Simplicity, simplicity, simplicity! I say, let your affairs be as two
or three, and not a hundred or a thousand; instead of a million count
half a dozen, and keep your accounts on your thumb-nail.
— Henry David Thoreau
In recent years, methods for evaluating defense have been springing up like
mushrooms after a spring rain. We’ve got
UZR and PMR and the
plus/minus system, all based on play-by-play data. Then there are the
zone rating-based systems, one from
Chris Dial, another by
stuff from folks working with the BIS zone rating data that we
publish here at THT. And let’s not forget those heroic attempts to
evaluate fielding using traditional stats:
Win Shares and FRAA.
The evaluation of defense is a fascinating subject, and I’ve read
through much of the material that documents the above
systems. And you know what? I still don’t know which one works
best or, more generally, how well any of them work.
These systems are either a) very complicated or b) not fully
explained (usually both), so it’s very hard to wrap your head around them. I know,
So, I’ve decided to go back to basics, and I’m starting with infield
defense. I’ve got some precise hit location data for the 2005 and
2006 seasons that I obtained from
mlb.com and I want to see if I can take a Thoreau-vian look at it, see
if I can evaluate infield defense “on my thumb-nail.”
Where do ground balls go?
This seems like a very simple question, but I’ve never seen anybody
give the answer.
For example, we are told that shortstop is the most
important infield position (I’m excluding catcher from the infield),
presumably because more balls get hit to the shortstop than to any
other infield position. That’s true, but how many more? And
sabermetric wisdom has it that first base defense isn’t that
important, simply because first basemen
field fewer balls than the other positions. Ok, but how many fewer? Do
they field half as many as the third baseman? Eighty percent as many?
I’ve never seen these questions answered, so I
decided to answer them myself. Armed with my hit location data,
I’m going to divide the infield up into 22 thin wedges or zones. I
chose the number 22 because STATS,Inc. uses the same zoning for their
zone rating stat. The variable that I’ll use to describe where a
ground ball is hit is the angle that the ball trajectory makes with the third
base line. It’s easy to see what I mean by looking at the graphic on
the right. A ball right down the third base line has angle=0, while a
ball hit over second base has angle=45, and so on.
Then I just counted up the number of ground balls hit into each
slice. Simple, right? Thoreau would be proud. The plot below shows
the results for the roughly 100,000 ground balls hit during the 2005-2006
seasons (bunts have been excluded). The red and green curves
show the results for right- and left-handed batters separately.
I don’t know about you, but I find this plot fascinating (I need to
get out more, I know). First of all, I wasn’t expecting this shape to
the ground ball distribution. I expected to see two humps around the
shortstop and second base positions, but I am surprised to see
that double-peak structure on the left side. Another curious thing is
that, for a right-handed batter, it looks like almost as many balls
are hit towards the third baseman as are at the shortstop, maybe even
I also didn’t realize how few balls were actually hit up
the middle. As you can see from the RHB and LHB curves, batters
overwhelmingly tend to pull ground balls, which I knew. What I didn’t
know is that a right-handed batter will hit more balls at the second
baseman then he will up the middle (see the peak in the red curve near
60). Same thing for a lefty hitting balls towards short.
Who fields the grounders?
O.K., we’ve seen where batters hit ground balls; now we’ll have a look
at how often they get turned into outs and who does the turning. The
following graphic shows just that: the blue curve is just the
distribution of all ground balls, it’s the same as we saw in the
previous plot. In red, we see the balls that were converted into
outs (including plays scored as fielder’s choice). The dotted lines
show where each infield position recorded his outs.
Hmmm, there’s lots of food for thought here. For example, you can see
that there is quite a bit of overlap between the area covered by the
third baseman and the area covered by the shortstop (and the same is
true on the other side of the infield). We’ve all seen
the third baseman cut in front of the shortstop on a slow chopper many
times. This overlap region makes it difficult to assign credit
to specific fielders for this kind of play.
On the other hand, there’s very little overlap between the areas
covered by the shortstop and second baseman. That’s not surprising to
me, but apparently some smart people are not aware of the fact.
I came across the following in this year’s Baseball Prospectus
Annual, in a comment on the defense of Indians shortstop Jhonny
…it’s worth noting that Peralta didn’t have the benefit of great
support to his right and left; Boone lost almost as much ground in the
field as he did at the plate (according to both scouts and metrics),
while Ronnie Belliard‘s range at second left a lot to be
desired. [emphasis added]
Belliard’s range did indeed leave a lot to be desired,
but it had nothing to do with Peralta’s lack of same.
Shortstops field only
6% more balls than second baseman do, which doesn’t seem like much,
when you consider that shortstops are generally viewed as much more
important than second baseman.
Conversely, despite having almost as many balls hit toward
them, third baseman field far fewer ground balls than their shortstop
colleagues. This makes sense since the third baseman is
playing closer and has less time to react to hard-hit balls. It
is called the Hot Corner, after all. First baseman field
the fewest balls of all, 1) because fewer are hit their way and 2)
because they often play out of position in order to hold a runner on
Team Infield Defense
Since I don’t really know how to divvy up credit (or blame)
for individual fielders, how about if we look at team infield defense?
Check out this graph:
To start off, focus on the blue curve in the upper plot. This is the
mlb average fraction of balls turned into outs as a function of
where the ball was hit. The dips in the blue curve show
show the “holes” where most hits get through. It’s also clear that balls hit towards the
shortstop or the second baseman are easier to field than balls hit at
the third or first baseman, i.e. the two peaks in the middle are
higher than the two lateral peaks.
Okay, now look at the red curve in the upper plot. That is what the
Cleveland Indians did in 2006. Tribe infielders performed below
average wherever the red curve is below the blue curve, which is just
about everywhere. It’s evident from this plot that Peralta and
Belliard showed quite poor range in 2006. Both were O.K. at balls hit at them,
but they were both below average when asked to move off their set
position. They were both particularly bad to their left.
The lower plot shows the number of plays made above or below average.
As noted on the graphic, the Indians turned 90 fewer ground balls into
outs than the average mlb team would have, given the same ground
balls. That’s an astonishingly bad performance, by far the worst of
any team in 2006. Furthermore, since the overlap between SS and 2B is
small and if we neglect the influence of pitcher fielding, we can
divide the total into left and right side of the infield. We see that
the Indians were equally bad on the two sides of second base.
I note that this plot is similar to the type of plot that David Pinto
produces with his
PMR system. David’s plots, however, are based on
his complex system and are shown separately for each player. In
trying to stick to my Thoreau-vian principles, I haven’t made a bunch
of adjustments, nor have I tried to apportion credit to individual
The 2006 Baltimore Orioles also were terrible, according to my simple
method. As you can see below, the O’s were uniformly terrible on
any ball hit anywhere near the center part of the diamond.
Both Miguel Tejada
and Brian Roberts, who played the majority of the Orioles games at SS and
2B, seemed to play too far towards the hole, leaving the middle
infield virtually uncovered. The O’s corner infielders, Mora and
(mostly) Millar, were pretty terrible also.
Why all this negativity?
Let’s look at the graphs for a couple of teams with good infield defense.
Everybody knows that Adam Everett is the best-fielding shortstop in
the game and my little pictures seem to bear that out.
Actually, the Houston infield looks pretty darn good across the board. I am
surprised to see average play coming out of second base, which was
mostly manned by Craig Biggio in 2006. Hmm, maybe this method is
too simple. Both Ensberg and Berkman got to a lot of ground balls last year.
I hadn’t heard much about the Rockies’ infield defense, but by my measure
it was excellent in 2006. The left side of Atkins and Barmes was
especially good, but Helton and Carroll on the right side held up
their share of the bargain.
This is not a system
I want to make clear that this is not a defensive evaluation
system. It only takes into account one aspect of ground balls, namely,
where they are hit. There are other variables that likely have an effect on
the ability of a player to turn a ground ball into an out: speed of
the batted ball is clearly one such variable. The number of outs and
possible runners on the bases affect positioning and hence the out
conversion rate. Other effects may also be important: the ballpark,
handedness of batter or pitcher, etc. I’ve ignored all those things,
because I want to see the “raw” data first, in its natural purity,
before it gets gussied up with adjustments.
Maybe in a future article, I’ll have a look at some possible
adjustments, try to get a feel for how big they are and if they are
really necessary. For now, I’ll leave you with a list of team infield
performance in 2006, based on my simple method.
Infield Plays Made Above Average in 2006 Team Total Left Right HOU 44 33 11 COL 43 35 8 DET 40 8 32 SDN 30 21 9 SLN 29 9 20 SFN 29 25 3 NYN 28 14 14 PHI 23 7 16 TOR 18 -10 28 FLO 15 10 5 MIL 5 13 -7 ARI 5 14 -9 CHA 2 18 -16 ATL 1 -1 1 BOS 0 8 -8 OAK 0 -7 7 SEA -3 -5 2 CHN -8 -10 2 LAN -8 6 -14 MIN -11 12 -22 TEX -12 -12 0 KCA -13 -29 16 NYA -14 -12 -2 ANA -15 -23 8 PIT -16 -14 -2 WAS -22 -10 -13 CIN -25 -22 -3 TBA -38 -10 -28 BAL -40 -26 -14 CLE -90 -47 -43
References & Resources
You can download a PDF file with infield defense graphs for all 30 teams here.