The four of them had been withering away for quite a while when Godric pulled out an equally withered hat:

“A hat? Why not a flying carpet?” humored Helga.
“It could be biased,” remarked Rowena, who had recently been studying muggle statistics.

Salazar stood up and examined the hat closely. “Well I’m not going to let that thing decide the fate of my school,” he declared coldly.

Godric simply sighed, but despair could be seen in his eyes. Despite all this, the wizard kept tinkering with his old hat, hoping the others would eventually see what it had to offer.