Sampras is obsessed with finishing the year at No. 1 for a record sixth consecutive time.
But between the mild-mannered American and his dream stands the Chilean once called the most hated man in tennis by Sports Illustrated.
"What other people think about me or say of me simply does not interest me," said Rios, who will end 1998 in front if he fares better than Sampras at this week's ATP Tour world championship. "I just go my own way."
The 22-year-old has had an outstanding season, becoming the first South American tennis player to top the men's rankings.
Rios held the No. 1 spot for two brief periods and he liked it.
"To prove wrong all the experts who had said a guy like me could not be the No. 1 was a great satisfaction," he said.
Before the Hanover event for the top eight players starting on Tuesday, Rios is in second place a mere 33 points behind Sampras, which makes the situation quite simple.
If he goes further than his rival in the tournament, the Chilean will return home as the world No. 1.
Obviously, the perfect scenario would be a final between Sampras and Rios with the top ranking as a reward for the winner.
Oddly enough, the two have not played each other for more than four years.
Their last match ws at the 1994 French Open. Sampras won it 7-6 7-6 6-4.
"It's pretty odd that we have not played in such a long time," said Sampras. "But we're No. 1 and two in the world and you only play in the finals. It's not easy to get there."
Living up to his reputation, Rios blasted the ATP Tour officials just before making the trip to the northern German city for the grand finale.
"They drill us as if we were in the army," he told German weekly Stern in an interview released on Thursday.
"If somebody breaks his racquet in anger, then a punishment machine is set in motion," he added. "That way, people are reduced to bloodless creatures."
Rios said competitive tennis was not exactly a friendly game.
"If somebody says he's got good friends on the circuit, that's nonsense," he said. "In this business it's like wild animals in a cage. It's every man for himself."
But the hot-blooded Chilean, who is consistently given the "Prix Citron" (Lemon Award) by journalists at the French Open for being the sourest player on the circuit, says he feels his behaviour has improved.
"In the last few months I got better," he said. "Maybe next year somebody else will get the prize."
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