An Unfair Advantage
The NFL overtime process is the most complicated and unfair tiebreaker system in sports. It is the only process that doesn't give each team an equal opportunity to score in the overtime period. Keep in mind that this is the most physical and injury prone of all sports, so football players don't really look forward to playing extra time that increases the risk of injury due to fatigue.
I grew up when the original rule was that all games during the regular season were ruled as a tie after the regulation four quarters were played. Then in 1974 they implemented a sudden death period where the first team to score wins the game. This had to be done in one 15 minute overtime period or the game would then be ruled a tie. Naturally, playoff games were the exception, where they played as many periods as necessary until a winner emerged. The biggest drawback to this rule was if the team that got the ball first scored, the other team didn't get a chance to get the ball.
How They Tried to Make It Fair For Both Teams
In 2010 the NFL amended the overtime rule to try and give both teams a chance of possessing the ball in overtime. They shortened the overtime period to 10 minutes and decided that if the team possessing the ball first scored a touchdown, the game was over. This did not give the defending team a chance to retaliate, but if the team with the first possession only scored a field goal, the defending team would get the ball and could either match the field goal, or score a touchdown to win. If they matched the field goal the game would continue until the next score or the overtime ended resulting in a tie.
The only way the defending team could win on the first possession is if they were to somehow get a safety or score on an interception or fumble recovery. So the coin toss became a very important element of the overtime process, as winning the toss determined who would get the ball first. I can't think of any other sport where both teams do not have a fair shot of scoring in an overtime situation.
How Other Sports Handle Ties
In basketball the teams play five minute overtime periods until a winner is reached. In baseball, extra innings are played with each team getting a chance to bat until one team outscores the other. Hockey is also a very physical sport and used to have tie games also, but now they have a five minute overtime period and then they go to a shootout until a winner is determined. You can name almost any sport and they have an overtime or tie-breaking process that is fair to both teams. Even boxing uses an extra round if there is a tie in some competitions.
The Simple Solution for Overtime
Surprisingly, the solution to NFL ties is simple. All they have to do is follow the college model. Each team gets the ball and starts at the opponents 25 yard line. if the first teams scores a touchdown, the other team gets the ball and has to match that touchdown. If the first team gets a field goal, the other team can match that field goal and the game continues, or score a touchdown to win. If they are still tied after two possessions, a team scoring a touchdown must then attempt a mandatory two point conversion.
This will work in the NFL with a few minor changes. The teams will start from the 50 yard line instead of the 25 yard line. As good as NFL kickers are, I would even consider them starting from their own 40 yard line, but I think the 50 yard line would help determine a winner faster. There would only be three possessions during the regular season, again taking the injury and fatigue factor into consideration, but I would keep the mandatory two point conversion after touchdowns on the third possession. Of course during playoff games they would play until a winner was determined.
This system works in college, but I feel starting from the 25 yard line is too easy for the pros. Also the extra point in the NFL is no longer automatic so kickers will feel the pressure also. This will make for some interesting coaching decisions. Even if a team doesn't get a first down during their possession, they are looking at a 55 yard or longer field goal. Hey NFL fans, let's get this rule change implemented next year.