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• ATP Finals: Perfect Zverev downs Alcaraz to reach semi-finals

  Alexander Zverev has booked his place in the ATP Finals semi-finals with a straight-sets win over Carlos Alcaraz, who is now facing elimination.

  The German secured the year-end number two spot in the ATP rankings after triumphing 7-6 (7-5) 6-4 in just under two hours to set up a meeting with Taylor Fritz in the final four.

  Zverev has now won each of his last eight matches and topped the John Newcombe Group but had to work hard for it, with Alcaraz successfully defending a set point to force a tie-break.

  The Spaniard struggled to match the pace in the second set though, losing his serve in the opening game, giving Zverev the control he needed to register his sixth career win against Alcaraz.

  Zverev avenged his French Open final loss to Alcaraz earlier this year, racking up his 69th win of 2024 in the process, but played down talk he is playing the best tennis of his life.

  "You guys need to relax a little bit," he said. "It has been three fantastic matches. I'm happy to be 3-0 in the group for sure, but the semi-finals now are going to be very difficult - no matter who I am against.

  "Taylor beat me the last few times we've played at the slams, but I'm looking forward to that match.

  "Carlos has beaten me too many times this year in important matches, so I'm happy I got this one. We have a pretty good rivalry, but a great friendship as well. It's always great to share the court with him."

  Alcaraz's chances of qualifying for the final four are slim, but he could progress based on the percentage of games won if Andrey Rublev beats Casper Ruud in straight sets later on Friday.

  Data Debrief: Out in front

  Zverev is looking to cap 2024 on a high by continuing his impressive run, and he is the first player to register 69+ wins in a single season since Andy Murray (78) in 2016.

  Since he made his first semi-final at the ATP Finals in 2018, only Novak Djokovic (five) has reached the semis of this event more often than the German (four).

• ATP Finals: Sinner completes perfect group stage with Medvedev win

  Jannik Sinner made it three wins from as many matches at the ATP Finals with a routine victory over Daniil Medvedev in his final group-stage outing.

  Sinner topped the Ilie Nastase Group and reached the last four with a perfect 3-0 record for the second season in a row, beating Medvedev 6-3 6-4 in 75 minutes.

  After a late break saw Sinner take the first set, Medvedev threatened a fightback by reeling off three straight games in the second, only to immediately concede another break.

  Speaking after the win, his eighth in 15 all-time meetings with Medvedev, Sinner credited his opponent for posing a tactical challenge.

  "I'm trying to find new ways to improve as a player," Sinner said. "I'm trying to win as many matches here as I can. Me and Daniil, we know each other very well. 

  "So, every time we step on court, we try to change something tactically. I felt like I was ready to see what he was going to do today.

  "I know what I have achieved during this year, so I try to step on court with a good mindset. I have beautiful people around me who support me daily, which for me is really important."

  Data Debrief: Sinner targeting exclusive club

  Sinner's victory ensured smooth passage to the next round, as he bids to replicate the achievements of Roger Federer and Novak Djokovic, the only previous players to win the Australian Open, US Open and ATP Finals in the same season.

  The win – Sinner's ninth in a row – saw him draw level with Alexander Zverev for the most victories on the ATP Tour this year, with 68. They are the first duo to both record at least 50 in a single year since Djokovic (82) and Andy Murray (51) in 2015.

• ATP Finals: Comeback win keeps Fritz in semi-final contention

  Taylor Fritz has put himself in a strong position to make it to the ATP Finals semis after a comeback win against Alex de Minaur.

  Fritz rallied in three sets to triumph 5-7 6-4 6-3 in just over two hours, sealing De Minaur's fate, as he crashed out having failed to win a match.

  The Australian made a strong start as he attempted to overturn the odds to reach the semi-finals in his maiden tournament and took control with a break late on, winning the final three games of the first set to take an early advantage.

  Fritz fought back, protecting his serve in the opening game before finding his edge late on, and though De Minaur valiantly defended two set points, he could not prevent a decider.

  The American eased into cruise control after that, taking a 4-1 lead with a three-game winning streak, from which he did not look back.

  "Even though I won the match I feel like there wasn't necessarily any moments when I changed too much," Fritz said.

  "He was all over me when I did a great job, but towards the end of the second set, I began to find my serve and I started serving much better.

  "When I wasn't creating the first serves, he was just killing me from the baseline. It just gave me a little bit of comfort to just stay in the match and not be under so much pressure all the time. It was still incredibly tough."

  His attention now turns to the late match in the Ilie Nastase Group between Jannik Sinner, who has already progressed to the final four, and Daniil Medvedev. The Russian must win in straight sets to progress, but if he drops a set or loses, Fritz will advance along with the world number one. 

  Data Debrief: On the brink

  Any further involvement at the ATP Finals for Fritz may hinge on favours from elsewhere, but he worked hard on Thursday to put himself within touching distance of the semi-finals for the second time.

  He struggled against the big serves of De Minaur, whose aggressive approach saw him outhit Fritz with 12 winners to seven, though he could not translate it into a win.

  It means that Fritz (nine) is the first American player to register 9+ wins against top-10 opponents in a single season since Pete Sampras (10) and Andre Agassi (12) in 1999.