Watching the Packers against the Eagles NFL playoff game I was struck when broadcaster Troy Aikman suggested that with four minutes remaining in the fourth quarter and down by 11 points the Eagles should attempt a field goal from the two yard line instead of going for a touchdown. Aikman's logic was that the Eagles needed to score twice - values of 3 and 8 though in either order - to send the game into overtime and instead of risking the chance of not getting any points it was better to take the 3 at that moment.
He's wrong. In the best situation for the Eagles - and what ended up happening - was that they would have their current possession and one more and need scores in each. Those possible scores were, 3 + 3*, 3 +8, 8 + 3, 8 + 7. What nearly happened except for one poorly thrown ball was the final option and the one Aikman neglected.
To think about this in terms of game theory where we value wins as 2, ties as 1 and losses as zero, kicking a field goal on the penultimate possession yields only .5 in value whereas a touchdown that turn gives 1.5.
Described action at the 5:40 mark.
*In the waning moments of a game no team would go for three points when they needed eight but this further proves Aikman's logical flaw. If they kicked a field goal from the one yard line any situation where they need to score a touchdown will be equal to or less likely because every distance is further than their previous opportunity.