harder on average it is to find an actual replacement 2B. I'd want to know that before I traded my 2B for a LF.
276. JoeD has the Imperial March Stuck in His Head Posted: December 21, 2008 at 09:25 PM (#3035384)
But if teams are paying more for it, then it's priced into the market, and it removes that player's added value, right?

So then we are right back to the production being equal. The concentration would only be of additional value to a team if they didn't have to pay for it. Perhaps I'm missing something though.

I don't think it's the same as Pennants Added. The concentration of wins is important in Pennants Added because adding a 10 win player to an 81 win team has more than 2x the chance of getting a team into a post season than adding a 5 win player over two years does. 91 and 81 wins back to back years will make the post-season more often than 86 and 86 wins will, on average. 96 and 86 makes more postseasons than 91 and 91, if you start with an 86 win team, etc.. I don't know that this applies to roster construction, especially if it's priced into the market anyway.

I would add that this 'peak' value is not nearly as important as most think, pennants added shows 10+0 being 11-12% more valuable than 5+5, IIRC).

Borrowing from James example in The Politics of Glory, Carlton > Sutton; Drysdale > Pappas; but Sutton > Drysdale.
277. Chris Dial Posted: December 21, 2008 at 09:28 PM (#3035386)
where Tango's approach is clearly more useful. MVP voters are trying to decide how valuable a player's offensive and defensive contributions are compared to players at different positions. The ability to play a more demanding position is a key factor, and Tango is telling us how much that's worth.
And I disagree because his values aren't accurate for a particular season. They are way off for 2008.
278. Chris Dial Posted: December 21, 2008 at 09:35 PM (#3035387)
Mefisto,
here is where OPD describes the alternatives, including psoitional movement. I disagree with the basic positional values. It assumes too much. Better, I think the scouting evaluation of a player has a better chance of identifying a fielder's ability to change positions (at all) than the adjustment Tango proffers.
279. SkyKing162 Posted: December 21, 2008 at 09:39 PM (#3035391)
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.
280. Jeff K. Posted: December 21, 2008 at 10:45 PM (#3035424)
But if teams are paying more for it, then it's priced into the market, and it removes that player's added value, right?

Wait, you're adding an externality. The contract market is completely separate. If we bring that in right now, there's no hope. You're not incorrect in what you're saying, but it's outside the scope of the discussion. The salary discussion came up as a side note (though a good one) in fret's #191.

I don't think it's the same as Pennants Added. The concentration of wins is important in Pennants Added because adding a 10 win player to an 81 win team has more than 2x the chance of getting a team into a post season than adding a 5 win player over two years does. 91 and 81 wins back to back years will make the post-season more often than 86 and 86 wins will, on average. 96 and 86 makes more postseasons than 91 and 91, if you start with an 86 win team, etc.. I don't know that this applies to roster construction, especially if it's priced into the market anyway.

Not the same, I was just going for the analogy. The point was just that in each case, concentrating value is beneficial. I think the analogy may overwhelm the small point, though.

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.

Yep. Or rather, imo, the relative difficulty of playing that position, as I've been saying.
281. Jeff K. Posted: December 21, 2008 at 10:49 PM (#3035425)
Jeff/198: I don't think you should know me. I'm a long-time lurker, posted occasionally in the past, these days more often. Twice I solved your diff-eq problems in the Lounge.

I'm now going to do my level best to continue completely forgetting about differential equations. Any of y'all that thought they were hard in college, try taking 8 years off and doing them in your first semester back. Unrecommended.

I wasn't clear. Tango says that the market is basically linear: a 4 WAR player gets paid twice as much as a 2 WAR player. I think that isn't true, and teams consider the 4 WAR player to be worth more than twice as much. The reason we can't get a handle on it is that we aren't good at comparing contracts of different length. I agree with what you said about discount rates etc.

I thought it was established that it was not linear, but rather exponential. It seems I have assumed more than the truth.
282. BeanoCook Posted: December 21, 2008 at 11:01 PM (#3035430)
Time for a tea break guys.
283. David Concepcion de la Desviacion Estandar (Dan R) Posted: December 21, 2008 at 11:22 PM (#3035446)
Nate Silver says it's exponential and Tangotiger says it's linear. I think it's just plain batty. I would say there are three separate markets: one for players who are average-to-below (0-2 WARP), another for those who are above average (2-4 WARP), and finally one for stars (over 4 WARP). Basically, it seems to me that average-to-below guys (who should average 4-5M) tend to get paid at the bottom of that range, the above-average guys (who should average 13-14M) get paid way too much (C. Lee, Soriano, Hunter, etc.), and the true stars (Beltrán, Santana etc.) get paid too little. There is something really crazy going on when Johan Santana only makes 20-25% more than Torii Hunter--he is literally twice as valuable.
284. DJ Endless Grudge Plays All The Hits (CW) Posted: December 21, 2008 at 11:30 PM (#3035451)
The difference between Silver and Tango is that BP's WARP 0 WARP is, and I'm just spitballing it here, -2 WAR? If you account for the difference in replacement level they seem to line up.
285. David Concepcion de la Desviacion Estandar (Dan R) Posted: December 21, 2008 at 11:34 PM (#3035455)
No, Nate did his study using a real replacement level, not the goofy Davenport one (which they are finally about to change on the DT cards anyway).
286. SkyKing162 Posted: December 22, 2008 at 12:06 AM (#3035472)
Nate's study: http://www.baseballprospectus.com/article.php?articleid=4535

BPro's Glossary:
For 2007, a player's MORP is estimated as follows:
1200000*(WARP^1.5) + 380000

Seems like he's using straight WARP to me, unless I'm missing something.
287. DJ Endless Grudge Plays All The Hits (CW) Posted: December 22, 2008 at 03:53 AM (#3035598)
I think I've figured out the sticking point here - of course, I've thoguht that before.

The way that I - and I think the majority of people in the discussion - look at a player's value is the difference between a player's production and the production of a team's alternatives. For a specific team analysis of free agent deals and trades, it may make sense to define a specific baseline - Wins Above Ryan Theriot or Wins Above Ryan Howard or what not.

But for a standard contextless value measure, what we traditionally do is use a commonly-accepted baseline - like replacement level or average - based on the idea of an average team.

In this case, then, we really don't care whether Zaun has a career year or get hurt in May, because he's not really "in-play" for the Twins. Mauer's value to the Twins is the Twins' wins minus their wins without Mauer.
288. Jeff K. Posted: December 22, 2008 at 04:51 AM (#3035637)
That makes sense as far as a description of your position goes. I would still say that I don't think that's correct (I seem to be in some weird space here that's halfway between Dial and the rest of y'all, which is odd as this seems to be polemic.) There are a number of problems with that, including that using that logic, you can't define replacement level as league average of replacement players. Those guys by definition are/were in the majors, hence are not freely available, hence are not "in-play". That logic bites both ways. Also, to go back to an earlier analogy, the fact that you neither own nor have the money or opportunity to buy the largest gold mine in the world doesn't mean its existence has no effect on the value of your gold bar. This is not the Ravenous Bugblatter Beast of Traal, a beast so mind-numbingly stupid that it assumes that if you can't see it, it can't see you, and so meaning the best way to get past it is to cover your own eyes so it thinks you are a figment of its imagination. Gregg Zaun exists and has value, and therefore affects the value of other catchers.
289. Tango Posted: December 22, 2008 at 03:21 PM (#3035783)
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.
290. Tango Posted: December 22, 2008 at 04:16 PM (#3035835)
For those interested in a comparison of my WAR converted to dollars and Nate's use of WARP to create MORP, you can check out posts 11 and 12 on my blog. You can also read the entirety of that thread if you want more.

Ahh... I know most of you don't RTFA, so I'll cut/paste those two posts:

war warp Me\$ MORP\$
1.00 2.40 4.2 4.9
2.00 3.40 8.0 7.9
3.00 4.40 11.8 11.5
4.00 5.40 15.6 15.5
5.00 6.40 19.4 19.8
6.00 7.40 23.2 24.6
7.00 8.40 27.0 29.6
8.00 9.40 30.8 35.0
9.00 10.40 34.6 40.6

The divergence happens at around the 6 WAR level. Other than Pujols, no one exceeds that. (THT has Santana and ARod at around 5.5, which is less than 1 MM difference between me and MORP\$).

And, since most of you that I was crazy to consider Pujols worth as much as I said he was in \$ terms (that if a player is tooooo good, that there’s some sort of “diminishing returns"), you guys are going to hate the ever-rising value of his MORP\$.

So, let’s all agree that linear is the easiest, safest cleanest way to work and think about this, and anything else will make you go through so many mathematical gymnastics that it makes you see something (like MORP/WARP do) that simply isn’t there.

...

Nate pointed out that it’s at the lower-end that you’ll see the biggest difference, and he’s right:

war warp Me\$ MORP\$
(1.00) 0.40 (3.4) 0.7
(0.50) 0.90 (1.5) 1.4
0.00 1.40 0.4 2.4
0.50 1.90 2.3 3.5
1.00 2.40 4.2 4.9
1.50 2.90 6.1 6.3
2.00 3.40 8.0 7.9

Those are huge gaps. And all that MORP does is show us how you have to decide whether to trust the superlow replacement level of WARP or mine in WAR.

I don’t see the benefit of the exponent in MORP, and just see the downside of the superlow repl level in WARP.
291.  Posted: December 22, 2008 at 05:03 PM (#3035863)
Basically, it seems to me that average-to-below guys (who should average 4-5M) tend to get paid at the bottom of that range, the above-average guys (who should average 13-14M) get paid way too much (C. Lee, Soriano, Hunter, etc.), and the true stars (Beltrán, Santana etc.) get paid too little.

That's how pricing in Rotisserie Baseball tends to work- In Rotisserie you have the advantage of being able to calculate what a players' salary "should" be-and you will still have this effect.
There are \$50 guys in Roto, they will not get \$50 (except in young or unstable leagues)- they will go for \$40
The guys who should go for \$20 will go for \$25 or higher.
The guys who "should" go for \$10-15, will split, some will go upwards of \$20, some will drop to \$5
The guys who "should" go for \$5-10 will go for \$1-3.
292. Tango Posted: December 22, 2008 at 05:06 PM (#3035866)
When I calculate Fantasy Baseball \$, I use the same linear method, and I get the more reasonable numbers (top-end near 35/40\$). So, I dispute the illustration in post 291.
293. David Concepcion de la Desviacion Estandar (Dan R) Posted: December 22, 2008 at 05:17 PM (#3035877)
JPWF13 is not saying what players should go for, he's saying what they do go for. And Johan Santana has not gone for under \$50 in my league (\$230 budget for 23 players in a 20 team league) since 2005.
294. Tango Posted: December 22, 2008 at 06:05 PM (#3035919)

There are \$50 guys in Roto, they will not get \$50 (except in young or unstable leagues)- they will go for \$40

... they will go for 40\$ (but "deserve" a fair price of 50\$).

***

If you are in a league where Santana is going for \$50+, then that's a league that you must be pretty happy to be in.
295.  Posted: December 22, 2008 at 06:31 PM (#3035947)
When I calculate Fantasy Baseball \$, I use the same linear method, and I get the more reasonable numbers (top-end near 35/40\$). So, I dispute the illustration in post 291.

How can you dispute it without knowing the league parameters?

If you are in a league where Santana is going for \$50+, then that's a league that you must be pretty happy to be in.

he went for 37 in mine

4 x 4
NL only Roto.

A player like Hanley Ramirez is easily "worth" \$50 in such a format- but he won't go for that high (not in my league anyway).

Back in his post 30s prime Barry B was a DiamondMind GOD, but no DiamondMind League using \$s would he go for his "true" value, he might be worth \$60 and the next best guy \$40, and the tier under that \$35- Bonds will get \$50, the next guy \$40, and the next tier will all get \$38...
296. David Concepcion de la Desviacion Estandar (Dan R) Posted: December 22, 2008 at 06:49 PM (#3035971)
Tango, I only know how to do dollar values for my league's parameters, but by my math \$50 isn't outlandish for Santana at all (using 2006-8 PECOTA and ZiPS projections), and I am somewhat handy with a spreadsheet. We are a highly competitive and active 20-team Rotisserie-scored league, with rosters C 1B 2B 3B SS CF OF OF Util 11 P and 3 Bench, 20 teams in the league, a \$230 budget for 23 players, and stat categories OBP SLG R RBI NetSB Wins ERA WHIP SO and NetSV. Max 162 games per position and 1,450 innings pitched. The cost is \$200 a team, with \$2400 going to the winner, \$1000 to second, \$400 to third, and \$200 to the team that improves the most in the second half. If you think the owners are so stupid that it's just easy money waiting for the taking, would you be interested in joining next year? Perhaps you could teach us all a lesson...

(There is no sarcasm or wounded pride here--I happen to think the league is quite competitive, but perhaps I just haven't been faced with the big boys yet).
297.  Posted: December 22, 2008 at 06:54 PM (#3035976)
If you think the owners are so stupid that it's just easy money waiting for the taking, would you be interested in joining next year? Perhaps you could teach us all a lesson...

Or join mine, please, my co-owners are a bunch of cutthroat lawyers - any deficiency they have in fixing dollar values to specific players is more than made up for by other abilities they ahve in trading, cheating, roster management, near cheating...
298. Tango Posted: December 22, 2008 at 07:46 PM (#3036018)
Thank you for the offers. Just to be clear, I never called anyone stupid, nor was this implied. I did say there was pricing inefficiency. Inefficiency does not imply stupidity.

I have my hands quite full with the 2009 Forecasters Challenge. Even if I wasn't involved in that though, I would not join any league that requires a daily or weekly following. Been there, done that in my college, and early work years. How anyone can does this with a family, my hat is off to you. Regardless, the Challenge simply would stop me from doing anything.

In addition, I provide the Marcel forecasts and the Fantasy Baseball dollars for the world to see, along with the full methodology on my blog. Here was the 2007 numbers (post 60), and for 2008. I'll be doing the same for 2009.
299. JoeD has the Imperial March Stuck in His Head Posted: December 22, 2008 at 07:57 PM (#3036035)
The roto analogies are interesting.

In our league, we have 15-man keepers (up to 3 years, with one extension before the last year of the deal, \$5 per season of extension is the raise - so a 4-year extension is a \$20 raise), \$263 budget for 24 players, 14-team NL only, and cheap minor leaguers; 5-round farm draft every year, when they get to the majors they get 1-3-5-9 as salaries their first four years.

In those circumstances, stars go for far more than they are actually worth - our 'inflation' is close to 50%. Pujols goes for \$60, as did Bonds. Johan went for \$62.
300. Tango Posted: December 22, 2008 at 08:46 PM (#3036089)
1-3-5-9 as salaries their first four years.

Well, that's the reason right there. You are limiting say Longoria to 18\$ the first 4 years total, when he would be worth alot more than that in the bidding (just in one year!).

Since you are allocating a fixed budget, and you "use it or lose it", you get to overbid, naturally.

Just taking a guess, if you have \$263, of which one-third "should" go to the 1-4 year players (just guessing), but you are only paying them half as much as they should be, that's an extra 45\$ that you get to spend. If you spread it to the other two-thirds of 263\$, it comes out to a 25% premium.

Again, this is just a simplistic illustration.
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