Down 0-30, Venus lets go an ace, a perfect serve-plus-one shot into the corner, a service winner on the T, and clinches with a big baseline shot that Sloane shanks back, long. 1-1. It looks like it’s going to be a ball game.

Miss Williams, if you please, and Miss Stephens. Are these the two best women at the U.S. Open? Suffice it to say, they have made it to the semis — as have Coco Vandeweghe and Madison Keys, who will play next on the center court of Arthur Ashe Stadium. It is the first time in more than a generation that we see semi-finals here where all the candidates are American.

About time, too. But if the reconstruction of American tennis has been a long-term project, it has been solid. There are many fine young American women in the sport, as shown in the juniors competition. Two very young Americans, Coco Gauff and Amanda Anisimova, whose ages add up to less than 30, are moving toward the final on the girls’ side.

The boys are doing well too, and the young men had nice runs in the main draw, notably Jared Donaldson, who is from nearby Rhode Island, and the College Park, Maryland native Frances Tiafoe, who almost beat Roger Federer, taking him the full five-set distance in the first round and thereby may be credited with helping wear down the greatest player of our times. Federer finally succumbed to fatigue and back pain in a four-setter the other day, scotching a chance for a first U.S. Open match-up against his great rival (and good friend) Rafa Nadal. The defeat was altogether honorable: it came at the hands of the man who beat him in 2009 to take the trophy, Juan-Martin del Potro.

Nadal and Federer, who have met at tournaments everywhere except this one over their many years of competition, were the most likely men to make it to the final, seeing as how everyone else at their level — Novak Djokovic, Andy Murray, Stan Wawrinka — dropped out before it started. So many players have been dropping out. Federer himself, mind, took the entire second half of the 2016 season off due to serious injuries, and Nadal had been through a series of injury-interrupted seasons until this year. This has provoked a running story the theme of which is whether the Tour has become too arduous. There is talk of modifying the best-of-five sets format of Grand Slam matches — perhaps by playing best-of-threes during the early rounds and going to five during the last two or three. (Which was the format in the early years of the U.S. Open, though not the others.)

Meanwhile, however, it will be Nadal v. Del Potro in the men’s semi; the winner almost guaranteed to take the trophy since the other semi is between Pablo Carreno-Busta and Kevin Anderson. And as to the women —

Well, as to the women, Miss Stephens holds and then breaks Miss Williams in the fourth to go up 3-1. She is playing what has to be called all-court-high-pressure tennis. She keeps the great veteran — who won her first U.S. Open in 2000, when Miss Stephens was a small child — on the baseline and limits her ability to deploy her power game.

She holds, breaks her again, holds, and it’s 6-1 in scarcely half an hour. No question about it, to beat Miss Williams, you have to keep her from getting those killer angles, because she will use them.

As we see in the second set. From sluggish and distracted, Miss Williams finds her spark, her speed, her power, above all her astonishing accuracy. Fully warmed up, she takes over, dictating practically every point, setting up the gorgeous crosscourt forehands that no one can reach and unleashing service aces whenever she wants, or so it seems. This is the champ who, you could argue, brought the power game into the women’s tour.

She didn’t — no single player did — but arguing the point allows you to remember how much tennis owes Venus Williams. When she is on her game, she combines power and grace that turns the sport into ballet. In another half-hour set, it’s 6-0 for her, and the match is even.

Venus Williams lost to her sister Serena in the final of the Australian Open last January. She has had a terrific year, a run to the fourth round at Roland-Garros and runner-up at Wimbledon, where she lost to Garbine Muguruza. Obviously it would be nice to finish the year with the trophy she last won in 2002. Miss Stephens has had a nice year too, all the sweeter for being a comeback following a long lay off due to injury and surgery.

Having each tried out opposite extremes, they settle into their best games. They are both playing fantastic tennis. Early break and break-back even the score at 2-2. Miss W. makes a bad mistake on an overhead volley, recovers, hits long — tiring? — , aces beautifully up the T to save the break point, then earns the ad with a backhand volley at the net. Then doubles to go back to deuce. Hangs in and holds.

But Sloane fights off two break points and serves an ace to the T in reply to Venus’s to hold the sixth game; and they are again even. A forehand out of bounds by Venus gives Sloane a break point, Venus saves it with a strong serve, takes the advantage with another one, but fails to convert when she hits a forehand down the line out of bounds. A superb rally gives Sloane the advantage and a second break point. Which Venus saves with a forehand winner. Another fantastic rally, a forehand duel, end with Venus netting one. Third break point. She rushes the net, nets a forehand, break: and Sloane is serving at 4-3.

But Venus is not done. She breaks back. She holds back. The tension is palpable. (Cliché, sorry.) They are both hitting hard, deep, gorgeous crosscourt shots from both wings. Miss Stephens knows she must avoid giving Miss Williams forehands. Miss Williams know she must keep Miss Stephens off balance, set up situations to put it away. Give her an angle, you doom your point. Miss Stephens knows this. She is very cute in her pink outfit. Miss Williams is her eternal graceful lithe lovely self. Let that not distract you, these are top athletes, best in the world. At 30-all, 4-5, Miss S. ends a simply fabulous baseline rally (25 shots, I think) with a backhand down the line which will be anthologized. Now leading 40-30, she converts with a superb lob to the baseline. In the next game, she breaks with a breath-taking race to the net to catch a drop shot which she sends back crosscourt almost parallel to the net, and it’s 6-5. No wonder they say the semis at the U.S. Open will bring out the best of the best (another cliché, sorry.)

Then it all happens fast. Serving for the match, she goes up 40-15 and on the next serve Miss Williams, unbelievably — given how high the level has been in this set — flubs a backhand return of (second) serve into the net. Sloane Stephens is in the final, her first ever at a Slam.