Analysis: Over the winter months Mayo bounced back impressively from their traumatic All-Ireland final defeat, producing several impressive performances during the league to beat Tyrone and Cork. They even edged Kerry for a semi-final place on scoring difference, though that seemed to suit Jack O'Connor at the time.

Considering the steady progress, it is strange they go into tomorrow's game completely written off by most observers and by many of their own supporters.

This is mainly because the same weakness Kerry exposed last September re-emerged in their toughest challenges to date this year. In the league semi-final, the Armagh pair Steven McDonnell and Ronan Clarke again exploited the full-back line with score after score from direct balls. I would expect an increased emphasis on protecting this line tomorrow, with someone shadowing in front of Colm Cooper to help his marker.

Then, against Galway in the Connacht final, their inability to hold ball up effectively meant poor-quality deliveries in to the forwards.

Mayo may have had 19 wides against Cavan but that actually hid several positive aspects, like the added physicality brought to the team by Austin O'Malley, Michael Moyles and Pat Kelly.

Also, the tactic of playing Ciarán McDonald alongside O'Malley at full forward looked effective when direct ball was played in. It was only when they went back to their old ways that they struggled.

With Trevor Mortimer also returning, if he recovers from a leg injury, a huge improvement from the last championship meeting against Kerry can be expected.

This is Kerry's first return to Croke Park since that marvellous display and, without setting the world alight since, O'Connor brings a team on course to delivering back-to-back All-Ireland titles.

Cooper, with a clinical display of score getting, ensured a poor team performance against Limerick in the Munster semi-final was not fatal. Then a much improved Cork side tested them for 50 minutes in the Munster final and it was only when Declan O'Sullivan goaled that the result seemed secure.

However, Kerry have an even stronger look about them. Darragh Ó Sé and Séamus Moynihan are restored after last year's injuries. And Johnny Crowley's retirement is compensated for by the presence of Mike Frank Russell.

Of course they still need to step up a gear, starting tomorrow. Only when pulling away from Cork in the second half of the Munster final did they reach the standards expected.

Sport has a knack of throwing up surprises but Kerry should progress.

The other quarter-final will be a much closer affair. After the Fermanagh defeat in the championship last year, Billy Morgan obviously made a decision to rebuild his team. There are five new forwards, and the likes of James Masters and John Hayes have brought a clinical aspect back to Cork football. With Brendan Jer O'Sullivan and Philip Clifford also playing well there is a good combination of youth and experience. Also, the half-back line, in particular Noel O'Leary, has been the launch pad that has allowed these new combinations to thrive.

This is countered by Galway moving Paul Clancy - the revelation of the summer - to centre back.

They come into this match in a strong position, having already won the Connacht title and an under-21 All-Ireland this year.

Several players have graduated from underage success, like Finian Hanley, Alan Burke and the midfield combination of Barry Cullinane and Niall Coleman. Half the battle will be won if the latter two, with the help of Joe Bergin, who seems to be back to his roving role of 2001, can eclipse Nicholas Murphy around the middle.

Thereafter, the ball in to Michael Donnellan and Pádraic Joyce should ensure they rack up more than the 10 points they needed to get past Mayo. They will have to.

Overall, especially with the return of Bergin, Galway should edge it.

As for today's qualifiers, whoever comes out of the Laois-Derry tie will feel they can go on to claim Sam Maguire. Derry have improved on last year, with Fergal Doherty coming back from injury, a solid full-back line and Paddy Bradley in sensational form.

Still, if Laois get out of the blocks quicker they have the determination and ability to earn a shot at Armagh.

Tyrone are the type of team that will bounce back from the Ulster final disappointment but the loss of Ryan McMenamin is significant; with Chris Lawn he had tightened up the full-back line. Monaghan, and in particular Thomas Freeman, will have to make hay here.

Monaghan have plenty of quality but with Stephen O'Neill on course to become player of the year and Brian McGuigan almost fully fit I expect the extra attacking class to get Tyrone through a tighter affair than is generally expected.