There are many posters here smarter than I am, and I’m sure even some who didn’t rely on a fraternity brother to help him breeze through Probabilities & Statistics.
Just the same, my pea brain head doesn’t understand it. I get the idea that deferring MIGHT give you back to back possessions - with a 20 minute break in between. But at the same time, taking the ball first, in a finite window of time (30 minutes), suggests to me that you have an increased chance of having more possessions in the first half than your opponent. Assuming possessions alternate, of course. And while it’s obviously true that the team which defers may grab an extra possession in the second half, I don’t see how it could lead to more possessions over the course of the game.
I always view the take/defer decision as one which must be made on several factors: relative strength of defense; relative strength of offense; weather conditions, when appropriate; strength of special team; home or away; emotional decisions, and “gut feel” for the players/game.
But, like I said, I’m looking at this like a fan. Not a statistician.