One thing that all master's seem to have in common is that, if you look in statistics, they have more good holes (birdies and eagles) points wise than bad holes. According to my statistics, I have 100 birdies to go if I am correct.
I could always be wrong, and you do need a low stroke average as it is an indicator of how well you are doing right now.
Since my game is very spotty, I doubt I'll be there in the master tier any time soon...