At this point in the season, it is clearly true that Yankees hitters are abnormal. Their abnormality refers not to their private lives (though no doubt some of them might qualify on that count, too) but to their bats. Baseball teams do not hit .300 for more than small fragments of time. They certainly don’t do it for full seasons. The Yankees have been doing it for the last 72 games, suggesting that this is not a fluke, and that this — not the offense that fluctuated from slightly above to slightly below average — is their true level of ability.

Only two teams have hit .300 over a full season since the superrabbit ball year of 1930: the 1936 Cleveland Indians and the 1950 Boston Red Sox. Those were the Red Sox of Fenway Park at its friendliest, of Ted Williams and Bobby Doerr. Billy Goodman, the utility infielder, won the batting title. Not only do the Yankees not have a hitter-friendly park, but their closest analogue to Goodman is Doug Mientkiewicz. He not only will not win the batting title, but was so bad that Brian Cashman probably prays nightly that Mientkiewicz will not come off the disabled list before November.

Yet, the Yankees are plugging away. From the beginning of the season until May 17, the Yankees hit .274 AVG/.351 OBA/.423 SLG and went 18–21. Since then, they’ve batted .300/.374/.488 and have won 43 of 72 contests. Narrowing the sample to just 54 games, the last third of the season, the Yankees have batted .304/.378/.492. No one else is close. Only the California Angles, the Detroit Tigers, and the Baltimore Orioles have stayed above the .270s during that span in the American League.

On-base percentage and slugging percentage give a better sense of offensive potency. The Red Sox (.278/.361/.435) have the second-highest on-base percentage in that time, and the Tigers the second-highest slugging percentage. No team has been as hot as the Yankees.

Back in April, many pundits assumed that the Yankees had a lineup that could score 1,000 runs (shorthand for having an offense that ranks with the all-time greats) without trying. They were wrong. The Yankees had the potential to do it, as they’re proving now, but first they had to get over that messy human tendency to not behave as we think or wish they would. They also had to get over some bad luck, and some nasty self-inflicted mistakes.

The Mientkiewicz experiment should finally kill the idea that a good offense can “carry” a bad hitter. A lineup is not a series of individual buildings. It is one unified structure in which each piece buttresses the next. If Lou Gehrig doesn’t get a hit then maybe Babe Ruth can, and if Babe Ruth makes an out then maybe Joe DiMaggio will pick the team up. Each time you pull out a good name for a bad one, you’ve eliminated a support. There is no team that can afford an out-machine at any position.

Bad luck included early injuries, and fallible humans included Johnny Damon, Robinson Cano, Melky Cabrera, and Bobby Abreu, all of whom have had severe, offense-killing slumps. Most of these are easily understood. Damon is becoming old and fragile; Cano’s lack of plate judgment can lead him into bad habits, and Cabrera is excitable and worried about hitting his way into a crowded lineup.

Abreu, though, is one of the most accomplished hitters of his time, and the way his approach at the plate collapsed is almost impossible to fathom. On the last day of May, his averages stood at .228/.313/.289. These are numbers that would lead many a right fielder to feelings of dishonor and perhaps ritual self-disembowelment.

Fortunately, Abreu knew no shame, because starting June 1 he has batted .338/.415/.557. A bit of creative platooning by Joe Torre has helped (Abreu has done nothing with lefties all season), but that by itself does not explain Abreu’s amazing resurgence. He wasn’t an old 33 and he wasn’t hurt: He was just completely, totally lost.

As were the Yankees. Now, though, they’re batting .291 as a team and though they won’t score 1,000 runs, they’re going to come within 50 runs of that figure, and perhaps win the wild card in the process. Whether they do or do not win the wild card, there’s a lesson to be learned about taking things for granted and about confusing the potential to achieve something with the will and strategy to do it. Normally it’s the statistically-oriented fans and writers who are accused of confusing human beings with the numbers on the backs of their baseball cards. This time it was the Yankees and the mainstream observers who made that mistake. They didn’t reckon on life being more complicated than the fantasy lineup they had put together.

Mr. Goldman writes the Pinstriped Bible for yesnetwork.com and is the author of “Forging Genius,” a biography of Casey Stengel.