Over at Advanced NFL Stats, they have some suggested rule changes for the NFL. One of them is for changing the overtime rules (#11). Their suggestion is for the home-team to automatically get the ball in overtime. This approach has one big advantage to it, that the teams know who will get the ball in overtime, so that they can play the game in regulation with that knowledge. The team that knows they will not get the ball will be more willing to play to win the game in regulation. The problem with their approach is that giving the advantage to the home team seems arbitrary.
My suggestion is to treat overtime as a third half, continuing the coin toss from the beginning of the game. Also if you defer until the second half, you lose out on choosing for the overtime. And if you really want the option in overtime, then you can choose to defer from the second-half choice. It balances out the original winner’s value in they would lose the ability to defer unless they are willing to sacrifice the overtime choice. Everything going into overtime is known ahead of time. It is not gimmicky like a lot of other approaches, i.e. the college football overtime system. It does not change things very much, so it is should not be too controversial.
I honestly do not know if anyone else has suggested this before. If I come across someone else who suggested this earlier, I will give him or her credit.