Wimbledon champion Roger Federer believes his improved mental strength will help him overtake Andre Agassi as the new world number one this week.

The Swiss world number two saved seven match points in his 4-6 6-3 7-6 first round victory over Scott Draper at the Cincinnati Masters Series on Tuesday, moving him a step closer to topping the rankings.

He needs to reach the semi-finals here to overhaul Agassi, and says it will be a resolute mind as much as his technical gifts that will make his dream possible.

"One thing I have improved on is coming from behind to win," the 22-year-old, whose mental approach has often been suspect, told reporters.

"I think that's something you've got to be able to do when you're at the top.

"It can make a huge difference between losing in the first round or getting to the semis. It happened like this last week (at the Montreal Masters Series) and hopefully the same thing will happen this week."

Federer, who leads the Champions Race, was originally told he needed to win just one match here to become world number one.

But after the ATP Tour deliberated and reworked their calculations on rankings points, he was given a revised goal.

"That's alright with me...What can I do about it?," he said. "I'm just going to hang in there."

Judging by his performance against Australian Draper, he is becoming quite good at that.

Draper had four successive match points in the final set tiebreak, but still Federer would not leave quietly, eventually triumphing 12-10 in the thrilling breaker.

"Normally it should be over when you are down 6-2 in the tiebreak," he said.

"So I'm really happy I came through. I was pretty relaxed out there -- at 6-2 down you're relaxed. When you get back to 7-7 it's not so relaxing because you want to win."

Draper, world number 114, refused to blame himself after the two hour, two minute defeat.

"As John Newcombe would say, 'I kept asking the questions and he kept coming up with the goods'," the 29-year-old said.

"But I can hold my head high...it's got to be one of my most memorable matches. It's certainly in my top three or four.

"He's the next possible world number one, I'm getting to the end of my career, so it's great to have matches of that excitement."

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