Biggest challenges await a focused Williams

It has been more than a year since Patrick Mouratoglou became that rare figure in Serena Williams' life: a coach outside her family circle.

The relationship - personal as well as professional - has been rewarding, and if there is one spot that symbolizes their mutual success, it is the new display case that sits in Mouratoglou's eponymous academy in the Paris suburbs.

It is filled, at Williams' insistence, with the trophies she has won since she and Mouratoglou began working together before Wimbledon last year.

"She's won so much, we're already making a second case," Mouratoglou said at the National Tennis Center on Thursday. "Wimbledon, the U.S. Open, the year-end championships, Miami, Charleston, Madrid, the French Open. They're all there."

Two more singles victories from Williams in New York, and there will be another major trophy to put in the new case.

It is tempting to get ahead of ourselves in light of Williams' dominance thus far. She has not dropped a set in five matches and was pushed only to 6-4 by Sloane Stephens in the opening set of their soon-to-be-lopsided fourth-round encounter.

This has been golden-age Williams: focused, stingy and unapologetically ruthless with a few growls and shrieks for punctuation but with self-containment providing the bulk of the narrative.

It looks, from the outside, like a fine place to be, but she knows deep down, just as we know deep down, that the players most capable of throwing a stone in her reflecting pool are still in the tournament.

In Friday's semifinals, Williams will face Li Na, one of the few women with the weapons and defenses to stay with Williams in a baseline punching contest.

Get through that, and Williams is likely to have to deal in the final with Victoria Azarenka, who faces the unseeded Italian veteran Flavia Pennetta in the other semifinal and who has beaten Williams in their last two outdoor hardcourt matches. She also nearly beat her here in last year's emotional journey of a final.

Li has beaten Williams only once, in 2008, and has not taken a set off her since 2009. But their three matches over the last two seasons have been competitive and occasionally spectacular. Though the fifth-seeded Li is still capable of midmatch walkabouts and not nearly as confident at the core as Williams, she has been producing bold patches of play here at age 31 as she continues her journey with veteran coach Carlos Rodriguez.

"She knows how to do many, many things," Mouratoglou said. "She does not have real weaknesses. OK, the forehand is not as good as the backhand, there are moments when the forehand catches a bit of a cold, but in general she's a complete player who moves well, is very athletic, returns well and is aggressive in the game and does not have too many holes. She's a dangerous player, no doubt."

Her relationship with Rodriguez becomes even more intriguing in a match like Friday's. Rodriguez has analyzed and plotted against Williams' game with perhaps more success than anyone. During his many years coaching the unimposing yet great Justine Henin, she won six of her 14 matches against Williams before retiring for good in 2011.

Rodriguez began working with Li in July 2012, and she might already have won a major title on his watch if she had not twisted her ankle with a one-set lead over Azarenka in this year's Australian Open final.

But for now her only Grand Slam singles title remains the one she won at the 2011 French Open before they joined forces.

"The connection with Justine was clearly very, very strong, and it worked for a long time with lots of success," Mouratoglou said. "Now if he's capable of reproducing these kinds of results with another player, it will show, really show, that he is extremely competent."

© 2013 New York Times News Service