Last month, we started a thing: Trying to identify, and then appreciate, the single best defensive game any player had that month. Partly an excuse to make sweet moving pictures, mostly an attempt to put excellent short-burst defense in perspective, so that we can intuit the value of a great defensive game just as easily as we can process Chris Davis’ 4-for-5 with three home runs. To do that we had to turn these defensive plays into something like numbers, and to do that we turned to Inside Edge, provider of defensive data to major-league clubs, media outlets, and elsewhere. Inside Edge rates each defensive opportunity thusly:

Routine: Greater than 90 percent chance that it will be fielded

Likely: 60 to 90 percent chance

Even: 40 to 60 percent chance

Unlikely: 10 to 40 percent chance

Remote: 1 to 10 percent chance

Impossible: 0 percent chance

With each play rated, then, we could pick a winner, and for May that winner is Aaron Hill, for the game he played on May 14th. Here’s what Aaron Hill’s defensive performance looked like in the box score of the next morning’s newspaper:

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The only defense that was deemed important enough to record in that game’s box score was: An error by Ian Desmond; an error by Chris Owings; a pickoff by Doug Fister. A slightly more detailed box score would note Jayson Werth’s outfield assist. Add one more level of detail and the box score would record the double play collaborations: A Rendon-D Espinosa-T Moore; I Desmond-T Moore. That’s it, though. Nothing on Aaron Hill.

So we proceed on our own. Ten baseballs were hit near Aaron Hill in this game.

1. Anthony Rendon, First Inning

Routine. If you watch closely, there are 10 people in this picture who have to perform some action during this play: The second-base umpire moves around to the other side of the bag in case there’s an errant throw leading to a play at second, for instance. The catcher moves over to back up the throw to first. Rendon runs to first, of course, and Goldschmidt covers first, and the first-base umpire shifts into position, and the first-base coach shuffles about to have a better angle on the throw and the play, while the right fielder halfheartedly backs up the grounder and the shortstop starts walking over to second base, also in case of a play caused by a poor throw, and the home plate umpire jogs out for some reason that probably makes sense. On any batted baseball, there are a dozen or so routine acts that the men on the field do routinely. Relative to all these people, Hill’s job was the least routine. It was still very routine. Inside Edge calls this one 90 to 100 percent likely to be made, so Hill gets credit for maybe 1/20th of an extra play here.

2. Nate McLouth, Third Inning

This one goes down as Even, a 40 to 60 percent chance of an average defender making it. Hill, as they say, makes it look easy; considerably easier than Nationals’ first-base coach Tony Tarasco makes his job look. There’s a moment that is a bit hard to see in the first GIF, but clearer in this second one, just as Hill stabs the ball,

when you can see the effort involved in keeping his balance. It’s a three-step move. In the first step, as he fully extends, his left foot turns a bit in at an angle to begin the spin and counter the momentum of his lunge; in the second, he has to make a very quick step so that his right foot can catch up and keep him from tumbling, while the momentum of his upper body carries him into an almost prostrate position, head facing the ground; then a strong plant on his left foot stabilizes the action. Slowed down, he seems to be on the edge of his balance and then in perfect posture within three very quick steps.

The Diamondbacks didn’t broadcast this game on TV, so the average Arizona fan didn’t get to see any of these plays; a diehard fan would have gotten to hear them, on the Diamondbacks radio broadcast. What does this play look like to a radio listener?

Greg Schulte: Groundball to the right side, nice play by Hill, going to his left, turns around and throws to Goldschmidt on a dandy fielding play there.

Tom Candiotti: Really nice play. Looks like it might get into right field, Hill ranging that way, spears it with one hand and then does the pirouette play.

For converting an “Even” chance, Hill gets credit for one half of an extra play over an average second baseman.

3. Anthony Rendon, Fourth Inning

Routine, even more routine than the first ball Rendon hit. There is nothing to say about this play, except did you ever notice that the screen behind home plate at Chase Field is a mirror showing the catcher’s butt? We’ll give Hill credit for 1/20th of an extra play.

4. Ian Desmond, Fifth Inning

That counts as a chance, though a remote chance; Hill was between one and 10 percent likely to make the play, and he didn’t. On the one hand, Hill doesn’t get the out. Dock him 1/20th of a play. On the other, after kicking it and chasing it down he ultimately ends up fielding a ball in shallow field, directly behind where a shortstop plays. What range!

This was the first hit Brandon McCarthy allowed, and it came in the fifth inning. Both announcing crews—the Nationals’ on TV, the Diamondbacks’ on radio—said flatly that Hill wouldn’t have thrown out Desmond even if he had fielded it. Maybe.

Desmond had taken seven steps when the ball hit Hill’s glove, and it takes about 16 for most guys to get to first, so figure Hill had around two seconds, or slightly more, to get it to first. It took him about two and a half to get rid of the ball and get it to first in this similarly wonderful play from last year.

5. Denard Span, Sixth Inning

Infield is in, but the play is otherwise routine, at least as far as we can see from this late-cut camerawork. So routine that shortstop Chris Owings turns away from the play even before it’s over. I think the runner at third should have been allowed to score because the Diamondbacks catcher is clearly blocking the plate, but I guess the new rules are confusing to everybody. Hill gets 1/20th of a play added to his ledger. So far we’ve got three routine plays, a pretty good play Hill makes, and a very tough one he doesn’t. How is this the defensive game of the month, you wonder.

6. Anthony Rendon, Sixth Inning

This play’s so unexpected that the cameraman cuts to the run scoring at home, which means we’ve got a really good insight into what Nate McLouth thought of this play. This is the third ball Rendon has punched to Hill (“to” Hill) in this game, and the first two were right at Hill, who barely had to move. This one was not.

A thing I learned recently, thanks to Mark Simon at ESPN: Baseball Info Solutions this year, at ESPN’s request, is tracking assists from “knees, stomach, or any other part of the body.” There is a leaderboard for these throws. This could, I assume, count as a throw from the knees, though if you watch it over and over you realize: He actually throws it from the air, having propelled himself entirely off the ground, like a fish crossing the street. (I have stills that can prove it.)

Here’s Schulte’s radio call: “Groundball to second again but it — …. — Diving stop Hill! Throws! Got him at first! What a play! Hill saved a run there with a diving play going to his left, got up and threw quickly to Goldie. What a play defensively by Aaron Hill, who’s made a couple today.”

And the Nationals’ TV guys:

Bob Carpenter: Right side it… is fielded by Hill.

F.P. Santangelo: What a play, are you kidding me.

Hill gets credit for one Unlikely play, or about three-quarters of a play more than the average defender would record there.

7. Danny Espinosa, Seventh Inning

Routine. Two things: 1. You have to give Matt Williams credit. These guys do run out routine groundballs. 2. The GIF is more fun when you imagine the first-base umpire is frozen by indecision.

Hill gets 1/20th of an out on his ledger.

8. Kevin Frandsen, Eighth Inning

I’m obsessed with this play, which Inside Edge classified as remote—a one to 10 percent chance that the defender makes it. A friend noted that it almost looks like a Keystone Kops sort of play: You’ve got the pitcher running toward the play and then having to stop, suddenly and a bit uncomfortably, as though he’d been hypnotized and wasn’t allowed to cross some imaginary line. You’ve got a first baseman who runs away from a slow grounder hit almost directly to him. You’ve got a baserunner swimming through dirt trying to get to the base instead of running right through it. And you've got Hill, who makes one of the least throw-like “throws” of the year, a sort of push/shovel/nudge/scoop/shove toward the first baseman. Of course, all of these look vaguely blooperesque in isolation but, aside from Frandsen’s momentum-killing slide, were necessary to a fairly complex highlight. Goldschmidt had to flee the ball; nobody else would get to the base in time, or at an angle at which he could deliver a throw. McCarthy had to stop, as it became clear in just the nick of time that he was going to impede Hill’s plans. Hill’s non-throw throw, the shovel/shove, took incredible balance and focus. And Frandsen made it all possible by slowing himself down by a step or two.

Schulte: A groundball toward first. —…—And Hill—…— To Goldie. And they got him at first base. Hill just kind of rolled that ball over.

Candiotti: Boy how about Aaron Hill, what a play. Goldie stayed right at the bag. Hill comes in and just kind of swats the ball like you’re playing a flip game.

That’s 95 percent of a play that Hill gets that an ordinary defender wouldn’t.

9. Danny Espinosa, Ninth Inning

Almost the same play that he made on Desmond earlier, but he fields it a little shallower and has a little more time to throw, so he can get up to his feet. The premise of this article and this series is that great defensive games go overlooked, but by this point both teams’ broadcasters are noting that Hill is doing something special.

Schulte: Boy another dandy play by Aaron Hill who took a run away.

Candiotti: That’s right Aaron saved another run right there. He has been spectacular in the field today.

Carpenter: Right side, well placed, Aaron Hill AGAIN. Arrest that man.

Santangelo: Aaron Hill today, he’s playing right out of his uniform.

That play was classified Unlikely, so give Hill another 3/4 of a play over average.

10. Nate McLouth, Ninth Inning

Sadly, one inch away from really making it a day. Hill took a long time dusting his uniform off after this one.

So knock a 20th of an out off for that Remote chance. Here’s what his day looked like:

Routine Plays: 4-for-4

Even Plays: 1-for-1

Unlikely Plays: 2-for-2

Remote Plays: 1-for-3

Summed, that’s slightly more than three plays that Aaron Hill made that an average defender wouldn’t have.

When the defensive metrics get together for their monthly poker night, Hill is a controversial topic; they actually had to instate a house rule that nobody is allowed to bring up Aaron Hill, because somebody always stormed off angrily and somebody always got his feelings hurt. In 2012, FRAA rated Hill a +23 defender—the 12th-best defensive season ever by a second baseman. That made Hill an MVP candidate, by WARP. Meanwhile, UZR thought he was just a couple runs better than average, and Defensive Runs Saved rated him significantly below average. A large difference is showing up again this year, particularly between FRAA and DRS, and over the past three years the two systems disagree about Hill’s defense by about 43 runs. Forty-three runs is roughly the difference between Derek Jeter and Elvis Andrus, so it’s a lot. One game won’t solve this disagreement, but here’s what Inside Edge’s metrics have said about Hill in those three years:

Of 19 qualified second baseman,

No player has made more Remote plays than Hill. He also has the most Remote chances, but only three players have converted a higher percentage.

No player has made more Unlikely plays than Hill, and no player has converted a higher percentage.

He’s right around the median for Even—40 to 60 percent—plays

No player has made fewer Likely (60 to 90 percent) plays than Hill.

And no player has made a higher percentage of Certain/Almost Certain plays than Hill.

So these aren’t necessarily gospel, but if we take them as trustworthy we’d say that Hill makes the extremely difficult play as well or better than any second baseman in the game. And he makes the routine play as well or better than any second baseman in the game. And he make the not-quite-routine play worse than or as badly as any second baseman in the game. That’s certainly interesting.