First, we need to establish a basic measure of Willingham's offensive value. A good, all-in-one stat to sum up a hitter's overall offensive value that I've used here before is runs created (RC). There are many ways to calculate RC, but they all of them do more or less the same thing, summing up the hitter's total offensive contribution and quantifying it as a total number of runs that they created for their team. Because I'm kinda lazy and not that good at math I like to use the most simple version: OBP x SLG x AB. Although there are far more sophisticated versions of RC that factor in things like stolen bases or performance in the clutch, this one is close enough for my purpose here and will usually get us within a run or two of the more sophisticated formulae.
Using Willingham's 2008 rates (.364 OBP / .470 SLG) and assuming a full season of let's say 500 ABs, his season total RC would be 85.5. The average NL LF (.350 OBP / .435 SLG) creates 76.1 runs in 500 AB, a difference of about 9.5 runs (which would be worth a little more than one additional win above average).
(Of course, the Nationals' LFs were nowhere near average last year, hitting a horrendous .303 OBP / .328 SLG on the year--jeez, just think of that. In 500 ABs, that production gives you 49.7 runs. I don't think it's possible that the Nationals could possibly repeat that kind of performance no matter what they do, but there it is, for reference.)
Now let's try to establish whether Willingham is in fact the stone-gloved outfielder Cameron says he is. Defensive stats are famously unreliable, but there are some good metrics out there that quantify how effectively fielders convert batted balls into outs.
First, let's look at Zone Rating. This stat simply divides the field up into zones and simply tallies up the percentage of plays a fielder makes on balls in his zone. Here are Willingham's ZR numbers for the last three years:
- 2006: .790 (18th out of 19 gold glove-qualified LFs--only Manny Ramirez was worse)
- 2007: .828 (10th out of 17)
- 2008: .847 (would be 6th out of 12 qualified LFs, if he'd qualified, which he didn't because of the back)
To measure Willingham's defensive deficiencies against his offensive contributi0ns, however, we need some way to translate these defensive stats into an apples-to-apples metric, like how many runs he creates offensively vs. how many runs he allows with his bad defense. We'll get to his offensive runs created further down in this post, but for now let's look at runs allowed.
Chris Dial, posting at the Baseball Think Factory, has done just this. You can read his methodology in detail here, but the basic idea is to take ZR and translate it into runs prevented or allowed. The bottom line is that Dial estimates based on zone rating that Willingham cost the Fish 15 runs in 2006, 9.2 runs in 2007 and 2.5 runs in 2008 versus what the average LF would do (keep in mind that because Dial's ZR to runs prevented calculation is a counting stat that Willingham's '08 defense would translate to about 4 runs below average for a full season).
In other words, based on this particular stat, Willingham's '06 defense would make him a 5.5 runs below average overall player, his '07 defense would make him an exactly average overall player, and his '08 defense would make him a 7 runs above average player.
Of course, the relative unreliablilty of defensive states like ZR requires us to look at a variety of methodologies. David Pinto's Probabilistic Model of Range (PMR) is like a super-charged version of zone rating. Pinto uses a variety of batted ball data and historical fielding outcomes to determine how likely it is that an average fielder would convert each ball in play into an out. Those calculations give him an "expected" number of outs, which he then compares that to the actual number of outs converted to establish each fielder's total number of outs coverted above or below average.The system is based on Mitchel Lichtman's Ultimate Zone Ratings system (which he stopped publishing after he was hired by the St. Louis Cardinals in 2004), and Pinto posts his results at his Baseball Musings site, with archives going back to 2004. If you're interested in a more detailed explanation of PMR, read here.
Here's what PMR says about our friend Josh:
- In 2008, 2551 balls were hit in play while Willingham was in left. He converted 166 of those into outs, versus 173.8 "expected outs," for a ratio of 95.51%, ranking 35th out of40 LFs with a minimum of 1000 balls in play.
- In 2007, 3653 balls were hit in play while Willingham was in left. He converted 211 of those into outs, versus 223.26 "expected outs," for a ratio of 94.51%, ranking 34th out of 42 LFs with a minimum of 1000 balls in play.
- In 2006, 3255 balls were hit in play while Willingham was in left. He converted 206 of those into outs, versus 210.68 "expected outs," for a ratio of 97.78%, ranking 27th out of 40 LFs with a minimum of 1000 balls in play.
To translate these numbers into runs prevented, we'll use a methodology created by Angels blogger Los Angeles Waterloo of Black Hawk and maintained this year by Beyond the Box Score's David Turkenkopf. You can read more about it here. The bottom line for Willingham is that he cost his team just 3 runs in 2006 compared to an average left-fielder. In 2008, Turkenkopf's calculations have Willingham at 6.48 runs below expected, which considering that he saw just 2551 balls in play (a full season would put him around 4100), that translates to about 10.4 runs for a full season. For some reason LAWBH's archive of his 2007 calculations for LFs isn't linked, so we don't have that. However we can see that his made outs to expected outs ratio in '07 was a bit worse than in '08, so he probably cost the Marlins somewhere around 11-13 runs in '07--just a guess.
Now let's turn to Rate2, a defensive stat invented by my buddy Ed's fantasy league-mate Clay Davenport (who also happens to write for Baseball Prospectus). It's a similar measurement to PMR, though I really don't know the detail on how the stat is derived. But in short Rate2 tells us how many runs above or below average the fielder is per 100 games. So for instance a fielder with a Rate2 of 90 would be costing his team 10 runs per 100 games.
Willingham's Rate2s are:
- 2006: 88
- 2007: 80
- 2008: 94
So putting it all together, Willingham is clearly a below average left fielder. There's some evidence that he's might be getting better, though that finding doesn't carry through all the methodologies. And there's a ton of variation within the different metrics that makes it hard to make firm conclusions.
So rather than trying to decide whether he's really going to cost us 30 runs or 3, I think it's probably fair to assume that he'll provide defense that is somewhere in the middle of these stats, costing us let's say somewhere around 12 runs in 2009. If he does that while putting up offensive numbers consistent with 2008 while playing a full season (which you'll recall we calculated about would put him at 9.5 RC above average), he'll be about 3.5 runs below average overall. You can think of this as something like the 2008 offensive produce of a Bengie Molina or Yunel Escobar, combined with dead average defense.
That still means he'd be about a 23-run improvement--about 3 additional wins--over the horror show we had in LF in '08. But it's hardly anything to get crazy about--any way you cut it, you're going to lose more games than you win with below average performance. But if your goal is to move from embarrassingly unwatchable to bad but respectable, Willingham should help us achieve that.
However, because it's prudent to at least be aware of the worst-case predictable scenario, let's consider what we'd be getting if he plays defense that's closer to those awful '07 and '06 Rate2 numbers or his '06 ZR stat and assume that he costs us more like 20 runs in the field in 2009. Further, let's assume (as we really ought to) that his offensive production slips a little with age, and that he falls to let's say .360 OBP / .465 SLG, which would be about consistent the erosion you'd expect for an age-30 player. That would mean that offensively he'd be giving us 83.7 RC in 500 AB, now just 7.5 RC above the average NL left-fielder. After knocking off the 20 runs he could give back defensively, now you're looking at a combined 12.5 runs below average player. You can think of that as the equivalent of Mark Teahen's 2008 offensive production combined with average defense--significantly south of what Willie Harris and Ryan Langerhans did in 2008. Ick. (Though that'd still be a whopping 14-run improvement over the unfathomably bad Nationals left-fielders of 2008, Wily Mo Pena being by far the biggest culprit.)
So to answer the question posed in the title of this post, I think Willingham's defense is a cause for concern. Not panic, but concern.
One final thought--I think based on Willingham's struggles in left, the idea of moving Willingham to first base might not only be a good idea in the event of a Nick Johnson injury. A move to first may become at some point in Willingham's time in DC a defensive necessity.