Ever since he reached the final of the Wimbledon Boys' event in 2018 at the age of 16, there have been high expectations around Draper.
Andy Murray - who became the first British man to win Wimbledon in 77 years back in 2013 - had undergone significant hip surgery at the start of 2018, and his decline as one of the world's best players was apparent.
Seven years later, Draper has stepped up to take the mantle of British tennis' great hope, much like Murray did when Tim Henman bowed out around two decades ago. And while he has the three-time Grand Slam champion to thank for ending that drought and easing some of the pressure, all eyes remain firmly glued on him as Wimbledon fast approaches.
Now this is the difficult part. British fandom and the media hold no prisoners. He will face a different type of pressure as he carries the weight of a nation on his back, regardless of how realistic his actual chances are of winning Wimbledon this year.
There is little doubt that Draper will, at some point in his life, probably be in a Wimbledon final. Alexander Bublik described his build like a UFC fighter, and his big-serving, big-hitting game, coupled with the fact that he is left-handed, is perfectly suited to the grass.
He has demonstrated his ability to battle with the best this year, beating Carlos Alcaraz, Taylor Fritz, Holger Rune and Lorenzo Musetti, to name just a few.
But the fact of the matter is, Draper's rise has been so rapid and so impressive that it is easy to forget that he has never been past the second round at Wimbledon before, and has just two wins in three visits.
He fell in the second round at the hands of a more experienced Brit, Cameron Norrie, last year, when all the hype was around Draper. He couldn't handle the occasion.
When he reached the US Open semi-final last season, he made headlines for the wrong reasons as he vomited several times at the back of the court against Jannik Sinner from the stress of the occasion (as well as the heat), showcasing that he is still a relative rookie at Grand Slam level.
Draper is a better player than he was back then, and he is learning how to manage his emotions and keep his composure during crunch time far better. But he hasn't suddenly garnered tonnes more experience.
He has also been handed an utterly nightmarish draw. The in-form and at times unplayable Bublik - who beat him recently at the French Open - is a potential third-round opponent, while breakout star Jakub Mensik could be lurking in the last 16.
Should he pass those two tests, a certain Novak Djokovic could await.
So as good as Draper is and as good as he can become, realistically, it is very unlikely that he will go from a best of the second round all the way to lifting the trophy at the end of the fortnight. Getting to the quarter-finals would be an immense achievement.
But that won't matter to those watching in the stadiums and at home on their sofas. Imagine he reaches the second week. He will be on the front and back pages of every newspaper in the country (does anyone even read them anymore?).
What makes Draper an even more captivating figure for the fans is the fact that he is a Londoner. While Murray was adored by the home faithful in the end, many weren't as warm to him at the very start. The Scot also made a few enemies when he once stated that he wanted 'anyone but England' to win the 2006 World Cup.
That certainly won't be the case for Draper. No one will feel torn over their support of him, and he won't have to worry about feeling like an outsider.
But he is excited as he enters the pressure cooker of Wimbledon's centre court.
Speaking after beating Holger Rune at the Hurlingham Club exhibition tournament this week, he said: "It's going to be a privilege to play as the British number one, that's what I've always wanted. I've wanted to make Centre Court my environment.
"I'm full of excitement knowing the crowd is right behind me, that I'm going to be playing on the courts I wanted to play on since I was young, watching Andy Murray, watching all these great players. It's sinking in that I'm there now: I've got the chance to show people what I can do."
Murray - who is a close friend of Draper - is also confident that he can deal with expectations.
“He has obviously shot up the rankings and had some amazing wins. It will obviously be a little bit different this year coming in as a top seed but he’ll deal with it well. He’s played in difficult environments and under pressure before, and I’m sure he’ll cope with it well," Murray stated this week.
Often, playing in front of your home crowd can be more help than hindrance. Draper has experienced that just this year, when he was taken to five sets by Thanasi Kokkinakis and Aleksandar Vukic at the Australian Open, as well as coming up against Gael Monfils and the French crowd at Roland Garros. So he will now have the opportunity to use that to his advantage.
This is something else he will have to channel from Murray. After his loss to Roger Federer in the 2012 final, an emotional Murray said: “Everybody always talks about the pressure of playing at Wimbledon, how tough it is, but the people watching make it so much easier to play."
How he deals with the limelight is going to be one of the most captivating storylines of Wimbledon, even if the local expectations will be unfair. But as he continues his rise to the top of men's tennis, it is something that he absolutely must learn to deal with.
Jack Draper: Welcome to the soap opera of British sport.