Brett Favre’s announcement that he has Parkinson’s disease is bringing renewed attention to the potential links between football and a risk of brain disease.

When people say Dolphins quarterback Tua Tagovailoa should retire after suffering his third concussion, they will point to Favre and his many concussions.

Mr. Favre, the former N.F.L. quarterback who fell from grace after Mississippi officials accused him of helping divert funds meant for low-income residents, announced the diagnosis before Congress.