He lost on Sunday in his opener to Roger Federer.
With Novak Djokovic and Andy Murray sidelined through injury, Federer is the only genuine star left in London and is the clear favorite to lift his seventh year-end title at the grand old age of 36.
The United States has been waiting 10 years for a win at the ATP Finals, few thought Jack Sock would be the man to deliver it.
With these two powerful customers desperate to keep their hopes alive after losing their opening matches, it was the American, in his debut finals, who held his nerve best in the decisive tiebreak after a compelling 2 hours 27 minutes contest.
Cilic, who won the 2014 U.S. Open, broke the American twice to win the first set but found himself adrift in the second as Sock levelled the round-robin match with two breaks of his own. I'm relieved that in the last match I can play freely against Cilic.
Sock, a partying pal of Nick Kyrgios but possibly more focused, said on his arrival from Bercy, where he had to win the tournament to qualify, "I'm playing with the house's money".
Trust in raw talent is no guarantee of victory in any sport, and it was tested to snapping point when Roger Federer survived a serious examination of his pedigree to advance to the semi-finals of the ATP World Tour Finals, while Jack Sock also stayed in the race.
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But Zverev is setting tongues wagging after an impressive year in which he has won five tournaments, and Federer was forced to repel three break points against the German as early as the opening game.
"It was a tough one for sure", Sock said after defeating Cilic for the third time without a defeat in their series. I'm very excited for his future.
"I'm not the type of guy that will just enter a draw and be happy to make the third round or the quarters or whatever".
"It's been an interesting morning so far, the fire alarm went off at 4am and we had to exit the building".
Sock was 3-0 down in the final set and looked exhausted and ragged for much of the match, but his touch, improvisation and fight didn't desert him.
With Cilic a 4-3 and a minibreak up, Sock produced the shot of the match as he sprinted forward to retrieve another near-dead net cord and didn't look back from there, winning the next three points to secure the match.