Nick Bollettieri: Veteran's mental reserves will test Federer's control

Andre Agassi's incredible win over Joachim Johansson yesterday not only set up a mouth-watering quarter-final against Roger Federer but reminded us again of Andre's formidable mind.

Andre Agassi's incredible win over Joachim Johansson yesterday not only set up a mouth-watering quarter-final against Roger Federer but reminded us again of Andre's formidable mind.

He was blitzed by the biggest missiles in the tennis world - Joachim hit 51 aces, a world record - and Andre was on the wrong end of 96 Swedish winners. All but a very few players would quickly have waved a white flag at that kind of barrage and gone off for a quiet lie-down in a darkened room.

Not Andre, who proved that mental resilience can make all the difference between success and failure. He convinced himself that if he hung in there long enough, he'd find his opening. He did. It was particularly impressive that his crucial breaks of serve in the fourth set - after three tie-break sets of no breaks - came after Joachim had broken him. The brain was mightier than the bomb.

Talking of mind power, here are five questions with cerebral themes that are crying out for answers as the tournament enters the second week.

Federer v Agassi: Who will win?

It's the dream match for the fans and TV companies, and the stakes couldn't be higher. Andre turns 35 in April and if he loses, it could be his last-ever match at the Australian Open, a tournament he has won four times. But what an incentive he has: the chance to beat a guy who's quite possibly the greatest tennis player we've ever seen.

Federer is almost invincible at the moment, and even a brief second-round wobble against Takao Suzuki - at his personal best - was rapidly overcome. The mental approach is important. Roger says he's glad to play Andre because he relishes facing a champ. I think that's bullshit. I believe he did prefer to face Andre, but only because he didn't want Johansson. Technically, Federer will win more points on serve than Andre. On returns, Andre has been the best in the world but Roger's darn good, too. So to weaknesses, where Andre's movement is slowing, but this might be negated if he can restrict Federer's own dominance of the court. It is a big ask. Andre will need to hit consistently deep to Roger's forehand and pressure his backhand through sustained rallies to break it down. Emotionally, I'm with Andre because of my long association with him and because he has been such a wonderful presence for the game. But if forced to bet, my money would be on Roger. He's the best in world. As Andre has said: "To stand any chance, you have to be at your absolute best and Roger has to be having an off-day."

Tim Henman: Still the revival man or in the last-chance saloon?

Tim was very honest about his limp three-sets defeat to Nikolai Davydenko, saying he got his ass kicked. He did, and I cannot help but conclude that it was a terrifying loss for him because of what it signified. He has retired from Davis Cup tennis to concentrate on trying to win a Slam, but the clock is ticking and he knows his chances are ebbing away. I have the greatest respect for him and he has proved he is a top player. He has also handled the pressure of British expectations. But it's tough to win a Slam and I can't see it.

Where's the silver lining for British tennis?

Elena Baltacha's against-the-odds progress to the third round was a personal triumph as spirit overcame adversity. If you could replicate her attitude and marry it with a decent development programme, Britain could follow Belgium, Russia and now China as producers of emerging talent. Just don't ask me for a timescale.

Who's the dominant Russian in the women's event?

One of the two who face each other in the bottom-half quarter-final, Maria Sharapova or Svetlana Kuznetsova. We know Maria's major weapons: power, determination, fight. But Svetlana is strong, hits the ball very hard on both sides, moves well, never drops the pace. And the pressure is all on Maria, the higher seed, the golden girl... and often a slow starter. I believe if Maria comes out blazing and starts well, she'll win in two sets to cement her supremacy. If she loses the first set, she'll have trouble.

Are the Williams sisters still in decline or back in business?

For the sake of the women's game, I hope they are back. The tour needs them to rediscover their desire. A resurgent season for Serena and Venus could make it a heck of a year. I'm sure that they are as sick and tired as anyone of all the doubts over their commitment. But I also see signs of improvement, so much so that I now think Serena could win this tournament, and certainly use her service power to beat Amélie Mauresmo in the quarter-finals.