Like most 16-year-olds, Mirra Andreeva has a few things to learn about controlling her emotions, as demonstrated by a couple of moments in her fourth-round exit here on Monday when her frustrations boiled over. But the Russian teenager’s level of maturity, in her game and particularly off the court, bode well for her future.

At this rate of progression it would be a big surprise if she is not contending for significant titles before long.

Andreeva, a qualifier, had a chance to lead Madison Keys by a set and 5-1 before the American found her game, winning 3-6, 7-6 (4), 6-2 to take her place in the quarter-finals for the second time, eight years after the first. Andreeva was warned for throwing her racket from some distance towards her chair at the close of the second set and near the end of the match received a second warning – and therefore a point penalty – when the umpire, Louise Engzell, judged she had thrown her racket as she fell. It seemed harsh at the time and more so with the benefit of the replay.

“I didn’t throw the racket, I slipped and then I fell,” Andreeva told the umpire. “It’s the wrong decision.” Later she expanded on the incident. “It’s a controversial point,” she said. “I didn’t have any intention to throw the racket. I slid. I thought that I will fall forward.

“Maybe it did look like I threw the racket. I don’t know. I didn’t see any videos yet. But that was her decision to make. She made the decision, so the match is over now.” And of the choice not to shake the umpire’s hand? “She didn’t do a right decision for me. That’s why I didn’t want to shake hands [with] her.”

Andreeva played her first WTA event as recently as May. She qualified and reached the third round at the French Open and her run here means she will rise to around No 64 when the rankings are updated after Wimbledon, giving her direct entry into all the biggest events.

Dealing with emotions on court is far from easy. Even Roger Federer had problems controlling himself when he was young. Initially, the realisation that others found things difficult was helpful for Andreeva but she thought temperament issues would pass with time. Eventually, she understood that she has to help herself.

“It’s kind of strange, but almost every time before I go to sleep, I turn off the lights and I just try to speak to myself just about the day, about everything,” she said. “That time after [losing at the] French Open, I spoke about the game. It helped me.

“I just speak to myself as I would speak to my mum or to my coach, but just to myself without anyone in the room. It works the same. But nobody’s listening except for you.”

That kind of maturity is rare at any age but especially for someone so young in a sport where the attention can be intense. Not to mention when you are followed around by Netflix cameras, capturing your every move, as Andreeva has been here. Despite the disappointment of losing from a winning position, she spoke with poise and confidence, answering everything in a thoughtful, charming manner.

The former doubles star Todd Woodbridge played his first grand slam event as a 16-year-old. On the BBC, the Australian compared the game and court smarts of Andreeva to that of Tracy Austin, who won two US Open titles as a teenager, but he said she needs time to find her way.

Woodbridge said: “I quite like that she’s fiery. But maybe it’s good that she didn’t squeeze through today. What she’s done at the French Open and Wimbledon is amazing but it’s easier [to handle the expectations] if you rise incrementally.”

Winning six matches here will have further boosted her confidence and Andreeva will head to the US for the hard-court season, where she also hopes to run into Andy Murray, her favourite player on the tour. “Maybe in a couple of months I will be ready to say hello,” she said, smiling.

Keys, who will play the No 2 seed, Aryna Sabalenka, a 6-4, 6-0 winner against Ekaterina Alexandrova, in the last eight, was asked what advice she would give Andreeva. “I would say ignore everyone and everything that they say unless you actually care about their opinion,” she said. Andreeva, it seems, has that side of things all sorted out.