If you get the ball first and end the half with the ball, you get +1 in that half.
But in the other half the other team gets the ball first and the best you can do it make the number even (barring an onside kick).
So I just don’t see the 2-possession difference,
Team A gets the opening kick, holds it for 30 minutes and scores.
Team B gets second half kick off, punts
Team A takes possession, holds end of game
Team A 2 possessions, Team B 1
(Back to the math of IU and OSU. if IU gets a 10-9 edge in possessions it projects to be 25-20, not 25-23 if both teams get 10.
Margin increases by playing to take away the extra possession.)
Chop it up however you want inside of that, the ability to be +1 is clear. Then you layer in the context of gaining mor points per possession than the other team because you are more skilled.
Now, real world football, the more skilled team has the larger per possession delta and by the mid 3rd quarter, early 4th quarter the lesser team is behind and has to play very predictably. It is clear to anyone paying attention that the lesser skilled team is running out of possessions.
The increase in win % by even 1 extra possession is worth the downside to the strategy of winning by efficiency and that does not capture the increase in win % when the last 2-3 possessions of the game are do or die, have to try and go fast, pass only constrained nightmares for the opponent.