There’s a moment in Jim Corbett’s Man-Eaters of Kumaon, which is unquestionably the greatest book ever written about hunting man-killing tigers in India, when the author encounters a snake. It’s a big snake, a king cobra, 13 or 14 feet long, and Corbett is alone, deep in the forest, tracking some fearsome jungle cat. The snake is drinking from a pool of water, and when it sees Corbett it raises its head two or three feet in the air and looks at him. “It was the most beautiful snake I had ever seen,” Corbett writes. “The throat, as it faced me, was a deep orange red shading to golden yellow where the body met the ground.” There’s a sort of shivery moment while Corbett and the big snake stare at each other across the pool. Corbett’s nervous, because king cobras are aggressive and he can’t shoot this one without revealing his location to the tiger hidden somewhere in the trees. But instead of attacking, the cobra closes its hood and starts to glide away.

At this point, like any good late-Victorian naturalist, Corbett decides that he’d better try to kill it. He picks up a stone, which fills his hand “as comfortably as a cricket ball,” and whips it at the cobra’s retreating head. The stone hits its mark, but all the impact does is make the cobra turn and rush him, so Corbett throws a second, bigger stone, which catches the snake on the neck. “After that,” he writes, “the rest was easy.” Killing the snake fills Corbett with a quasi-mystical joy. “For the first time in many days,” he says, “I had a feeling that my search for the man-eater would be successful.”

I have no idea what this means, but I think about it all the time, especially, for some reason, when I’m watching sports, and especially when I’m watching Roger Federer. It’s not Corbett throwing the rock that gets me so much as the weird magic of that moment right before it, the hunter and the cobra on opposite sides of the pool, just looking. There’s something about Federer’s game these days — some quality of vulnerable, but simultaneously mind-blowing, uncertainty — that seems to call strange images to mind. In his prime, Federer went way beyond everything, took tennis somewhere it had never been before, and now his decline’s taking place in a pretty freaky glade.

Anyway, at bottom, beneath media narratives and stats and everything else, isn’t that why we love watching the best athletes? Because they take us into the forest and put us face-to-face with something mysterious? Admittedly, you have to strip away a lot of barnacles to get to that point, a lot of accumulated theme music, truck commercials, exploding football helmets, and so on. But there’s something underneath all that stuff, some deep-down fantasy thing we go to top-level sports to get — whether it’s reconciliation with the body or simulated tribal combat or the dream of immortality — and some athletes just make you see it. As if you’d started with the Google Maps view of what it means to be human and zoomed way down through the treetops until you found yourself staring across that pool, tigers lurking somewhere off-screen, freedom like an incandescent animal.

The first time I felt that way about Roger Federer was 10 years ago, when he was 19 and playing Pete Sampras at Wimbledon. Now, in 2011, in his endless middle-sunset as a player, Federer has become something mysterious, an all-time great whose career feels increasingly fragile. But in July 2001, he was much more the hunter than the cobra.

In July 2001 Sampras was 29, the same age Federer is now, and very much in the autumn of his prime. He’d won seven of the past eight Wimbledons, including four in a row, and 13 of his eventual 14 Grand Slam titles. He was the top seed at the All-England Club, but the engines were trailing smoke: He started that year ranked no. 3 in the world, and ended it at no. 10.

Still, Sampras was a heavy favorite against a teenage Federer who had yet to crack the top 10, had won his first tournament (the Milan Indoor, where he beat professional footnote Julien Boutter in three sets) only a few months before, and still had a reputation for choking against elite players. I’ve never really thrilled to Sampras’ game — mostly for the usual “crude power vs. elegant angles” reasons, though also because he moved like a superhero who was pissed that he still had asthma — but like everyone else, I assumed he’d roll over the 15th-seeded Swiss kid. Federer, of course, wound up winning an epic match, 7-6(7), 5-7, 6-4, 6-7(2), 7-5.

Because this was the only competitive match that the two best tennis players of all eons and eras ever played against each other, it’s acquired legendary status and its own cult lore. I rewatched the match recently, and it’s impossible to see it today without experiencing it as a generational handoff, a hinge in the history of the game. It’s the Nixon-Kennedy debate of tennis, except that Federer wore less makeup (than Kennedy) and Sampras had less charisma (than Nixon). Every forehand has a phantom significance. There was even a hint of that significance at the time: In the match broadcast, John McEnroe can’t stop describing Federer as Sampras’ doppelgänger or twin (“this must be like looking in the mirror for Pete,” etc.), as though we’re somehow watching two incarnations of the same player at different moments in his life.

Given that the match involved Sampras, whose service games on grass had an average point length of around 0.0004 seconds, the rallies are surprisingly tactical. Like all intensely fought top-level matches, it turns into what feels like a fierce debate between conceptually simple and diametrically opposed ideas. The ball pocks off the rackets and almost sounds like words — as McEnroe might have noticed, it sounds like then and now. Sampras rips a big serve (then) down the center line to Federer’s ad side, which Federer just barely gets to, lunging for an off-balance backhand (now), which Sampras, who’s of course crept in toward net, awkwardly parries (then) back to Federer’s ad corner, forcing Federer to scoop the backhand off the ground (now), which sets Sampras up for an easy forehand drop shot (then), which Federer implausibly runs down, flicking a cross-court forehand (now) that Sampras has to stretch out to his full-body-plus-racket length to hit back (THEN), a looping forehand winner into Federer’s ad court, Federer marooned by the net on the wrong side.

But every time you think now isn’t ready for the moment, Federer coolly does something that makes then look like the distant past. With Federer serving at 4-4 in the fifth set, Sampras wins his first break point of the set on a vicious down-the-line backhand. If he takes the next point, he serves for the match. This is the point, in other words, where everyone crumbles against Sampras. Federer drops in a so-so serve. Sampras, who’s definitely going to win, whips it back toward Federer’s feet, and Federer, who’s definitely going to lose, sends back a slow forehand toward where Sampras is already lying in wait, and Sampras lines it up for a hard cross-court backhand that’s definitely going to leave Federer, who’s planted in the middle of the court, no room to get in a return. Only Federer manages to block it back with one of those little backhand flicks that start up by the shoulder, and he flicks it out to Sampras’ left just as Sampras is edging right to close down the court, and Sampras has to lunge against his own weight for the backhand, but he can’t get there. And when you watch this at full speed it looks like the ball just goes NOW and skips past him, and you — or your 2001 self, the one that knew Sampras would win — stare in disbelief, and McEnroe can only mutter something about how “big-time” Federer’s shot was. Federer goes on to win this game and his next service game and then break Sampras at 6-5 to take the match, at which point he falls to the ground like he’s just won the tournament, which, in fact, as a sign of how early this is, he wouldn’t do for two more years.

After the match, the Sports Illustrated write-up focused on Sampras, of course, describing him as “defeated and dethroned” as he sat slumped in his changeover chair, stuffing sweaty towels into his bag. Actually, he just looks numb, numb and exhausted, while the kid in the other chair, whose whole career is ahead of him, sobs for joy.

They both seem stunned, which is not the same thing as surprised, by what time can do to you.

The saddest moment in the career of a great athlete is the one when he’s tagged with the word “still.” One day you’re fast. One day you’re slow. There’s an in-between day when you’re “still fast,” and that’s the day when everything hollows out.

Think about this. You know people get old. You know things change. And you know that that’s especially true in sports, where in tennis, for example, a 29-year-old can be unironically described as having entered his twilight years. But because the physical gifts of top-level athletes are so incredible, and because their skills are so ingrained that they seem like they’ve always been there, you fool yourself into thinking of them as stable essences who are essentially immortal. They might have good streaks and bad streaks, or develop their games in one direction or another, but their basic abilities feel constant. Then one day you’re watching a game and you think, “Wait, has Kobe lost a step? Well, no, he can still get to the basket ”

Roger Federer has spent longer as a “still” athlete than any great player I can remember. You could even argue that it’s one of the signs of his greatness. Other top players hit the “still” moment, hang around for a little longer, and then whoosh, they’re gone, broken up into memorial clips and Hall of Fame inductions, classic rock bands who’ve sold their copyrights. Federer, after three straight years of diminished results — 11 to 12 singles titles a year from 2004 to 2006, then eight in 2007, and four to five every year since — is well, still really amazing. He’s still near his best, which means he’s still playing some of the best tennis the world has ever seen. If anything, he’s improved his serve to compensate for what’s maybe been a slight decline in his movement and shot-making — although, as McEnroe pointed out during the French Open, his movement is “still great.” Heading into Wimbledon, historically his best tournament, he warmed up at the French by sensationally ending Djokovic’s 41-match winning streak and playing as well as Paris has ever seen him play against Nadal.

But because he’s been “still great” for so long — because we keep seeing the end coming, even if it never actually comes — Federer has also acquired an aura of weird sadness over the past few years that’s hard to reconcile with the way we used to think about him. And even though that’s only been possible because he’s still so good, it’s a jarring development, because at his peak, Federer was probably the best athlete in the world at making greatness look utterly natural. Nobody seemed more effortless, or more graceful, or more beyond time than Federer from, say, 2003 to 2007. Now we’ve seen him lose 350 French Open finals to Nadal, fall hopelessly behind in their personal rivalry, and struggle to keep younger players like Djokovic and Andy Murray from overtaking him. Had his decline been quicker — had he spent less time in that slow glide down through “still” — a lot of that never would have happened, and we’d have gone on seeing him as the invincible icon he once was. As it is, he’s been on the precipice for so long that we’ve stopped seeing him and started seeing only the precipice.

What this means, though, is that Federer has become something rarer and stranger, something arguably even more interesting. He’s still good enough to win any tournament he enters, but he’s always surrounded by that vague sadness, the result of his no longer being free from time. He’s become something like the world’s leading practitioner of mortality as a tactical position. He doesn’t exactly inspire the “rooting for the old guy” cliché because he’s manifestly not old; what he’s doing right now is completely different from, say, Nicklaus winning the Masters at 46. That was a resurrection, a public spectacle. Watching Federer increasingly feels like looking in on something private. It’s as if his game is just somewhere else, on some secret corner of the map where it can stage its weird encounter between beauty and death.

And yes, that sounds pretentious, but then death is never as far out of the frame as you think it is in sports. The English codified boxing and hunting at the same time and early 19th-century sportswriters covered both, along with dogfighting, cockfighting, and any other sport that promised a reasonable likelihood of blood being spilled on sawdust. Those F-16s flying over Monday Night Football aren’t exactly instruments of peace, and to go by our favorite sports metaphors, what we’re watching when we turn on a game is a lot of killing, dismantling, destroying, eviscerating, shredding, and annihilating. The cricket ball is also a stone. Somebody’s always getting killed in sports; it’s only a matter of timing.

When Federer beat Sampras 10 years ago it was a grueling match, but a quick death. Sampras didn’t disappear overnight, but having his best tournament, the place where he’d always been untouchable, taken away from him by a teenager put an end to his “still” phase; after that, he was just straight-up in decline. As if to underscore the point, the SI headline after the match was “Changing of the guard.” For one reason or another, no one’s produced a “changing of the guard”-style moment against Federer, not even Nadal. As a result, Federer’s protracted “death” would make a great career for most tennis players. It’s only sad for us.

Brian Phillips writes about soccer for Slate and edits The Run of Play. You can find him on Twitter: @runofplay.