Infield Defense, Part 2 — The Next Step

Last time I had a look at infield defense in a simple and
straightfoward way. I divided the infield into 22 narrow
pie wedges (or zones) and, for each team, counted the number of
balls hit into each zone and the number of those balls that were
converted to outs.

My goal was to learn something about the anatomy of infield defense:
where the grounders are hit, how do grounders from right- and
left-handed batters differ, which zones are covered by which
positions. I did not adjust my results,
because, as I wrote last time, “I wanted to see the ‘raw’ data
first, in its natural purity, before it got gussied up with
adjustments.” I presented some results on team infield defense, based
on my simple method.

But, is the method too simple? Am I neglecting important effects
that need to be taken into account? Keeping things simple is good
because it allows you to see what is going on, but is it
correct? Defensive systems based on play-by-play data
typically make several adjustments, which means they not only take
into account where a ball is hit, but also other factors. The UZR
defensive system adjusts for “handedness of batter and pitcher, speed of ball,
runners on base and outs, park factors, and G/F tendencies of the
pitcher (ground ball pitchers tend to allow easier-to-field GBs, even
after controlling for speed of ball, according to STATS).”

Wow, that’s a lot of adjusting. I think it’ll be instructive to have a
close look at some of these effects and see how big the
adjustments are. I’ll say right up front that I have a hunch that
there’s just too much adjusting going on here. And this is not to pick
on UZR; other systems make similar adjustments. Hey, that’s what we
analysts do—we try to go beyond the basic notions and figure
out all the subtleties. But, I think we sometimes get so wrapped up
in the
adjustments, we might end up obscuring the reality.

Ground balls from right- and left-handed batters

So, let’s have a look at an effect that is usually adjusted for: the
handedness of the batter. Which side of the plate a batter swings
from has a very big
effect on where the ground balls tend to go, as you might expect. We
can see that clearly in the following graphic, which maps out ground
balls for MLB during the 2006 season:

Here’s how to read the
graph: The variable plotted on the horizontal axis is the angle that
the ball makes with the third base line: angle=0 means a grounder
right over the 3B bag, angle=45 is straight up the middle, a grounder
hit at an angle of 75 degrees is headed toward the hole between second
and first base. The vertical axis is number of grounders, and the blue
curves show the total number of ground balls hit. The solid red
curves show the number of those that were turned into outs, and the
colored dashed lines show which positions made the outs (pitcher outs
not shown). Oh, and the
upper plot is for right-handed batters and the lower plot is for
lefties. One other point: I’m not interested in little nubbers and
swinging bunts (right now), so I only include in these plots balls that travel
at least 50 feet.

It’s no surprise that batters tend to pull ground balls, so we see the
majority of balls hit to the left side by RHB and to the right side
for LHB. If you
look closely, you can see the different positioning of the infielders,
depending on the handedness of the batter. The curve describing the SS
outs, for example, is slightly more to the left (i.e. towards the
hole) against righties. There are similar shifts for the other
infielders, as well.

Note
that this effect, in and of itself, does not require any adjustment to
my simple defensive measure. That’s because I’m already taking
into account where each ball is hit. But, there may be other reasons
for making a left/right adjustment. A pulled ground ball may be more
difficult to field, because it will tend to be hit harder, than a ball
hit to the opposite field. So, it’s possible that a third baseman, for example,
will have a tougher time fielding grounders by right-handed batters
compared to left-handed batters. Seems logical.

OK, so let’s have a look at that. The next graphic is similar to the
previous one, but now on the vertical axis I show the fraction of
ground balls that are turned into outs.

Hmm, the curves for RHB and LHB don’t look so different, do they? If they
are different, that would mean some kind of adjustment might be
necessary. If you look carefully, though, you do see a
difference. Look at the third base area, the first four or five points
on the plot: It looks like third basemen turn a greater proportion of
grounders from RHB into outs, relative to grounders off the bats of
lefties. A similar, but opposite effect can be discerned near first
base.

We can make a better comparison if we overlay the RHB and LHB curves
on the same plot. Now the blue curve is for right-handed batters and
the red curve is for lefties. The bottom plot shows the difference
between the two curves.

Now it’s evident that third basemen have a more difficult time with grounders
from lefties, while the opposite is true of first basemen. Hey,
that’s just the opposite of what we postulated above. Seems like
grounders hit the opposite way are more difficult to field. Maybe opposite field grounders aren’t hit
more softly than those pulled. Or maybe third basemen play closer when a lefty is up and that
causes them to miss more grounders. Sounds like this should be looked into more closely sometime.
Not today, though.

Note that I don’t believe this is a positioning effect. Sure, third
basemen are likely to play further from the line when a lefty is up,
thereby reducing the fraction of balls down the line that they
field. However, in that case, I would expect to see an increase in the
out fraction somewhere toward the hole. What we see, though, is that
the red curve lies below the blue curve for the whole third base
region. So, it’s not just a positioning issue.

Over at first base we see the same thing, i.e. opposite-field
grounders are more difficult to field, although there the effect is
not so pronounced. For middle infielders, the two curves seem to be
separated by a horizontal shift — which indicates a shift of
position—it’s not obvious if grounders from lefties or
righties are more difficult for them. Overall, though, grounders from
left-handed batters are turned into outs slightly less frequently than
those of righties.

Do some teams face (a lot) more lefties than others?

OK, we know now that third basemen do better against RHB and first
basemen against lefties. But do teams face significantly different
numbers of lefty batters? Doesn’t that just all average out over the
course of the season? The answer is a resounding “No!” In 2006 the
Pirates featured four left-handed starting pitchers at times and
opposing managers tended to load their lineups with righty batters.
At the other extreme, the Diamondbacks pitching staff was
overwhelmingly right-handed last year, so they faced many more lefty
hitters than the average team. The following table shows the
proportion of left-handed batters that hit ground balls against
selected teams:

+------+------+------+----------+
| Team | GB   | LHB  | LHB_frac |
+------+------+------+----------+
| ARI  | 1968 |  991 |    0.504 |
| SDN  | 1603 |  769 |    0.480 |
| COL  | 2021 |  935 |    0.463 |
... 

| LAN  | 1924 |  780 |    0.405 |  <-- MLB average
...

| CHA  | 1910 |  687 |    0.360 |
| DET  | 1822 |  619 |    0.340 |
| PIT  | 1844 |  530 |    0.287 |
+------+------+------+----------+

Remember, facing fewer lefty batters is potentially 1) a slight overall advantage
for the infield, 2) a more substantial advantage for the third
baseman and 3) a slight disadvantage for the first baseman. We're not
sure how the L/R affects the middle infielders.
Still with me? Good, we're ready to make an adjustment.

Adjusting for mixture of LHB

Recall how the basic calculation is made: Take the outs made in a
given zone and subtract the outs expected, based on the MLB average
out fraction. This is done in each of the 22 infield zones and
everything is added up to get the team totals.

To adjust for the L/R tendencies of opposing batters, you apply the
same procedure, but first you split the data into two groups,
depending on the handedness of the batter. You calculate plays above
average for each group separately and then you add the two answers to
get the total. The key point here is that the "MLB average" is calculated separately for right- and
left-handed batters.

So, how much difference does this adjustment make? Let's check the
most extreme teams, the Diamondbacks and the Pirates. The Diamondbacks
faced the largest proportion of lefty batters, so we expect that the
simple method, without the L/R adjustment, will underestimate their
team infield performance, in particular their third basemen. The two
graphs to the right show the D'Backs infield performance without (above) and with
(below) the L/R adjustment.

Although the two graphs look very similar, close inspection will
reveal that the blue curve is different in the two plots. On
the upper plot, the blue curve shows the overall MLB average, while on the
lower plot the blue curve represents the MLB average, for the same
mix of right- and left-handed batters that the D'Backs actually had.

If you look closely, you can see a difference in the two plots in the second base area
(50-70 degrees).
The simple method shows
Orlando Hudson as well below average going to his right, where the
blue curve is decidely above the red one. After making the L/R
adjustment, though, we see that that the blue curve is a
bit lower, meaning that Hudson had harder-to-field balls than
average. He still appears to be below average, but not as much as we
previously estimated.

It's not so evident on the graphs, but Arizona third basemen gain
about two plays due to the correction, while their first basemen lose one
play. Overall the D'Backs rating goes from +5 to +10, as noted on the
plots. (The "Left" and "Right" on the plots refer to the left and
right side of the infield—not to be confused with left- or
right-handed batters.)

The Pirates were at the other extreme—very few left-handed
batters faced—so we were probably overrating their team
defense with the previous method. When we apply the L/R correction,
the Pirates overall rating goes from -16 to -18 plays above
average, which is what we expected. The two graphs look the same to the naked eye, so I don't
show them.

Now, I haven't really worked out how to divide up the infield and
assign zones to the different positions. That's a subject for another
day, but I would like to get a feel for how the L/R adjustment affects
the different parts of the infield. So, let's call the first four
zones the 3B area, the last four zones the 1B area and split up the
middle evenly between SS and 2B (see picture at right). Then, the
adjustment in each area comes out like this:

       3B    SS    2B    1B  Overall
PIT  -1.7  -0.2  -1.7   1.3    -2.3
ARI   2.1   0.9   3.9  -1.5    +5.4

Recall, that these are the two teams where we expect the biggest
adjustments. Most teams will have much smaller adjustments and most
individual players will see their ratings change by less than one
play. It's not that big a deal, after all, is it?

I guess your answer to that question depends on your viewpoint. Here
are some hard numbers: The biggest overall correction applies to the
Orioles, whose defense wasn't as bad as I made it out to be in my last
article. The L/R adjustment changes Baltimore's team rating from -40
to -32. This large adjustment is interesting for two reasons: (1) the Orioles were about
average in terms of LHB faced last year and )2) second baseman Brian
Roberts had a similar graph to Arizona's Orlando Hudson; i.e., he
seemed to play way over in the hole, apparently letting lots of balls
get through up the middle. (I showed the Orioles' infield graph in my

previous article).

It seems we're seeing some kind of
interplay between positioning and the L/R batter mix. I bet looking
at these team plots for RHB and LHB separately will shed some light on
the issue, but I'm going to tackle that one another time.

The average correction, up or down, for all teams was 2.2 plays. Only
five teams out of 30 had a correction larger than three plays.

Wrapping up

I was surprised at how small, in general, the adjustment for the
mixture of left- and right-handed batters turned out. I was expecting
something much larger. It makes me think that other corrections, such
as pitcher handedness or home park will matter even less, but of
course I won't know that for sure until I look at those issues.

Here's the new ranking of team defense, after making the L/R
adjustment described above:

Infield Plays Made Above Average 2006 - with L/R adjustment
Team     Total      Left     Right
DET        42         9        34
HOU        42        31        10
COL        42        35         7
NYN        30        16        13
SDN        30        23         7
SFN        28        26         2
SLN        27         8        20
PHI        24         6        18
TOR        16       -10        26
FLO        12         7         5
ARI        10        17        -7
CHA         4        19       -15
ATL         3         2         0
MIL         1        11        -9
BOS         0         6        -6
OAK        -1        -8         7
SEA        -6        -9         2
CHN        -6        -7         1
LAN        -8         5       -13
TEX        -9       -10         0
ANA       -11       -20         9
MIN       -12        11       -23
KCA       -14       -29        15
NYA       -16       -12        -4
PIT       -18       -16        -2
WAS       -24       -12       -13
CIN       -26       -20        -5
BAL       -32       -23        -8
TBA       -42       -13       -29
CLE       -87       -45       -42
Left - left side of the infield
Right - right side of the infield

References & Resources
Many thanks to Tom Tango and others who discussed my previous article here.