New York Yankee Alex Rodriguez. (JOHN GRESS/REUTERS)

David Epstein is a Sports Illustrated senior writer and the author of “The Sports Gene.”

Alex Rodriguez has long worn his ego, and his insecurity, on his pinstriped sleeve.

When I began reporting on him in 2008, tracking the movements of the conspicuous black Mercedes with the “Alex Rodriguez” dealership license-plate holder, I found that the Yankees third baseman would occasionally turn to his retinue of buddies to ask how he looked. Good, they would assure him.

One of Rodriguez’s former hitting coaches told me at the time that A-Rod was extremely hardworking but that much of his postgame film-watching was “so he can hear what the announcer’s saying about him.”

His private trainer in Coral Gables, Fla., who worked in a converted storage locker festooned with mirrors, told me that Rodriguez would ask who was “cooler,” Yankee shortstop Derek Jeter or rock star Lenny Kravitz — which may have led Rodriguez to hire Kravitz’s onetime manager.

So I wasn’t terribly surprised when my Sports Illustrated colleague Selena Roberts and I learned from sources in 2009 that Rodriguez had tested positive for steroids six years earlier. And I certainly wasn’t surprised to hear in April that he had ties to the anti-aging clinic Biogensis.

In his vanity, Rodriguez is like the vast majority of people who use performance-enhancing drugs: gym-goers who want to be bigger, faster, stronger — and younger. He plays a game in which aging is unusually rapid, even by sports standards. And he’s a star in an era when steroids have created an unrealistic picture of the 30-something slugger — a picture that some players, and the executives who sign them, have trouble letting go.

When Yale economist Ray C. Fair mathematically modeled how hitters age, using the stats of every batter who played at least 10 full seasons between 1921 and 2004, he found that the typical peak is around age 28. By 29, as a group, hitters are in decline. (Pitchers tend to peak even earlier, around age 26.)

Rodriguez certainly seemed to be at the height of his game when he was 28: He won the MVP and Gold Glove awards in 2003 (and failed that drug test). He was still going strong four years later, when the Yankees gave him a new contract for 10 years and $275 million. But the idea that he would still be worth $20 million a year a decade hence, at age 42, defies logic and most of baseball history.

Indeed, A-Rod returned to the Yankees this past week after his second hip surgery. Even players who are assiduous in caring for their bodies, such as Derek Jeter, eventually become injury-prone. And as I learned while reporting my new book on the genetics of sports, aging in baseball is much more than creaky joints and threadbare cartilage.

Twenty-nine is about the age at which visual acuity often begins to deteriorate. And visual acuity is critical for hitters. Big league hitters have no faster reaction times than teachers, doctors or lawyers. But they have an average visual acuity of about 20/12, meaning they can see from 20 feet away what I have to scoot up to 12 feet to discern. That superior vision helps them pick up on anticipatory cues such as the “flicker,” or the flashing pattern of seams on a ball as it spins toward them. Subconsciously registering the flicker allows them to predict where the ball will go well before it’s halfway to home plate.

If a big league hitter begins to lose his superior visual acuity and can’t pick up the flicker early enough to see the future, he’s left trying to react to the ball. And since initiating muscular action takes one-fifth of a second, or half the flight time of a major league fastball, reacting can lead to swinging too late.

In addition to declining sight, as we age the fast-twitch muscle fibers that are required for explosive movements shrink more rapidly than do the more plodding slow-twitch fibers. Most people’s muscles are slightly more than half slow-twitch fibers. But the fiber-type mixes of athletes tend to fit their sports. The calf muscles of sprinters are often 75 percent or more fast-twitch fibers. Rodriguez, who once upon a time was a lithe, base-stealing threat, may have had the advantage of a high proportion of fast-twitch muscle fibers.

Aging means that big league hitters become, well, more normal. That may not provoke a lot of sympathy. But imagine, at an age when many people are just figuring out their career trajectories, losing the superpowers that were bestowed by nature and intense practice. It’s like the Daniel Keyes story “Flowers for Algernon”: Low-IQ grunt Charlie Gordon is made brilliant through an experimental surgical technique. He falls in love with a teacher, but soon the effects of the surgery begin to fade and he returns to his prior state, losing the ability to read and write. To make matters more excruciating, Gordon remembers what it was like to be a genius.

By age 40, major league hitters are down 10 percent from their peak in terms of OPS, “on-base plus slugging,” perhaps the best mainstream measure of performance. Proportionally, that decline dwarfs even the deteriorations of track sprinters and high jumpers. As Charles Barkley succinctly put it last year: “Father Time is undefeated.”

But in his analysis, the economist Fair identified 18 hitters who, for a while anyway, kept Father Time at bay. From that group, all but one (Charlie Gehringer) retired after 1989 — in or near the steroid era. The list of age-defying outliers includes a notorious who’s who: Mark McGwire, Barry Bonds, Ken Caminiti, Rafael Palmeiro and Sammy Sosa. Clearly, some of the stars of the steroid era used drugs to compensate for, or protect, what Father Time was absconding with.

Even with that knowledge, baseball executives continue to sign players to preposterous contracts that will take them well past their natural primes. Take, for example, the nine-figure, five-year contract signed in December by outfielder Josh Hamilton, who at 32 already appears to be in decline. It was probably a bad investment. But the stars of the steroid era constructed an unrealistic picture of the aging hitter that persists today.

Age was clearly on Rodriguez’s mind this past week. In his first news conference after the announcement of his pending suspension, he noted that the previous seven months had been a “nightmare” because of the steroids accusations and a “tough surgery and a rehab program.” Then he smirked: “And being 38.”

Moments later, he gushed that returning to baseball after the rehab made him feel “like I was 18 years old.”

The problem for A-Rod, and what probably brought him to Biogenesis, is that when he’s being honest, he feels like he’s 38.

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