Last week (or because this gets weird with time zones, three weeks ago) in Korea, the Kia Tigers of KBO (the professional baseball league in Korea) employed a rather interesting shift. It’s not entirely clear why from the footage released, but Deadspin documented that the Tigers tried to play their third baseman behind the catcher. The Tigers were tied with the KT Wiz 5-5 in the top of the ninth. Apparently, with two out and runners at second and third, they tried the rather unorthodox shift only to have the third baseman be told to go back to his home at the hot corner by the umpire.

According to Deadspin writer Barry Petchesky, “Since it’s the top of the ninth in a tie game, I can only assume the Tigers have decided that protecting against a wild pitch or passed ball is more important than having four infielders. (I would love to see the sabermetrics on that.)”

Warning! Gory Mathematical Details Ahead!

First off, let’s start off by pointing out that this sort of shift would be illegal in MLB. The rules of baseball explicitly state that fielders must be stationed in fair territory, except for the catcher. But, if it were allowed, would it make sense?

A commenter at Deadspin pointed out that with two outs and first base open, it was likely that the Tigers were going to intentionally walk the next batter and just wanted the third baseman back there in case of an intentional ball that got away. It’s a rare occurrence, but it basically costs nothing to have the third baseman back there, because the ball isn’t going to be put into play on an IBB. But what if he was actually back there as a second catcher to guard against a real live wild pitch. Would that make sense?

Of course, it would only make sense in a very specific set of circumstances, mostly the bottom of the ninth (or later) with a runner on third and a tie score. There would probably have to be fewer than two outs. At that point, the only thing that matters for the visiting (fielding) team is making sure that the runner on third doesn’t score. If he does, they lose. It’s not a great situation to be in, but in life, you have to play the hand that you are dealt. The problem is that now, the batter is probably looking at an infield drawn in and the possibility of winning the game on a simple sacrifice fly. Sometimes teams in this situation will employ a legal, but surprisingly under-used shift—playing a five-man infield—but let’s look at this more extreme shift.

Let’s start with the easy part. Let’s say that putting an extra defender back behind home plate would effectively neutralize the risk that a passed ball or wild pitch would score the run. The catcher wouldn’t have to track the ball down and the pitcher not have to charge in to try to catch a throw on the run and tag the runner. The backstop guy could field the errant pitch and the catcher could just stay and cover home if the runner makes a dash. In 2014, there were 342 PB and 1686 WP in MLB, for a total of 2,034 balls at the backstop. There were 79,764 PA with runners on. (Remember: wild pitches sometimes happen with no one, but no one cares or notes it), so we have a rate of 2.6 percent of “eligible” PA that featured a PB or WP. By putting a backstop guard back there, a team would “buy” a 2.6 percent reduction in the chances that the runner would score in this particular plate appearance. Pretty good.

Well, whom should they stick back there? I don’t think that the third baseman is the best guy for the job. Personally, I’d pick the slowest outfielder, probably the left fielder. The reason is that when a team is in this extreme situation, the shape of the field changes. Not physically, mind you, but functionally. Consider that if the batter lifts a fly ball to the wall in left field, a normally playing left fielder might be able to track back and catch the ball, but the runner at third will tag up and run home easily. There’s no point in the left fielder catching that ball, because you still lose the game. Why bother positioning him in such a way that he could make that play? In fact, anything in the outfield that is beyond the outfielder’s range to throw the ball catch and throw the ball home in time to nail the runner is useless to defend. If we assume that the maximum range where an outfielder could still either deter a runner from going at third or throw him out is roughly 250 feet (a somewhat educated guess on my part), then the defending team might as well not defend anything past 250 feet. The field now effectively has fences that are 250 feet away from home plate. Beyond that is as good as a home run. That’s a tough spot to be in. Remember when people used to complain about bandbox stadiums and all the home runs that were hit and how the high scoring was ruining baseball? (Remember?)

The silver lining is that the defense doesn’t really have much area to defend. Is it possible that two outfielders could handle it? Let’s use some geometry!

We know that the foul lines create a 90 degree angle at home plate. Let’s assume that anything on the infield skin is the “responsibility” of the infielders. The rounded part of the skin is actually 95 foot radius from the pitcher’s rubber, so on a line straight through second base from home, you’d travel 155 feet. Just using that as a radius, you’d get an infield that has an area of 18,869 square feet (area of a circle is pi * radius^2) and because the foul line creates a right angle, it’s ¼ of a circle). The total area that needs to be defended (remember 250 feet from home plate) is 49,087 square feet. That means that the outfielders have to cover about 30,000 square feet.

We know an average baserunner can make it down the line in 4.3 seconds from home to first. That’s 90 feet. So, he could cover roughly 85 feet in four seconds, and your average fly ball hangs up for about four seconds. (Actually, the kind of fly ball that would go to the short outfield probably hangs up longer specifically because it is hit with more of a vertical launch angle.) That means that if our two outfielders have even average legs, they can cover a circular area of 22,698 square feet each, which means that the two outfielders could conceivably cover about 45,000 square feet, more than the area we assume that they have to cover in general. The outfield isn’t shaped like two giant circles though. So, let me break out Microsoft Paint and show you why I wasn’t an art major before we continue.

Our purple outfielders (must be the Rockies!) would probably want to play a little back toward the imaginary fence line. If a ball was hit over their heads, they’d want to be able to track back and have time to get behind the ball so that they could catch, set, and throw in one motion. The red area in my crude outfield doesn’t matter any more, because in that area, we assume that even if the outfielders caught it the sac fly would be a fait accompli. Those black circles around them are their theoretical range. They would probably overlap a bit and that’s not to scale (in any sense of the word), but you can quickly see that you can overlay two reasonably big circles and there wouldn’t be a lot of room left that mattered that wasn’t covered. Maybe some, but is it worth covering?

We’ll assume that there’s some patch of ground that a third outfielder could cover that the other two couldn’t, but let’s see how often that would come into play. In 2014, 31.2 percent of plate appearances didn’t involve the defense (strikeouts, walks, HBP, home runs), although they could have involved a passed ball/wild pitch. The left fielder would not be missed here.

· Of the 68.8 percent of plate appearances remaining, roughly 40 percent of those were groundballs, which if they got to the outfield, would be base hits anyway and the run would score, so the left fielder being there or not being there doesn’t matter.

· We’re down to 41.3 percent of all plate appearances. Another 20 percent of balls in play (13.8 percent of all PA’s) would be line drives. From 2010-2014, 68.5 percent of line drives fell for hits anyway, and that’s with a three man outfield playing at normal depth. 16.2 percent of line drives were snagged by infielders, leaving 15.3 percent of line drives that were caught for outs by outfielders. Now, our outfielders will be playing shallow to begin with, which means that they would have even less time than normal outfielders to respond to a line drive (not that you get much hang time with liners). That means that some of the 15.3 percent that they would normally catch at normal depth won’t be caught here. Even if we ignore that, we know that line drives are more about whether it gets hit at you than any sort of defensive ability. If we make the assumption that because the left fielder is gone, we’ll lose a third of our line drive catching capacity, that’s 5.1 percent of line drives not caught, due to the absence of the left fielder, or 0.7 percent of all plate appearances where the left fielder could have made a difference by being in actual left field.

· Now, the fly balls (the remaining 27.6 percent of PA’s). In the Retrosheet data from 1993 to 1999, we actually have decent ball location data for where fly balls came down, using a grid system. If you look on that grid, you’ll see that beyond the infield skin, there are five levels of the outfield grass, starting with the one that goes from 5D to 3D, and moving on out further. During that time period, when there was a runner on third with less than one out and a ball was hit to an outfielder (who caught it) in the innermost ring, the runner on third scored 3.5 percent of the time. In the second ring, the success rate was 20.8 percent. In the third ring, it was 91.7 percent. (In the outer two rings, success rates were above 99 percent.) Really, only balls hit in those first two rings give us any chance that the outfielder would throw the runner out. Again, from 1993-1999, 64.3 percent of all fly balls were hit into this “too far” zone. That means that only in about 8.2 percent of plate appearances where we could expect to see a ball hit into the zone where an outfielder could make a catch and throw the runner out (or hold him at third). We’re pretty sure that we have most of that area covered.

· We know that putting the left fielder behind home plate saves a run in 2.6 percent of plate appearances. We know that not having him in left field lets a run score on a non-caught line drive 0.7 percent of the time, so right now, the left fielder as backstop guard is winning by 1.9 percent. To negate that 1.9 percent advantage, we’d have to make the case that if the left fielder were in the outfield for the 8.2 percent of plate appearances in which a ball was hit into the “not too far” zone, he could make a play about 23 percent of the time (1.9 / 8.2) that the other two couldn’t make by themselves. Given that the amount of turf that has to be defended in the outfield small enough (30,000 sq ft) that one outfielder standing in the middle could (at least theoretically) cover 2/3 of it (assumed range of 22,000 sq ft), it’s not likely that the left fielder would actually prove to be that useful. There just isn’t 25 percent of the field that our left fielder could have to all to himself.

Oddly enough, the idea of using a left fielder in this situation as a backstop guard actually sounds like it would be a more advantageous strategy than a traditional three-man outfield. But here’s a question: Is it better to put him behind the plate as wild pitch insurance or is it better to put him in the middle of the diamond as a fifth infielder. We know that the effects of taking him out of the outfield will be the same either way, but behind the plate, he prevents a run scoring 2.6 percent of the time. What would he do in the middle of the diamond as an extra infielder?

Infielders snag 16.2 percent of line drives, (probably less with them playing in, but let’s go with it). We know that whether an infielder catches the ball is mostly to do with luck. So, let’s just assume that adding another infielder boosts their line drive catching ability by 25 percent (4.1 percent of line drives). Because we assume that 13.8 percent of plate appearances are line drives, we assume that the left fielder-middle infielder saves a run by snagging a line drive in 0.6 percent of plate appearances.

As to knocking down a few grounders, 13.6 percent of grounders went straight up the middle from 1993-1999 (zones 4M and 6M). About half of them went for hits with a four-man infield. Because the infield would be playing in, that number would probably go up, but let’s go with it. 27.6 percent of all plate appearances ended in grounders, 13.6 percent of those went up the middle, that’s 3.8 percent of plate appearances in which an extra infielder might come in handy. We know that playing at regular depth, the 2B and SS manage to get to that ball and record an out (usually at first) 50 percent of the time. However, while playing in and having to come home, their success rate would be much lower (assuming no fifth infielder). I’m going to simply cut it in half and say 25 percent, which brings us to 2.8 percent of plate appearances where our left fielder standing between the shortstop and second baseman might be able to pick up the ball and throw home to get the runner at third, but the keystone combo wouldn’t. Now, the left fielder will also be playing in (very far in!), so his success rate won’t be great either. In order to break even with stationing the left fielder as a passed ball preventer, we’d have to assume that the left fielder would be able to convert 71 percent of the ground balls straight up the middle into an out at home (or that he could hold the runner at third). Plausible, but it’s amazing how close a shave it is.

Shift Your Entire Way of Thinking

The bottom-of-the-ninth, tie game, runner-on-third, less-than-two-outs scenario isn’t going to be common, but it happens from time to time. I was actually surprised when I saw the Deadspin story. The Kia Tigers get major extra credit for creative thinking! I had never thought of having a second catcher, but after doing some math, I can see a pretty good case for doing it (other than that it’s illegal). At the very least, the left fielder as backup backstop is about equal to the left fielder as fifth infielder strategy. Both are better than leaving him in left field… which is what usually happens.

We see that playing a five-man infield is a strategy that prevents the winning run from scoring an extra 1 percent of the time (in this extreme situation), compared to leaving the left fielder in left field. I’m left wondering why it’s so rarely used when the situation calls for it.

No one ever really talks about the danger of passed balls, but in this particular situation, a passed ball is a) as good as a home run and b) one of things that a team can sorta prevent, especially since it doesn’t have to worry much about preventing balls from dropping in most of the outfield. And in this situation, it makes sense to pour resources into preventing a passed ball, even if it would look really weird on TV. (The left fielder would be dancing behind the umpire and catcher in the center field camera shot!) If a pitcher was a little more prone to being wild, it might even be the obvious choice of a strategy once you’ve done the math… if it were legal.

Hey, MLB…

Special thanks to the Effectively Wild Facebook Group for pointing out the Deadspin article..

Thank you for reading

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This was a really fun article! I particularly loved the illustration.

There is a tiny typo in the 4th paragraph under "Gory Math" where it "should" read "wild pitches sometimes happen with no one ON," but I think you should leave it because it conveys a certain existential angst that seems somehow appropriate for an article centered around a rule that doesn't exist, almost like a koan. "If wild pitches sometimes happen with no one, are they really wild?"
I printed your drawing off and hid it under my mattress.
I know people keep talking about a site re-design, getting excited about new writing talent, and debating proper usage of cFIP and DRA. But what we really need around here is more of Russell's artwork.
I showed that drawing to my wife and we made a bet about how long it would take until someone suggested that those weren't Colorado Rockies. I had much more faith in you guys. ;)
You mean they're more Grand Tetons? Do they even have a team there? :-)
russell, your drawing looks like the owl from a cartoon I used to watch growing up.

A little kid was supposed to be practicing classical music but was corrupted by Owl Jolson, who taught him to play jazz: "I wanna singa, about the moon-a and a June-a and the spring-a..."
Russell, given your pseudonym, I thought it was a slice of pizza.
Is there a rule here against having more than one player behind the home plate area? Could a third-baseman play in foul territory at all?
no. all players, save for the catcher, must be in fair territory when the ball is put in play.
Russell said this: "When the ball is put in play at the start of, or during a game, all fielders other than the catcher shall be on fair territory."

And the rulebook says this: "5.02 (4.03) Fielding Positions
When the ball is put in play at the start of, or during a game, all fielders other than the catcher shall be on fair territory."

So, yes, there is a rule. And no, the 3B cannot play in four territory at all.
I don't know why, but this reminds me of something in football...

Why don't offenses put a fast linebacker or a strong safety behind everyone in a victory formation? This seems like a better strategy than hoping your running back has the ability to tackle the defender who might pick up a loose fumble during from the snap.
Reasonable thought. A lot of teams go with a WR, probably because, well, that's what you do... Might be they figure the fastest WR might be able to get to the ball first, or else can run the other guy down, and, even if he can't make the tackle, could force him out of bounds, which is just as good...
Well, if you just have to be in fair territory when the ball is put in play a team could have it's 'extra catcher', or whatever this player shifting for a backup was and have them stand right in front of the hitter before the intentional ball was thrown, then as the pitch was released, charge to the backstop incase the ball got away and was a wild pitch...

It would look stupid but might save a run and certainly fits under the MLB rules...
What about a shift where the second baseman runs up behind the pitcher and jumps around and waves his arms from just behind the arm slot where the batter is looking for the pitch?
Actually, I'm pretty sure that's explicitly illegal as well.

Probably the kind of thing the 1890's Orioles (McGraw, et al.) would have tried at least once...
Awesome article.

Because of behavioral change for the pitcher and catcher, I just don't believe 2.3% of plate appearances with a runner on 3B have a PB or WP where the runner scores.

MAYBE the backstop dude gives the pitcher confidence to throw breaking pitches in the dirt and this has a HUGE effect to support the shift...

It was a really fun read and the pic looks like a surprised guy with red hair.
Wouldn't putting the third baseman behind the catcher allow to the runner to get an enormous lead and just steal home? I assume that the SS would have to hold him on third to prevent this, and if that's the case, that creates a huge hole on the left side.
Although I guess if they were intentionally walking the runner it wouldn't matter because they wouldn't have to worry about the batter putting the ball in play, duh.
If this was legal, it could give a big boost to one group: knuckleball relief pitchers. While throwing a knuckler isn't particularly tiring, there must be some pitchers out there who can only keep it in control for an inning or two. Or if a replacement-level reliever could learn a knuckler, he could become much more valuable. If teams could do a better job preventing passed balls in high-leverage situations with men on base, they could deploy these relievers with less risk in late innings.

Who doesn't think that MLB would be a better place with more knuckleballers?