Making a case for the DF?

[Wally Mo Pena]

Continuing my series of columns devoted to making baseball stats more meaningful and useful to fans, I turn my attention to defense, the forgotten Chinese food of the statistical fridge. Or something like that.

It seems to me that in this day in age, defense can be accounted for pretty easily with two stats. First you have Zone Rating (ZR), which is a play-by-play stat that requires stat-heads in some bunker/dungeon to log every ball put in play in every game. I’m glad I don’t have to do it, but it’s nice that someone does. So, how ZR works is simple: the field is divided into “zones,” one for each defensive position, and the ZR is simply the percentage of balls hit into the zone that a player gets to. Thus 1-ZR is the percentage of balls a player didn’t get to in his zone, and from that you can figure out how many extra hits a player allowed defensively by not getting to balls.

Now to me, I don’t see any real difference between extra hits and errors, which are addressed by the second key defensive stat, the Fielding Percentage (FP). The FP is the percentage of balls that a player gets to that are successfully played, i.e. not errors. Again, 1-FP is the percentage of balls that are played into errors, and from that you can calculate the number of “extra hits” allowed by a player when he gets to balls.

With this foundation I’ve designed a way of making these numbers a little more accessible, for each position. Understand that what follows isn’t the be all end all of accuracy. My methods use a series of approximations that the pros would scoff at, but my aim is to get more out of the numbers in a reasonable way. So with that in mind: I was able to come up with projections for how many balls will be hit each position (Zone Chances = ZC) over a season, and also the “maximum” ZR for each position since some positions are more difficult than others (+ZR), from historical data:

     ZC   +ZR
1B: 225, .925
2B: 800, .890
3B: 525, .830
SS: 775, .900
LF: 300, .930
CF: 375, .950
RF: 300, .930

Now a formula can be worked out to project “extra hits” (-dHits) that a player allowed over a season compared to the best possible defender at that position:

(ZC * ZR*(1-FP)) + (ZC * (+ZR-ZR)) = -dHits

I went one more step with this. It seems fair to me that to gauge a player’s total value, you could take away the extra hits that a player gives up in the field from the hits they put up at the plate. From historical distributions it looks like the average hit is worth 1.2 bases. Over a normal 550 AB season, an extra hit that gets you 1.2 bases would be worth just about .004 points of OPS. So it could said that every –dHit is worth .004 –dOPS, and that OPS-dOPS could give you a total ratedOPS.

I’ve calculated the ratedOPS for top five qualified OPS producers at each position (other that P or C) for the 2005 season, with some pretty interesting results. The table below shows Zone Rating, Fielding Percentage, extra hits allowed, OPS given up, OPS, and ratedOPS. I’ve also included the two top ZR players at their positions whose ratedOPS is higher than some of the top 5 OPS producers.

Player	ZR	FP	-dHits	-dOPS	OPS	ratedOPS
Lee	.871	.996	14.1	.056	1.080	1.023
Pujols	.865	.992	16.2	.064	1.039	.974
Delgado	.827	.989	25.2	.100	.981	.880
Helton*	.916	.996	4.0	.015	.979	.963
Giambi	.750	.988	42.5	.170	.975	.804
							
Utley	.874	.978	28.2	.112	.915	.802
Roberts	.843	.988	45.7	.182	.903	.720
Kent	.817	.978	72.8	.291	.889	.597
Polanco	.857	.995	29.8	.119	.830	.710
Giles	.800	.984	82.2	.328	.826	.497
							
Ellis*	.875	.989	19.7	.078	.861	.782
							
Rodriguez	.735	.971	61.1	.244	1.031	.786
Ensberg	.804	.964	28.8	.115	.945	.829
Ramirez	.756	.947	59.9	.239	.926	.686
Wright	.775	.948	50.0	.200	.912	.711
Glaus	.766	.946	55.3	.221	.885	.663
							
Young	.807	.974	88.3	.353	.899	.545
Peralta	.852	.970	57.0	.228	.885	.656
Tejada	.818	.971	81.9	.327	.865	.537
Jeter	.830	.979	67.6	.271	.839	.567
Lopez	.836	.970	69.0	.276	.838	.561
							
Wilson*	.884	.982	24.7	.098	.662	.563
							
Ramirez	.729	.974	65.9	.263	.982	.718
Bay	.864	.996	20.8	.083	.961	.877
Cabrera	.826	.976	37.1	.148	.947	.798
Dunn	.859	.981	26.2	.104	.927	.822
Burrell	.882	.972	21.8	.087	.892	.804
							
Jr.	.805	.990	57.4	.229	.942	.712
Jones	.873	.995	30.5	.122	.922	.799
Edmonds	.888	.994	25.2	.100	.918	.817
Sizemore	.908	.992	18.5	.073	.832	.758
Damon	.874	.985	33.4	.133	.805	.671
							
Guerrero	.880	.988	18.1	.072	.959	.886
Giles	.889	.987	15.8	.063	.905	.841
Sheffield	.820	.988	36.0	.143	.891	.747
Jenkins	.894	.984	15.1	.060	.888	.827
Abreu	.852	.986	27.0	.107	.879	.771

*Denotes top Zone Rated player at that position

It’s pretty amazing the effect that defense has when looked at in this way. Some players like Giles and Young are giving back over .300 on their OPS. It makes it pretty clear why you position bad defenders at the corner positions. Giambi at 1st, as bad as he is, costs the Yanks fewer hits than A-Rod at 3rd. Or take Derek Lee (.871, .996) and Andruw Jones (.873, .995), and see that Lee gave up 16 fewer –dHits. Also notice that the only two positions where a fielding ace made it into the top 5 of ratedOPS were the middle infield. I have yet to figure out the best ratedOPS players from last year, but I’ll post it when I do.

Obviously the OPS put up by DHs wouldn't be affected, and it makes you wonder, is a DF in baseball's future? Michael Young and his .545 ratedOPS could certainly use one, or at least a move to left field.

The stats that I used are publicly available on ESPN.com, and the formula I use is very simple, though it could certainly be improved. Since it’s so clear how important defense can be, I think it would be great if we could get something like –dOPS talked about and displayed in tv broadcasts, along with all the rest of the stats they show. It would really make it a lot easier to interpret the impact of player’s defensive ability.

[Porter]

Incredible stuff Wally.

Rep++ When i can give rep again tonight.

[volzok]

Good article Wally. Way to expand on your post from the Reds board. + rep.

[redsrbetter]

Dang Griffey's defense really hurts him.

Great job once again Wally. It is insane to see the difference in a hitter's OPS vs. their rated OPS. Griffey gave up so many dHits last season that his rated OPS really sank. I really like this formula. It will be interesting to see how bad the Reds play into this after this season.

I have always wanted to see a calculation of sorts on how much an error can effect the outcome of a game no matter how well you perform at the plate. There are a lot of times where I say that a player has to get the game back on track with his bat because he made a costly error. I can mean that more in a statistical sense now with this formula.

Felipe Lopez and Dunn were horrible as well last year. I can expect Felo to get better, but Dunn has already made a horrible year for himself even if he doesn't make another error all season. Its a shame when you have a guy that is a monster at the plate and his OPS is insane due to his incredible ability to walk and hit for power. Yet, it looks like crap once you rate the .004 OPS given up after a dHit was allowed.

Very interesting stuff man. This only makes me want to get pissed at the Reds defense even more. +rep.

[Saber]

Wouldn't it make a whole lot more sense to compare players to the average defender at their position rather than the best? So Alex Rodriguez sucks at third depending on what kind of year Ryan Zimmerman will have?

[Wally Mo Pena]

i thought about doing something with the average, but in the end it just made less sense to me. The +ZR that i present isn't the best player that year, it's a hypothetical "best" ZR for each position that i computed from historical stats. That way, everyone gives up some extra hits compared to the "ideal" fielder (i'm imagining hermes cuising around center on winged sandles or something), and it's a one directional scale that you can use for any year without having to recompute the average.

In the end, you could use the average ZR and FP, it would basically be the same, it would just move the scale.

[Saber]

You have to move the scale. You've created a system in which everyone loses because they aren't historically and abnormally great on defense. It turns a player who's helping his team with his defense into one who's only hurting them less. That doesn't make much sense.

[Fishercat]

Amazing job with the calculations.

Still, I wonder what the LgAvg rOPS so it could be used to compare players. Since, as saber pointed out, it isn't normalized to the average player, rather based on the perfect fielder (meaning a perfect ZR for their position, or +ZR and FP). And this certainly isn't the stat deity inside of me, but I just can't see Jack Wilson being such a good defensive player and Miguel Tejada being so bad as to make one worth more than the other, though I'm not one to disprove this article.

[love_that_reefer]

I honestly think the last thing baseball fans are more bogus stats. You clearly did your homework and that is to be respected but just just doesn't do anyone justice.

[missionhockey21]

I honestly think the last thing baseball fans are more bogus stats. You clearly did your homework and that is to be respected but just just doesn't do anyone justice.

Bogus stats? Baseball needs more statistics to represent fielding in a more clear cut way to the fans. And hell, even managers more so. Fielding stats are no where near the level they are for pitching and batting.

[missionhockey21]

Let me begin by saying that I am not well versed when it comes to fielding statistics. Rarely you will ever see me argue for a player using fielding stats (although I am of the mindset that outside of horrendous defense, a good bat is worth the sacrifice, but I never have statistical backing for that.) Outside of the aforementioned ZR and FP, I am clueless. But it is something I would like to learn a bit more in-depthly to have a complete and well-rounded view of the game (since I consider my knowledge elsewhere at least respectable.) And I don't think I am completely alone on this either. So here are some my un-enlightened comments (although hopefully I am a bit more enlightened now) regarding your article Wally.

Is the +ZR from historical data an average of that position? If not, what does it consist of? I was unclear on that, but then again I am pretty tired. But using historical data to make a position projection list is quite ingenious and at least for myself, it gives a sort of benchmark of what to expect or hope for since there doesn't really seem to be a stat level in fielding that is expected as there are with run production or pitching (not that you can't tell what is good or not, just not something everyone is projecting or measuring up against... at least I don't do that.)

The -dhits stat is also extremely interesting and another way for the average fan to get a better picture of what a certain player did. But I think it would be more effective to look at the average ZR for the position that year in comparison to the player being measured since the best player creates too high of a standard to compare other players to.

With the ratedOPS, I have to presume you were largely influenced by our bumbling boys when thinking up that one Wally. How often do we see a guy like Dunn or Ed E give up a run due to shoddy D, but then see them get it back with one swing of the bat? Some of it's not terribly shocking, like D Lee not losing a ton in rated OPS due to his big range and great glove at 1st. And even though I was expecting Jr. to be a pretty big drop-off, but seeing that huge of one is pretty rough. Then you have guys like Marcus Giles who just has such a large drop-off and makes my appreciation for Utley's gritty play all that much more when you consider the value he is adding to the Phillies at that position. And given the range a SS has to face, those we're somewhat surprising but I guess expected. And even though I realize the talent that Jhonny Peralta is with the bat, it's impressive to see he's the only SS there with a ratedOPS over .600

All in all, this is my favorite article of yours yet.

Top-notch work, thanks for sharing. +rep

[Wally Mo Pena]

well, i like how i've put it together, it makes sense to me, but the comments get directly at two things i mention in the article.

1. the stats are out there and if someone wants to put together something else in the same direction, i'm sure what i've done can be improved on.

2. i'm also sure the professional analysts have something way sweeter and more accurate than what i've done or the suggested improvements, and going on forever trying to find the perfect solution for fans doesn't make much sense. In the end, there is a point where practicality takes precedence over accuracy, and for me that point was computing averages for every position for every year that i wanted to check out.

My way is, as they say, quick and dirty. but it gets the point across.

that said, here's a little something for the nay sayers. The ratedOPS for SS in 2005 based on average ZR and FP for 2005 (.839, .975):

Player      ZR     FP     -dHits      -dOPS     OPS     ratedOPS
Young	0.807	0.974	25.4	0.101	0.899	0.797
Peralta	0.852	0.97	-6.8	-0.027	0.885	0.912
Tejada	0.818	0.971	18.8	0.075	0.865	0.790
Jeter	0.830	0.979	4.4	0.017	0.839	0.821
Lopez	0.836	0.97	5.6	0.022	0.838	0.815

wilson	0.884	0.982	-39.7    -0.158	0.662	0.821

there the negative numbers are hits saved and OPS gained. But in this model, everyone is getting helped by renteria's 30 errors rather than setting the standard at 0 errors.

so whatever, it's all basically the same it's just the difference of seeing positive numbers instead of negative numbers. i guess saber's just a half-full kind of guy.

[redsrbetter]

Bogus stats? Baseball needs more statistics to represent fielding in a more clear cut way to the fans. And hell, even managers more so. Fielding stats are no where near the level they are for pitching and batting.

Exactly, think of all the stress stats like this could put on poor fielders. It would wake them up and have them concentrate on other aspects of the game. You are not an all around player if you can't play your position. Of course a DH is different, but a position player needs to help his team out both on the field and at the plate.

I think if we were to concentrate on fielding stats like this more, we would see a vast improvement in some of these guys FP. A lot of people may think that if it didn't give up and unearned run, then it wasn't all that bad. Well, if you are prone to that kind of thinking, you may try and shake off an error that is costly as well. Or you could make the pitcher start off in a different part of the order than he wanted to the nest inning. Or you may cause your pitcher to lose focus because he is so miffed at the added baserunner due to the fielder's incompetence.

Fielding is a huge part of the game and it needs to be looked at in a deeper level. Wally did a great job digging deep and it should be looked at this way from the ballplayers themselves.

[love_that_reefer]

Yes bogus stats because that's what they are. Defense cannot be measured in numbers but can help make some points along the way. The only way to measure it is by watching the games. Hell Arod might have better numbers than Eric Chavez but does that make him a better third baseman. Too many stats and stat junkies.

[love_that_reefer]

Exactly, think of all the stress stats like this could put on poor fielders. It would wake them up and have them concentrate on other aspects of the game. You are not an all around player if you can't play your position. Of course a DH is different, but a position player needs to help his team out both on the field and at the plate.

I think if we were to concentrate on fielding stats like this more, we would see a vast improvement in some of these guys FP. A lot of people may think that if it didn't give up and unearned run, then it wasn't all that bad. Well, if you are prone to that kind of thinking, you may try and shake off an error that is costly as well. Or you could make the pitcher start off in a different part of the order than he wanted to the nest inning. Or you may cause your pitcher to lose focus because he is so miffed at the added baserunner due to the fielder's incompetence.

Fielding is a huge part of the game and it needs to be looked at in a deeper level. Wally did a great job digging deep and it should be looked at this way from the ballplayers themselves.

You honestly think these guys don't want to get better fielding the ball anyway without these so called stats? That's just flat out ridiculous. Stats are just numbers and are no true way to evaluate anyone's talent. They are there for arguements sake. Too much stock in stats is not a good thing.