Yep I believe you are right on this one shouldn't really matter it's just a strategy but it couldn't hurt to try changing strategies this coach has a hard time doing that obviously cannot make in-game adjustments or halftime adjustments of course that's because halftime is filled with going to the bathroom and other necessities other than winning the football game
I know a guy that was obsessed with the coin flip concept.
He is a statistics expert and works primarily in wireless communications technology development.
I have not talked to him in a couple of years. From what I recall, he looked at win/loss vs coin flip but he added some other variables. Some of the added variables were young QB vs veteran, great run offenses vs great pass offenses, "bad" teams vs "good" teams, win/loss in regards to point spreads, etc..
I think one simple analysis was where he removed all wins by teams that covered the points spread and removed all losses by teams that lost by the expected points or more based on the point spread. The remaining data was just the teams that didn't meet the expectations of the spread. My recollection is that in this scenario, the coins flip vs win/loss was far in favor of teams thatgot the ball first.