Don’t ever accuse the United States Tennis Association of rigging the U.S. Open draw to favor its own players.

The draws are official, and the Americans are officially out of luck. The three best American men in the field — Andy Roddick, James Blake, and Sam Querrey — ended up in the same half as Roger Federer, who will seek an Open era-record fourth consecutive U.S. Open title beginning Monday. Venus and Serena Williams were drawn together, too, in the same half as the other top contenders in the field.

Roddick and Federer, last year’s finalists, should butt heads in the quarterfinals, so long as Roddick survives possible encounters with two of the tour’s biggest hitters: Ivo Karlovic and Tomas Berdych. Blake and Querrey are on track to meet in the third round; the winner would have a reasonable path to a semifinal appearance against Federer (Marcos Baghdatis and Nikolay Davydenko would be their chief obstacles). Federer doesn’t have the easiest road, either. After facing qualifiers in his first two rounds, he’ll likely have to contend with former top junior Jarkko Nieminen, either Juan Carlos Ferrero or Richard Gasquet, and then Roddick.

While none of this is welcome news to fans of American players, Rafael Nadal couldn’t be happier about it. This is the best U.S. Open draw of the Spaniard’s career. Depending on the extent of his recent injuries, he might struggle in the second round against the aggressive Janko Tipsarevic. But from there Nadal has as clear a path as he could hope for until the semifinals, where he might face no. 3 seed Novak Djokovic. Djokovic, round for round, has the most difficult draw among the men: First, former top contender Mario Ancic (recovering from mononucleosis); then Radek Stepanek, the former fiancé of Martina Hingis and a dangerous hard court player; then later Lleyton Hewitt, who is playing superb tennis of late, and then perhaps Tommy Robredo or Mikhail Youzhny, who defeated Nadal en route to the semifinals here last year.

The women’s draw is top heavy, too. Five of the six likely winning contenders — top seed Justine Henin, Serbians Jelena Jankovic and Ana Ivanovic, and the Williams sisters — landed in the top half of the draw. To reach the final, Henin might have to defeat Serena Williams in the quarterfinals and perhaps Venus Williams in the semifinals. Ivanovic, the no. 5 seed, has it worst of all. She’ll likely have to defeat Venus Williams, Jankovic, and the winner of Henin and Serena Williams to advance to the final.

Defending champion and no. 2 seed Maria Sharapova, meanwhile, only has to contend with several fellow Russians (Nadia Petrova, Svetlana Kuznetsova, and Anna Chakvetadze ) against whom she has a combined 1 3–4 record. Chances are good that we’ll see an all-Russian quarterfinal in this half of the draw. Nicole Vaidisova — who has struggled with injuries this year — Martina Hingis, Daniela Hantuchova, and Patty Schnyder have the best chances of breaking up that party.

Perhaps you are wondering how it is that Roddick, the no. 5 seed, could draw the top seed in the quarterfinals. In a more rigid system, that honor would be reserved for the no. 8 seed; no. 2 would play no. 7, and so on. But the system used by the U.S. Open in recent years combines a computer and a random drawing, so luck plays a role.

Before USTA officials arrived at the Empire State Building yesterday to announce the draw, a computer had placed Federer at the top and Nadal at the bottom, and then the other 96 players — a collection of unseeded men and yet-to-be-determined qualifiers — in between. Choice spots are left open for the remaining 30 seeds. Seeds three and four receive the most favorable treatment. They get either one of two spots in the draw, in the quarter opposite the top seed or the quarter opposite the second seed. Seeds five, six, seven, and eight are treated as equals. Each man has a one in two chance of landing in the top or bottom half of the draw, and a one in four chance of landing in the same quarter as the top seed. Roddick’s name was drawn first, so he got Federer.

If Roddick is going to win the U. S. Open, chances are he’ll have to beat Federer at some point. As Patrick McEnroe, co-host of the draw ceremony with Mary Joe Fernandez, pointed out yesterday, one might as well play Federer in the quarterfinals as the finals — perhaps the world no. 1 will still be a few winners short of his best stuff. The annoying part for Roddick, of course, is that last week, he was the no. 4 ranked player in the world, which would have guaranteed that he couldn’t meet Federer until at least the semifinals. His early loss in Cincinnati, a title he won last year, cost him one spot in the rankings.

Looking at the rest of the draw, there are several intriguing firstround matches for those visiting the tournament during its first few days. John Isner, the 6-foot-9-inch college standout who reached the finals in Washington, D.C., this summer, faces Nieminen. Donald Young plays Chris Guccione, a 6-foot-7-inch Australian with a booming serve. Tim Henman, the 32-year-old Brit, couldn’t have been happy to see Dmitry Tursunov’s name above his: The Russian holds a 5–1 record against him. Justin Gimelstob drew Roddick as a first-round opponent for the second straight major (Roddick won in straight sets at Wimbledon).

Finding a compelling first-round women’s match is usually a much more difficult task, and this year is no exception. Alicia Molik and Maria Kirilenko ought to put on a decent show. Two young Americans would be worth a visit, too. Alexa Glatch plays Marion Bartoli, the surprise Wimbledon finalist. Ashley Weinhold, the 17-year-old who won the girls National Championship in Berkeley, Calif., last weekend, plays Anna Chakvetadze, the no. 6 seed.

Mr. Perrotta is a senior editor at Tennis magazine. He can be reached at tperrotta@nysun.com.