[magic is] about as effective as prayer...
I believe in neither. However, I came across an interesting reversal of an old story about prayer yesterday.
The original version takes this format: a devout man's house is hit by floods. He climbs on the roof and prays to God to save him. A rowing boat turns up and the occupants invite him to climb aboard. Being devout, he say, "No, thank you. God will save me." He similarly refuses assistance from another rowing boat and, later from a helicopter, before finally drowning. Later, in heaven, he confronts God: "I was devout, I believed, and I prayed to you in my hour of need, and you let me drown." "I can't understand it," says God, "I sent two rowing boats and a helicopter." (There are many versions of this, going back at least to classical Greek times.)
The interesting reversal: An Alaskan
atheist is caught out in a blizzard and loses his way. Fearing that he will freeze to death, he breaks his own rules and prays desperately to God to save him, saying, "Save me, and I will believe in you." He slips into unconsciousness, and wakes up later in his cabin having been carried in by two Inuit men who had found him.
Later, he is telling the story to a religious friend. His friend says, "So, you must believe in God now. After all, you're here to prove it."
"No, says the man, I was just found by two Inuit men who were passing."
The point being that events happen and we choose whether to ascribe them to prayer, or magic (etc.) according to our pre-existing beliefs and expectations.
So, yes, you are right: magic is probably about as effective as prayer. The real question is, how effective is that?