Ozzie Smith is widely regarded as the best defensive shortstop (and somewhat by extension, the best defensive player) of his era. Anything that was hit into that no-man's land between second and third was gobbled up by the Wizard. In a game that adores offensive numbers, there was something so special about Ozzie's glovework that he ended up in the Hall of Fame despite a career .262/.337/.328 triple slash line.

Plenty of plus-glove shortstops have played in the big leagues over the past few years. Some of them were of the plus-plus-glove, minus-minus-bat variety (Brendan Ryan, Paul Janish), while others have been of the plus-glove, just enough bat to make people believe he's a leadoff hitter type (Andrelton Simmons). And then there's Manny Machado, who has yet to actually play at short in the big leagues.

Teams have always seemed to understand that a particularly good defender is worth a lot, especially at shortstop. Neifi Perez and Felix Fermin played for years, and it certainly wasn't because of their offensive prowess. It hasn't been until recently that we've been able to fully appreciate the value that a good defender can bring. After all, I own t-shirts that are older than the first edition of The Fielding Bible.

Defensive metrics (and baseball metrics in general) still have one big problem. While we can estimate how many outs a fielder personally contributed based on the number of balls he did or did not get to, fielding, unlike hitting, is not an individual endeavor. It's not quite basketball, where all five players on a team might be involved in the play at any time, but what one player does on the field might impact what another does. If the shortstop has a lot of range, it might affect where the third baseman plays. If a center fielder covers a lot of ground, it might make the men on his left and right look better than (or not as bad as) they really are.

In 2000, former BP writer Keith Woolner posed this question as one of baseball's unanswered problems. Can we quantify the secondary effects that a good fielder has on his teammates? Seems a shame to leave an unanswered question unanswered.

Warning! Gory Mathematical Details Ahead!
Most of the publicly available fielding indices are actually based on raw data that are not made public (or at least not made public to me). Fortunately, we do have data from 1993-1999 from Retrosheet that includes the rough location of each batted ball hit during that time. Ideally, our data set would be more fine-grained than this, and there's probably some bias inherent in these data. Then again, ideally, I would be napping in a hammock on a tropical island right now.

I limited the sample to all ground balls with valid hit location data. I looked only at grounders that made it to the dirt part of the infield, and possibly further. For each position, I looked at ground balls that were hit to the main zone of responsibility (so, for the shortstop, the '6' zone on the Project Scoresheet chart), and the zone immediately to the right and to the left. I figured each fielder's success rate in reaching balls hit into those zones. (Later, I changed it to whether the out was recorded. It didn't affect the overall results much.) This served as a rough range factor for each fielder present on the diamond.

I also figured the pitcher's BABIP on ground balls for the year, the batter's BABIP, and the BABIP in general for balls hit on the ground to that particular zone. In this way, we'll be able to control for hitters who hit the ball really hard, pitchers who give up a lot of hard contact, and the fact that some balls are harder to get to than others. All rates were converted to the natural log of the odds ratio.

I then selected all ground balls that were in the "first baseman" area (i.e., the '3L' zone, '3', and '34'). I created a binary logistic regression that controlled for BABIP on grounders to that specific zone, the batter and pitcher BABIP, and of course, the rough "range rating" created above. Then, I entered the range ratings that the other three infielders had for ground balls hit into their zones. As you might have guessed, I repeated the process for the three other infield spots. Only ground balls that featured a pitcher who had given up at least 100 grounders, a batter who had hit 100, and four infielders who had each seen at least 100 grounders in their general area were included in the regression. I later dropped that to a minimum of 50, and it didn't make much difference.

Remember that the set of ground balls under study here are all aimed mostly toward the first baseman, so while there might be some effect for the second baseman, we surely wouldn't expect the fielding chops of the shortstop to come into play here, right? The theory has always been that having an elite defender for a teammate who stands near you makes it easier for you to cheat a little bit away from him and to concentrate your efforts on a different part of the diamond. In doing so, a guy who is actually just pedestrian might look like a pretty good defender on paper.

Surely enough, there was a significant effect of having a defensive whiz for a teammate. A negative one.

Yes. A significant negative effect. Having an elite second baseman actually made the shortstop a little worse, and this in a regression that controlled for the location of the ball, batter, pitcher, and the shortstop's own talent. Even after controlling for all those variables (which all pointed in the direction that they should), there were still significant (and negative) effects for other fielders. Second baseman and shortstops got in each other's way. Oddly enough, a good second baseman actually made the third baseman worse, and vice versa.

In fairness, there was one exception. A good second baseman seemed to make the first baseman more efficient. There were also a few non-significant findings, such as shortstop and third basemen having no effect on each other in either direction. But I was a little shocked by this. I thought that there might be some quirk of my methodology that produced these weird results. However, I tried lowering the inclusion criteria to 50 grounders per actor. I tried including only one "extra" fielder at a time in the regression. I tried pulling out the pitcher and batter controls. I tried changing the "range" variable of whether the infielder got to the ball into a "defensive efficiency" that required an out to be made. I tried penalizing the third baseman for a ball in the '56' hole that the shortstop got to. I tried not penalizing him. I tried rewarding him. I used raw percentages as inputs rather than logged odds ratios. Same basic results each time.

An elite infielder can actually make the fielders around him worse, and at least from 1993-1999, that's what he did, on average. Now, let's talk about matters of scale here. It's still worth it to add an elite defender to a defense. I looked at the effect of raising the second baseman's efficiency by five percentage points, which would take a second baseman from below average to Gold Glove territory. It zapped about a percentage point from the shortstop from what we might expect of him given otherwise equivalent circumstances. The rest of the effects were of a similar size.

We Have an Emergency!
There's a well-known effect in psychology called the bystander effect that might explain some of what's going on. Suppose you’re walking alone and you come across a man who has fallen down and is hurt. Would you help him? Now, imagine that instead of walking alone, you are walking with a few friends and come across the same man. If you were alone, it is more likely that you would help, and you would do so more quickly. When there are other people around, psychologists suggest that there is a "diffusion of responsibility." Someone should probably help the poor guy, but is it your responsibility when there are others around? (Pro tip: this is why if you are ever in an emergency situation, you should never yell, "Someone call 911!" People will look around at each other. Instead, make eye contact with someone, point, and say, "You, in the silly hat, I need you to call 911.")

I have to wonder if something similar is happening on the infield. Sure, on paper, having a good defender on the infield allows the other infielders to shift their positioning a little to cover a bit more ground. But that ignores the reality of what goes on in someone's head. People do not often make decisions based on maximizing efficiency, but instead on minimizing cognitive load. If I don't have to worry about something, I won't. If the shortstop gets to anything within five miles of him, then I don't have to work really hard at third base. It wouldn't often take the form of a fielder just refusing to go after a ball. In the "injured man" scenario, someone from the group usually helps him, but the response times are longer. Maybe that's what happens here. There's a small lag in the reaction time. And on ground balls, a couple tenths of a second of reaction time can mean the difference between a groundout and a single. It's not like infielders have five minutes to get to the ball.

What I think is telling is that good fielding second basemen have an effect on third basemen (and vice versa). In response to knowing that one of them has good range, the shortstop probably does cheat a little bit, perhaps away from Mark Ellis at second base. The third baseman knows that Ellis is a virtuoso at his craft, and he knows that the shortstop is cheating a couple of steps toward him. It might not even be something that he's aware of. And on the flip side, that same regression tells us that the third baseman who knows that the rest of the infielders have limited range might take it a little more upon himself to get to that ball.

And maybe there's something to be said about baseball's fascination with guys who "go all out" and who "only have one speed: full throttle." A guy, perhaps, who treats every ball like he's the one who's supposed to get it and the fate of the free world depends on him getting the job done. Managers have sung the praises of such players for years. And for the longest time, we've just kind of assumed that while such efforts were cute and made for a great story, they were inefficient—kind of like we've always assumed that a good defender made everyone else around him better. Maybe that take-charge attitude is a natural counter to the diffusion of responsibility and has a real benefit.

I will be the first to admit that the diffusion of responsibility piece is conjecture, but it's not bad conjecture. Let's go with the point for a moment. There has been work done on how to get past the diffusion of responsibility, and mostly, it comes down to pointing out the tendency to diffuse and saying "No really, you need to act." In one area where it really counts, the identification and reporting of child abuse, there are even laws that require that people in certain professions must report (under penalty of jail time for a withheld report). This is one case where awareness of the issue might help quite a bit. Above, I spoke of teams bleeding off a percentage point’s worth of efficiency on ground balls. (A quick reminder: one percentage point is 10 points of BABIP!) If a team can recover even some of that, it's value that comes at the cost of a couple (free) conversations.