This situation happened in the Giants-Dallas game.
Let's say an offense runs a play that results in 4th and 1 in an area where they would likely go for it, because a punt would be unproductive on average and a FG is low probability. That could be something like the 37-40 yard line.
The offense commits a 10 yard penalty. That could create something like 3rd and 13, 3rd and 17 or 3rd and 20.
There would be some value of 3rd and X where one would think that it is better to let the offense have 3rd down again. What should X be? In the Dallas-Giants game, Garrett decided to give the Giants 3rd and 17 over 4th and 1.
I have some ideas about how I would evaluate this, but I'd like to open for discussion first. It's best to start off by assuming the offense and defense are involved are average, and that Perry Fewell is not your defensive coordinator.
so you would always take a 5-yard or 10-yard penalty in the above example, right?
I'm sure coaches have a number for X in your question but field position, score, confidence in your defense at that moment also play a part.
Next we let Y equal to the total weight of the defensive line players and subtract from that the total weight of the offensive line players and divide that by the weight of the running back it becomes very clear.
If X is greater than Y thank you take the penalty but if Y is greater than X you decline. If X turns out to be equal to Y you have to fire Fewell.