Lots of the usual teeth gnashing after the game this weekend where the Vikings "didn't get a chance in overtime." The basic complaint is that the team that wins the coin flip has a huge advantage, ultimately deciding the game, and that this is unfair.
First, the stats cited vary, but the winner of the coin flip does not always win the game on the first possession. Indeed, the stat is something like 60% or so, which is not really that unfair.
Second, defense is part of the game, and if you cannot stop the other team when the stakes are high, then too bad.
Third, if you don't want to face the possibility of losing a game in overtime because of a coin flip, win in regulation! The Vikings had their chance to win--but Favre unsurprisingly threw the game away with a foolish interception. So, I don't pity the Vikings. They could have won if they held until the ball then and/or in previous drives.
Is it fair that in some games, the ball's bounces happen to fair one team rather than the other? Again, if you want to prevent that from happening, don't fumble, don't throw passes that are likely to be tipped, etc.
If one wants to change overtime at all, it would seem to me that the best change would be to require a team to score by anything other than a single field goal. Two field goals, a safety, a touchdown, but if you want the other side to have a decent shot at it, then just make it so that a field goal does not do the trick. If a team gives up a TD, which does not happen on every drive, then they should lose. But a field goal is a cheap way to score, although not this year with the random event of the field goal kickers blowing big kicks through out the league.