Mookie Betts's Glove Was in the Field of Play

I got the tl;dr out of the way in the title.

I've written previously about the value of multiple points of view (literal points of view in this case, but I think it's valuable for figurative points of view, too).  Last night, in Game 4 between the Boston Red Sox and the Houston Astros, was another example.

Here's the situation as it was in Houston (the location is kind of interesting, though not really important to the ruling).  It's the bottom of the first, and the Astros are already down 2–0, but they have George Springer on first after a one-out single, and Jose Altuve up to bat.  Altuve hits a deep fly to right, and Red Sox right fielder Mookie Betts reaches up and seems about to make the play, when his glove is closed shut by a fan's hand.  The ball bounces back into right field, where Betts retrieves it and fires it back into the infield.  Altuve ends up on second, and Springer (who presumably had to wait to see if Betts made the catch) stands on third.

Umpire Joe West initially calls a home run, and then appears to indicate interference (as shown here at the 8:48 mark).  The umpires collectively go to the replay, and after a delay of a few minutes, they call Altuve out, and order Springer to return to first.  After Marwin González is hit by a pitch, Yuli Gurriel flies out more conventionally to right and the Red Sox escape without further damage.

In the aftermath of the Red Sox' 8–6 victory, however, there was considerable controversy over whether the interference call was the right one.  The ruling was that because Betts's glove did not exit the field of play—that is, it did not cross the imaginary plane of the outfield fence—he was interfered with.  Had the glove been beyond the fence, then any contact with the fans would not have been considered interference.

The problem is that it's far from obvious where Betts's glove was at the moment of contact.  The Red Sox observed (as did some others) that Betts's body had yet to reach the fence, but the Astros pointed out that Betts was reaching backward for the ball.  Both sides agreed that the ball would have gone into the stands were it not for Betts, and both sides agreed that Betts had a good chance of catching the ball.  (I've seen a few fans claiming that Betts simply closed his glove early, but neither I nor any professional commentator seems to find that credible. See here at the 0:45 mark for a pretty clear video of Betts's glove being closed by a fan's hand.)

Incidentally, whether Betts would have caught the ball doesn't have any bearing on the correct call. West's call was predicated only on whether the fans interfered with Betts's fielding in the field of play. The approved ruling associated with Rule 6.01(e) reads:

If spectator interference clearly prevents a fielder from catching a fly ball, the umpire shall call the batter out.

The comment on that rule goes on to clarify:

No interference shall be allowed when a fielder reaches over a fence, railing, rope or into a stand to catch a ball. He does so at his own risk. However, should a spectator reach out on the playing field side of such fence, railing or rope, and plainly prevent the fielder from catching the ball, then the batsman should be called out for the spectator’s interference.

That's what made the correct interpretation of the replays so vital.

Nevertheless, both sides also thought the replays confirmed their conclusion, each perhaps pretending to a greater certainty than they really felt.  They're really not that conclusive either way, at first glance, and it was important, probably, that the call on the field was interference.  Here's a shot from one angle, for instance (the left-field camera, I think):

Can you tell where Betts's glove is in relation to the fence?  I can't.

Well, we don't have to tell from that shot alone.  Here's a second shot from another angle (maybe the first-base camera):

Hmm, it's not obvious from that shot either.

Once again, though, we don't have to rely on either shot in isolation; fortunately, the two images together will tell us what we need to know.  Both shots show the play a split-second after the fan had made contact with the glove, and with the ball just about to strike the outside of the glove.  The fans are still looking up because they're not trained to follow the ball into the glove, and because that baseball is moving fast, but that white blur is the ball in both photos.

How does this help us?  Well, let's take a look at where the glove is in relation to the wall.   Here are the same two shots, but with the same location marked on the outfield wall padding:

Notice where the glove is in relation to that mark in the two images.  It's to the right of that mark from the point of view of the left-field camera, but it's just about in line with the mark (or maybe a little to the left) from the point of view of the first-base camera.  It's simple triangulation: If the glove is directly above the fence, then it should be in the same position with respect to the mark from both views.  If it's in front of the fence, it should appear further to the right in the first view (from left field), and if it's beyond the fence, it should appear further to the left in the first view.

Since it's further to the right in the first view, the glove must have been in front of the fence at that moment, and the interference call is the right one.  (I was mildly surprised to discover this, by the way.  If I had to guess, I would have guessed that the glove was beyond the fence—but I would have been pretty loathe to guess.)  Without knowing more about the location of the cameras relative to the wall, we can't be sure how much in front it was, but at any rate, the contact was made in the field of play.

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ETA: Here's a third, intermediate view—from the third base camera, I think—further confirming the findings:

Cicada Recurrence and the Allee Effect

One of the best-known phenomena in the insect world is the unusual recurrence of various populations of cicada.  There aren't any cicadas out here on the West Coast, where I live, but they are endemic to the Northeast.  The periodical cicadas (there are non-periodical cicadas, apparently) are notorious for having life cycles that are synchronized to one of two (relatively) large primes: 13 years and 17 years.  The big question, of course, is why: Why do cicadas have life cycles that are synchronized in this fashion?

One could divide the 13-year cicadas into 13 distinct subgroups, depending on which year they emerged, and divide the 17-year cicadas into 17 subgroups along the same principle.  Physical observation of cicadas, as shown in the Wikipedia plot summary, reveals that only about half of the 13+17 = 30 subgroups actually manifest in the United States (where the cicada is native), however, with two subgroups becoming extinct within the last century or two.  Nonetheless, the periodicity is well enough established that there should be a rational explanation of this phenomenon.

 One historically proposed reason for the synchronization has been that the long recurrence time limits exposure of the species above ground to predators, and that when they are exposed, there are so many of them that predators cannot possibly decimate them (a fact well attested by the unfortunate farmers who have to deal with them), thereby ensuring the continued existence of the population.  Although this is surely part of the answer, it only explains why the period is long; it doesn't explain why the period isn't 12 or 15, for instance, rather than 13 or 17.  These latter periods would only provide additional benefit if the likely predators of the cicada likewise had a life cycle punctuated by years of inactivity, which turns out not to be so.

A more successful explanation involves hybridization.  It is hypothesized that whatever mechanism governs the return of the population after however many years is based on a biological clock that is adjusted to activate periodically, and that if a 13-year cicada were to mate with a 17-year cicada, the result would be a substantial number of cicadas with unpredictable, but likely shorter, periods.  (Too long, and the individuals would die of old age, anyway.)  Such offspring would be more vulnerable to predation, so there is an evolutionary premium placed against hybridization.  Computer simulation studies show, however, that if we assume an initial species-wide distribution of a variety of periods—some prime-numbered, some composite—the prime-numbered periods remain, but so do some of the composite periods.

This 2009 paper, by Tanaka et al., explains away the remaining composite periods by means of something called the Allee effect.  In many population dynamics analyses, it is assumed that the fewer instances of a species exist, the more likely any instance is to survive—it being presumed that there is no disadvantage owing to an excess of resources.  There may be no such disadvantage, but it is nonetheless the case that there are situations where the reverse is true, for small populations: the greater the population, the more likely any individual is to survive to reproduce, because it benefits from the increased support and robustness of the larger population, up until the point where that larger population represents more competition than cooperation.  This reverse but very natural-seeming tendency constitutes the Allee effect.

Tanaka and company simulated the cicada species under a very simple hybridization model, both with and without the Allee effect, starting with subgroups with a range of periods varying from 10 through 20 years.  They found that without the Allee effect, there was broad survival of all of the cicada subgroups, with the 16-year subgroup thriving the best.  But with the Allee effect, the result was startlingly different: Only those cicada subgroups with periods of 13, 17, or 19 years survived, depending on some of the initial parameters.

Since the actual mechanism of the periodicity is not well understood yet, this study is more suggestive than dispositive, but the results are provocative.