Mayo's situation is sort of unique, last year showed they could come off a basis of a mediocre league, poor defeat to Galway, look like muck in qualifiers, and still come so close to winning Sam. One of the all-time most successful teams only bet them by a point after 2 games.
Their focus is entirely on the last 3, maybe 2 games of the summer, nothing else. They are probably 2nd best team in the country because of Kerrys transition. Tyrone remain unproven. So they believe they will reach the final yet again. They have lost so many major games, most narrowly, or after replays in the last few years that there is nothing else left. They are gone beyond the league being anything more than treading water, maybe trying out some tactics, and the qualifiers to some extent.
They have rebuilt their defensive structure successfully, apart from the calamity of the goalkeepers in the replay. They believe they need another couple of scores against the best team they have to meet. Or else for Dublin to bomb on a given day. They would probably have won Sam last year but for 2 of the most freakish goals ever seen in a major game, on a day when everything else went right for them. Perhaps there is really a curse.
There was a time when a league win may have layed a foundation for them but possibly not either, due to their generally poor handling of hype/media over the years.