"Generals always prepare to fight the last war, especially if they won it". (Georges Clemenceau)
If we want to enjoy similar success to what we saw under Martinez, Rodgers and Laudrup, there's no point trying to recreate the exact same circumstances, we need to understand the core principles that were at work.
I agree with
@rockinj - playing football on the grass is a necessary condition for our success because it's what our supporters identify with, it creates a 'buzz' and keeps them off the manager's back. It's not a sufficient condition for success and it doesn't really matter if we play it fast or slow, have 80% possession or 45%. As long as we do it with style and don't hoof the ball, people will declare it is a return to 'The Swansea Way' (whatever that means).
I wish I could tell you what the core principles are, because then I could earn a fortune advising football clubs. My guess would be a harmonious dressing room with leaders the players look up to, stability at board/senior management level, the right blend of developing our own youth talent and hiring in ugly ducklings, enough of whom turn into Swans to keep us afloat, and a manager who is a left-field choice. That, more than anything, is what we've been trying to do since Laudrup was sacked, and arguably we've only managed it once since then (Potter), and even he wasn't that left-field.
"No man ever steps in the same river twice, for it's not the same river and he's not the same man." (Heraclitus)