Last Sunday I posed a problem concerning when a NFL coach should play for a win in regulation. The solution suggested the Atlanta coach may not have maximized his team's winning chances. This is plausible as coaches appear somewhat reluctant to take short term risks even when this would maximize their team's chances. This is reinforced by the amount of criticism a coach will receive when a gamble fails. Consider the criticism Belichick received for his recent defensible decision to go for a fourth down conversion.
However the problem calculation is only as good as the assumptions. One key assumption was the chances in overtime would have been equal. The Atlanta coach may have felt the Giants would have been demoralized by blowing a late lead giving his team the edge in overtime. As it turned out the Giants won the coin flip and immediately drove for the winning field goal. When this happens the losing team generally feels the coin flip is overly important. In fact the coin flip winner seems to win about 60% of the time. Suggestions are periodically made to change the rules to diminish the importance of winning the toss in overtime but they haven't attracted much support. Perhaps because the most common proposal giving each team a possession has obvious problems of its own.
A very simple change would be to move the kickoff spot forward to the 35 yard line for the overtime kickoff. Before the 1994 rule change moving the spot from the 35 to the 30 the overtime winning percentage was about 50% regardless of which team won the toss. I am fond of making the coaches bid for field position. The coach bidding closest to his end zone would get the ball. If nothing else this would provide ample fodder for second guessers.
I came up with the auction idea myself but others have proposed similar schemes. See here and here .