When Stannis arrived at the wall in episode S04E10 of Game of Thrones he had about 10,000 soldiers with him, I am wiling to give him a freedom of doubt and grant him 10,000 more for the argument sake. Mance Rayder in the previous episodes was rumored to be having an army of 100,000 soldiers which is still 5 times more than my exaggerated count and 10 times more than the actual count but when Stannis arrived they dismantled them very quickly leading to Mance Rayder surrendering.
I know Stannis is a ruthless battle general but still that army of 100,000 shouldn't have given up that easily or Is there something else I am failing to account for?