A .453 batting average; .597 on-base percentage; .986 slugging percentage. Thirty-three homers and 93 runs batted in in 212 at-bats.

You look at the numbers, squint, and then look again. These are Baseball Stars numbers, a video game creation, with abilities cranked up to the max. There’s no way a professional baseball player could have done this.

Except someone did. His name is Jose Abreu. He just might be the best hitter in the world. And you’ve probably never heard of him.

Abreu plays for Cienfuegos in Serie Nacional, Cuba’s top baseball league. He put up those unfathomable numbers last year, despite Serie Nacional’s schedule only lasting 90 games. Not that Abreu played in all of those games. He missed 23 contests with bursitis in his shoulder. In other words he cranked 33 balls out of the park in 67 games. That’s a pace of 80 homers over a 162-game schedule.

That 2010-11 campaign capped a meteoric rise for Abreu. The hulking first baseman (he’s listed at 6-foot-3, 240 pounds but is almost certainly bigger than that) broke in as a 17-year-old in 2004. Abreu wasn’t great in that first brush with pro ball. He struck out six times more often than he walked, didn’t hit for much power, and was so defensively limited that he DH’d all year. But he also hit .271 that season, a respectable result even in a league slanted toward offense. That he did this at age 17 was all the more remarkable.

As Abreu matured, so did his numbers. By his third season, he was one of the league’s better hitters. He hit .337/.423/.538 that year, numbers that would make him an MVP candidate were they posted on an MLB roster. Baseball Prospectus co-founder Clay Davenport devised a stat called Equivalent Average (EqA), which takes all of a hitter’s contributions (power, on-base ability, etc.), compares those results to league norms, and calibrates them on a scale that mirrors batting average. A .260 EqA is about average, .300 is very good, .350 is fantastic, .400 is astronomical. Abreu posted an EqA of .308 during the 2005-06 season the year he turned 19.

It’s in the past two and a half seasons that Abreu’s become a bona fide superstar. In 2009-10, he hit .399/.555/.822, good for a .396 EqA. Through 54 games this year, he’s crushing Serie Nacional pitching to the tune of .371/.526/.724, leading the league in OBP and ranking second in slugging.

But last season’s numbers were the ones that broke the scale. Davenport runs translations for Serie Nacional players, just as he does for Japanese league players, minor leaguers, and others not in the majors. He considers the competition in Serie Nacional to be equivalent to high-A ball in North America’s minor leagues — the Carolina, California, and Florida leagues. After comparing a player’s performance to the rest of his league, Davenport then must establish how players from that league did when they graduated to higher levels. Once he has a good idea of how players typically change between leagues, he translates an average major league player to Serie Nacional. The Cuban player’s translation thus comes from looking at how far above or below the average major leaguer he would be.

Miguel Cabrera was the best hitter in Major League Baseball in 2011. Jose Abreu, even after adjusting his numbers to reflect A-ball competition, blew Cabrera out of the water.

“I don’t know that I’d name him the ‘best hitter in the world’ based on a 60-game performance,” said Davenport. “But yes, I’d say there’s a chance.”

To understand how you might be hearing Jose Abreu’s name for the first time, it’s worth getting to know how baseball is covered in Cuba, and who has access to its inner workings. The answers to these questions: It isn’t, and virtually no one outside Cuba.

Michael Lewis traveled to Cuba in 2008 for a Vanity Fair story on Cuban baseball. To do so, he enlisted the help of a retired Canadian high school teacher named Kit Krieger; gaining entry into Cuba as an American journalist on assignment without the help of a government-friendly Cuban baseball zealot like Krieger would have been nearly impossible. Per Lewis, Cuban journalists don’t cover the sport all that closely, either, eschewing interviews with players and managers in favor of their own opinions. Which is fine, of course. But those of us who want to learn about Cuban baseball get surprisingly reliable, well-kept stats plus very few details about style of play, or anything specific that happened in a game.

Even if you’re a major league scout trying to get into Cuba to see a player in person, best of luck. “I’ve seen guys try it,” then-Braves scout Chuck McMichael told Lewis. “I’ve seen guys try to get a radar gun in. And they get put right back on the plane going out.”

What those scouts know, but don’t get to see in person, is the canyon-sized gap between the best and worst Serie Nacional players, and the uneven competition that dominates league play. That Abreu broke into the league at age 17, for instance, is hardly an aberration. Many Cuban players get the call at an early age. In a nation of just over 11 million people, you won’t find many top-shelf players especially in areas outside Havana and other baseball hotbeds. Players play for their native provinces in Serie Nacional competition. If a given province can’t find elite players in their prime years, throwing kids or broken-down older players on the field becomes their next-best option. For elite sluggers like Abreu, recent A’s signee Yoenis Cespedes, and this season’s home run leader, Alfredo Despaigne, that can mean facing an electric arm like Aroldis Chapman one day, a gray-haired junkballer the next.

Player age itself is a sore subject when it comes to Cuban players. The ages of Orlando Hernandez and his half-brother Livan upon their defections to the U.S. quickly became a running joke. El Duque supposedly pitched his final game just before his 42nd birthday, but there are people in the game who’ll swear he was closer to 50 than 40 when he hung ’em up. Livan Hernandez is supposedly eight months younger than Derek Jeter, which is as plausible a story as getting an elaborate Jeter-themed gift basket from Crabtree & Evelyn. The Cuban government has little incentive to make its prized players seem younger than they are and thus more attractive to major league teams. Still, concerns about age-fibbing persist.

There are other factors complicating Serie Nacional results. The league recently switched to Mizuno-150 baseballs, much livelier models than the Mizuno-200 or Rawlings balls found in other countries. Throw in recent defections by Chapman, Yunesky Maya, and a number of useful pitchers who never signed with major league teams, and you have an environment ripe for Bondsian numbers. When Abreu and Cespedes both broke the single-season home run record last season, it came at the expense of Despaigne’s record, set just two years earlier.

“The talent pool is so restricted,” said Ben Badler, a writer for Baseball America who follows Serie Nacional. “Guys who, if they left Cuba and tried to sign with a major league team, either wouldn’t get signed or wouldn’t make it out of rookie ball. Some would become solid organizational players. Then you’ve got someone like Jose Abreu, who could step into a major league uniform tomorrow and immediately be an above-average major league player.”

OK, so just how far above average are we talking?

David Forst, assistant general manager for the Oakland A’s, has some thoughts on the subject. Over the past few years, the A’s have repeatedly lost free-agent bidding wars, even after making the highest bids. They offered Lance Berkman a two-year deal; he took a one-year deal instead, then hit like a fringe MVP candidate for the Cardinals. They offered Rafael Furcal four years; he took three to play for the Dodgers. Adrian Beltre snubbed Oakland, twice. So desperate were the A’s to get somebody to take their free-agent money that they gave a broken-down Ben Sheets $10 million two years ago. Predictably, he got hurt, making just 20 starts that season. He hasn’t pitched in a major league game since.

It’s against that backdrop that the A’s agreed to a four-year, $36 million deal for Cespedes. We’ve documented the 26-year-old outfielder before: He has tools on top of tools on top of tools. He’s an athlete so impressive, his agent produced the single best 20-minute video in the history of Western civilization, an orgy of flexing, stand-up sit-ups, violent swings, and star wipes. There are some talent evaluators who’ve seen Cespedes take weak swings in international competition and who doubt the integrity of Serie Nacional stats enough to declare him a future bust. Others, including the A’s, see a five-tool package at a prime age for major league performance, and envision a future star. Oakland will take a chance on someone like Cespedes, and scout someone like Abreu as aggressively as a Cuban player can possibly be scouted, knowing the team needs to take chances on high-variance players to overcome its disadvantages in revenue streams and signing of established major league stars.

Forst confirms that A’s scouts can’t get anywhere near Cuba to see live Serie Nacional action. But he also notes that Cuban players gain much more exposure in international competition now than they did 10 or 15 years ago. Abreu has played in five major international tournaments in the past two and a half years, and that’s after getting cut from the 2009 World Baseball Classic roster. Thanks to those tournaments, the A’s have compiled multiple scouting reports on him.

Oakland and other teams agree that Abreu isn’t nearly the all-around athlete that someone like Cespedes is. He’s a first baseman at best and maybe a DH if and when he makes the big leagues. He doesn’t run well. His body is not exactly chiseled. His stats have been inflated somewhat by intentional walks (a league-leading 32 in 2009-10, and 21 last season) and hit-by-pitches (30 in 2009-10, 21 last season, though Abreu might have an easier time sustaining high HBP numbers than league-leading intentional walk totals in the majors). Even Abreu’s hit tool, while playable, might not be superstar-level.

“Is he Barry Bonds? No,” Forst said. “If you do a comprehensive survey of the clubs, they’d say he is not the best hitter on the planet.”

But?

“There are legitimate comparisons to Ryan Howard.”

So the wildly optimistic view is that it’s possible — not likely, but possible — that Abreu might be as good at — or better at — than Miguel Cabrera. And the more realistic and pervasive view is that he could hit like Ryan Howard, a star first baseman entering year one of a five-year, $125 million contract who has launched 262 homers over the past six seasons.

Which is, in a word, stupefying.

There’s so little in the sports world now that’s unknowable, so few arguments that can’t be settled by a quick trip to Baseball-Reference and its sister sites. As Chuck Klosterman asked last week on the B.S. Report: “Aren’t we almost accustomed to watching sports in a way that’s no longer supposed to be subjective?”

He was talking about Jeremy Lin. But in Lin’s case, anyone could drop by Harvard’s field house for a game, even catch him occasionally on TV. We had information from the NBA’s scouting combine and summer tournaments. Though he didn’t see much live game action, Lin got plenty of run in practice, where coaches got to see him match up against starting point guards. Yes, he’s been a gigantic, pleasant surprise, a breath of fresh air for a Knicks team that needed it, in a season that nearly never happened. But Lin came out of nowhere to make two straight Sports Illustrated covers because NBA talent evaluators screwed up and teams wouldn’t give him a chance, not because the information wasn’t out there for people to see.

Scouts do have information on Abreu. But in many respects, it’s flawed and difficult to interpret. The only time a team can see him live is in those international competitions. Yes, there’s value in tracking his performance in the Baseball World Cup or Intercontinental Cup play. But when he’s facing a baseball-rich country one day, Liechtenstein the next, you can only tell so much. There are some video reports out there, which certainly help. And there are those stats. Those dazzling, breathtaking stats.

Try as he might, Davenport’s Cuban translations remain much less reliable than what he can do with, say, Japanese league players. He has more examples of players coming over from Japan. He also has far more examples of major league players going to play in Japan (a lot) than he does major leaguers going to play in Cuba (zero). There are huge psychological barriers that any player coming from a foreign league must overcome, getting used to a brand-new culture, or just resisting the convenience and temptation of American fast food, especially on a minor leaguer’s per diem. With Cuban players, there’s an added mental hurdle: knowing you’ve abandoned your family for a shot at the big leagues.

“In a general way, the place [stats] don’t take us is to knowledge of the future,” said sabermetric pioneer and Red Sox senior advisor Bill James. “Much of what we do is ‘predicting the future,’ but it’s not really prediction; it’s merely projecting present realities into the future.”

When it comes to Abreu, scouts can’t be sure what those realities are. And for regular schmoes like us who have little or no access to scouting information, those realities are damn near impossible to figure out.

That might soon change. Fidel Castro has retired from politics. The Cold War is long over, and the U.S. has already started to loosen restrictions on travel to Cuba. If Cuba’s the last refuge for baseball’s unknown, it might not be for much longer.

So let’s enjoy Jose Abreu while we still can. Let’s dream on a hitter so big, so powerful, he just might be better than anyone else on Earth. The information explosion has made us more knowledgeable sports fans than we could have ever imagined. But it’s OK to root for a mystery. Especially if it’s one of the last ones we ever see.