The concept of “old” is mutable in many of the sports we follow. The swimmer Michael Phelps, perhaps the greatest U.S. Olympian ever, climbed out of the water after a race a couple of months ago and said to reporters, “I feel like an old man coming out of the pool sometimes.” Phelps, who turns 26 at the end of the month, is indeed past his prime, but mainly because of the course he and his coach set. Phelps trained six consecutive years over one period without taking a single day off, a regimen that produced 16 medals at the last two summer Olympics, including eight golds in 2008 in Beijing. He is stronger than he has ever been and just about as lean — 197 pounds as opposed to the 193 he weighed at his first Olympics, when he was 15. If all it took was physical attributes, Phelps could probably match his accomplishments from Beijing. But he can no longer summon the focus and motivation to train like he did. Phelps plans to swim in London in 2012, but in fewer events. “There’s a volitional and psychological window,” Phelps’s coach, Bob Bowman, told me. “It closes. A lot of it has to do with the effort you put in up to that point.”

A version of the same syndrome — in the vernacular, “burnout” — may be afflicting Tiger Woods, who looks like a very old 35-year-old in a sport in which 35 isn’t that old. Yes, Woods has suffered numerous injuries as well as an incalculable impact on his performance from chaos in his personal life. But it is also true that he has been hyperfocused on golf for an unusually long time — in essence, a professional since he was 2, when he carried a tiny golf bag onto the set of “The Mike Douglas Show” and, with Bob Hope looking over his shoulder, demonstrated his swing. Lots of things are no doubt troubling Woods, but 33 years of high-intensity golf in 35 years of life is quite likely part of the problem.

Pro basketball, with its focus on the extreme athleticism of its players, is marketed as a young man’s game, but at the championship level, it is just as often a sport for old men. Nearly every year, one of the older teams in the league — versions of the stereotypical old heads at the “Y” — advances to and often wins the N.B.A. finals. Earlier this month, the Dallas Mavericks — led by the 33-year-old Dirk Nowitzki, the 38-year-old Jason Kidd, in his 17th season in the league, and several other key players well into their 30s — prevailed in the finals over the 26-year-old LeBron James and the much younger Miami Heat. In basketball, a player who loses his man on defense can get help from a teammate. Crafty older players find ways to compensate for their loss of quickness. Cleverness matters. (Fake shot, induce overeager youngster off his feet to attempt block, lean forward as he lands on you — advance to foul line for two free throws.)

Baseball offers no such workarounds. It is said to be the hardest game to understand, the most nuanced. And yet, for all the rich literature paying it homage, from Roth, Updike and Malamud to countless lesser literary figures, it is, at its core, about one thing only: pitcher versus hitter, an unforgiving competitive dynamic.

“How can you think and hit at the same time?” Yogi Berra once said, which like many of the quotes attributed to the former Yankees catcher, even the malapropisms, contains an essential truth. You can’t think and hit because there’s not time for both.

In 1987, A. Bartlett Giamatti, then president of the National League and soon to become baseball’s commissioner, was curious to know more about the science of the pitcher-hitter duel. He asked an old friend, the Yale professor Robert Adair, to do some research and gave him the title, no doubt with a wink, Physicist to the National League. Adair ended up producing a book, “The Physics of Baseball,” that is surprisingly accessible and even funny at times. If any aspiring young player were to read it, he might give up the idea of trying to make a living hitting a baseball, because it seems nearly impossible.

At 90 miles per hour, average major-league speed, a baseball leaves the pitcher’s hand and travels about 56 feet to home plate in 0.4 seconds, or 400 milliseconds. The batter’s eyes must first find the ball, Adair writes, then sensory cells in the retina encode information on its speed and trajectory and send it to the brain. This all takes about 75 milliseconds, during which the pitched ball has traveled nine feet.