NEW YORK - Garbiñe Muguruza, Simona Halep and Ashleigh Barty, each a former or current World No.1, remain three of the most versatile players in the game. Each has won two Grand Slam titles and remain a threat in any event they enter. 

For all three, though, each of those major wins came on the natural surfaces: the clay at Roland Garros and the grass of Wimbledon. But so far they have come up empty in Grand Slam hardcourt events, which on the surface seems puzzling considering combined they own 25 titles on the concrete. 

Halep came close at the 2018 Australian Open, falling in three sets to Caroline Wozniacki in the final, while Muguruza lost in three to Sofia Kenin in the championship match two years later at the same event. Barty's best hardcourt Grand Slam run came as a semifinalist at the 2020 Australian Open.   

Why have they not been able to break through in Australia or the US Open?

"I feel you need that X factor that clay court brings and grass courts are unpredictable. But on hard court everybody plays well."

- Garbiñe Muguruza

"I don't think they are the hardest ones -- They are all hard," Muguruza said. The No.9 seed is into her second Round of 16 at the US Open, having made her first in 2017. "I think everybody plays well on hard court, it's more equal. So I feel like there can be more winners.

"The other [Slams] you need to have something in your game. You have to be more than just hitting the ball and hitting hard. I feel you need that X factor that clay court brings and grass courts are unpredictable." 

"But on hard court everybody plays well. So there is no theory, really. It's just funny that three players just happened [to do] that.

"I don't think there's anything specific to it. It's just sometimes you have to get the timing right. Things have to fall in your place. You have to get a bit of luck."

- Ashleigh Barty

This year, top-seeded Barty is bidding to advance past the Round of 16 in New York for the first time. The US Open is the only Slam at which she has yet to make a semifinal. Of her 13 titles, eight have come on hard courts, including two Miami wins, the WTA Finals and Cincinnati just two weeks ago. 

"Yeah, it's an interesting one," Barty said when asked about the trio's quest for a hardcourt major. "Obviously the occasions can make you feel different. You can't hide behind the fact that for me playing in Australia is different to what Simo or Garbiñe feel when they play in Australia. When they're playing in Europe it's different to how I feel when I play in Europe.

"I think all in all, we've won titles on hard courts, we've all won big titles on hard courts. I don't think there's anything specific to it. It's just sometimes you have to get the timing right. Things have to fall in your place. You have to get a bit of luck."

This year, Halep is into the second round of the US Open for the first time since 2016, but success in New York has been limited. Playing her 11th US Open main draw, Halep is into the second week for a fourth time. Her best result came in 2015, when she progressed to the semifinals but lost to eventual champion Flavia Pennetta.

In recent years, the Romanian was snake-bitten in the early rounds with tough and tricky draws. As the No.2 seed in 2017, she drew the ignominious task of taking on Maria Sharapova in the first round, where Halep lost a dramatic three-setter under the lights on Ashe. The next year, it was a hot-handed Kaia Kanepi who blasted winners on the brand new Louis Armstrong Stadium to knock then No.1 seed Halep out of the tournament. In 2019, Taylor Townsend stunned Halep with a stunning barrage of serve-and-volleys to end her tournament in the second round.

After winning her second-round match over Kristina Kucova, Halep, who is nursing an upper leg injury, joked about her recent US Open results. "Already is a better result than when I was healthy, so it's a good thing to be in the third round here."

Halep is as stumped as anyone else as to why she, Barty, and Muguruza have yet to translate their hardcourt success in New York.

"I cannot explain why," Halep said. "It's just maybe because we didn't trust that much that on hard court we can win. But also, at the same time, we won other tournaments, big tournaments on hard, so probably it's a matter of time and we have just to wait and to believe that it's gonna come.

"Hopefully one of us can win a hard court Grand Slam. But it's nice to be in these top three. They are very nice players."

Aside from her French Open and Wimbledon wins, Muguruza has won all six of her other titles on hard courts. She's conquered three of the biggest hardcourt events on tour, with titles in Beijing, Cincinnati and Dubai. But the Spaniard has always been honest when it came to the challenge of the US Open. The tournament and city's energy can be unsettling for some players, but Muguruza said this year her mind is clearer.

"The past years I was very -- in Spanish we say you're a little bit cross, your brain is a little bit not working very well," Muguruza said after her third-round win over Victoria Azarenka. "I felt negativity was more than positivity in the previous years.

"This year, I just prepared well and said, Hey, at some point it's going to change, this might be the year. I feel also having went through those couple of first tough matches gave me also the feeling that, Hey, I can do well here. I think going through the first rounds always gives you that confidence. In the previous years I didn't manage to go through those opening rounds."

Then again, maybe hardcourt Slams are difficult to win because Slams are difficult to win. Simple as that.

"You have to be able to navigate your way through a two-week tournament, which is not easy," Barty said. "Sometimes the single-week tournaments are easy to get a bit of a flow. You play every day. You just get in this monotonous rhythm of warmup, practice, play. That same thing over and over.

"But for two weeks, that's a long time. It is a very long time to stay focused, to stay specific to what you want. And the Grand Slams [is] where the best quality tennis players come to one event and try and beat each other. 

"I hope for all of us we're not far off. You keep putting yourself in that position time and time again, keep showing up, having a crack, and that's kind of all you can ask."