That was also — strange but true — the last time Li played anyone in the top 10, and she quite rightly said that Saturday’s final would give her a chance to judge how much she had really improved in recent months.

“This time here, really can see,” Li said. “Really happy I can play against her again.”

Li remains the paragon of a hot-and-cold talent. The latest proof was her wild 7-5, 2-6, 6-3 victory over Dominika Cibulkova late Thursday night. With the wind and Li’s confidence gusting, it was a match filled with explosive shot-making and smack-your-forehead gaffes. The night was encapsulated by Li’s final service game, in which she produced two double faults into the breeze, one in which her second serve struck the bottom of the net and one in which her second serve bounced before striking the net.

Yet she still managed to prevail. More impressively to those who have watched Li self-immolate through the years, she did so without blowing a gasket, without berating herself, her entourage or the fates.

That hardly means the internal dialogue was all peace and love, but her composure was still meaningful, constructive and encouraging. Li agreed that a younger version of herself would have gone crazy in a match as inherently frustrating as that one.

She credits maturity and self-awareness. She credits Rodriguez and their intense daily communication. But even with the Australian Open title in hand, Rodriguez sounds as if he is still waiting for the true payoff.

“We discuss things a lot with the understanding that tennis is so very mental,” he said in an interview after the semifinal. “The challenge is to get the best out of yourself in situations like this. Tonight, she managed to win without playing a great match, and that’s a good sign. But I expect more from her based on what I know she can do: more quality, more consistency. I left the table still hungry tonight because I didn’t see what I’m used to seeing in training.”

He wants her more, much more, at the net. He wants her to project more confidence and desire on court.