### Explaining some new math

December, 19, 2008
12/19/08
2:23
PM ET
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.

What it does mean, though, is that the gap between Concepcion and Perez, offensively, is likely made up for more so by defense and adjusting for the difficulty of the position.

If Concepcion in a given year with 700 PA was -8 runs batting and +10 runs fielding, and Perez is +15 runs hitting and +3 runs fielding, it looks as though Tony was vastly superior. However, the adjustments need to come into play, because +10 at SS is MUCH better than +3 at 1B. It's not an advantage of +7 runs, it's +7 runs added onto how much more difficult it is to play SS. Via Tango's work, SS is +7.5 runs vs. -12.5 runs for 1B, so we're talking about a +20 run swing.

Therefore, in this theoretical season, Conception is -8 + 10 + 7.5, or +9.5 runs above average (+29.5 above replacement), and Perez is +15 +3 -12.5, or +5.5 runs above average (+25.5 above replacement). Even though he was much better offensively and not sluggish defensively in this hypothetical, because 1B is not nearly as difficult as SS, the gap diminishes, or even goes in the other direction.

Me: Let's continue on this line of reasoning … Wouldn't we wind up concluding that there are too many first basemen in the Hall of Fame and not nearly enough shortstops? Do we now believe that Omar Vizquel belongs in the Hall of Fame and Jim Thome does not?

Eric: Yeah, that would essentially be the case, assuming that the HOF voting takes everything into account. Unfortunately, it doesn't, so you have guys who stunk in the field but hit 500 HR making it into the HOF, while tremendous fielders who were likely much closer in overall value (factoring in baserunning, as well) having to become icons in the field to even get noticed.

I always come back to Adam Everett when I talk to my dad or [grandfather] about this. It is very easy to see who was the best offensive player from 2004-07, but I would say 95 percent of this country has no idea just how good Everett was on defense. I would really have to see Vizquel's numbers defensively to ensure they match his reputation, and I don't know when [Baseball Info Solution's John] Dewan started doing the +/-, but in terms of overall value, yeah, there are bound to be plenty of SS/2B who are vastly undervalued compared to 1B.

If you had a 1B and an SS who could put up identical offensive lines, wouldn't you want the SS because it is a much tougher position? That's really the point of this, and it definitely means the answer to your question is a yes. I would rather have an average-hitting SS with a fantastic glove than a 1B with above-average (not Pujols or Berkman, but above-average) offense yet a poor glove.

Me: Understood, but I'm still trying to get a handle on the utility of all this information. Is it simply about accurately measuring the real-world value of Adam Everett? And would you argue that Everett (for example) has been terribly underpaid in his career, in terms of dollars per win?

Eric: Yeah, in terms of measuring the OVERALL value. The basic point is that, if you have a +10 run SS and a +7 run LF, the SS has an advantage of way more than just 3 runs, because the position is so much harder to play. Tango's research showed that it's a swing of about +20 runs. So a +10 SS, with positional adjustments taken into account, is actually closer to +18 runs better defensively than the LF. 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.

As far as Everett is concerned, his offensive runs from 2004-06 are -6, -18, -26, but with UZR numbers of +10, +13, +24.

With the adjustments and value over replacement prorated, he comes out at +2.3 Wins Above Replacement, +1.8 WAR and +2.1 WAR, so his fair market values in those years were north of \$7 million (granted, he's been under team control for most of his career). As a free agent this year without the injury last season, we may have seen a more reasonable deal, but at just \$1 mil he is a steal.

So the utility is that it levels the field of play between fielders at different positions. Two players with identical runs saved, but one at 1B and one at SS, are by no means equally valuable fielders, and the adjustments help us understand that.

Me: Thanks a mil, Eric. If you're saying what I think you're saying and you're right, inevitably a number of teams are going to use the same math when valuing players, and we may see a real surge in the salaries of great shortstops, particularly.