Harry och Dumbledore pratar om det kort i slutet av Secret of Secrets :
"So I should be in Slytherin," Harry said, looking desperately into Dumbledore's face. "The Sorting Hat could see Slytherin's power in me, and it -"
"Put you in Gryffindor," said Dumbledore calmly. "Listen to me, Harry. You happen to have many qualities Salazar Slytherin prized in his hand-picked students. His own very rare gift, Parseltongue - resourcefulness - determination - a certain disregard for rules," he added, his mustache quivering again. "Yet the Sorting Hat placed you in Gryffindor. You know why that was. Think."
"It only put me in Gryffindor," said Harry in a defeated voice, "because I asked not to go in Slytherin..."
(källa: Harry Potter och Secrets Chamber , kapitel 18, Dobbys belöning )
Så det verkar som att hatten var väldigt starkt benägen att placera Harry i Slytherin, men Harrys intensiva vilja att undvika det ödet försvagade det för att placera honom i Gryffindor istället.