One of the NFL playoff games today was tied at the end of the fourth quarter and so went into overtime. While I suspect there are not many sports fans among JFW readers, I must once against register my objections to the NFL's overtime system and trumpet my own idea for an alternative. (Non-football-fans can use the opportunity of this uninteresting post to go check out something better on the Internet; given the "dude, whatever" attitude probably aswirl in your head at the moment, might I suggest this music video? At a minute-and-a-half, it's timed to be roughly equivalent to how long it would take the average reader to reach the end of this post.)
The way the NFL currently resolves ties is that they start an overtime period just like it was the start of the first quarter, and the first team to score any points wins. As you might suspect, this system gives a massive advantage to whatever team gets the ball first in overtime, and, indeed, teams that win the coin toss and so get the ball first win something like 60-70% of NFL overtime games. Generally speaking, if your method of breaking ties is associated with the outcome of a coin toss, it's not optimally meritocratic. NFL overtimes also have this unfortunate feature where one could conceivably get locked into a situation in which neither team is able to score and the overtime goes on interminably. Indeed, during the regular season the NFL actually declares any overtime not resolved after any extra quarter of play to be tied, meaning that the NFL's method of breaking ties does not necessarily break the tie.
Fans of college football know that college football has a different and better method of breaking ties that are based on giving each team a possession starting on the opposition's 25-yard line. If the first team scores a field goal on its possession, then the second team loses if it scores nothing, wins if it scores a touchdown, and the teams go to another overtime round if the second team scores a field goal. This system reduces but maintains the disadvantages of the NFL system. There is an advantage in this system to going second, so the winner of the coin toss still has an edge. Plus, again, since an overtime doesn't necessarily resolve the tie, the game can once again stretch on for some unspecified period of time.
In my system, there would still be a coin toss. However, what would happen is that the loser of the coin toss would have to specify a number of yards, for example, "12 yards." The winner of the toss would then have to decide whether they wanted offense or defense. The team on offense would get the ball on the opposition's 12-yard line. They would get the standard four downs with which to score a touchdown from that distance. If they score a touchdown, they win; if they fail to score a touchdown, the team of defense wins. In either case, the game is decided by the offenses, defenses, and coaches (not, alternatively, by a kicker, who is already too influential in the NFL); it is decided in four plays; and it is decided in a way that confers very little advantage* to the team that wins the coin toss.
* Indeed, other than whatever psychological advantage winning a coin toss might confer, I believe the only reason the coin toss would confer any advantage at all would be that presumably, for simplicity's sake, the team that lost the coin toss would be required to choose an integer (i.e., 12) rather than continuous (i.e., 12.6734) number of yards.