No. The original writers came up with the title first, then just made up an easy to film movie around it.
^^^^Whoever wrote that above is wrong because the story goes like this, a boy got beat up by 13 other boys, They thought he was dead and they threw him into Crystal Lake. At night, he swam to the surface. One of his friends was using the bathroom by the lake and he saw him, he tried to talk to him but he could not. The little boy had gotten a knife and a mask from the cultural center at the campsite and he went to the cabin the 13 boys were at. He killed all of them while asleep and he left. In the morning, the counselors went to see the boys and they saw that they were dead. they called the police and investigated but never told the kids parents of the happenings. This all happened in the late 1920's early 1930's . The camp you see in the movie in the 1980's Friday the 13th is actually Camp Keowa located in New York State and at Ten Mile River. It is said that the mask used in the movie, was thrown and is at the bottom of the lake. This story was passed on by the boy who was in the bathroom when he saw his friend go kill them, then his son passed it on to his son in the 1980's and then it was passed on to the guy who I met.