Football season is beginning, which gives me a nice time for me to agree with all of those who regard NFL overtimes as a mess, and propose my own solution.
According to the bad old system, everything started with a coin flip, with the lucky winner getting to determine whether they'd kick off or receive the kick. The first team to score would win, which meant there was a nontrivial advantage in choosing to receive. So coin flips were playing an unduly large role in determining the outcome of the game. Candyland is a fine game for people who want chance to determine outcomes, but I don't want that in pro football. Victory should go to the best athletes with the smartest strategy, not to those who make lucky guesses about gyrating bits of metal.
There's a new, more complicated, and probably better system now where you do the coin flip as before and have the lucky winner choose, but each team is guaranteed to be on offense, unless the team that gets the ball first scores a touchdown. I'm not totally sure which team this favors, but I'm sure it'll be figured out in due course. Chris Chase thinks it'll help the team that kicks off and gets the ball second, which seems about right to me. And in any case, we're still in Candyland. Random chance is playing too big a role in determining the outcome.
So here's my solution: Determine who gets the ball first by bidding. Have the home team's coach name an even number, and the visiting team's coach name an odd number. The team whose coach bids the lower number gets the ball at their yard line corresponding to that number. So if the home team's coach says 8, and the visitors' coach says 5, the visiting team gets the ball at their own 5. And from there, it's sudden-death overtime, with the first scorer winning. No Candyland, just coaches playing head games against each other, and players taking over from there.
Added bonus: I've heard that the league is interested in reducing the number of kickoffs that happen during the game, for the good reason that kickoffs present a lot of injury risk. This solution eliminates overtime kickoffs, and is to be preferred for that reason.