The 104-year-old race is still reeling from the ouster of former overall leader Michael Rasmussen, who left a pack of dispirited riders heading toward Paris, burdened by the latest jolt to the sport.
Not Contador and Evans.
The two riders, each going for a first victory in this event, realize the 35-mile race against the clock could decide the winner.
"In this time trial, everything can change - my entire life can change," Contador said.
Added Evans: "We will know all the answers out on the road tomorrow."
Contador has a time cushion and in Discovery Channel sporting director Johan Bruyneel, a cool head who helped Lance Armstrong to seven straight Tour wins.
The odds are heavily in Contador's favor, and Predictor-Lotto sporting director Hendrik Redant knows it.
"I saw him (Contador) this morning by the bus, and he seemed to be quite nervous," Redant said. "He is not allowed to fail now. He can only win. So for a young guy ... he has to stay calm. He's now the favorite."
The 24-year-old Contador would be the Tour's youngest winner since Jan Ullrich in 1997.
"Tomorrow is the most difficult day of my career as an athlete," Contador said after Friday's 18th stage, which was won by Sandy Casar.
Redant stepped up the mind games further.
"It's a big gap (1:50), but if you lose that you have a really big failure," Redant said. "He's a young guy, and it would be fine for cycling if a young guy like that can win the Tour. But it's a lot of stress ... and for him I hope he can cope with it. I know Cadel is very relaxed, he's very confident, and that's a big advantage of course."
Bruyneel turned the tables on Evans.
"Evans has to have a great day, and things would have to go really badly for Contador," Bruyneel said. "The best will win."