Between 2000-2007 there were 124 OT games in the regular season. Of those 124 games, 37 ended on the first drive. That's just less then 30% so it's not like the majority of games end without the other team ever having touched the ball. (http://www.advancednflstats.com/2008...lip-in-ot.html)
Besides, you have 4 quarters to win the game. If you're afraid you'll lose in OT because of a coin flip then do something to win the game during those first 4 quarters.