Infield Defense, Part 2 — The Next Stepby John Walsh
May 24, 2007
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:
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.
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.
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 +5.4Recall, 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.
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 and Resources
Many thanks to Tom Tango and others who discussed my previous article here.
John Walsh dabbles in baseball analysis in his spare time. He welcomes questions and comments via e-mail.