American tennis star Jessica Pegula on being 'normal' despite her family's billions.. and how she's taken inspiration from Coco Gauff and Novak Djokovic

Earlier this US Open, Jessica Pegula did something that millions of New Yorkers do every day.

A video posted to her Instagram account showed her riding the subway - except, unlike most straphangers, she was lugging tennis bags and preparing to play in her eighth main draw in Queens.

'To me it's normal,' said Pegula, the current world No. 5 and daughter of billionaires Kim and Terry. 'And people are like, 'Oh my god, I can't believe you did that.' And I'm like, well, why? I like taking the train. I like taking the subway.

'It's just kind of funny when people assume that I fly private everywhere, or that I have a chauffeur driving me around since I was five,' she added. 'I'm like, what? Or I have a butler... that's not how it works,' she said. 

Pegula, who spoke exclusively to Mail Sport after her second round win vs. fellow American Sofia Kenin, is an affable personality who - like her WTA peers - has been training for a pro career since she was a kid.

Jessica Pegula's family is worth billions but she thinks fans sometimes get it wrong about her

But it's easy to see where the assumptions come from.

Pegula's father, Terry, sold most of his natural gas company for a whopping $4.7billion in 2010, according to Bloomberg, and the family purchased the NFL's Buffalo Bills four years later.

A headline last summer even blamed her sixth straight Slam quarterfinal defeat on a missing 'dynamic' that her 'family billions can't buy' after she was eliminated from Wimbledon.

As the 30-year-old pointed out, though, her family's extreme wealth didn't come until she was a teenager, and she believes that people at times 'have a picture in their head' about her that gets it wrong.

'People jump to these conclusions that are so over the top. I grew up pretty normal, and a lot of that [her family becoming billionaires] didn't happen to me until I was already older and playing. My goal since I was six or seven was to be number one in the world. So that was before a lot of this other stuff happened. I mean, before that, I was just a normal kid growing up in Pittsburgh, Pennsylvania, taking lessons after school. So I think that's just the kind of difference that maybe the casual fan kind of doesn't grasp as well.

'It's usually some random people online that, I don't know, probably don't have anything better to do,' she added of the barbs involving her family's wealth. 'But I would say, I think everyone on tour knows me really well, and obviously knows it's not easy. So I don't think there's a lack of respect there from anyone that I work with, at least.'

Pegula, left is seen with her family after her parents Terry (center) and Kim (right) bought the Buffalo Bills in 2014

Pegula advanced to the third round after defeating American Sofia Kenin on Thursday

That should be the case, as Pegula has carved out an impressive career and established herself as the second-highest ranked American woman behind Coco Gauff.

She's made it to the last eight of each Slam - but no further than that - as questions have naturally arisen about her ability to break through.

Pegula led 4-1 with a break point in the final set of last year's Wimbledon quarterfinal vs. Marketa Vondrousova before ultimately losing the match, and eventually changed coaches in February after exiting Queens in last year's round of 16.

In discussing the decision to part ways with ex-coach David Witt, she previously said that she was edging towards the 'ending of my career phase.'  Since that change, her year has been up and down as she was ousted from the second rounds of this year's Australian Open and Wimbledon, before she surged to the final in Cincinnati earlier this month.

Nonetheless, she seemed optimistic as she spoke from the Billie Jean King National Tennis Center - and is drawing inspiration from a male player seven years her senior.

'Seeing someone like Novak [Djokovic] play and still obviously be one of the best players in the game right now... at such a late age, definitely, I think you see people doing well [at] later ages, and that definitely helps you.

'Obviously turning 30, I'm not going backwards,' she continued. 'So I think it's just stepping into a new set of life and challenges and maturity, and just wanting to know that I gave myself time to maybe try some other things.'

Pegula has also gleaned motivation from the other end of the age spectrum.

She's spent extensive time playing doubles with and getting to know 20-year-old Gauff, and was pleased to see her claim her first Slam last summer in Queens.

Along with Gauff, the soon-to-be-retired Danielle Collins, Emma Navarro and Madison Keys, Pegula is one of five American women ranked in the top 20 right now. But she of course wants to be the next one to have their moment in the spotlight.

'I thought it was really nice last year watching her win that,' she said of Gauff. 'Obviously, I would love to win one too. But it definitely helps when you're playing with someone and practicing with someone, and then you see them do well. It's definitely motivating. 

Pegula and Coco Gauff have gotten to know each other as doubles partners, and the former said she was happy to see her fellow American win last year's US Open

Pegula cited Novak Djokovic, 37, as an inspiration as she enters a different phase of her career

'And I felt like that's something a lot of the American girls are doing right now. I mean, there's a lot of us, and we're all seeing each other do really well, and when you see that, it makes you feel like you can do the same things. So it's always motivating and inspiring to see.

Pegula has taken down two American players this tournament in Kenin and Shelby Rogers, and Spain's Jessica Bouzas Maneiro awaits in the third round on Saturday.

The specters of her previous quarterfinal shortcomings will of course loom the further she gets in this tournament but for now - after already achieving her best Slam finish this season - she's living in the present.

'I have to trust that if I keep putting myself in those situations, that I'll be able to get through,' she said.

'...Of course, I would love to get over the hump, but at the same time, I gotta get there first.'