After Saturday’s heartbreaking loss in the U.S. Open semifinals, it seems fair to ask whether Roger Federer missed his last and best chance to add to his collection of Grand Slam titles.

On second thought, maybe it isn’t fair. Roger Federer is the world’s third-best tennis player. He served for the match twice on Saturday.

He didn’t beat Novak Djokovic, but he had won their semifinal at the French Open.

Rafael Nadal? Well, he’s been a longstanding problem for Federer. But he did defeat Nadal in London last November. With the right breaks, Federer is still capable of winning a Grand Slam title.

But it won’t be easy. What, exactly, are the odds?

Apart from Nadal and Djokovic, the key factor working against Federer is his biological clock. Tennis players peak at a fairly young age. In the Open Era (since 1968), the average age of men’s Grand Slam winners is 24.4 years old.

Perhaps not coincidentally, that number bisects the age that Nadal (25) and Djokovic (24) are right now. (Maybe you should spring for tickets to Monday’s final: both players are probably close to the absolute peak of their abilities.)

But thirty-something players — Federer turned 30 in August — have won occasionally. They’ve claimed 18 of the 174 Grand Slam titles during this period, or about 10 percent.

One way to frame the question is this. How likely is a tennis player who is ranked third in the world as of his 30th birthday to win another Grand Slam before he retires?

I looked up the ranking as of age 30 for every men’s player who ranked in the world’s top 5 at any point during the Open Era. (For 1973 onward, I used the A.T.P. rankings. For 1968 through 1972, before the A.T.P. rankings were unveiled, I relied on unofficial rankings instead.)

Five players — Andre Agassi, Jimmy Connors, Rod Laver, Ivan Lendl and Ken Rosewall — were still ranked No. 1 in the world as of their 30th birthday. Four of them won at least one more Grand Slam title after turning 30, Lendl being the odd man out.

John Newcombe, the only player to be ranked No. 2 as of his 30th birthday, brought home one more title: the Australian Open in 1975.

After that, things get spottier. Arthur Ashe, ranked fourth in the world on his 30th birthday, did win one: Wimbledon in 1975. So did Pete Sampras, whose rating had already dropped to 12th by the time he turned 30, but who won the U.S. Open as a 31-year-old in 2002.

But Tom Okker, who was ranked third when he turned 30 in 1974, failed to win a Grand Slam. (Okker also had not won a Grand Slam before turning 30, so this wasn’t a new problem for him.) Guillermo Vilas, fourth in the world as of his 30th birthday, did not win another title. John McEnroe and Ilie Nastase both played some capable tennis after turning 30 — but neither won another major title.

Bjorn Borg was already retired by the time he turned 30. Boris Becker, Mats Wilander and Stefan Edberg weren’t retired, but they may as well have been.

Still, Federer’s odds aren’t so bad. A statistical analysis that uses a player’s ranking as of his 30th birthday as its input puts them slightly in his favor, suggesting that he has a 58 percent chance of winning another Grand Slam.

That strikes me as a touch optimistic. There isn’t usually as much differentiation between the No. 3 player in world and the top two as there is right now.

On the other hand, there also isn’t usually as much differentiation between No. 3 and the players ranked fourth and below as there is right now.

Here’s the key question, I think. We know that beating Nadal or Djokovic is going to require some luck on Federer’s behalf. We also know that he can still win sets and matches against them, and that given enough opportunities, the breaks are liable to go his way at some point. But can Federer put himself in a position to get lucky?

Meaning, can he count on getting to the semifinals of major tournaments without too much problem?

So far, this hasn’t been too much of an issue. Federer has lost to a couple of good-but-not-great opponents on the circuit this year. But he’s generally come to play in majors, having made it to the semifinals in four out of the last five Grand Slam tournaments.

If he does that several more times, he may pull one of them out.

Handicappers make Federer a 4-1 underdog against winning Australia in January, a 6-1 underdog against winning Wimbledon next year, and a 16-to-1 underdog against winning the French Open. I can’t find odds on next year’s U.S. Open quite yet, but since it’s the same surface as Australia, I’d assume you’d be looking at similar numbers, about 4-1 against.

Maybe you shouldn’t take those figures literally — these sorts of bets include a fair amount of “juice” for the casino, especially for popular brands like the Roger Federer brand. But if you do, it implies that there’s a 48 percent chance that Federer wins one of the next four majors, even though he might be an underdog in each one individually.

And he still might have a few opportunities after that. Although they’re unlikely to be as good as the one he missed on Saturday.