CORTLAND, N.Y.—When Michael Vick signed a one-year contract with the Jets in March, fans immediately started daydreaming. Their team now had one of the most exhilarating players ever to step on a football field. He would presumably start over Geno Smith, who as a rookie was arguably the NFL's worst starting quarterback.

That presumption gained traction when head coach Rex Ryan announced that there would be an open competition for the starting quarterback job. But in May, Vick surprised everyone, his coach included, when he...