Over-seeding an athletic field has it's own set of constraints not at all like a pasture or hayfield. It's essential to seed without disturbing the integrety of the existing turf so as to remain in service. In most cases, the seasonal play will overlap the proper time to seed. If that turf was poor quality, it would be stripped completly before seeding or sodding. (I've been involved in rebuilding a couple high school football fields and one college football practice facility.)
No doubt a power seeder is the best option in MANY cases. However, there are several instrances where they aren't the best answer. Also, there are instances where light tillage is the ONLY answer followed by over-seeding directly into the tilled soil.
Finally, the OP doesn't have a power seeder, a disc, or ANY implements for the task at hand. He's asking about ALL available options. One particular poster is so dead set that it's his way or NOTHING, he's overlooking many viable options that are time tested and proven successful by countless millions of farmers, landscapers, and hobbiest/home-owners worldwide.
Some of us go into everything with an open mind and long years of practical experience. Others only believe in what limited experience and a few minutes on the internet tells them.