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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).

• Kyrgios confirms return to competitive tennis in Brisbane

  Nick Kyrgios confirmed he is returning to competitive tennis at the Brisbane International at the end of December.

  The Australian announced in October that he was planning to return at the World Tennis League event in Abu Dhabi.

  Kyrgios has played just one ATP Tour singles match in the last two years, having suffered with wrist, knee and foot injuries that have kept him off the court.

  That lone outing came in Stuttgart in June 2023, where he suffered a straight-sets defeat to Wu Yibing.

  "Honestly, this is probably the best I've felt in two years," Kyrgios told Australian television channel 9News.

  "I played that amazing year in 2022. Then, at the finals in Wimbledon and the US Open, that's when I started feeling some issues in my wrist. I had that wrist reconstruction, and now I'm feeling amazing.

  "It was a 15% miracle chance that I was going to get back to playing at this level and here we are.

  "To get back out there in front of the home fans is going to be sick."

  Kyrgios previously won the Brisbane International in 2018 and will be making his fourth appearance at the tournament as he steps up his preparation for the Australian Open.

  He previously said he was aiming for a grand slam title when he returns, having lost his only previous such final to Novak Djokovic at Wimbledon in 2022.

  "I am feeling fit and healthy, and I am excited for my return to tennis following some time out of the sport," Kyrgios added.

• 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.