Still, she is 18-0 so far in 2015 (with one withdrawal), and watching her fight past third-seeded Simona Halep in a classic match Thursday and overwhelm Suárez Navarro in a dud Saturday made it clear that she has the will and the skill to run the table as she chases Margaret Court’s record of 24 Grand Slam singles titles. (Williams is at 19.)

“We’ll see,” said her coach, Patrick Mouratoglou. “Listen, if she wants to get to 23, 24, 25 Grand Slam singles titles, she had better not miss occasions.”

Could this be the year? Sure, it could. Will it be the year? The odds are, of course, against it. No woman has completed a Grand Slam since Steffi Graf in 1988, no man since Rod Laver in 1969.

“Obviously, anyone that wins the Australian Open wants to win a Grand Slam,” Williams said Saturday without so much as an arched eyebrow. “I’ve won the Australian Open six times, and I have not done that yet. I’m not saying this is the year or not the year. Who knows?”

Her off days can be hard to predict. Injuries are always a concern, but even at this stage of her career, she is improving. With the help of racket and string technology, she is creating sharper angles. Her volleys, although still not works of art, have become more consistent. Her single-handed backhand chip is generally crisper and more versatile, as evidenced by the lunging back-to-the-net winner she hit down the line on a crucial point against Sabine Lisicki in the quarterfinals.

“She can play offense, obviously, but now the defense has gotten better,” Martina Navratilova said after handing Williams the trophy in Key Biscayne on Saturday. “She’s as eager as ever, and it’s been really cool to see. It’s great to see somebody want it that badly, to do everything they can possibly do to be the best they can be. I really respect that from her. She’s been doing that the last three years remarkably well.”

It is also remarkable that Williams is not the only singles player with a reasonable chance at a Grand Slam this year. Novak Djokovic won the Australian Open and has been winning convincingly, even on off nights. At 27, he is in his prime and well aware that although he is unlikely to catch Roger Federer or Rafael Nadal in Grand Slam singles titles, he could elevate himself to a category all his own in this era by winning the Grand Slam.