Source: http://win.wizkids.com/bb/viewtopic....1d1c1a248588de

pug_nacious wrote:
When does the player choose to roll for this effect? Do they do it when the attack is declared or do they do it after the opponent makes the attack roll?

WK: The roll is made after the attack roll has been finalized. This would be after all rerolls and/or die replacements have been applied.

If the roll is a critical hit and Thanos uses his ability, does the hit still automatically miss Thanos?

WK: No. Thanos becomes hit by the attack. Note that he can still use his effect to potentially deal damage to the attacker.