Federer said: "I feel like these streaks just happen".
But Anderson, playing in his first Wimbledon quarter-final, finally made the 20-time Grand Slam champion look human.
Roger Federer's hopes of a ninth Wimbledon title bit the dust as South African Kevin Anderson recovered from two sets down to win a quarter-final cliffhanger 2-6 6-7 (5) 7-5 6-4 13-11 on a tension-filled Court One on Wednesday.
"I'm ecstatic. That's what you work so hard for". "I nearly could have". Anderson held for 5-all, broke to 6-5 with a violent return victor off a 97 miles per hour second serve, then staved off three break points and closed the set with a 133 miles per hour ace.
The comeback was just beginning.
"I had my chances", Federer said, "so it's disappointing".More news: Harold Varner III tied for lead at the Greenbriar
Djokovic wrested back the momentum for good after coming from 0-40 down at 2-2 in the third set to hold serve, and then breaking his Japanese opponent in the next game.
The World Cup showpiece will take place on Sunday at 18:00 (local time), which is 16:00 BST, meaning it is likely to kick off during the men's grass-court final, which eight-time champion Federer is a heavy favourite to be a part of. But there was more. So much more. Federer was attempting to reach his 13th semifinal at Wimbledon and move closer to title No. 9, both of which would have broken his own records.
While Anderson is known for his booming serve, it's Federer's serve that has proved impenetrable at this year's Championships - the Swiss is yet to drop serve and has held in his past 81 service games, dating back to the first set of his semi-final against Czech Tomas Berdych last year. Only my second time out on Centre Court.
"I'm not quite sure what to say, I had to try my best to keep fighting", Anderson told the BBC. "That's the worst feeling you can have as a tennis player".
Nishikori, who had won only two matches in 15 meetings with the 12-time major victor, broke for 1-0 in the fourth but was broken straight back. The South African saved three break points before taking the set 7-5. But have you seen him play a classic cricketing shot?
Novak Djokovic wasn't definitely happy about having to play on No. 1 Court as third and last match of the day on Monday.More news: Theresa May presses on with Brexit plan after high-profile resignations
The 32-year-old, who reached last year's U.S. Open final, will face either Milos Raonic or John Isner in the semis. That earned a code violation from chair umpire Carlos Ramos.
"I think the first warning was unnecessary", said Djokovic, who was sanctioned in the second set for spearing his racquet into the court.
That didn't seem to affect his focus, though, and neither did a time violation he was given when serving at 4-2, 30-30 in the fourth set.
However, his attention is now on Wimbledon, where the world number one has reached the quarter-finals and will take on Juan Martin del Potro on Wednesday.
"I'm a big player, big serve".More news: Centre’s change in stance on Section 377 of IPC
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