On Sept. 10, 2012, Jhoulys Chacin was facing the ninth-place hitter in the San Francisco Giants' lineup with two on and two out. Chacin's opponent was a typical pitcher: a lifetime .147/.181/.196 hitter, owner of one career home run in nearly 200 plate appearances, close to an automatic out. After falling behind 2-0, Chacin threw a fastball for a strike. His target for the 2-1 fastball was down the middle, as it would be. This was a pitcher facing a pitcher.

He threw that fastball down the middle ...

... and Madison Bumgarner hit it 427 feet.

Bumgarner was not, as it turns out, a typical pitcher. How atypical he was would emerge, though how atypical he is remains unanswerable. As Chacin prepares to face Bumgarner again on Saturday, he has to answer a question that Bumgarner's manager, his opponents, and many of us who watch the game would love to see answered: Is Bumgarner good at hitting for a pitcher, or is he genuinely good at hitting?

Most baseball analysis depends on large samples. In the absence of large samples, most baseball analysis depends on regressing to the mean. If a player goes 2-for-5 in his major league debut, we're smart enough to know he probably isn't the best hitter since Ted Williams; the best guess is he's average, and the more plate appearances we see, the more we adjust from there. Think horses, not zebras.

A pitcher who goes 2-for-5, meanwhile, probably isn't the best hitter since Ted Williams, and probably isn't a league-average hitter, either. The best guess is that he's a typical pitcher, a guy who'll bat around .130 with no power and tons of strikeouts. The more plate appearances we see, the more we can adjust. Bumgarner, who has never batted 100 times in a season, can't provide large samples, because in baseball large sample sizes are often measured in the thousands. At the same time, as a pitcher who hits 112 mph home runs in pairs, he can't necessarily be regressed to the league-average pitcher.

In the absence of large samples, we guess, we extrapolate, we get cautious, or we get hyperbolic. Sometimes we lose our minds, and sometimes we keep our minds locked up so tight we don't have any fun.

.542 career OPS before today https://t.co/u5td5Ngm8x — robneyer (@robneyer) April 2, 2017

So what do you say about an outlier who bats only a few dozen times a year? We asked around to try to figure it out.

1. He's fun as heck, but he's actually pretty bad (for a hitter).

Bumgarner has batted 524 times in his career, and his career slash line is .187/.236/.327. That's great -- for a pitcher! It's the seventh-best OPS among active pitchers, and the proportion of that slash line that comes from dingers has produced some truly marvelous fun facts. But his career stats are similar to those of catcher Jeff Mathis, an offensive punchline who has hit .198/.255/.310 in his career.

Mathis pinch hits occasionally, but rarely. That's true, too, of Bumgarner, and if Bumgarner is fun as heck but not a good hitter, this is appropriate.

"We indeed have Bumgarner as the best hitting pitcher in the game, though he's far from any sort of singularity," write Adam Guttridge and David Ogren of NEIFI Analytics, which consults for major league teams, via email. They point out that a year ago, Zack Greinke was the king of pitchers hitting:

2013-15 aggregate leaders (minimum 120 plate appearances):

Greinke: 87 wRC-plus

Bumgarner: 72

Travis Wood: 62

But in 2016, Greinke's wRC-plus (an all-in-one offensive stat that is adjusted for ballpark, with 100 representing average) dropped to 20. So did Wood's.

"It's clear that whatever amount of regression may be needed, Bumgarner's proper regression point cannot be the average hitter," Guttridge and Ogren write. "Regressing him towards the average hitter would actually make him look better, not worse. Which is implausible."

2. He used to be bad (for a hitter), but now he's genuinely pretty good (even for a hitter).

Since the start of 2014, Bumgarner has hit .234/.284/.459 in a pitcher's park. After homering twice in the season opener, his weighted on-base average -- another all-in-one hitting stat -- is, at .320, tied with Ian Desmond over that period. Bumgarner's wRC-plus is 105, tied with Carlos Gonzalez. If you think about Bumgarner this way, he's clearly the best hitter on the Giants' bench, a batter who should be pinch hitting dozens of times a year and DHing in interleague play. According to the ZiPS projection system, nobody on the Giants' bench projects to produce a .320 wOBA this year:

But Bumgarner's .320 wOBA comes in just 259 plate appearances, with endpoints chosen specifically to make him look as good as possible. They're spread out over three-plus years, but it's still only 259 plate appearances. For any other hitter with a sample size of 259 plate appearances, we'd regress those numbers significantly to his career norms. Unfortunately, regressing Bumgarner's numbers to his career numbers means bringing in data that's five, six, even nine years old, and that ignores the real possibility that Bumgarner has developed as a hitter since then.

"The regression is the key part of it," argues one team's in-house statistician. "The sample size isn't that bad. I've got 325 PA over the previous four years. I can work with that. What I would do is run the projection looking at him as a regular hitter, then the same but regressing him to other pitchers, just to see how big the gap is, how much the regression changes things."

It helps to know his history. In high school, Bumgarner played for nationally ranked South Caldwell High (Hudson, N.C.). He was the school's ace and best hitter. He led the team in home runs and batted second in the lineup even on days he didn't pitch. In 2007, he faced a draft prospect named Sam Runion in a highly anticipated matchup. Bumgarner homered against Runion, a second-round pick that June. Bumgarner later hit a walk-off, title-clinching home run in his final high school at-bat. According to reports at the time, he was to be the designated hitter at the University of North Carolina if he hadn't signed with the Giants.

A hitter of this caliber would typically follow a predictable development path: He'd go to college or the low minors, getting hundreds of at-bats every year. Once he'd shown he could hit at one level, he'd move up to the next level and have thousands of plate appearances before finally facing major league pitching. Or he'd wash out when he hit his limit. But Bumgarner skipped all that, because he was a pitcher. In the two years between high school and his major league debut, he batted only nine times. (He hit .429/.500/.857 in those Double-A plate appearances.)

It makes sense, then, that he would be overmatched as a major leaguer. It also makes sense because he debuted in his age-19 season, an age at which even Mike Trout looked overmatched. Bumgarner was just a month past his 23rd birthday when he hit that 2012 home run against Chacin -- younger than Byron Buxton is now, younger than the average Double-A hitter. The Giants' announcers at the time talked about his booming batting practice displays -- in at least one, he got a standing ovation -- so he had the power. But he had almost no hitting development or experience against top pitchers. He was young enough to be a prospect.

In 2014, he changed his swing. He opened up his stance and moved his hands farther back. He added a huge leg kick in place of a soft, inconsistent toe tap, giving his swing more load and a more effective timing mechanism. He switched to a massive Marucci bat used by his new teammate, Mike Morse. Bumgarner became more aggressive, swinging at 56 percent of pitches after swinging at just 46 percent in the three seasons prior. He pulled 45 percent of balls he put in play, up from 40 percent in his career before that. He hit more fly balls. There's a simple story to tell that says he became a different hitter, and in many ways it's similar to the stories we've heard about Daniel Murphy, Josh Donaldson, Justin Turner, J.D. Martinez and others: reworked swings, fly ball approach, swing plane to match the flight of the pitch, and a repudiation of the old wisdom that batters should hit down on the ball. If you buy that story for Bumgarner, you might feel comfortable ignoring what came before 2014.

3. He's pretty good (even for a hitter), and maybe he's getting better.

If we're being skeptical of small samples, maybe we should be especially skeptical of his 2016 performance, when he hit just .186 and homered only three times.

He had the lowest contact rate of his career last year. He whiffed more often than almost any hitter in the game, and more than most pitchers did.

But he crushed the ball. His average exit velocity was, at 92.4 mph, the same as Paul Goldschmidt's. Bumgarner's average ground ball was as hard as Miguel Cabrera's, the 20th-best out of 513 hitters. His average ball hit in the air was harder than Kris Bryant's, 95th in baseball. Bumgarner's launch angle was slightly higher than the major league average for all hitters. And, for the first time, he started walking -- 10 times in 95 plate appearances, well above the league average.

"Is Madison Bumgarner good at hitting for a pitcher, or is he genuinely good at hitting?"

Then came Sunday, when he homered twice and walked on a 3-2 curveball. We can't learn much about one game, but Bumgarner possibly hits the ball harder than any other pitcher in baseball. In 2016, pitchers put 3,000 balls in play, and not a single one was harder than 110 mph off the bat. Bumgarner hit two balls Sunday, and they were both above 112 mph.

This might not tell us everything -- the hardest-hit ball by a pitcher last year was by Jon Lester, one of the league's worst-hitting pitchers -- but it adds to the inconclusive argument that Bumgarner's peer group is not pitchers. Most pitchers -- maybe all pitchers -- are simply not capable of what he is capable of. It might be that a lot of hitters aren't, either.

4. He was good (for a hitter), but only because he's a pitcher.

Pitchers have it relatively easy when they go to the plate, and that's true of Bumgarner, too.

On average, a typical right-handed batter will see about 31 percent of pitches off the plate inside. Only 49 percent of pitches he sees will be in the zone, and only 54 percent will be fastballs.

But the typical right-handed pitcher will see only 26 percent of pitches come inside. Some 57 percent of the pitches he sees will be in the zone, and 67 percent will be fastballs. Pitchers at the plate rarely have to deal with opponents who even bother with a plan against them.

Teams prepare advance scouting reports for only "a small handful" of pitchers at the plate, according to one team source. "It'll range from 'he can handle the bat a little' (probably one to two guys per NL team) to 'make some pitches to this guy' (maybe 10 guys total) to 'you actually need a scouting report.' Very few guys get a detailed report. Probably Bumgarner and maybe another guy or two."

Last year, the league adjusted to Bumgarner. Only 56 percent of the pitches he saw were fastballs, down from 62 percent in 2015, 68 percent in 2014, and about 72 percent in the years before that. Nearly 40 percent of the pitches were breaking balls, up from 21 percent in 2013. The last time Chacin faced Bumgarner, there were no more fastballs down the middle. Chacin threw four breaking balls and two fastballs at the top of the zone, because his opponent was no longer a typical pitcher:

Bumgarner is a fastball hitter. Thirteen of his 16 career homers have come on heaters, and only two have come on breaking balls (in about half as many pitches). He's seen 228 curveballs in his career, 122 for strikes, and managed no more than a pair of singles.

For a normal hitter, this wouldn't mean much. We'd assume that pitchers couldn't suddenly start throwing him all curveballs or he'd adjust. We'd assume that they're already throwing him as many as they feel comfortable throwing. But this is the challenge of projecting Bumgarner: He's not a normal hitter. He doesn't have thousands of at-bats under his belt. He hasn't passed all the stress tests that minor league development puts guys under. And he hasn't been pitched like a normal batter at all. Maybe he's bad against curveballs because he just hasn't seen enough of them, and that'll be the next leap he makes. Or maybe he'll never learn to hit curveballs, while his opponents learn to throw a lot more of them.

Ultimately, projections require one of two things, and preferably both: a lot of data, or a presumption that the player is a normal player. We will never have a lot of data about Bumgarner. And there's a real possibility that he's not normal at all.

"I'd focus on exit speed, launch angle and swing-and-misses," offers Tom Tango, a co-author of "The Book" and senior data architect for MLB Advanced Media, via email. "I think those three things are a huge determinant as to what population a pitcher (or any hitter) belongs to. For example, if you have a P, C and 1B, that have the same EV, LA and whiff rate, should they still be in a different population?"

By exit velocity and launch angle, Bumgarner is a real hitter. But by whiff rate, he's a pitcher. And the quality of his contact is complicated by the fact that for most of his career opposing pitchers may have pitched to him as they would a pitcher.

"I think we also need to keep in mind that the mathematical model we use for regressing toward the mean of the population may not work real well for pitcher hitting," writes Mitchel Lichtman, one of Tango's co-authors and a consultant to major league teams, also via email. "The typical model for regressing (adding X number of league-average PA) assumes a normal distribution of talent within that population. Clearly there isn't (a normal distribution) with regard to pitchers hitting."

So, for now, we shrug, because we can. Giants manager Bruce Bochy needs to answer this question. Chacin, and the rest of Bumgarner's opponents, need to answer this question. We'd like to answer the question too, but in lieu of that, we can appreciate the ambiguity. The ambiguity, after all, is so much of what makes Bumgarner's home runs interesting. We know he's not as good a hitter as Edwin Encarnacion or Brandon Belt or Dexter Fowler or any number of actually, definitely good hitters. Yet we enjoy watching him slug dingers more than we enjoy watching any of those guys do it. As Major League Baseball tries to figure out what makes the game fun, it might keep that weird fact in mind.