The Boston Red Sox haven’t given their fans much to cheer about this summer so we’ve had to take our pleasure where we could find it, for example, by watching Alex Rodriguez of the Yankees struggle to hit his 600th career home run — again and again and again.

Rodriguez hit his 599th home run on July 22, bringing himself and his fans to the brink of celebration. And then, for 12 long days, he not only failed to drive the ball out of the park and into the history books, he also went hitless for 17 consecutive at-bats. This wasn’t the first time Rodriguez has stood at the precipice, and then stood there some more: after hitting his 499th home run in 2007, he came to the plate an excruciating 28 times before finally hitting his 500th.

What made all this so frustrating for New Yorkers (and so delicious for Bostonians) was that everyone felt certain that Rodriguez would have slammed several homers in the past two weeks if only they hadn’t mattered so much. Watching him struggle to break the numerical barrier was like watching a man frozen with fear on the last step of a tall ladder: we knew, and he knew, that the last step was exactly the same as all the steps before it — so why couldn’t he just take it?

One of the ironies of human psychology is that desperately wanting something can make attaining that thing all the more difficult. When stakes go up, performance often goes down. In one study, subjects practiced sinking a putt and got better as they went along — better, that is, until the experimenter offered them a cash reward for their next shot, at which point their performance took a nosedive.

This is because we pay close attention to what we’re doing when what we’re doing matters, and though close attention is helpful when our task is novel or complex, it is positively destructive when our task is simple and well practiced. Golfers in another study were told either to take their time and think about their stroke or to step up and swing as quickly as possible. Although novice golfers did better when they took their time, expert golfers did worse.

The lesson from the laboratory is clear: thinking about tasks that don’t require thought isn’t just pointless, it’s debilitating. It may be wise to watch our fingers when we’re doing surgery or shaving the family dog, but not when we’re driving or typing, because once our brains learn to do something automatically they don’t appreciate interference. The moment we start thinking about when to step on the clutch or hit the alt key, our once-seamless performance becomes slow, clumsy or impossible.

That’s why milestones can be millstones. When Rodriguez stepped to the plate in recent days, he may not have heard the roar of the crowd as much as the sound of a record book opening and a pencil being sharpened. The more important his next homer became, the more he probably thought about how to hit it. The more he thought, the less he hit; the less he hit, the more he thought, and the cycle spun on.

Until Wednesday, that is, when Rodriguez finally hit his 600th home run. Forty-six agonizing at-bats separated that homer from the one before it, but the moment the ball sailed over the center field fence, Yankee fans knew that a great burden had been lifted, a great slugger had been liberated, and that a great bat would once again be free to find the ball — naturally, effortlessly, and in its own sweet time.

Or maybe not.

After all, 600 is an important number only because it’s round, and several of the numbers that follow are much more significant. For instance, Rodriguez is the seventh greatest home-run hitter of all time and hitting 600 didn’t change that. But hitting No. 610 will, because it will push him past the retired Sammy Sosa and into sixth place; hitting 631 would let him overtake Ken Griffey Jr. and put him in fifth place. Should that happen, there are a few more legends whom Rodriguez must lap on his way to supremacy: Willie Mays at 660, Babe Ruth at 714, Hank Aaron at 755 and the reigning champion Barry Bonds at 762.

Rodriguez won’t get any competition from a Red Sox hitter as he works his way up the list, but that’s O.K. Red Sox fans are nothing if not good sports. Which is why on Friday, when the Red Sox play the Yankees, we will applaud Alex Rodriguez — not just to acknowledge his new achievement, but also to remind him of the unbelievably, incredibly, really very large historical significance of each and every one of his future trips to the plate.