Final answer:
The football coach's plan violates the principle of random assignment in experimental design, compromising the experiment's validity due to potential self-selection bias.
Step-by-step explanation:
The coach's plan violates the principle of random assignment. In an ideal experimental design, participants are randomly assigned to different treatment groups to ensure that any effects observed are due to the treatment itself and not to preexisting differences between individuals who selected different treatments. Without random assignment, the experiment can be affected by self-selection bias, where the characteristics of the players who choose one treatment over another may influence the results, rather than the treatment itself.