I am not sure conservative versus aggressive would show up in the percentage of first downs on any given down by pass or run.
Where it does show up is in yardage gained and points scored. When you combine the yardage from the play and the rate of success, to get a likely yardage for a choice run v pass, passing comes out ahead. More so when you track the points gained.
There are downsides to choosing passing and not all game situations are alike. But in the first and third quarters, passing is more productive.
You can see some of this here:
http://archive.advancedfootballanaly...cess-rate.html
Burke is saying coaches think in a one step, success or no, proposition. Their success rate is whether or not the play achieved its goal. It correlates well with actual game choices and play calling. Generally, teams look to get halfway to the first down first and second down. Third down success is to convert. But those calculations ignore the unequal payoffs of passing versus running regarding keeping drives alive and scoring.
Basically, the coach cannot have a calculator or computer on the sideline telling them when they have maximized their payoffs. But they can, through institutional memory, training and observation (film review and live game setting) see what plays worked and what didn't.
They are literally counting (or stacking) success, not assessing probability.