Tuesday, November 18, 2008

Willingham's Defense: A Cause for Concern, Panic, or No Worries at All?

Fangraphs' Dave Cameron made the case the other day that much of Willingham's offensive value is offset by his bad defense. As a fan of Josh Willingham, Sam I am, if not the deal that brought him here, this claim, I thought, required some examination and elaboration.

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)
It would appear based on ZR that Willingham is bad, but getting better, though we should note that the '08 improvement happened with a smaller sample size '08 because of his back issue.

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.
Well, so much for Willingham getting better defensively. By this measure, his played his best defense in 2006 and bottomed out as one of the worst LFs in baseball the last two seasons.

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
In other words, projected over a full season of 150 games, he cost his team 18 runs in '06, a massive 30 runs in '07, and 9 runs in '08. Like ZR, Rate2 thinks Willingham tightened up his defense significantly last season.

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.


JayB said...


Thank you for keeping the great work flowing. That said, I think you believe you could do away with the game on the field and just play it in Excel.

I think the stats you use are a tool but not a very good one. These are the same tools that show that Lopez should be worth X wins for the Nats......That Kearns should be worth Y Runs......We know now all that worked out.

Coaches matter and so to the players around others, like Zim....that is why Lopez in 2008 shows the intangibles matter and so does the attitude of players.....your stats take none of this into account. Josh W will lead to many more wins that your stats show because it changes the chemistry of the team......But if you want to do stats, how does Milledge in rate in your system? His defense is the worst in baseball in CF how does this translate to wins.....would we be better cutting him than playing him in your world?

Steven said...

JayB--I'm not sure I totally follow your point. Based on runs created, for instance, Kearns and Lopez were awful in '08.

Let me try to respond to you this way: the stats we're looking at here are all backward-looking. They don't proscribe the future. I think that what's happened in the past is instructive and certainly tells us *something* about what to expect in the future. But like the stock market past performance is no guarantee of future earnings. In Willingham's case, we can look for trend lines and guess about aging patterns and other things that help project future performance, but really everything I'm doing in this post is just establishing an overall metric of Willingham's total value, with offense and defense factored in.

Similarly, these stats only get at actual quantifiable events on the field, not, as you say, the intangibles, which are of debatable importance, but certainly I agree they're worth something. But it's just not what I'm talking about here. We could at some point try to quantify his leadership value, but if Willingham, for instance, has X wins worth of leadership value, that would be on top of (or subracted from--I don't personally have any knowledge of whether he'll be a pos or neg) whatever his on-field contributions (or deficits) add up to. You just would have to factor that in separately.

Steven said...

Re: Milledge--you're certainly right that his relatively poor defense has to be factored in. One could make a pretty compelling argument that in 2008, we'd have been better with Willie Harris as the every day CF from opening day.

However Lastings's age and a whole bunch of other observables and data points suggest that his offense and defense will all improve quite a bit over the next 1-5 years, and therefore factoring the short term and long-term benefits I would have gone ape shit if Manny had played Willie over Lastings.

JayB said...

Interestingly on Milledge....if we had any kind of LF option other than Harris I would have been happy to have Nats play Harris in CF instead of Milledge. I do not think Milledge will improve in CF....ever, he does not have the work ethic needed to improve. Hell he even says, he thinks he is a great CF already. I think that Nats are finally coming around to this line of thinking and if so then playing Milledge in CF every day last year was a complete waste as I said all along.

My point on the stats you are using is that they do not take into account the intangibles of baseball. They fail to take into account the chemistry of a team.......Nats need leadership to improve. Zim and Kearns provide no leadership. With Vet leadership, (not D Young type of leadership please), then the players all around the Vet improve. Your stats would have supported the Lopez, Kearns deal and predicted a much improved Nats club after the deal, but in 2007 and 2008 as we know, that did not happen. Not because of injury but because of chemistry. This show us that intangibles matter a lot and this is something the stats miss every time.

JayB said...

On Kearns, go back and read his comments at the time of the trade......"I miss my family, I am not sure if I can play somewhere else without my old buddies. I will always be a Red.......on and on......Just showed a total lack of confidence and leadership from day one.

Lopez, on the other hand said he was too good to be playing for a second rate team. He basically said he was not going to try hard until he got onto a team that could win......3 years later that is just what happened.....none of that shows in your stats that predict how many runs someone is worth and how many wins that runs translated into......thus in my view they are not worth much.

JayB said...

Oh and Leadership.....Leaders are players who produce on the field every day....not Robert Fick, Not A. Boone, not players who have 15 HRs and 55 RBI's as a career highs....not Ronnie B. or W. Harris......this team needs someone to lead them like Tex.......but if not Tex then someone like Willingham who has hit 25 HRs is a nice start.

Steve Shoup said...

JayB: I think thats a bit of Cherry picking you are doing there. I don't remember the comments from Kearns but so what if he said that? Those comments have NOTHING to do with leadership. He is from Kentucky he was playing for his hometown team, a team that drafted him and took care of him, and he left a team full of friends. Why is the reaction of him missing all of that a sign of a poor teammate and leader??? If you grew up rooting for the Nats and they drafted and developed you, you wouldn't have some hesitation about leaving all of that?? If Kearns wasn't such a good teammate and really didn't want to be here why did he sign a multiple year contract?? He could have been a free agent right now had he not signed that contract and gone back to the reds but no he wanted to play in Washington.

I also never remember Lopez saying he wouldn't try hard. I recall comments he made about the way he was used what posistion he played ect. But I can never recall him "pulling a Manny". As for the rest of what you said about not getting leadership from bench/role players I do agree with that.

John O'Connor said...


What leads you to the conclusion that Milledge lacks in work effort? Everything I've read makes me think that he is sonmebody who will (and does) work hard.

I think Milledge gets tarred with a lot of negatives that don't seem to fit him, all based on a couple of arguably bad guys who were his teammates in New York.

JayB said...

Kearns is not a leader, his time in DC shows that and the comments on being traded give some insight, but you’re right, not as relevant as his performance here. As for signing on here......he got much more money from GM Jim then he ever would have if he was a free agent.....does anyone want Kearns at $8 Million next year?

Lopez did say that one reason he was not playing well is that unlike the Reds, the Nats were not playing in games that were important and that makes it hard to focus. To me that just tells you all you need to know about Lopez.

If Milledge did have a strong work ethic he it would show in pregame....watch him.....walks, talks, underarms throws, basket catches balls.....he is not in CF learning how to go back on a ball....I have seen him just wave a balls and not move a foot. Biggest problem is he believes he is already a great outfielder. He has said a number of times he will be a Gold Glove CF.......hello....if that were to happen it would be have to be done on old fashion hard work.....not something you see from him at 4:30 PM on the day of a game.

Granted I believe the coaching staff was to blame for some of this lack of direction. If Milledge had a manager and coaches that required him to work instead of making excuses for him in CF then we could at least remove that doubt from the picture of why he was the worst CF in baseball last year.

Steve Shoup said...

JayB: I wasn't using the Kearns contract as an example of a 'good signing' or a 'smart move by bowden' I was using it as an example of him wanting to play here. Yes no team now would want to pay Kearns $8 mil but at the time it seemed like a pretty solid deal if Kearns had 25 HR's each of the last 2 seasons you better believe he'd be making more than $8 mil a year.

As for Lopez, i'd love it if you could site your source b/c while i'm never gonna nominate him for teammate of the year I have doubts about him saying " that one reason he was not playing well is that unlike the Reds, the Nats were not playing in games that were important and that makes it hard to focus." Exactly how many meaningful games did he play with the Blue Jays and Reds?

As for Milledge I do remember some of the comments about him saying he wants to be a GG Centerfielder but I can never recall him saying that he already was. Some of those comments if i am recalling correctly came during like his introductory press conference or talks with fans (ESPN zone ect) which is more for the fans than saying he truely believes it. Of course he is going to say stuff like that he is trying to energize the fan base. It would be different if he talked to Chico and said "I am the best CF in the league I make Tori Hunter look like a rookie" Until he does say that I say cut him some slack. It was his first full year and he def has the tools needed for the posistion. I think with the right coaching and attitude by Milledge he can be an above average fielder.

JayB said...

That was tough....you want me to find you the Milledge quotes as well, look just last month when he said he had improved to the point that he was one of the better CF in the league........

Lopez About coming from St. Louis to Washington:

"It's like night and day. You go from somewhere that's dead last and the energy is not there. You come here and as soon as I walked in I felt that energy. That inspires you, that motivates you to play well. ... They were trying to develop young players. I was not in their plans for the future."

On not hitting:

"Like I said, the motivation - just being dead last, I guess. Like going out there knowing you're probably going to lose isn't motivating. That's tough. That's tough, for me."

These are the things that Steven's Stat focus just miss the mark on completely.....

Will said...

Steven, did you factor in the defensive stats of the Nationals LFs last year? According to Turkenkopf's LMR, the Nationals LFs were the 4th best in baseball. If you compare the runs saved by the Nats LF in 2008 vs the runs saved by Willingham, I think you'd get a different result.

A side note- the LMR rankings put Wily Mo as the 15th best LF out of 40, which makes me a little skeptical of these stats.

Will said...

Whoops, I meant PMR not LMR in the above post.

Jayb, if you're referring to the MLB.com interview with Milledge, you're misquoting him. Here's what he said:
I don't think it's fair, to be honest. I didn't feel I had enough time to be whatever they wanted me to be out there. I just came from left and right field the last two seasons I was in the big leagues. Playing center field in Washington is not so easy, as well. At the same time, I think I played pretty well in center field.
There were plays where I should have got to the ball, but I was out of position. You can't do anything about it when you play a guy [to hit to the opposite field] and he pulls the ball. At the end of the season, I started to get comfortable and started to have a little more success in center field.
People are going to say what they want to say about me, but I'm not a corner guy. I'm definitely a premier center fielder as long as I get the opportunity and get my repetitions.

He clearly explained that he has the potential to be one of the best, but that "as long as" is the key to what he said. Moving back and forth between center and the corner positions wasn't easy for him, and given more time in center, he's confident that he'll be one of the best CFs.

Either way, I'd prefer he say "I'm the best CF in the league", than "I'm not a very good CF". But maybe it's just me.

Steven said...

will--I did not factor in the Nationals 08 defense last year. It's a good point. Though the offense was so bad no amount of defense would have altered the underlying point, but in the interests of precision and consistent analysis, I should have at least acknowledged that.

Steven said...

on the reliability of PMR, it generally seems pretty good, but you're right the Pena thing seems weird. It could be a sample size issue I suppose. But that's why I think you need to look at a range of defensive metrics. None of them even claim to be perfect.

On these quotes, I think you guys should assume that athletes aren't the best communicators in the world. Maybe it's not worth putting TOO much stock in what they say? Especially the non-native English speakers. Just sayin'.

JayB said...

"I'm definitely a premier center fielder as long as I get the opportunity and get my repetitions."

This one of many Milledge Quotes I have seen.....Steven he is a native English Speaker......problem is what he did not say. He did not say I need to change how I approach the game. I need to stop goofing off and focus on what others see as my weakness. He did not say I need to listen to my coaches. He did not say I need to learn from Vets who came before me. He did not say I need to become a professional player, one who works everyday to improve what others I respect see as my problem areas.....he is saying he has no weakness and all he needs is the opportunity. That is the problem.

Will said...

Jayb, seriously? Did you actually read the interview? Because he did say most of that stuff.
[I didn't think I could go] the opposite way. I had a lot of success going the other way this year. I actually have more power than I thought I had to right field. [Hitting coach] Lenny Harris kept reminding me to go the other way. It really didn't click in until I had good results.
Yes, he does listen to his coaches.

I told [former first-base coach] Jerry Morales in Spring Training that I needed a lot of work out here. I worked hard from Spring Training to the end of the season. I told him I needed a lot of work because I hadn't played center field in two years. So I need the repetitions. I knew myself that I was going to struggle a bit. I didn't let everybody know about it, but I let Jerry know. It was a little difficult for me, because I didn't play out there. At the same time, I continued to work hard and made some great plays out there.
He's working hard to improve his defense, and he's consulting with the coaches!

You could say we need pitching and you can say we need a big-name guy, but at the same time, we have to play together to win. We have to know ourselves and play together. I don't think we knew how to play together this year.
We have a great group of guys. After losing 102 games, there were no fights. You can't ask for much more.

He knows that everyone must play as a team, and is confident that they will get better.

I learned a lot from Lenny. He made me a better hitter. I will continue to talk to Lenny, whether he is with the organization or not. We share common knowledge of the game. I like his hitting style. I have a problem when I can't be with the guy, who really helped me and polished me up to be an even better player.
[Manny Acta] handles the team great and he knows how to handle young guys. The biggest thing is, he knows how to communicate with guys.
He's still listening to the coaches.

For him to say ALL that in just one interview is pretty impressive for a 24 year old. I didn't have to go scrounging through all his past statements, it's all there right in front of you.
You don't have to like the guy, but at least back it up with some valid reasons.

JayB said...

I am talking about Defense and CF.....Yes he said some of the right things but he does not do them.....I watch him carefully many times a year, before games mostely. I am a season ticket holder. I watched close to 160 games in person or on TV. The only comment that reflects accurately about how he really feels about what he must do to improve is the one made that says all he needs to do is playing time. Stats show he was the worst CF in the National League. Observations shows he does not work at improving his game in CF.......why....because he feels he has all the skills needed and if he just plays in enough games he will be a “premier centerfielder”.....That show me someone who will never get it......The Nats seem to agree with me based on comments I read....yes he could be a CF but after one year experiment Nats seem to believe he does not have the work ethic needed to make that happen....in my view....your is different...OK let us see what happens this year.

Steve Shoup said...

I think even though the Nats defense in left last year was strong it shouldn't factor in that much. The Nats leftfield defense was so strong b/c Willie Harris played 86 games out there. Harris led all left fielders in plus/minus in only playing half the season. Now thats not to take anything away from Harris he is a great player to have on a team but he is not a left fielder neither his .761 OPS (quite the career high) or .667 career are that good for a left fielder. Harris should move back to the infield and play in center to give Milledge an off day or two.

Our outfield as it is right now we have 5 players, Pena, Kearns, Willingham, Dukes and Milledge. The best offensive potential would be Pena, Dukes, Willingham, the best defensive potential would be Milledge, Dukes, Kearns. The best overall and long term potential would be Willingham, Milledge, Dukes and thats what I think it should be. Pena is dead weight on the roster and Kearns is vastly overpaid. Maybe longterm Milledge will have to move off Centerfield but I'm willing to give him another year or two to see if he can figure it out.