Dave I have no idea how you're coming up with a 50% chance of stopping a team for a three and out. Are you saying that, for any drive, a team has a 1 out of 2 shot of stopping them for a "3-and-out"? So you're saying that 1/2 of all drives are 3-and-outs?
At end of game situations, I think so, yes. ...at least close to 50%. When a team is trying to burn three TOs, they don't play the same style as with their regular offense. Of course stopping a team 3-and-out is more difficult in the middle of a game, but at the end, one team is more likely to run and you can bring up your safeties, because there is absolutely no threat of a deep ball. It's almost like running a goalline defense at midfield.
Also - a 50% chance of driving the field with no timeouts on any drive?
"Driving the field" in that situation would only be 20-30 yards and you'd have 4 downs to do it, since you aren't going to punt. I think that it's also about 50-50.
98% came from the opposite of 2% (converting a onside kick, without taking into account driving and kicking a FG). But obviously that is wrong as that website I found stats 1 out of 4:78 for onside kick conversions in the last 10 years.
This is a misunderstanding of the question, so I will let it go.