If teams lose the coin toss, PLAY DEFENSE!
What you don’t want is for the coin flip to decide who wins. You also don’t want the coin flip to give one team a significant advantage. If the game play is such that it skews towards the offense, and the offense statistically has a significantly higher than 50% chance to score on the initial possession, then sudden death OTs are affected too much by the coin flip.
Here’s my solution then: losers don’t get paid!
It wasn’t overwhelming, but it was disproportionate: about 61% of the time, the team that won the coin flip won the game.