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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 06:01 AM | 301 comment(s) Login to Bookmark
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   1. Zac Schmitt Posted: December 20, 2008 at 07:20 AM (#3034543)
Huh, I didn’t realize that positional adjustments is considered so ‘new’.


i was also confused that rob neyer seemed surprised at something that caused me, a sabermetric novice who only has a rudimentary understanding of what goes on in the community at large, to say "yeah, of course." but i can only imagine that rob is playing ignorant so as to get the question answered for his readers, sort of like how in movies where a bunch of scientists are talking there's always one who randomly doesn't know something he probably should just so the other guys can explain it to him (and thereby the audience).

here a question: a poor fielding shortstop or catcher might be "more valuable" than a better fielding first baseman (say the shortstop below replacement level and the first baseman is below average but above replacement level). depending on the exact numbers, once you adjust the shortstop might be "more valuable," but is he really more valuable than the team since he's not playing his position well?
   2. Justin T., Director of Somethin Posted: December 20, 2008 at 07:47 AM (#3034545)
I think positional adjustments sound new because we have long known that lesser fielders play the corners, for example, and so it seems this is not a new concept.

Yet, I think that this particular thing they are talking about is new. However, Seidman either really crappily explained it in that email with Rob or it is far more complex than it seems it should be. Because after reading that, it does seem like it should be simple, but something is keeping me from really getting it.
   3. Tripon Posted: December 20, 2008 at 07:56 AM (#3034546)
I'm suprised that 2nd baseman and 3rd baseman get the same adjustment, doesn't seem 3rd basemen can switch over to 2nd base as easy as 2nd basemen can to 3rd.
   4. Jeff K. Posted: December 20, 2008 at 08:01 AM (#3034547)
Positional adjustments aren't remotely new. Positional adjustments in this particular format are new, or are at least new to me. This is applying a normalizer to defense, which (again, to the best of my knowledge) hasn't been done. In the past, you've taken a guy's hitting, adjusted *that* for position, added his defense, added baserunning, and called it a day. What this does is explicitly value the fact that it's easier to be a first baseman purely defensively speaking than it is a shortstop.

So instead of saying player A is 30 BRAA, 10 FRAA, 10 BaseRunningAA, player B is 25/15/5, but the 25 is more valuable than the 30 because player B is a shortstop and shortstops tend to be weaker hitters than first basemen like A, you're saying that whole thing and now adding the fact that the 15 is more than 5 more valuable than the 10 FRAA for player A.
   5. Ivan Grushenko of Hong Kong Posted: December 20, 2008 at 08:12 AM (#3034549)
I thought positional adjustments were already built into VORP and RARP based on the replacement level of offense for that position. It's not entirely clear to me why it's better to use these somewhat arbitrary sounding numbers instead of an empirically derived one.
   6. robneyer Posted: December 20, 2008 at 08:12 AM (#3034550)
What Jeff K. said.

And no, I was not feigning ignorance. I've really had to be hit over the head a few times with this stuff, but now I do think I get it.

And Ivan, you may be right about VORP, but it's useful to understand that (for example) Carl Crawford probably isn't really a more valuable fielder than Carlos Beltran (even though his FRAA or his UZR might suggest that he is). -r
   7. Justin T., Director of Somethin Posted: December 20, 2008 at 08:13 AM (#3034551)
But what's the point? Why consider an average fielding first baseman to be more than a full run less valuable because a random second baseman could go over there and play the position better? Shouldn't a first baseman be compared to his peers at the position rather than a theoretical slap hitter who could outperform him there?
   8. Jeff K. Posted: December 20, 2008 at 08:13 AM (#3034552)
(EDIT: This is Re: #5) Because you can't get the positional difference of defensive value just by looking at offensive numbers. The claim would be that two adjustments need to be made, not just one, to properly adjust for position.
   9. Jeff K. Posted: December 20, 2008 at 08:18 AM (#3034554)
But what's the point? Why consider an average fielding first baseman to be more than a full run less valuable because a random second baseman could go over there and play the position better? Shouldn't a first baseman be compared to his peers at the position rather than a theoretical slap hitter who could outperform him there?

Justin, now that I know you're a finance major like I was, I know you understand the concept of differing marginal values. Just like the difference between a 200 OPS+ and a 190 OPS+ is more valuable than the difference between 110 and 100, the claim here is that being 7.5 runs over average defensively at short is more valuable than 7.5 runs over average at first. It's not that you're comparing him to second basemen now. It's that the 7.5 run difference is harder t accomplish at short than 1b, and hence, more valuable. You can't straightline compare the two as we've been doing lo these many years.

6. robneyer Posted: December 20, 2008 at 03:12 AM (#3034550)
What Jeff K. said.


Quoted in a Posnanski column on Bill James and now this? I can die, if not a happy man, somewhat less disgruntled...
   10. Justin T., Director of Somethin Posted: December 20, 2008 at 08:18 AM (#3034556)
So instead of saying player A is 30 BRAA, 10 FRAA, 10 BaseRunningAA, player B is 25/15/5, but the 25 is more valuable than the 30 because player B is a shortstop and shortstops tend to be weaker hitters than first basemen like A

Reading Jeff's #4 again, is it the case that using previous methodology, Player A would be 30/10/10 and Player B would be 40/0/5 because the positional adjustment was built into the offense?
   11. Jeff K. Posted: December 20, 2008 at 08:31 AM (#3034559)
No, not really. If we keep Player A where he is and make the adjustment purely to player B, A is 30/10/10, B would have his offense adjusted upward. Let me do one thing and change B's FRAA and baserunning to 10, as well, I think it makes it easier to talk about. So, raw numbers of BRAA/FRAA/BaseRunAA (and these are generic terms I'm using, not anything actual like BPro's FRAA) are A = 30/10/10, B = 25/10/10. And let's say that the positional adjustment to BRAA is +5 as far as the difference between a shortstop and a first baseman. So after adjustments, A stays 30/10/10, now B is 30/10/10. Here is where we have always stopped. So we would say each player is 50 runs above average and they are of equal value.

The claim, and I use that term because I'm not positive I believe it yet, is that this is untrue. We aren't properly valuing their defensive contributions. Because it's harder to be +10 AA at SS than 1b, we have to place more value on it. So now, A is 30/10/10, and B is 30/15/10. And hence, B is more valuable.

I like what Rob said about Crawford and Beltran.
   12. Justin T., Director of Somethin Posted: December 20, 2008 at 08:32 AM (#3034560)
I certainly get that a +7.5 run defender at SS is harder to come by than a +7.5 run 1B. So yeah, the defense at short is more scarce and therefore more valuable if you can get your hands on it. But if there were a team that had Carl Crawford in left at +15 runs and Beltran also playing CF at +15, isn't that team still saving 30 runs no matter what? Beltran is saving 15 runs more than Johnny Damon would, and Crawford is saving 15 more runs than Jason Michaels would, but if Damon played LF he would be 10 runs better than Michaels.

Maybe the problem is that I always thought positional adjustments were there and they were not. I think I always thought a +15 rating for a LF was easier to come by than +15 for a CF. Was this not the case? I mean, I never thought that if Albert Pujols was +15 at 1B that implied he could play SS and be a +15.
   13. Tripon Posted: December 20, 2008 at 08:33 AM (#3034561)
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.


So a team full of Willie Bloomquist would be utterly average?
   14. Jeff K. Posted: December 20, 2008 at 08:37 AM (#3034562)
So a team full of Willie Bloomquist would be utterly average?

No, look at the terms. It'd be utterly Willie. :)
   15. Jeff K. Posted: December 20, 2008 at 08:41 AM (#3034563)
Maybe the problem is that I always thought positional adjustments were there and they were not. I think I always thought a +15 rating for a LF was easier to come by than +15 for a CF. Was this not the case? I mean, I never thought that if Albert Pujols was +15 at 1B that implied he could play SS and be a +15.

No, of course not. But you added that 15 to Pujols the same as you added 15 to Rey Sanchez. And yes, the team with Crawford and Beltran is saving 30 runs, but those 30 runs are not "created" equally, so to speak. I think that a good analogy would be low run environments vs. high. If Ty Cobb in 1905 is 30 BRAA, and Todd Hundley in 1998 is 30 BRAA, those are not of equal value. The 30 BRAA in 1908, given league scoring, is of course more valuable. Apply the same concept to defensive positional context.
   16. Justin T., Director of Somethin Posted: December 20, 2008 at 08:54 AM (#3034565)
Well, I'm gonna sleep on it. It's more skepticism than lack of understanding at this point.
   17. Drexl Spivey Posted: December 20, 2008 at 09:01 AM (#3034568)
I love articles explaining new stats on ESPN. It's dumbed down just enough for the average reader to be confused/enlightened by the article.

For example: "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."
   18. Jeff K. Posted: December 20, 2008 at 09:43 AM (#3034576)
I don't see it as all that confusing, just hard to explain, as witnessed by Eric's attempt and then mine in #4. It intuitively made sense to me immediately on reading the blurb here, even if, as I said earlier, I'm not sure I agree with it. I'm willing to buy the concept that we shouldn't do straightline comparisons and that there should be some defensive positional adjustment, but like Justin said, 20 whole runs of difference between SS and 1b, natively, built into the system? That seems high.

Now, if you're unfamiliar with positional adjustments (or hell, adjustments for park, era, league...) this is not the one I'd want to start with.
   19. Jeff K. Posted: December 20, 2008 at 10:14 AM (#3034581)
I hadn't read the article until just now:

A stat like VORP is already adjusted before you see the final product, but in using UZR or Dewan's system, we would need to adjust for the difficulty level of playing certain positions; so (for example) Ryan Howard's +1 run at 1B isn't even close to a +5 by Feliz at 3B.

I don't see how this can be right. VORP is adjusted, yes, but it is only adjusted to normalize offense across positions, not defense as well. Whatever defensive stat you use to construct whatever your own personal version of VORP is, you should still have to adjust for defensive positional context, else I don't see where the advancement is.
   20. JoeHova Posted: December 20, 2008 at 11:11 AM (#3034586)
I understand the concept of this, what I don't get is where the numbers come from. With offensive numbers it is easy to see how the average 1st baseman is worth 30 (or whatever it really is) runs over the average SS. How do we know the average SS is worth (exactly) 20 more runs than the average 1st baseman defensively? We don't seem to be comparing apples to apples in that case, unlike with hitting. Where does the 20 runs number come from and how confident are we in that being an accurate estimate? Why not 40 runs? Or 10? Or anything else? I have to admit that I'm skeptical about the exactitude of these numbers. If they are really based on anything concrete, how likely is it that 2nd, 3rd, and CF are worth exactly the same defensive adjustment? I know that Tango says the numbers are based on the performance of players who switched positions, but even knowing that vague outline still leaves many questions to be answered, especially because Tango has also given the positional adjustments as +1 win for catcher, +.5 for SS/CF, +0 for 2B/3B, -.5 for LF/RF, -1 for 1B and -1.5 for DH.

I'm probably missing something, but lately it seems like the people who are working with defensive numbers are treating them more like gospel than they deserve to be treated at this point. I think anybody who starts promulgating a new stat has the duty to explain why the stat has value and how it came to be calculated. I'm not saying that people are necessarily failing to do that, I'm just saying that the burden is on the prosecution.
   21. jyjjy Posted: December 20, 2008 at 02:37 PM (#3034601)
I'm not getting this really...
I understand the concept but it seems like you either adjust positionally for offense or defense not both. The whole point of adjusting offense for position is to give them credit for playing a harder position. It is inherently harder to play shortstop or catcher defensively, so sure, give them credit for that, but it doesn't make it inherently harder to hit a baseball when you play shortstop. You can either compare a player versus average for the position on both sides of the ball or you make a adjustment based on how much harder it is to field the position as described in the article, not both. Comparing to an average player at the position seems worlds more valid than these (seemingly)arbitrary positional modifiers. Is the point of this then just a quick, rough comparison of the relative defensive value of players at different positions?
As for marginal values that's a complex topic that perhaps should be applied to every statistic, not just defense... but I don't see how that's accomplished with what's being described here in any case.
   22. GGC don't think it can get longer than a novella Posted: December 20, 2008 at 02:54 PM (#3034607)
I don't think positional adjustments would be neccesary (sp) if you expressed a player's value as a won-loss record or used loss shares along with win shares, but I don't spend all day thinking about this type of stuff like some do here.
   23. BFFB Posted: December 20, 2008 at 03:16 PM (#3034618)
On immediate reading it just seems to me that the adjustment is conceptualising something which doesn't actually exist other than in the theoretical. Capturing the theoretical value of a player as opposed to the actual measured value.

Or from a practical standpoint, it doesn't matter where a run is saved when measuring defense as long as it is saved. As long as both player A and player B save the same number of runs relative to positional average it's not important that player B's position is harder than Player A's.
   24. villageidiom Posted: December 20, 2008 at 03:43 PM (#3034624)
I had been working on something a year or so ago, like this:

1. Take the individual components of Tango's "Fans' Scouting Report" - hands, first step, etc. - and see to what extent each component correlates with defensive stats at their given position.

2. Use all of that to estimate how well each MLB player could do at any other position.

Then, either
3a. Adjust all players to a common position, then evaluate defensive value there; or
3b. Devise a positional adjustment along the lines of what's being discussed here.

I dropped it because (a) life got in the way; (b) to do this, it helps to have defensive stats you can believe in, and there was enough disparity in defensive stats to throw off the correlations; (c) I can't tell if, to the extent there was little correlation, the lack of correlation with defensive stats was because defensive stats were shaky, or that Tango's FSR components aren't as position-independent as he'd hoped. At the time the FSR ratings - and a number of defensive stats - were still in their infancy, so it was hard to look at multiple years. And, again, (a).

If someone else wants to take it up, I won't be offended.

- - - -

FWIW, initial conclusions were:

(a) Ichiro! might be able to handle CF. (His FSR numbers and defensive stats reflected RF.)
(b) The Yankees' problem was not that Jeter was playing SS, but that the entire defense was built for offense. Jeter could be an A or A- fielder at other positions, instead of the C or so he was at SS; but nobody else on the roster was performing like someone who could handle SS.
   25. Misirlou's been working for the drug squad Posted: December 20, 2008 at 03:46 PM (#3034627)
I understand the concept but it seems like you either adjust positionally for offense or defense not both. The whole point of adjusting offense for position is to give them credit for playing a harder position. It is inherently harder to play shortstop or catcher defensively, so sure, give them credit for that, but it doesn't make it inherently harder to hit a baseball when you play shortstop.


The problem is, if I understand the issue, is that before you would look at Pujols as a +15 defender at 1B and a hypothetical SS who is a +15 defender at SS and conclude they are of equal value defensively. Now, suppose that SS is the same hitter as Pujols, the old methodology would proclaim them of equal value. Intuitively, this is not correct and always bothered me.
   26. pkb33 Posted: December 20, 2008 at 04:06 PM (#3034635)
the claim here is that being 7.5 runs over average defensively at short is more valuable than 7.5 runs over average at first.

That is a claim that there is different distribution of skills at different positions, e.g. that the bell-curves are very different. That may be correct, but there's nothing in what I've seen research-wise on this that supports that, imo.

The problem is, if I understand the issue, is that before you would look at Pujols as a +15 defender at 1B and a hypothetical SS who is a +15 defender at SS and conclude they are of equal value defensively. Now, suppose that SS is the same hitter as Pujols, the old methodology would proclaim them of equal value. Intuitively, this is not correct and always bothered me.

That's not the case. If they had the same offensive numbers then the SS would have a VORP (or RAA, or whatever) significantly higher because the positional baseline offensive production would be much different. And thus, would appear to be a significantly more valuable player.

What's interesting here is that we are looking at defense in both an absolute and a relative sense.

The positional adjustment described here is giving us a total value for the player on the defensive end of the spectrum (it's comparing the player's positional value and the skill at the position relative to peers).

This makes sense to me, but it also reflects a managerial choice. For example, we can say that Carl Crawford was worth less defensively in 2008 than (say) Carlos Beltran because he was deployed in LF instead of CF. What we can't say, though, is that he's an inferior defensive player true-talent wise because we don't know. We can only use the adjustment to look at the actual.

So, let's take that same mindset to the offensive side.

Arguably, if we're doing this to address what the player actually contributed during the season---based on where a team actually deployed the player---we should also adjust offensive numbers to reflect lineup position shouldn't we? That reflects an actual contribution, too.
   27. Tricky Dick Posted: December 20, 2008 at 04:29 PM (#3034643)
Or from a practical standpoint, it doesn't matter where a run is saved when measuring defense as long as it is saved. As long as both player A and player B save the same number of runs relative to positional average it's not important that player B's position is harder than Player A's


It seems to me that this might make a difference, though, if you are trying to put a dollar value on the worth of the players. For instance, suppose a team has a fixed sum of money to fill two slots, a shortstop and a first baseman, and needs a method to determine the best use of budget to fill both positions. In theory the team's valuation should consider that the same "runs saved" defensive contribution from the shortstop may be very rare, although it is relatively easy to find among 1st basemen. Like someone stated above, this is a form of marginal valuation.

However, based on what I can tell, it would seem difficult to come up with solid numbers to assess the defensive value differences by position.
   28. Mefisto Posted: December 20, 2008 at 04:58 PM (#3034649)
That's not the case. If they had the same offensive numbers then the SS would have a VORP (or RAA, or whatever) significantly higher because the positional baseline offensive production would be much different. And thus, would appear to be a significantly more valuable player.


Yes, but using offensive numbers to set the baseline is an indirect way to get at the difference in difficulty between SS and 1B. IOW, a 130+ SS will be a much better hitter than the average SS, while a 130+ 1B will be not very far above average for a 1B. The reason for doing that is to try to get at the fact that it's a lot harder to play SS than it is to play 1B.

Tango's suggestion is to stop trying to measure defense indirectly like this. Instead, try to come up with the relative value, in runs, of the difficulty of playing each position. Think of it as reflecting the number of plays made and the relative difficulty of those plays. That way we're measuring apples against apples rather than using oranges to estimate apples.
   29. Dan Szymborski Posted: December 20, 2008 at 05:22 PM (#3034662)
Instead, try to come up with the relative value, in runs, of the difficulty of playing each position.

I see this approach as way too doctrinaire. Value isn't based on difficulty directly, but merely indirectly to the extent that difficulty of a position affects availability of players. We measure the availability already, there's no reason to go to a more rigid method that less takes into account actual conditions.

It's similar to crude oil and gold. Historically, the ratio between gold and oil prices trends towards 15:1. That's useful information, but most of the time, you're not in an "average" situation and you have to take into account conditions on the ground.

And that's what the normal approach does in baseball. Talent is not distributed in the same way in each era.

It's not comparing oranges to estimate apples at all. We're not trying to measure relative difficulty, but relative value. Players only have value compared to players that could theoretically replace them, not constructs of difficulty.
   30. David Cameron Posted: December 20, 2008 at 05:22 PM (#3034663)
Let's see if I can make this a little easier to understand.

Traditionally, we've always compared hitters to a position specific baseline. With VORP, it's marginal value over a replacement level second baseman, where replacement level 2B offense is calculated off of the actual results of how ML second baseman hit that year. This is true at each position.

So, generally, we'd say that a player who is +10 VORP at SS is equal in value to a player who is +10 VORP at second base. You see people make arguments like this all the time.

The problem. however, is that there's an implicit assumption in doing things that way that the sum of the defensive differences between any two positions are equal to the offensive differences within a given year. That just is hardly ever true, and leads to incorrect valuations of players.

Let's use an example from last year. NL second baseman hit .271/.338/.408 last year, while NL shortstops hit .276/.334/.404. There's hardly any difference between the offensive level of the two positions, so a position-adjusted offensive number would return similar values for players who had the same line at SS and 2B. Let's say that we said that a player was +10 runs better than the average SS offensively, and average defensively for a shortstop, so we'd call him +10 runs overall. Now, we have a player who is +10 runs better than an average 2B offensively, but +5 runs better than an average defensive second baseman, so we'd call him +15 runs better overall.

In this instance, the offense plus defense would conclude that the second baseman was more valuable. However, we know that an average defensive SS is a much better player than an average defensive 2B. That gets lost in the shuffle when you compare them to the offensive average of each position and the two positions produce similar offensive output.

That's why a lot of us have gotten away from position-adjusted offensive numbers, such as VORP, and are breaking things down by component. Compare offense to average hitter (not average for position, just league average), then add a defensive metric, then toss in a fixed position adjustment that doesn't fluctuate based on yearly performance, and you get runs above/below an average player. It's just a better way to do things.
   31. Dan Szymborski Posted: December 20, 2008 at 05:31 PM (#3034665)
ompare offense to average hitter (not average for position, just league average), then add a defensive metric, then toss in a fixed position adjustment that doesn't fluctuate based on yearly performance,

That's a bug, not a feature. Baseline value isn't fixed.
   32. this space for rent Posted: December 20, 2008 at 05:31 PM (#3034666)
Comparing to an average player at the position seems worlds more valid than these (seemingly)arbitrary positional modifiers.


One of the problems that these "arbitrary" positional modifiers attempt to address is the fact that offensive and defensive skills are likely somewhat correlated.

To put it another way, most folks here would agree that RF > LF > 1B on the defensive spectrum. But if you look at 2008, AL RFs outhit both AL LFs and AL 1B by a decent margin.

If you use VORP, you either (a) tweak replacement level by basing it on something other than average offensive performance at the position or (b) wind up with VORP telling you that a 1B with an X OPS+ is more valuable than a RF with an X OPS+. The latter conclusion directly contradicts the normal defensive spectrum.

Defensive positional modifiers get away from that, by measuring (albeit perhaps arbitrarily) the value of playing RF v. 1B completely apart from the offensive production of those two positions. If a full-time 1B and RF post the same OPS+, the RF is 5 runs more valuable overall according to positional adjustments.

Of course, you could also use these positional adjustments to set replacement level. Start with a baseline replacement level of X RC/600 PA, adjust that based on defensive difficulty, and you have your positional replacement level to use with VORP. The math is the same; it's the definition of replacement level (or average, depending on what you're measuring) that changes.
   33. The Mighty Quinn Posted: December 20, 2008 at 05:46 PM (#3034671)
Excellent summary Dave. I think some people could use a little primer on how Tango arrived at these positional adjustments, some seem to think he's just pulling them out of thin air.
   34. David Cameron Posted: December 20, 2008 at 05:51 PM (#3034673)
That's a bug, not a feature. Baseline value isn't fixed.

In regards to the talent level at certain positions, it is far more fixed than variable - fluctuations within the talent distribution will never exceed some fundamental laws. LF will never be equal defensively to CF. 2B will never be equal defensively to SS. When the metrics miss this important difference, they're wrong.
   35. Mefisto Posted: December 20, 2008 at 05:54 PM (#3034674)
We're not trying to measure relative difficulty, but relative value. Players only have value compared to players that could theoretically replace them, not constructs of difficulty.


I think David Cameron's post responds to this pretty well. I'll just add that I think you've implicitly defined the class of "players that could theoretically replace them" in a way that's too limited and that would cause us to miss important aspects of value. As Bill James pointed out early on, a defender's ability to save runs depends who we compare him to. Compared to a replacement SS, Mark Belanger saved quite a few. Compared to having Boog Powell at SS, he saved a roughly infinite number.

It's that latter point which is lost by looking solely to "replacement level" substitutes. The fact is that Boog Powell can't play SS, while Belanger could. That gives Belanger real value which isn't captured by comparing him solely to others who belong to the class "can play SS". Using a positional adjustment based on defensive difficulty is a way to capture that value.
   36. Justin T., Director of Somethin Posted: December 20, 2008 at 05:55 PM (#3034675)
Players only have value compared to players that could theoretically replace them, not constructs of difficulty.

This is what I keep coming back to in this internal struggle of mine.
   37. Joey Numbaz (Scruff) Posted: December 20, 2008 at 06:06 PM (#3034681)
Let's use an example from last year. NL second baseman hit .271/.338/.408 last year, while NL shortstops hit .276/.334/.404. There's hardly any difference between the offensive level of the two positions, so a position-adjusted offensive number would return similar values for players who had the same line at SS and 2B. Let's say that we said that a player was +10 runs better than the average SS offensively, and average defensively for a shortstop, so we'd call him +10 runs overall. Now, we have a player who is +10 runs better than an average 2B offensively, but +5 runs better than an average defensive second baseman, so we'd call him +15 runs better overall.


Except that you shouldn't be using average to set the baseline. You should be using the bottom end regulars to set the baseline. This is generally a much better (but not perfect) proxy for replacement level.

If not, star-gluts at a position will throw you off.

I would also think you should be using all of MLB, not just the arbitrary AL/NL to make the comparison.
   38. Dan Szymborski Posted: December 20, 2008 at 06:15 PM (#3034685)
It's that latter point which is lost by looking solely to "replacement level" substitutes. The fact is that Boog Powell can't play SS, while Belanger could. That gives Belanger real value which isn't captured by comparing him solely to others who belong to the class "can play SS". Using a positional adjustment based on defensive difficulty is a way to capture that value.

We compare him to those that could replace him, other players that could reasonably play shortstop. We compare his defense to those that can reasonably play shortstop and then we compare his offense to those that can reasonably play shortstop.

We make comparisons of this type in every aspect in our daily lives without any problems. When I buy a 4-door sedan, I don't have trouble making valuation compared to other 4-door sedans I could reasonably buy, not to $500,000 sports cars or ride-on mowers. When I buy soup and it's the worst soup available, I don't evaluate them on price as being "less than saffron" but "tastier than feces" but instead to other soups I could buy.

What we're talking about here is rigid and inflexible, based on the conceit that value is based on some absolute difference in difficulty.
   39. Dan Szymborski Posted: December 20, 2008 at 06:18 PM (#3034686)
n regards to the talent level at certain positions, it is far more fixed than variable - fluctuations within the talent distribution will never exceed some fundamental laws. LF will never be equal defensively to CF. 2B will never be equal defensively to SS. When the metrics miss this important difference, they're wrong.

But the relative availability of talent is variable. Value is not based on difficulty.

This is putting the cart before the horse. When has replacement level CF ever been better than LF/RF in recent years? Or SS better than 2B? Where is the logic in comparing a player to a fictional construct of a player instead of actual players in order to correct a problem that does not exist?
   40. Chris Dial Posted: December 20, 2008 at 06:22 PM (#3034688)
In this instance, the offense plus defense would conclude that the second baseman was more valuable. However, we know that an average defensive SS is a much better player than an average defensive 2B. That gets lost in the shuffle when you compare them to the offensive average of each position and the two positions produce similar offensive output.
I'd argue in the season jsut played he was more valuable. I think that's correct.

Using a positional adjustment based on defensive difficulty is a way to capture that value.
My understanding is that Tango's method (and really, he "invented" this, brilliantly so, with strong underlying data) actually means you compare SS as hitters to 1B as hitters, and then merely adjust that, rather than comparing SS to SS.

Tango and I have talked about this many times, and basically he and I disagree which is a better treatment. I am ready to be convinced, but the argument Dave makes and others convinces me more that it isn't correct.

The baseline of SS production versus 1B production varies seasonally. Right, if you want to see which salary was better, that might matter, but I want to know who was a better player, and I haven't seen any evidence that a stat like OPD does a worse job than the O+D+Pos. It could for some other uses, but I don't think it works for a seasonal comparison because it uses fixed numbers rather than the season variation (which is a little painful for me to write because I don't use single season PFs - I think they are different.)
   41. Chris Dial Posted: December 20, 2008 at 06:25 PM (#3034689)
Except that you shouldn't be using average to set the baseline. You should be using the bottom end regulars to set the baseline. This is generally a much better (but not perfect) proxy for replacement level.
It doesn't matter if the comparisons are built in season, IMO.

If not, star-gluts at a position will throw you off.
I recognize this makes some numbers funky, but I am not sure why it throws me "off". Off what?

I would also think you should be using all of MLB, not just the arbitrary AL/NL to make the comparison.
I strongly disagree. There are differences in defensive performance by league.
   42. Golfing Great Mitch Cumstein Posted: December 20, 2008 at 06:31 PM (#3034693)
Nice explanation Dave.

No, of course not. But you added that 15 to Pujols the same as you added 15 to Rey Sanchez. And yes, the team with Crawford and Beltran is saving 30 runs, but those 30 runs are not "created" equally, so to speak. I think that a good analogy would be low run environments vs. high. If Ty Cobb in 1905 is 30 BRAA, and Todd Hundley in 1998 is 30 BRAA, those are not of equal value. The 30 BRAA in 1908, given league scoring, is of course more valuable. Apply the same concept to defensive positional context.

I don't see how this comparison holds up. I understand 30 BRAA in a 2 runs/game environment has more value than 30 BRAA in a 4 runs/game environment. But how are the same number of defensive runs in the same scoring environment any more valuable?
   43. Chris Dial Posted: December 20, 2008 at 06:31 PM (#3034694)
I also want to second the description Jeff K. way above. This usage of positional adjustment is VERY new and not widely used. There are disciples that use it (and Tango is worthy), but BPro is clearly the most common usage with VORP, and I don't use it either.
   44. Blackadder Posted: December 20, 2008 at 06:35 PM (#3034696)
It should be mentioned that since Tango changed his positional adjustments a few months ago--taking into account the difficulty of playing non-first base infield positions for left handed fielders--they are now pretty close to the empirically derived positional replacement levels that Dan Rosenheck is using. As such, this disagreement, while certainly conceptually important, does not have huge implications for player valuations, at least for current players. In some sense, I think the way Dan does it is "right", in that what ultimately matters for measuring value has to be the quality of the player who could replace for the player in question for essentially no cost. One could raise legitimate empirical questions as to whether Dan's methods actually measure what they purport to, but that still has to be what one is ultimately concerned about.
   45. Joey Numbaz (Scruff) Posted: December 20, 2008 at 06:39 PM (#3034698)
n regards to the talent level at certain positions, it is far more fixed than variable - fluctuations within the talent distribution will never exceed some fundamental laws. LF will never be equal defensively to CF. 2B will never be equal defensively to SS. When the metrics miss this important difference, they're wrong.


I would also add that this isn't true, the game changes. RF in the 19th century was the equivalent of the modern DH. . . 3B used to be more valuable than 2B. 1B used to be more valuable than LF or RF.

In the era of turf parks, SS, 2B and CF became much tougher defensively than they are now. If you don't believe look at what those guys hit during that time-frame, compared with other eras. Those managers and GMs weren't dumb, you needed better fielders (and thus worse hitters) to be able to handle the position.

Who knows how the game will change over the next 100 years? You need a system that can adjust to changing conditions on the fly, not one that is rigid.
   46. The District Attorney Posted: December 20, 2008 at 06:41 PM (#3034699)
When has replacement level CF ever been better than LF/RF in recent years? Or SS better than 2B? Where is the logic in comparing a player to a fictional construct of a player instead of actual players in order to correct a problem that does not exist?
I don't think it has anything to do at all with trying to "cover" for when SS outhit 2B. It just has to do with this conversation, which could apply at any time:

A: Okay, this guy is a second baseman, and he's 10 runs better than the average second baseman. So that's his value.
B: But why are you comparing him just to the second basemen? What about the shortstops? Pretty much all of them could play second base too. Shouldn't you be comparing him to them also?

I've had that conversation in my own head a lot, so this new way makes a lot of sense to me.
   47. Mefisto Posted: December 20, 2008 at 06:42 PM (#3034700)
We compare him to those that could replace him, other players that could reasonably play shortstop. We compare his defense to those that can reasonably play shortstop and then we compare his offense to those that can reasonably play shortstop.


But this misses something very important: it's more difficult to play SS than it is to play any other position. There's more defensive responsibility there. We need to capture that difficulty somehow. If we use offense as a proxy for capturing that distinction, we're trying to describe an apple by evaluating an orange. Ideally, we'd measure that extra responsibility directly rather than indirectly.

This is NOT a dispute about the need to compare SS and 2B, it's about the proper way to make that comparison. Current measures use offensive performance as a proxy; that's the indirect way (I'd even say it's wrong when, as Palmer does, it uses average performance as a baseline rather than replacement value). Tango's trying to get a direct way to measure something everybody agrees needs to be measured.
   48. Chris Dial Posted: December 20, 2008 at 06:49 PM (#3034703)
But why are you comparing him just to the second basemen? What about the shortstops? Pretty much all of them could play second base too. Shouldn't you be comparing him to them also?

I've had that conversation in my own head a lot, so this new way makes a lot of sense to me.
What are I am only comparing him to 2B because only 2Bs played 2Bs. His value is *directly* comparable to the other performances at 2B. The SS on his team is "responsible" for his performance relative to the other SS. If you want to talk about how *next season* you might sign a SS to play 2B and how he'd compare to your 2B, that's different. Then *and only then* is the positional adjustment for defensive difference needed. What's the gap defensively there? a handful?

Also, overall, I am not 100% convinced it is easier to play SS. The double play goes a long way to close the fielding gap (I think). It's a differnt discussion that I haven't pursued, but we need to think longer about that. Defensive stats (like mine or MGLs) don't properly account for DP turning "difficulty".
   49. Mefisto Posted: December 20, 2008 at 06:52 PM (#3034706)
3B used to be more valuable than 2B.


I see this said a lot, but I don't think it's true, and it gets at something important for this debate. If you look at the number of plays being made by 2B and 3B, they don't change much over the years. To take a purely arbitrary example, in 1906 and 1907, Johnny Evers was making 200 plays per year more than Harry Steinfeldt. That pretty strongly suggests to me that managers were mis-evaluating the defensive spectrum, not that the spectrum itself has changed.

If we limit ourselves to estimating defensive value by offensive performance, we'd miss the fact that 2B were actually making many more plays. It's only by using a direct measure like Tango does that we capture this distinction.
   50. Chris Dial Posted: December 20, 2008 at 06:55 PM (#3034709)
And Mefisto, I am very happy to hear your opinion on this. I value it.
   51. Chris Dial Posted: December 20, 2008 at 06:56 PM (#3034710)
But why are you comparing him just to the second basemen? What about the shortstops? Pretty much all of them could play second base too. Shouldn't you be comparing him to them also?

I've had that conversation in my own head a lot, so this new way makes a lot of sense to me.
It's more related to the usage of the bunt versus not. Routine plays still were distributed evenly (evenly pctage wise 2Bs and SS still got lots mroe chances, but the 3B chances were more difficult), but a weak 3B would be bunted on more often. I think statheads underrate Pie Traynor for this reason.
   52. The District Attorney Posted: December 20, 2008 at 07:01 PM (#3034711)
If you want to talk about how *next season* you might sign a SS to play 2B and how he'd compare to your 2B, that's different.
I don't see how it's different. I would say that "how valuable is this player?", "if we brought in another guy to replace him, would that be better?", "if we traded him, how much should we be looking to get back?", etc. are all restatements of the same question.
   53. Joey Numbaz (Scruff) Posted: December 20, 2008 at 07:04 PM (#3034713)
I see this said a lot, but I don't think it's true, and it gets at something important for this debate. If you look at the number of plays being made by 2B and 3B, they don't change much over the years. To take a purely arbitrary example, in 1906 and 1907, Johnny Evers was making 200 plays per year more than Harry Steinfeldt. That pretty strongly suggests to me that managers were mis-evaluating the defensive spectrum, not that the spectrum itself has changed.


Johnny Evers plays were easy. 2B is a very easy position when you aren't expected to turn a DP. I played 2B in little league because I had no arm. The 3B were ALWAYS better players, before turning the DP became a huge part of the position. They were hitting and running all the time, making the pivot much less important.

Look at how 2B hit back then. If 2B wasn't easier, those managers sure were giving up a lot of offense at 3B. Were they all idiots? Players were faster, because there weren't power hitters. You needed a great arm to play 3B. Etc. It's not very hard to see how they were more valuable if you look carefully.
   54. Chris Dial Posted: December 20, 2008 at 07:04 PM (#3034714)
I don't see how it's different. I would say that "how valuable is this player?", "if we brought in another guy to replace him, would that be better?", "if we traded him, how much should we be looking to get back?", etc. are all restatements of the same question.
I don't think that's the right way to look at it. When we say Albert Pujols was the Most Valuable Player in 2008, it has nothing to do with "if we brought in another guy to replace him, would that be better?", "if we traded him, how much should we be looking to get back?".

Those aren't remotely close to restatements of the same question. They might if you added salary in your evaluation for the MVP, but I suspect you do not.
   55. Joey Numbaz (Scruff) Posted: December 20, 2008 at 07:04 PM (#3034715)
And mefisto, 1B make more plays than anyone. Is that a sign of it's difficulty?
   56. Chris Dial Posted: December 20, 2008 at 07:05 PM (#3034716)
Also, thanks to everyone. This is a great discussion, and really, THIS is the backbone of this site.

The only explanation: IT'S A TRAP!
   57. The District Attorney Posted: December 20, 2008 at 07:14 PM (#3034720)
When we say Albert Pujols was the Most Valuable Player in 2008, it has nothing to do with "if we brought in another guy to replace him, would that be better?", "if we traded him, how much should we be looking to get back?".

Those aren't remotely close to restatements of the same question. They might if you added salary in your evaluation for the MVP, but I suspect you do not.
Okay, so then it's the difference between whether you're trying to do "accounting" where you account for everything that happened in '08 and have it all add up to the real-life wins, or whether you're trying to figure out a player's value independent of some of the specific circumstances in which he found himself in '08.

That makes sense. I would certainly disagree, though, that we almost always do the former and hardly ever have any interest in the latter. We pretty clearly have great interest in both.
   58. Mefisto Posted: December 20, 2008 at 08:03 PM (#3034731)
And Mefisto, I am very happy to hear your opinion on this. I value it.


I'm happy to give my opinions. :)

Johnny Evers plays were easy.


We, of course, don't have any way to know this. And see below.

If 2B wasn't easier, those managers sure were giving up a lot of offense at 3B. Were they all idiots?


Absolutely not. Managers were trying to judge positional difficulty merely by watching. That turns out to be very hard to do. It's like trying to come up with the odds for poker simply by playing the game (an example I think MGL gave once). In the absence of hard data, this is a very difficult problem. Making it even harder to evaluate is the fact that not all plays are created equal (as you noted). It is true that the plays a 3B makes are harder, on average, than those a 2B makes. But we know today that the extra difficulty pretty much balances out the fact that a 2B makes so many more. As Tango's numbers show, the two positions turn out equal. That's the real benefit of his approach, namely that we realize something we might not have recognized.

The managers then weren't stupid, any more than physicists in 1900 were stupid. They just were lower down on the learning curve.

And mefisto, 1B make more plays than anyone. Is that a sign of it's difficulty?


Clearly not, and I should have been more precise. 2B have many more assists than 3B (more PO too). 1B have lots more PO, but many fewer assists.
   59. Joey Numbaz (Scruff) Posted: December 20, 2008 at 08:31 PM (#3034741)
Mefisto . . . this still doesn't account for the fact the game was different back then.

If people are using the hit and run, sacrifice and steal nearly every time a runner is on 1B, one would have to admit the turning the DP skill drops in value.

And if 3B/2B are equal in the modern game, is it that far of a leap to see that in the deadball era 3B had more value?

What about the prevalance of turf in the 1970s and 1980s. There are very clear signs that more defensive ability was needed to play up the middle in that era - how do the adjustments proposed deal with that.

The game of baseball is absolutely not static. It evolves. Over time certain skills become more valuable than others. If the adjustments don't account for this, they are missing something.
   60. snapper (history's 42nd greatest monster) Posted: December 20, 2008 at 08:44 PM (#3034743)
The game of baseball is absolutely not static. It evolves. Over time certain skills become more valuable than others. If the adjustments don't account for this, they are missing something.

I like the direct positional adjustments, but, I agree it definitely must be recalculated on a regular basis (not assumed to be some some of universal constant.

What really convinces me is this example. Say, there were 6 prime age ARod clones in a league at one time putting up a 150 OPS+ and 10 FRAA. And one Albert Pujols, putting up a 150 OPS+ and 10 FRAA, and a bunch of normal 115 OPS+ 1Bs with in aggregate average defense.

If you adjust for positional offense, Pujols will look better than the ARod clones. If you compare to league average offense (then add defense) Pujols will look equal to the clones.

But, we all intuitively know that the ARods could move to 1B, and be better fielders than Pujols. And, Pujols would be a train wreck at SS. To get the relative values right, you have to directly adjust for "degree of difficulty". Your good defenders at prime positions can always move down the spectrum. Your good defenders at 1B/RF/LF generally can't move up the spectrum.
   61. Joey Numbaz (Scruff) Posted: December 20, 2008 at 08:57 PM (#3034747)
If you compare to league average offense (then add defense) Pujols will look equal to the clones.


I know you aren't saying we should do it this way, but I think it's obvious that you cannot do it this way. I can't imagine any system that uses league average to calibrate the baseline will work. That's what I meant earlier when I said you'd be 'off'.

If you look at the bell curve, the 6 A-Rods are way to the right. Everyone gets this.

So if you are using the bottom 20% let's say to calibrate replacement level at a position (DanR uses the bottom 3/8); the 5 extra A-Rods, only move you from using number 25-30 to number 20-25, which isn't nearly as big of a difference as using #10 instead of #15 - which is where you get moved to if you are using 'average' as your baseline.

You have to account for the fact that stars aren't always evenly distributed by position.
   62. Joey Numbaz (Scruff) Posted: December 20, 2008 at 09:18 PM (#3034754)
I think position player value is pretty simple to measure, in theory:

1) Batting Value over Replacement level hitters (all positions treated equally).

2) Fielding Value over Replacement level fielders at the same position. Generally the baseline (replacement level) here is average, although Nate Silver suggests for SS it's a little below average. Tango thinks the method Nate used to come to this conclusion is somewhat flawed.

3) A fielding position constant - this is where the SS moves ahead of the 1B, assuming both are equally valuable based on #1 and #2 (snapper's example in post 60). This fluctuates over time at different position depending on the types of players in the league, the parks, the baseballs, manager strategies that are in vogue, etc..

We have #1 figured out pretty well. #2 is improving, and will get better over time.

The question is how to come up with 3.

DanR does it by taking the bottom 3/8 of regulars at a position. If I understand correctly Tango is trying to find this without using batting and this would be ideal - if it were to fluctuate based on the evolution of the game.

But I think they are both coming up with similar numbers anyway, that's the gist of post 44 right?

Am I missing something - I'm trying to make sure I understand exactly where we are right now.
   63. Mefisto Posted: December 20, 2008 at 09:36 PM (#3034758)
this still doesn't account for the fact the game was different back then.


This is just assuming your conclusion. The question we're trying to answer is whether, in fact, the game was different then (at least in this particular way; there's no doubt it was different in lots of other ways). The key point I'd make is this: despite the claims that 3B was a more important defensive position then, the ratio of assists made by 2B and 3B was not any different then than it is now. That suggests pretty strongly that the relative importance hasn't changed that much. I do agree that there were fewer double plays, but there were also lots more errors (and more by 3B than by 2B). How it all adds up can't be precisely known. My point is that we shouldn't just accept the claim, we should measure it.

I can't imagine any system that uses league average to calibrate the baseline will work.


Pete Palmer uses league average as the baseline.

I think position player value is pretty simple to measure, in theory:

1) Batting Value over Replacement level hitters (all positions treated equally).

2) Fielding Value over Replacement level fielders at the same position. Generally the baseline (replacement level) here is average, although Nate Silver suggests for SS it's a little below average. Tango thinks the method Nate used to come to this conclusion is somewhat flawed.

3) A fielding position constant - this is where the SS moves ahead of the 1B, assuming both are equally valuable based on #1 and #2 (snapper's example in post 60). This fluctuates over time at different position depending on the types of players in the league, the parks, the baseballs, manager strategies that are in vogue, etc..


I agree that these are relevant factors (I'd add baserunning and arm also, though we aren't really talking about those here). Where I disagree is how to calculate #3. IMO, we shouldn't be using offensive metrics to estimate defensive value. We should be measuring defense by itself. That's what Tango's system attempts to do.

The game of baseball is absolutely not static. It evolves. Over time certain skills become more valuable than others. If the adjustments don't account for this, they are missing something.


I completely agree. That's why we need a LOT more work on the dead ball era.
   64. Blackadder Posted: December 20, 2008 at 09:38 PM (#3034759)
That's right Joe. The biggest differences are

1) Dan sees the SS to 2B/3B as around .8 or .9 wins, while Tango has it as .5 wins

2) Dan sees the CF to corner gap as around .6 wins, Tango as a full win difference.

These discrepancies aren't enormous, of course, and it is somewhat encouraging that two such different methodologies come to relatively similar conclusions. Still, they aren't insignificant either, especially when looking over a long career, so one would in the end like to know which, if either, was "right".
   65. Darren Posted: December 20, 2008 at 09:44 PM (#3034761)
What really convinces me is this example. Say, there were 6 prime age ARod clones in a league at one time putting up a 150 OPS+ and 10 FRAA. And one Albert Pujols, putting up a 150 OPS+ and 10 FRAA, and a bunch of normal 115 OPS+ 1Bs with in aggregate average defense.


We call this theoretical time the early 2000s.
   66. Joey Numbaz (Scruff) Posted: December 20, 2008 at 09:45 PM (#3034763)
I do agree that there were fewer double plays, but there were also lots more errors (and more by 3B than by 2B).


This is evidence for 3B being tougher. SS make more errors than anyone, right? With lousy gloves and faster runners, 3B has much less room for error (pun intended) than 2B does.

I don't think raw numbers of plays are the way to measure it at all. Degree of difficulty is a much more important factor in the equation.

My point is that we shouldn't just accept the claim, we should measure it.


We have. If you assume managers act rationally, you can tell a lot by how players that played a position hit. There is a clear tradeoff between fielding and hitting availability at each position. The tougher the baseline of fielding ability needed to play the position, the worse the players chosen generally hit. I think this is a much more robust way of looking at the issue than just the number of assists and putouts players made.
   67. Willie Mayspedester Posted: December 20, 2008 at 09:53 PM (#3034766)
Would the same positional context need to be taken into account for baserunning as well? You would think that baserunning ability would not be equal for all positions and would also be independent of hitting and fielding abilities. For example Adam Dunn used to steal a few bases but was always a bad fielder.

Another example would be Matt Holliday for the A's. I've been thinking that his addition to the team would pretty large considering his replacement of Jack Cust. Next year he's replacing a valuable hitter who loses value in both fielding and baserunning. Now that the A's can hide Cust's glove at DH with somebody above average at fielding and baserunning would probably add at least a couple wins.

My question can be simplified to this... Is it more valuable to have a a plus baserunner at a position with a lower baserunning replacement value? Carl Crawford or Rickey Henderson would be other good examples. I guess you could just include it into offense for that position.
   68. Tango Posted: December 20, 2008 at 10:08 PM (#3034770)
Good thread, the kind of thread that attracted me to the old Primer. I'll just reply on those that directly referenced me, and then I'll make another post later for the rest of the thread.

***

So a team full of Willie Bloomquist would be utterly average?


As fielders, yes.

It doesn't necessarily have to be Willie. It's always nice to have a real face to the issue. Willie plays all the positions, and he looks average, and he has overall, pretty average numbers. Plus, my readers voted him the worst player in baseball two years ago, so I have a special affinity for this guy. If you want to use someone else, Melvin Mora, or whoever, feel free to bring a better name forward. I used to call this player "Hubie Raines", in honor of Hubie Brooks and Tim Raines.

This was first brought forward in 2003/2004, and one of the first articles on the subject is here:
http://tangotiger.net/UZR9903TT.html

My blog is filled with such "multiple position" comparison. Only recently have I included the lefthanded issue, which brought the CF down a peg, and in-line with 2B/3B.

I'm probably missing something, but lately it seems like the people who are working with defensive numbers are treating them more like gospel than they deserve to be treated at this point.


I go out of my way to say that they are not gospel and that lots of work needs to be done here.

I think anybody who starts promulgating a new stat has the duty to explain why the stat has value and how it came to be calculated.


I "promulgate" on my blog. If you think more people should cite their references more, you should take it up with them. In this case, you should shoot the messenger! Seriously, as Bill James once said, if it sounds like you are walking into the middle of a conversation, it's because you are. It would be nice if we have everything in one spot. It's just not always possible for us amateurs to find that time to get everything summarized.

I am ready to be convinced, but the argument Dave makes and others convinces me more that it isn't correct.


A good article and followup can be had here. We just need some time. I know I would enjoy the discussion with Chris and Dan R and several others.

Now, let me comment on the rest...
   69. Tango Posted: December 20, 2008 at 10:50 PM (#3034786)
VORP is adjusted, yes, but it is only adjusted to normalize offense across positions, not defense as well.


Untrue.

The idea behind what VORP does is to "neutralize" the offensive disparity among positions so that you can simply add in the fielding value relative to position (which is what SuperVORP is). The end result is that you don't have a positional bias.

Otherwise, if you simply do: offense above average (without regard for position) and defense above positional average, then the average 1B will be far higher than the average SS (by some 20-25 runs or more).

Chris with OPD (offense plus defense) ensures that the average at each position is exactly equal. He does that because his presumption is that a position is a position, like QB, RB, DT. I don't do that because baseball players are alot more fluid in their movement, like Left Defensemen and Right Defensemen, or Left Wing and Right Wing in hockey. No one in the NHL would measure Centers against other Centers. You WOULD do Forward against Forward. So, you really have "pools" of positions: C, IF, OF, 1B/DH. (In baseball, the pool on the right includes the pool on the left.)

Anyway, like I said, we can have a long discussion about this.

The problem. however, is that there's an implicit assumption in doing things that way that the sum of the defensive differences between any two positions are equal to the offensive differences within a given year. That just is hardly ever true, and leads to incorrect valuations of players.


Right, my position entirely.

LF will never be equal defensively to CF. 2B will never be equal defensively to SS. When the metrics miss this important difference, they're wrong.


People may also be surprised to know that the average RF hitter was WORSE than the average CF hitter in the 1950s. Would it make any sense that the average CF (off+def) equals the average RF in this case? You'd have to believe that the average RF was a better fielder in the 1950s.

To say nothing of when Brian Giles gets the bad luck of having Barry Bonds in his NL LF pool, and the next year he has the good luck of not having him in the NL RF pool.

And if you consider the DH/1B issue?

How about high school? Would you want the average SS there to be equal to the average 2B? OPD sets that as a requirement. Now, Chris may say that the SS from one team is competing with the SS of the other team. But, when he makes his list, he includes all players, and so if you have an average high school SS and an average high school 2B, they both come out equal in Chris' list.

That's why I can't go along with positional adjustments that make it a requirement that the average at each position is always identical under all circumstances.


What we're talking about here is rigid and inflexible, based on the conceit that value is based on some absolute difference in difficulty.


These adjustments apply only to the time period it was based upon (2003-2008). If for example the 1970s was filled with a ton of fantastic fielding SS, I'd have different adjustments. So, Dan's presumption here is in fact not a presumption of my system.

***

If there's anything else that I need to directly reference, please let me know.

***

In summary, I ask the question: "How does this player field compared to Willie Bloomquist, or some composite who is average in all tools respect (speed, strength, agility, etc), and who is equally experienced at all positions?"

Since this is the common baseline that we are comparing all baseball players against, we can make the apples-to-apples comparison. And that's what those positional adjustments do.
   70. Mefisto Posted: December 20, 2008 at 11:19 PM (#3034797)
This is evidence for 3B being tougher. ... With lousy gloves and faster runners, 3B has much less room for error (pun intended) than 2B does.


Agreed.

I don't think raw numbers of plays are the way to measure it at all. Degree of difficulty is a much more important factor in the equation.


While I absolutely agree that number of plays isn't enough by itself, the fact is that 2B in the deadball era were making 200 more assists each year than 3B were. That suggests that we'd have to consider 3B WAAAAY more difficult in order for the positions to be even.

Maybe they were. But the right way to test that is not by their relative offensive contributions; that's too indirect a measure. The right way is Tango's way. As he says, his estimates are era-dependent. Until someone does a good study of the deadball era which directly measures the difference, I'm going to remain agnostic on the question whether 3B was, in fact, more valuable defensively.

If you assume managers act rationally, you can tell a lot by how players that played a position hit.


It's not so much a matter of rationality, it's a matter of the data they put into their reasoning process. Sure they're rational (though Bill Bergen is hard to explain on that basis), but they didn't have PBP data to actually measure what was happening on the field. They had to rely solely on what they saw. As I said above, it's very hard to sort out the relative importance of two positions when one makes a lot more plays but the other's plays are harder. Those are incommensurate factors and people in general aren't very good at weighting them without more systematic methods than simple observation.

There is a clear tradeoff between fielding and hitting availability at each position. The tougher the baseline of fielding ability needed to play the position, the worse the players chosen generally hit. I think this is a much more robust way of looking at the issue than just the number of assists and putouts players made.


Well that's certainly NOT my position, nor is it Tango's. The measure is not the number of assists made; I just mentioned that to show that the number of plays made at a position hasn't changed much over the years. That's suggestive but not conclusive. As I've agreed, it's important to account for difficulty as well. I just want to do that directly, rather than use offensive ability as a proxy. That's a bad choice because it depends on the accuracy (not the rationality) of a manager's observations.
   71. Chris Dial Posted: December 20, 2008 at 11:28 PM (#3034801)
Would you want the average SS there to be equal to the average 2B? OPD sets that as a requirement.
No, it doesn't. It just appears that way. The average SS creates/saves runs against average the same amount as a 2B does. that is not the same thing as saying they are "equal". They *do* create/save equal number of runs. I don't find that to be a controversial position. Of course, assumes that "average" is the baseline. Were my baseline a % replacement level, your statement wouldn't necessarily follow.

An average 2B creates/saves runs the same as an average SS as compared to the league average 2B or SS as applicable. I don't think that's quite the same. I have, in this argument before, simply posted the raw values rather than adjusted against average (but then people talk about zero being the baseline - you can't please everyone , and usually not anyone). If you use zero, you can clealry see that a SS isn't "equal" to a 2B.
   72. Jeff K. Posted: December 20, 2008 at 11:55 PM (#3034814)
VORP is adjusted, yes, but it is only adjusted to normalize offense across positions, not defense as well.

Untrue.

The idea behind what VORP does is to "neutralize" the offensive disparity among positions so that you can simply add in the fielding value relative to position (which is what SuperVORP is). The end result is that you don't have a positional bias.


I understand that. But your last sentence is what I understand to be the point of what you're trying to do (and yes, I realize the irony of arguing with you about what your point was. :) ) VORP's attempt is to completely neutralize the context of position. The problem is that we shouldn't neutralize that context. A 2b with a VORP of 50 is more valuable than a RF with a VORP of 50, because VORP has normalized out a part that makes him more valuable.

Here's the progression, with the last part being my understanding of what you're trying to do:

Old - No adjustments whatsoever
VORP - Adjust hitting by position, add AdjHitting+Defense+Baserunning
New - Adjust hitting by position, add defensive positional modifier, add AdjHitting+AdjDefense+Baserunning

No?
   73. Tango Posted: December 21, 2008 at 12:05 AM (#3034821)
I don't think that's quite the same.


Ok, so let me ask the question: if you have a 2B who hits as well as the average 2B and who fields as well as the average 2B and you have a SS who hits as well as the average SS and who fields as well as the average SS, will they both, when you produce an "overall" list of all nonpitchers, be listed side-by-side as equals?
   74. Honkie Kong Posted: December 21, 2008 at 12:05 AM (#3034823)
The average SS creates/saves runs against average the same amount as a 2B does. that is not the same thing as saying they are "equal". They *do* create/save equal number of runs. I don't find that to be a controversial position. Of course, assumes that "average" is the baseline. Were my baseline a % replacement level, your statement wouldn't necessarily follow.

This is exactly what I can't follow. Are we talking about a scenario where what would happen if Frank Thomas played SS? Or are we more interested in what would happen if player X went down for 30 games?

Because we shouldn't need a construct for the latter situation. Take the average ( offence and defence ) of all players who have played games at Position X, but appeared there less than 50 times that year. That SHOULD be your replacement level.
Once that is defined, we should not need positional adjustments, as the replacement level should give us an idea of the available talent in the market ( This is making a very big assumption that the baseball player movement is governed by an efficient market ).
   75. Honkie Kong Posted: December 21, 2008 at 12:08 AM (#3034825)
And following onto #74, there are obviously issues with the methodology. If Jeter goes down for a few games, and ARod plays 30 games at SS, there will be a change in the replacement level of SS. I don't know if that is something we want reflected.

Or if Chipper Jones plays SS in a shift, is it counted as a game at SS?
   76. Tango Posted: December 21, 2008 at 12:11 AM (#3034828)
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".
   77. Tango Posted: December 21, 2008 at 12:13 AM (#3034829)
To reiterate and bold:

In summary, I ask the question: "How does this player field compared to Willie Bloomquist, or some composite who is average in all tools respect (speed, strength, agility, etc), and who is equally experienced at all positions?"

Since this is the common baseline that we are comparing all baseball players against, we can make the apples-to-apples comparison. And that's what those positional adjustments do.
   78. Exploring Leftist Conservatism since 2008 (ark..) Posted: December 21, 2008 at 12:15 AM (#3034831)
here a question: a poor fielding shortstop or catcher might be "more valuable" than a better fielding first baseman (say the shortstop below replacement level and the first baseman is below average but above replacement level). depending on the exact numbers, once you adjust the shortstop might be "more valuable," but is he really more valuable than the team since he's not playing his position well?
This is why, in my HOF analysis of him, I treat Jeter as a slightly subpar defender at 3b.
   79. Honkie Kong Posted: December 21, 2008 at 12:26 AM (#3034836)
Since this is the common baseline that we are comparing all baseball players against, we can make the apples-to-apples comparison. And that's what those positional adjustments do.

Not to belabor the point, but this is where I am getting a disconnect. I might just be a little dense today, so a little patience please.
Why do we need a fictional Hubie Raines/Willie Bloomquist figure? Every team has their version of that figure, who is plugged into holes opened up by injury. Ryan Freel or Omar Infante or Eric Bruntlett or Willie Harris. The list goes on.
What we do know however is the average production of these characters over a season at various positions in terms of solid numbers without names. So averaging all these characters over a season should give us a replacement level production at the position.

Assume this were not true. Then if say Chase Utley went down, and I don't have a replacement level player, I will trade for one ( say Iguchi if he were available), and thus set the replacement level value at 2B. Now the market of available players at a position should set its replacement level. So then you can directly compare 2Bs v 2Bs..or if you want a hypothetical replacementlevel figure, you average out the replacement level production at all positions, and normalise the replacement level for each position.

The way I understand it, you are not approaching it in the way I posited above, so maybe my disconnect.
   80. Chris Dial Posted: December 21, 2008 at 12:29 AM (#3034838)
if you have a 2B who hits as well as the average 2B and who fields as well as the average 2B and you have a SS who hits as well as the average SS and who fields as well as the average SS, will they both, when you produce an "overall" list of all nonpitchers, be listed side-by-side as equals?
Yes. And for their respective teams, their performance was that.
   81. Famous Original Joe C Posted: December 21, 2008 at 12:31 AM (#3034841)
I've just skimmed this thread, and no one has answered JoeHova's questions from #20. My apologies if I missed it.

But where do the numbers come from? Why is the adjustment from SS to 1B 20 runs? What data was analyzed to come up with that? How much variance is there?

Reposting what JoeHova said as well, because I thought it warranted saying twice:

I'm probably missing something, but lately it seems like the people who are working with defensive numbers are treating them more like gospel than they deserve to be treated at this point. I think anybody who starts promulgating a new stat has the duty to explain why the stat has value and how it came to be calculated. I'm not saying that people are necessarily failing to do that, I'm just saying that the burden is on the prosecution.

Can anyone point me to whatever study or studies these numbers are based on? I've been reading Tango's stuff for years, and he's done alot of great work, but I can't just buy these numbers that have such precision attached to them (7.5 runs? Why not just 7 or 8? Is your precision really that good?) as gospel without understanding how they were developed.
   82. Chris Dial Posted: December 21, 2008 at 12:31 AM (#3034842)
This is exactly what I can't follow. Are we talking about a scenario where what would happen if Frank Thomas played SS? Or are we more interested in what would happen if player X went down for 30 games?
Neither. We are saying 'Here's the performance of Dan Uggla. Compared to his peers (NL 2B), he outperformed them by X runs." It isn't about a "What if?" scenario. It is a reality question. What did Dan Uggla do, compared to the othe rplayers that played 2B. Every team has to have a 2B. No SS plays 2B. Because if they are playing 2B, then they are a 2B, not a SS. there are few - very few - Willie Bloomquists.
   83. Honkie Kong Posted: December 21, 2008 at 12:34 AM (#3034844)
Yes. And for their respective teams, their performance was that.

Not true is it, atleast not semantically? Shouldn't the value of a SS who is average but has lower replacement level be higher than a 2B who was average but has a higher replacement level, atleast to the team?

As individual players in no team context, your statement should have validity.

EDIT : Not to clutter up the thread, in response to #82. I was of the opinion that you wanted to compare non-pitchers across positions. I thought that was the whole idea behind positional adjustments.
   84. Joey Numbaz (Scruff) Posted: December 21, 2008 at 12:38 AM (#3034847)
This is why, in my HOF analysis of him, I treat Jeter as a slightly subpar defender at 3b.


Why on earth would anyone do this? He's a SS. You can't treat him as a 3B . . . you need to figure out his actual value as a SS, anything else is a wildly inaccurate shortcut, IMO.
   85. Joey Numbaz (Scruff) Posted: December 21, 2008 at 12:47 AM (#3034854)
If I were moving Jeter around, I'd treat him as a good 2B. His arm wouldn't be an issue, and he's athletic enough that he'd likely be great on the DP. I think he'd be a much better 2B than 3B; not that it matters anyway, since he's a SS.
   86. SkyKing162 Posted: December 21, 2008 at 01:12 AM (#3034872)
Neither. We are saying 'Here's the performance of Dan Uggla. Compared to his peers (NL 2B), he outperformed them by X runs."


Why are his peers only NL 2B? Why not MLB 2B? Why not MLB middle-infielders? Why not MLB infielders? Why not all MLB position players?

And, what about all the players who played multiple positions? Who are Blake DeWitt's peers? Does all of his offensive performance count as a "peer" for other 2B and 3B? Or only his time hitting while fielding those individual positions?

Those aren't rhetorical attacking questions, I'm sincerely interested in the way your position would address those questions.
   87. SkyKing162 Posted: December 21, 2008 at 01:16 AM (#3034873)
I think [Jeter]'d be a much better 2B than 3B


But Jeter's TALL!
   88. BFFB Posted: December 21, 2008 at 01:19 AM (#3034875)
VORP - Adjust hitting by position, add AdjHitting+Defense+Baserunning
New - Adjust hitting by position, add defensive positional modifier, add AdjHitting+AdjDefense+Baserunning


is this not making the same "adjustment" from different start points, that in the "new" method you are double counting (or penalising)?
   89. SkyKing162 Posted: December 21, 2008 at 01:26 AM (#3034878)
If it's helpful:

1. Offense
2. Position
3. Fielding

Some ways to combine things...

Offense + Position = VORP (hitting valued by position)
Position + Fielding = Defense
VORP + Fielding = Total Value
Offense + Defense = Total Value

It's all just fun with the associative property (with some difficult details and philosophies to work out.)
   90. Chris Dial Posted: December 21, 2008 at 01:31 AM (#3034879)
Why are his peers only NL 2B? Why not MLB 2B? Why not MLB middle-infielders? Why not MLB infielders? Why not all MLB position players?
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.

And, what about all the players who played multiple positions? Who are Blake DeWitt's peers? Does all of his offensive performance count as a "peer" for other 2B and 3B? Or only his time hitting while fielding those individual positions?
Fortunately, these players are extremely few, and their PAs are rarely evenly split *and* players that play multiple positions generally play "similar" positions. I categorize a player like that *for offense* with the group he played the most defense as. His Defensive Innings is what I use to assign his offensive performance above average. Yes, there are very few for whom this will result in a few runs "off", but not many. His defense is balanced against the position he played it against. So Blake DeWitt's defense as a 3B is compared only to other NL 3B (and so on and so forth).

The error bars of offensive and defensive measurement are certainyl wide enough that if OPS says DeWitt is +30 runs above average, and wOBA says +28 runs and VORP says +26 runs above average, we're entering the realm of a quibble over a fineness none of the metrics can attain. YES, OPD could be slightly more refined in this respect *BUT* one of my key rules in working to develop a metric like this is that it is verifiable by ANYONE. My calculations are completely transparent and can be duplicated by anyone. The extra complications required to achieve VORP (or other adjustments of breaking ABs by position played) just don't add a layer of accuracy that, IMO, justify the extra work for the vast majority (what - 700 of 750 players?), particularly in most cases the differnces will be less than a run (due mostly to the fact that players that play many positions usually don't get many PAs). There are a few exceptions, but I don't think they justify the legwork.

And as there is some error in all methods, OPD stands up (confession time: I am changing the calculation due to an issue Tango and terpnats mentioned at THE BOOK BLOG) to all of them within a run or two. I was undervaluing doubles, but that's being corrected.
   91. Chris Dial Posted: December 21, 2008 at 01:35 AM (#3034880)
Those aren't rhetorical attacking questions, I'm sincerely interested in the way your position would address those questions.
NP. I hope my response doesn't take on that tone. I do get excited, and may seem short, but it's really about passion, not personal attacks.
   92. Tango Posted: December 21, 2008 at 01:44 AM (#3034883)
Chris/80: in that event then, your response would be the same for the 1950s, a time when RF were outhit by CF, correct?

And this is why I can't accept it.

If we know that the average CF is a better hitter than the average RF, and we "know" that the average CF is a better fielder than the average RF, then I can't accept that the average CF is equal to the average RF. But in your system, that's what you end up with, because the average at each position will always rank as side-by-side equals (given equal playing time).

How do you reconcile this issue in high school?
   93. Chris Dial Posted: December 21, 2008 at 01:55 AM (#3034886)
in that event then, your response would be the same for the 1950s, a time when RF were outhit by CF, correct?

And this is why I can't accept it.

If we know that the average CF is a better hitter than the average RF, and we "know" that the average CF is a better fielder than the average RF, then I can't accept that the average CF is equal to the average RF. But in your system, that's what you end up with, because the average at each position will always rank as side-by-side equals (given equal playing time).
THat's because they are. I don't know why you can't accept it. Their contributions on the field outpace their counterparts equally. They *are* equal with respect to what we are measuring, and that is how much they help their team win on the field. I think you may be trying to measure something else.
   94. Chris Dial Posted: December 21, 2008 at 01:56 AM (#3034887)
How do you reconcile this issue in high school?
Really, this question doesn't make any sense to me. Reconcile what?
   95. SkyKing162 Posted: December 21, 2008 at 01:56 AM (#3034888)
I agree that in today's game, offensive adjustments and defensive adjustments are within our error bars. 3B and DH seem to be the only significant exceptions.

But, hypothetically, what if GM's went crazy and decided to play suboptimal players at 2B? Say 2Bs are now AA-caliber, so that Uggla is a superstar in relation to the rest of the pack. Does he deserve credit for that? Yes, he is a relative advantage in one of those football style pro/con checklists when comparing teams. But is HE more valuable, or have the Marlins just made a better decision than other teams. If the Braves move their SS Escobar to 2B and bring up a replacement-level SS, their team improves and Escobar rates as way more valuable. But is he? Or are the Braves just smarter? Isn't the real upgrade from the crappy AA-level 2B to the passable SS? Escobar is who he is.
   96. Chris Dial Posted: December 21, 2008 at 02:00 AM (#3034890)
There is a "baseline of talent" to play in MLB. No such thing exists in HS. The talent spread in MLB approaches zero compared to HS.
   97. SkyKing162 Posted: December 21, 2008 at 02:02 AM (#3034891)
Chris, how do you approach DH value? You've probably addressed this multiple times before, sorry.
   98. Chris Dial Posted: December 21, 2008 at 02:07 AM (#3034895)
But is HE more valuable
Absolutely.
If the Braves move their SS Escobar to 2B and bring up a replacement-level SS, their team improves and Escobar rates as way more valuable. But is he?
Absolutely. His value to his team is increased. His value is increased. He is more valuable.
   99. The District Attorney Posted: December 21, 2008 at 02:08 AM (#3034896)
I don't understand what the "every team needs to have a second baseman" argument is supposed to prove. Yes, you need to have a second baseman¹. One of the ways that you can get one is to get a player who had been playing shortstop, and make him a second baseman.² You can replace a second baseman with a shortstop. That is why you would want to consider the shortstops' abilities when you consider the second basemens'.

I understand that, if your goal is to account for what happened last year, you can compare only like positions to like positions and still have it all "add up". But 1) that becomes of little use once you move away from the "accounting for last year" scenario (What are our team's strengths and weaknesses? Who is more valuable to our franchise? If we're "timelining" and thus not assuming that every year of baseball history is zero-sum, who is greater, Player X from 1950 or Player Y from 2000?, etc. -- all of these questions are better answered by the more abstract method than by the "accounting" method), and 2) although you can make things add up that way, I don't see why it's actually preferable to do so.

¹ Although you don't, actually, right? You just need to field nine players. If anything, that argues further for the second positional adjustment, IMO, since if you followed that argument to its conclusion, it would lead you to "Uggla's identity is one of the hitters on the team", not "Uggla's identity is a second baseman."
² And as a bonus, said player will likely be a better defensive 2B than he was a SS.
   100. Chris Dial Posted: December 21, 2008 at 02:10 AM (#3034897)
Chris, how do you approach DH value? You've probably addressed this multiple times before, sorry.
I have. And I hate the DH. Fortunately there are very few of them. I basically give them a zero defensively, because that's what they contribute. That's another reason to keep the leagues separate. Usually they play some defense, and then that's what they have contributed to their team's winning.
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