The Swiss star has triumphed at the season ending event, which features the top eight men’s players, on six previous occasions.

He looked untroubled during the opening set of his first group match against Sock at the O2 Arena.

The 36-year-old, who missed last year’s tournament through injury, broke Sock immediately in the tie.

Federer held serve with ease to take the opener 6-4 against Sock, who qualified for the event by winning the Paris Masters earlier this month.

The American held his nerve in the second set as he fought off five break points to set up a tie-break.

Sock had failed to put Federer’s serve under much duress throughout the encounter, which ultimately told as the Swiss star won the tie break to secure a 6-4, 7-6 victory.

"I got off to a great start, my big hope was I was going to be able to play a bit more freely after that,” said Federer, following his 50^th win of the season.

“The second set was tight, I missed some opportunities, the breaker could have gone either way and in the end he helped me with some double faults and some mistakes.

"I’m really happy that I got through somehow."

Germany’s Alexander Zverev beat Marin Cilic later in the second match in Group B, which has been named the Boris Becker Group in honour of the German player.

Zverev claimed the opening set 6-4, but was unable to stop his Croatia rival taking the second 6-3.

With the momentum, it appeared Cilic would take the victory as he broke for a 3-1 lead in the decider.

Zverev stormed back to win five of the final six games to win 6-4, 3-6, 6-4.

The Pete Sampras Group will begin tomorrow, with Austria’s Dominic Thiem set to meet Bulgaria’s Grigor Dmitrov.

Belgium’s David Goffin will then face Spain’s Rafael Nadal.

Nadal was presented a trophy today after ending the year as world number one.

There are doubts over his fitness before the tournament, with the Spaniard admitting his preparations were “not perfect” due to a knee injury.