Frances Tiafoe and Taylor Fritz have both had breakthrough seasons on the ATP World Tour in 2018, qualifying for the prestigious Next Gen ATP Finals. They are also on track to finish the year inside the Top 50 of the ATP Rankings for the first time. The last time two Americans aged 21 and under have done that came 15 years ago, when Andy Roddick, Mardy Fish and Tiafoe’s coach, Robby Ginepri, accomplished the feat.

That’s a massive achievement, and for more than the reason you’d expect.

“When I was 14, 15, if you would’ve asked me if Taylor would play tennis, I would not have believed it,” Tiafoe joked.

To an extent, even Fritz thought along the same lines. Tiafoe lost just three games against Fritz in a junior final in Tulsa, Oklahoma five years ago, after all. Fritz, the son of Kathy May Fritz, who reached the Top 10 in the world, went to regular high school in California at first.

“I always thought I was probably much better than I actually was when I was at that age, like, 14, 15 years old,” Fritz said.

Then he moved to Florida to train at a USTA facility. And that’s when he saw that there were players his age who could not only match him, but beat him.

“That’s when I realised that, wow, if I actually wanted to be a pro, I’m going to have to be better than those guys. And so I really went to work, and I had those guys to build off,” Fritz said. “I just worked really, really hard. And, they will all tell you Tommy [Paul], Reilly [Opelka], [Stefan] Kozlov, Frances, I wasn’t even close to being in the same league as those guys.

“It’s crazy, I guess, looking back now at where I am now and all the things I expect of myself now, and back then it seemed so far. All of this that I’m doing right now just seemed impossible.”

In a way, Tiafoe’s rise was not all that likely, either. The story has been told plenty — growing up in Maryland, Tiafoe spent much of his time at the Junior Tennis Champions Center in College Park, where his father was a janitor. He’d wander the facility as a young boy, watching players train while trying to understand their coach’s tips, then going to hit against the wall daily to try to learn the sport.

And now, Tiafoe is someone who other kids are looking up to. The 20-year-old became the youngest American ATP World Tour champion in more than a decade earlier this year at the Delray Beach Open.

Tiafoe’s coach, Ginepri, has been in his shoes, and in a sense, has been where his charge wants to be, climbing as high as No. 15 in the ATP Rankings and lifting three tour-level titles.

“It kind of comes back full circle in a way. I try to coach Frances with a lot of experiences from when I played, the do’s and the don’ts. But it’s just been a lot of fun working with him,” Ginepri said. “He comes every day with a smile on his face and works pretty hard, so he’s been improving. It’s been a great year for him. He’s the second-youngest after Andy [Roddick] to win his first title, in Delray. So it’s a good shadow to follow. He’s got a big upside career in front of him if he keeps putting in the work.”

And Ginepri also knows what it feels like to be moving towards the top of the game with other compatriots. Roddick finished that 2003 season World No. 1, and Fish would eventually reach the Top 10, too. They pushed each other to greater heights.

“Frances kind of pulled out in front of Taylor a little bit this year, but Taylor’s right behind,” Ginepri said of the pair, as the friends are now separated by just seven spots. “He’s had some injuries, some setbacks, but his game’s just as good as Frances’ so they’re going to be neck and neck and hopefully we’ll get a few more Americans up there.”

Last year, for instance, Jared Donaldson qualified for the Next Gen ATP Finals. There are currently eight Americans 23 and under inside the Top 200 of the ATP Rankings. And they’re all pushing each other forward.

And it hasn’t always been easy. Fritz, currently at a career-best World No. 47, climbed as high as No. 53 in 2016, when he was named the ATP Star of Tomorrow presented by Emirates. Injuries then slowed his progress and forced him outside the Top 100 before building back up again.

Fritz’s coach, David Nainkin, says that inevitably, friends know how one another is performing. And when one does well, the other sees that.

“It’s great to see Frances break out and win an [ATP World Tour] 250 in Delray,” Nainkin said. “They’re definitely great friends, but great rivals. They want to see each other do better, which will certainly push them.”

While Tiafoe is in Group A and Fritz is in Group B in Milan, both still have opportunities to reach the semi-finals, as they each hold a 1-1 record in round-robin play. And while the Americans hope to fly their flag high the rest of the week at the Fiera Milano, they know that there is still more to come for them in the future.

“Hopefully me and Taylor don’t get complacent,” Tiafoe said. “I think there’s way more me and him can do. I’m going to be pushing him.”

Alex de Minaur became the second player to guarantee his spot in the last four of the Next Gen ATP Finals on Wednesday, defeating 2017 finalist Andrey Rublev 4-1, 3-4(5), 4-1, 4-2.

“It was great. I knew coming in it was going to be a really tough match and I was going to have to play some really good tennis and not leave too many balls short because his forehand is seriously one of the most dangerous weapons out there on the Tour,” De Minaur said. “I’m really happy with my win. I thought I executed my gameplan really well and served really well.”

De Minaur came out swinging, losing just three service points in the first set. And despite a hiccup in the second-set tie-break, the Aussie was broken just once in the match, while he broke the Russian four times to earn a berth in the semi-finals.

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“It’s not over yet. Every match counts,” De Minaur said. “I’m very happy with my win today and it’s been a great year, but tomorrow’s another day and you’ve got to get back out there and keep doing the same.”

De Minaur, who is at a career-best No. 31 in the ATP Rankings, is the second seed here in Milan. And he will look to complete round-robin play undefeated on Thursday evening when he plays fourth seed Taylor Fritz. The pair has not faced off in a FedEx ATP Head2Head match, but De Minaur defeated Fritz earlier this year at an ATP Challenger Tour event in Surbiton.

While Rublev, the 2017 Umag champion, will be disappointed, he is 1-1 in Group B play. The fifth seed beat Fritz in a five-set thriller on Tuesday, and he will try to earn his second win at the Fiera Milano this year when he clashes against home favourite Liam Caruana.

Stefanos Tsitsipas came in as the favourite at the Next Gen ATP Finals, competing as the top seed. And the Greek showed why on Wednesday, beating third-seeded Frances Tiafoe 4-3((3), 4-3(5), 4-2 to become the first player to guarantee his spot in the Milan semi-finals.

“I never dropped my performance, I always stayed at 100 per cent almost, so [I am] very satisfied that I managed to stay calm and play every point like a match point,” Tsitsipas said. “Hopefully I can play like this in every match that I’ll be playing here at the Next Gen ATP Finals.”

One year ago, Tsitsipas was an alternate at this event. And after two impressive performances against strong Group A opponents, the 21-year-old knows he will have a chance to play for a spot in the championship match. But first, on Thursday, Tsitsipas will have an opportunity to go undefeated in round-robin play when he faces Polish No. 1 Hubert Hurkacz.

There will be plenty at stake in that duel, as undefeated champions at the Fiera Milano receive $407,000. Tsitsipas has never played Hurkacz in a professional match.

The Greek will be the favourite in that clash based off his performance against Tiafoe, this year’s Delray Beach Open champion. It was the pair’s first FedEx ATP Head2Head meeting, but Tsitsipas also defeated Tiafoe last year in Tokyo qualifying, winning that match in straight sets as well. The Greek won 78 per cent of his service points on Next Gen Arena, saving both break points he faced en route to a 70-minute victory.

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In the first two sets, there was nearly nothing between the two players. In fact, before the tie-breaks, Tiafoe had won more points than Tsitsipas. But the recent Intrum Stockholm Open titlist got out to early leads on both occasions and did well on his serve to keep Tiafoe from sneaking back into the match.

“I believe having a good start in a tie-break, having a lead with a mini-break, maybe, helps a lot. When you can just stay more focused and calm on what you’re doing — it’s tough when you’re close in the score — so I try to focus when I get a good lead at the beginning and be aggressive. That’s the most important thing.”

After the second set, Tiafoe utlised one of the tournament’s innovations, speaking to coach Robby Ginepri via their headsets. And his fellow American tried to encourage Tiafoe to sneak forward when possible and control play.

“Keep this guy on the run,” Ginepri said. ”It’s good level, [you’ve] just got to execute in the tie-breaks a little better. Hey, keep your swag out there, don’t get down. This is a long match right now. You’ve got it. Let’s go.”

But Tsitsipas’ offensive pressure proved too much, playing aggressively off the forehand wing. And after earning the only break of the match, the top seed held out for the triumph.

If logic determined the outcome of tennis matches, Marin Cilic would have an outstanding record at the Nitto ATP Finals. The Croatian loves playing in Britain, thrives on indoor hard courts and has a habit of winning titles in the latter stages of the season. In other words, the season finale should be right up Cilic’s street.

The glorious unpredictability of sport is underlined by Cilic’s surprisingly modest record here at The O2. In his three previous visits to the Greenwich Peninsula he had just one win to show from his nine matches. His lone victory, over Kei Nishikori two years ago, was in a concluding group match when he already knew he had no chance of qualifying for the semi‑finals.

But Cilic is too experienced a campaigner to allow a quirk of form like that to put him in a negative frame of mind. He has enjoyed an outstanding season on the ATP World Tour, finding the year-round consistency that has sometimes eluded him in the past. One of his season highlights was reaching the final of the Australian Open, while another was winning the Fever-Tree Championships at The Queen’s Club in London, extending to 11 his run of successive years in which he has landed at least one ATP World Tour title.

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Over the course of his career, London has been a particularly productive city for Cilic, who has reached the final at The Queen’s Club four times and won the title there twice, with his first victory in west London coming in 2012. Grass clearly suits his game, as he demonstrated in the summer of 2017 by reaching the Wimbledon final, only to suffer a painful foot blister that contributed significantly to his straight-sets defeat to Roger Federer.

Capable of adapting his game to any surface, Cilic is among an elite group of players who have gathered titles on grass, hard and clay courts. But it is on indoor hard courts that he has prospered; eight of his 18 career titles have come on that surface. He is a four-time champion in the Croatian capital of Zagreb and has also won in Moscow twice, as well as once each in St. Petersburg and Basel. The latter four tournaments were all won in the period between the US Open and the end of the season, making his lack of success here all the more puzzling.

Although all three of his defeats at last year’s Nitto ATP Finals were close – he won a set against Alexander Zverev, Jack Sock and Federer – Cilic thinks he may have paid the price for a heavy workload in the closing weeks of the season. He arrived in London having made the semi-finals in Tokyo, Shanghai and Basel and the quarter-finals in Paris. “Last year when I came to London, I felt just a little bit drained,” Cilic has said. “Even though I played well at the end of the year, I had a lot of matches and it just took a little bit of extra energy out of me. Mentally, as well, it was difficult to sustain that over and over again.”

Cilic hopes to have learned from last year and went into the closing weeks of this season with plans to reduce the length of his practice sessions, the idea being they are shorter but more intensive. “I think you just have to focus day by day, obviously listen to your body as much as you can with your team to work and to balance the training,” said Cilic, who will lead Croatia in next week’s Davis Cup final against France in Lille.

Cilic came flying out of the blocks this year, reaching his third Grand Slam final at January’s Australian Open, only to lose to Federer once more after five hard-fought sets. After a quiet period his results again picked up on clay with runs to the quarter-finals of his home ATP World Tour Masters 1000 tournament in Monte-Carlo, the semi-finals of the Masters 1000 in Rome and the quarter-finals at Roland Garros.

That form continued at The Queen’s Club, where he defeated Djokovic in the final, but he then suffered his earliest Wimbledon defeat for seven years when he was beaten by Argentina’s Guido Pella in the second round. It was the first time since 2011 that he had lost to someone other than Federer, Djokovic or Andy Murray at the All England Club. After Wimbledon, Cilic went out to Rafael Nadal in the Toronto quarter-finals and to Djokovic in the Cincinnati semi-finals before losing a four-hour marathon against Nishikori in the last eight at the US Open.

While Cilic turned 30 in September, he is the youngest active man to have won a Grand Slam singles title, by virtue of his success at the 2014 US Open. Although he might have won many more majors and titles on the ATP World Tour had he been in a different era, Cilic believes competing against the likes of Federer, Nadal and Djokovic has made him a better player. “I feel they are pushing me to be a little bit better, day after day, match after match,” he has said. “I think we are all trying our best, pushing ourselves. Even the top guys, Roger and Rafa, they are setting an example, as well as Novak, who has come back and is playing well. I think there is a big group of players now that are very eager to win, very motivated.”