It's usually a big moment in the game if Andrew Miller is pitching, and April 21, 2018, was no exception. Miller was protecting a one-run Indians lead in the eighth inning, with two runners on and two men out. He had two strikes on the Orioles' Adam Jones, and tried to put him away with a fastball. "Ninety-seven," a broadcaster calmly noted. It was, according to Statcast*, Miller's fastest fastball of the year by quite a bit.

Every pitcher has a fastball. And, of course, every pitcher with a fastball has a fastest ball, the one pitch he threw harder than all the other fastballs. A flamethrower like Aroldis Chapman (average fastball last year: 98.9 mph) has a fastest ball (104.4), and just as surely a finesse pitcher like Kyle Hendricks (86.8, 90.9) does too. On average, a major league pitcher throws his fastest fastball about 3 mph harder than he throws his average fastball. That pitch from Miller was a little more than 4 mph harder than his fastball average, a half-mile harder than his second-fastest pitch, a mile and a half faster than his third.

There are 575 pitchers who, last year, threw at least 250 pitches. We put each pitcher's fastest pitch into a spreadsheet -- 575 lines, one for each pitcher -- to try to answer some questions: What do we make of these fastest fastballs? When are they thrown, and why, and to whom, and to what effect? We will answer those questions, after giving you the chance to hypothesize with a game of multiple-choice:

1. When in counts are these fastest fastballs thrown?

A. They're thrown when the pitcher is ahead in the count, especially with two strikes. The pitcher is using his fastest fastball as a strikeout pitch, a way to get a swinging third strike while he has the luxury of being a little wild.

B. They're thrown when the pitcher is behind in the count, especially 2-0 and 3-1. He knows the batter is geared up for a fastball, he knows he has to throw a fastball, and so he throws extra hard -- power on power, a true challenge pitch.

C. They're pretty evenly distributed. There's not much intent here, and a pitcher's fastest fastball is really just his fastball, thrown in a moment when he just nails his form.

The answer is:

A, and by a lot. A fastball thrown in a two-strike count is more than five times likelier to be a pitcher's fastest pitch of the season than a fastball thrown in any other count. The most common count is 0-2; the second most is 2-2, then 1-2, then 3-2, and only then come all the other counts. A fastball thrown in an 0-2 count is 30 times more likely to be a pitcher's fastest fastball than a fastball thrown on 3-0, nearly 20 times more likely than a fastball thrown on 2-0, more than four times as likely as a fastball thrown on 0-1.

Bartolo Colon, for example, averaged just 87.4 mph with his fastball last year. But one day in Texas he had Didi Gregorius in an 0-2 count. Colon threw that fastball 93.7 mph, more than 6 mph harder than his usual. It was the biggest average-to-fastest margin by any pitcher in baseball. (Gregorius lined out hard to center field.)

Using this pitch with two strikes makes sense. (But then, all the hypotheses made sense!) A pitcher's very, very fastest fastball is almost like a specialty pitch: He doesn't want to throw it all the time, for various reasons, but on two strikes it works to give a batter something new, late in a count, when there's a premium on swinging strikes.

2. When in innings are these pitches thrown?

A. They're thrown mostly with men on base. These are the most crucial situations, and a pitcher pulls out his very best stuff to get out of trouble.

B. They're thrown mostly early in innings, often to the first batter of an inning, when the pitcher has some strut coming out of the dugout, before he has been tired out by his time on the mound.

C. They're thrown mostly with two outs, when a pitcher has gotten into a rhythm on the mound and he really wants to put a punctuation mark on an inning.

The answer is:

C. The fastest fastball is more than three times as likely to come on a two-out fastball as a none-out fastball. (One-out fastballs are in the middle.) Put this fact and the one before it together and we get this: A fastball thrown with two outs and two strikes is our most common fastest-fastball scenario.

Chris Sale's fastest fastball is a good example: It came in June, against the Mariners, and it was his final pitch of a seven-inning start. He struck out Mike Zunino swinging with that pitch, then marched off the mound with the lean of an ace who'd just polished off a masterpiece: seven innings, no runs, four hits, and 13 strikeouts, the last one on a 100.5 mph pitch that was nearly 6 mph harder than his average fastball. (Sale had the third-biggest jump from his average fastball to his fastest fastball last year.) His second-hardest fastball of the year would have been an even better example: It came in the same game, also against Zunino. Sale had struck out the first two batters of the inning on six pitches, then jumped ahead Zunino 0-2, and with a chance at his first-ever immaculate inning -- and just the 93rd in major league history -- he missed the zone for a ball. He came back with his 10th pitch of the inning, at 100.4, to get Zunino. Same result: Stomp off the mound, etc. Sale's eight fastest pitches last year all came on two strikes; five came with two outs.

Fastest fastballs aren't thrown any more frequently with runners on base than with bases empty. As long as we're throwing out untested hypotheses -- perhaps because a pitcher is more likely to throw this pitch when he's in a groove? From the windup? When he's less worried about a wild pitch?

3. Whom are these pitches thrown to?

A. Mike Trout, the best hitter in baseball. You just have to bring a little extra against him.

B. Bryce Harper, the most, how would you say, divisive hitter in baseball. He's got a target on him.

C. Chris Davis, the most strikeout-prone batter in baseball. If these fastest fastballs truly come from pitchers hunting K's, it could just be as simple as Davis being the busiest game in town.

D. Jose Peraza, an option so out of nowhere I couldn't possibly have come up with him unless he is the correct answer. Anyway, a harder fastball might be more likely to be a wilder one, and a straighter one, and you'd rather make a straight-and-centered mistake to Peraza than to Trout.

The answer is:

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B -- Bryce Harper, by a lot, relatively speaking. Trout saw two fastest fastballs (by Kendall Graveman and Erik Goeddel). Davis saw one (Tim Hill). Peraza saw one (Chris Volstad).

Harper, meanwhile, saw 11 -- as many as those three guys and the No. 2 player on the whole danged spreadsheet, Manny Machado, combined. Joe Musgrove, Aaron Sanchez, John Gant, Brandon McCarthy, Jimmie Sherfy, Dillon Peters, Alex Wood, Seranthony Dominguez, Andrew Suarez, Arodys Vizcaino and Zac Curtis all throttled up against Harper: Nine times, Harper swung, putting just one in play (for a fly out) and striking out thrice.

There's a bunch of noise here -- these are rare events -- but one's intuition would probably expect that the top of this list would be a bunch of stars, and it does skew toward that. Harper and Machado being at the top is a powerful suggestion that the order of this list means something.

1. Bryce Harper, 11

2. Machado, 7

2. Ronald Acuna Jr., 7

4. Willson Contreras, 6

4. Jesus Aguilar, 6

6. Eight players tied with 5: Paul Goldschmidt, Francisco Lindor, Odubel Herrera, J.D. Martinez, Amed Rosario, Brian Dozier, Justin Upton, Jose Altuve

4. So, what happens?

A. These pitches are wild but effective (at getting swinging strikes and bad contact)

B. These pitches are wild and also ineffective

C. These pitches are not wild but also aren't very effective

D. These pitches are not wild and are effective

E. These pitches are actually just like all the other pitches

The answer will be somewhat open to interpretation, depending on how different something must be before you consider it different enough to mention. But here are the basics:

The average fastball across the majors is a strike 65% of the time, gets whiffs on 19% of swings, is put in play on 39% of swings and, when it is put in play, allows a .338 batting average and .560 slugging percentage.

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The average fastest fastball, meanwhile, was a strike 63 percent of the time, got whiffs on 20% of swings, was put in play on 32% of swings and, when it was put in play, allowed a .422 batting average and .600 slugging percentage.

That's a bit of a mixed bag, complicated by the sample smallness of fastest fastballs, and complicated further by a whole bunch of other factors (such as the effect of the count, and the better quality of hitters in the sample, and the fact that on this spreadsheet Jimmie Sherfy threw as many pitches (1) as Max Scherzer). But to my eye the answer is closest to E: They're mostly just like the other pitches. Slightly wilder, more likely to get a whiff, more likely to be fouled off but also more likely to be hit hard -- all of it, though, just slightly, and probably leaning against the pitcher's best interests. If we take that to be the case, then we can understand why these fastest pitches are each pitcher's outliers, rather than what they try to do all the time on every pitch: There isn't a ton of benefit to throwing at the outer bounds of one's ability, except perhaps situationally. And, of course, if they tried to throw this hard every time, they'd presumably get tired more quickly, perhaps get hurt more often. So they don't. These are just their occasional fastest.

To understand a little bit better, we went to the man who started this story: Andrew Miller. He wouldn't have recalled this as his fastest pitch of the year, but it made some sense to him that it would turn up: big situation, two strikes and two outs. It was a two-seamer -- which he feels like he throws a little bit harder, but hardly ever -- because he wanted to show a quality hitter like Jones a little wrinkle. More than all that, though, it made sense to him because, at the time, it felt like "my mechanics were falling in line. I felt like I was figuring it out. And usually I don't throw the two-seamer unless I'm really locked in."

In other words, he had to feel like he was in the right place to really reach back. He rarely throws a pitch as hard as he can. He doesn't feel like he can command it as well, he isn't sure his stuff plays as well, and he worries that really exerting himself will cause him to lose his mechanics. Throwing his very hardest tends to get him in trouble more than anything, he says. But this day he felt like he had it in him. "To me, that's just me feeling really good where I'm at. I sold out for velocity. The thought inside my head was, 'I'm going to throw one by him.' I was ready to take off."

"It obviously didn't work," he says. Jones fouled the pitch away to stay alive. On the next pitch, a slider, Miller got the strikeout.

*Nothing can measure millions of pitch velocities, in 30 different parks, with perfect precision and accuracy. We used Statcast data, and we spot-checked against Brooks Baseball's velocities (and watched many of these pitches) to make sure everything looked about right. But it's probably best to assume a few of these "Fastest" pitches might have actually been a pitcher's second, or third, or fourth fastest. Close enough to have fun with. "Average" fastball velocities, also from Statcast, included four- and two-seamers, but not cutters.