Thiem beat Kei Nishikori 6-1, 6-4 to keep alive his slim hopes of reaching the semi-finals but will need Kevin Anderson to beat Federer, and convincingly so. If the Swiss wins a set he is through, otherwise he needs to win five games if neither set ends 7-5 or six if one does.
The 37-year-old not winning the games he requires would appear to be an unlikely scenario and Thiem, who lost his first two matches to Anderson and Federer, admitted he did not believe he deserved to finish in the top two.
“I mean, I messed it up the two previous matches myself,” he said. “I didn't really think about it also today in the match. I wanted to play well again. That's what I did part of times today in the match.
“You never know what happens tonight, but I don't think it's going to happen.
“I'm not sure if I'm going to watch it. No, I will watch it because it's a good match in general.
“To be honest, I'm not hoping for it because it's not very realistic. I think both of these two players really deserve to go up. That's how it's going to be at the end.”
Thiem’s convincing victory ended a bruising 48 hours for Nishikori, who had beaten Federer on the opening night at the O2 but won just six of 30 games and went within a single game of a double bagel against Anderson on Tuesday.
“I was the same in the last match, too, but there were too many unforced errors for me,” Nishikori conceded. “I think I made it really easy today.”