Why is the intensity of Hawking radiation dependent on the size of the black hole it comes from?

I am asking for a non mathematical answer. I think I have a pretty good understanding of physics without the maths, which unfortunately eludes my understanding. It may be the answer would be obvious if I understood the maths, but I don't. As I see it, the event horizon has the same property for any size of black hole; it is the point from which light cannot escape. Given that this property is the same regardless of the size of the hole, it seems reasonable to suppose that the intensity of the Hawking radiation would be constant per unit area of the horizon. I know I am wrong, but I don't know why. A non mathematical explanation would be appreciated.