In the second game is no chance at Anderson was gone - Federer on his serve with the first ball won 92% of his hands, and two breaks brought him out of the group from the first place (6:4, 6:3).
"I'm very happy, the first match with Kei was tough and I never got going, but with my back against the wall maybe it's easier for me to play", said Federer. I fought hard, spoke a lot with my team to come up with a good game plan against Dominic [Thiem] and Kevin also today.
Six-time champion Roger Federer put a troubled start to his 16th ATP Finals behind him as he outclassed Dominic Thiem 6-2 6-3 on Tuesday to stay on course for the knockout stage.
Federer sealed his 20th major title after beating Marin Cilic - but only after the roof of Rod Laver Arena was shut before play commenced, despite the temperature being below the 40-degree mark needed to trigger its closure based on the tournament's heat rule.
The second set went with serve until the seventh game, when Federer produced an immaculate sliced backhand that landed on the line to earn a break.
The Swiss broke the giant South African's serve four times in a comprehensive 6-4, 6-3 victory at London's O2 Arena even though Anderson had not faced a single break point in his two earlier round-robin victories.
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"But I always wanted to go out with a bang, win the match and if I go through, great".
Four months ago, the two men played out a dramatic quarterfinal at Wimbledon, Anderson saving a match point after less than two hours and going on to win a 13-11 final set against the defending champion. I'm happy it all worked out.
Federer will now play the runner-up of Group Gustavo Kuerten, with Anderson taking on the victor. "He deserved that win at Wimbledon but hopefully I'll get my revenge", Federer said of his Anderson rematch.
"There were too many unforced errors for me".
Roger Federer insists he isn't thinking about the opportunity of winning his 100th career title after he progressed to the semi-finals of the ATP Finals in London. Federer held steady until 3-3 in the first set when Anderson played an unusually poor service game, allowing him to break to the delight of another huge midweek crowd by the Thames.
With this win, Federer will head into the next stage from the first place in Lleyton Hewitt group, and his opponent might be Novak Djokovic, who is now first in the Gustavo Kuerten group.
Federer was more concerned with the way he rediscovered his form to convincingly beat Thiem, admitting his head had not been right in a straight sets defeat by Nishikori.