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• ATP Finals: Alcaraz out as Ruud progresses with Rublev win

  Carlos Alcaraz was dumped out of the ATP Finals as Casper Ruud sank Andrey Rublev to reach the semi-finals of the Turin event on Friday.

  Following his defeat to Jannik Sinner earlier on Friday, Alcaraz could only advance by virtue of percentage of games won if Ruud was beaten in straight sets.

  However, Ruud dashed those hopes by taking an opening set in which he won 80% of his first-serve points (16/20) and did not give up a single break point.

  While Rublev fought back to level things up in the second set, Ruud came on strong in the third set, ultimately triumphing 6-4 5-7 6-2 in one hour and 45 minutes.

  Speaking after the match, Ruud said: "Tennis is interesting sometimes. I don't know what I am doing better this week than the past few weeks... the only thing is serving, I am serving really well.

  "It is tough to play the best players in the world but nice because you feel you are an underdog and can play free. You know if you don't bring your A level you will likely lose.

  "I knew coming into this match that a set was enough to qualify, so I was a bit nervous at the start. So when I got that first set I could breathe a little."

  Data Debrief: Career-best for Ruud

  Ruud's victory was his sixth over a top-10 opponent in ATP Tour-level events in 2024, surpassing his previous best in a single calendar year (five in 2022).

  With Sinner his next opponent in the semi-finals on Saturday, Ruud will hope to continue his impressive form against the best the sport has to offer.

• Swiatek and Raducanu help Poland, Great Britain advance at Billie Jean King Cup Finals

  Iga Swiatek and Emma Raducanu were both victorious as Poland and Great Britain won their first-round ties at the Billie Jean King Cup Finals on Friday.

  Poland won both of their singles matches against Spain in Malaga, while Britain did likewise versus Germany to seal their own spot in the competition's last eight. 

  World number two Swiatek clinched Poland's progress with a 6-3 6-7 (6-8) 6-1 victory over Paula Badosa, after Magda Linette had put them ahead by beating Sara Sorribes Tormo in a gruelling three-hour, 51-minute affair.

  Speaking after her own win, Swiatek hailed the endurance of team-mate Linette, who triumphed 7-6 (8-6) 2-6 6-4.

  "I wouldn't say that I pushed us to the quarter-finals, because Magda pushed us to the quarter-finals, so we did it together," the five-time grand slam champion said.

  "I'm glad that we won a match as Team Poland. I felt like it was my best match since the US Open. I knew that I could come back in the third set and try to win it for Poland."

  Later on Friday, Great Britain were propelled to victory by Raducanu and Katie Boulter, both of whom were straight-sets victors.

  Raducanu, playing her first match in almost two months after recovering from a foot injury, beat Jule Niemeier 6-4 6-4.

  The 2021 US Open champion started well and her effective serve was a key feature of the opening set, though she later required six match points to get over the line as Niemeier refused to go down without a fight.

  Britain will face defending champions Canada in the last eight after Boulter raced to an impressive 6-1 6-2 victory over Laura Siegemund, ensuring there was no need for Olivia Nicholls and Heather Watson to team up for a deciding doubles match.

• 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).