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I don't think this is a serious question. Mud isn't the same everywhere, even in the same place the quantity of water contained can vary within meters, the kind of soil, the tyres you have, the driver, the state of the truck... Everything factors in in this equation you're trying to ask. All you can do is try and have at least another truck to pull you out if you happen to get stuck. I'll tell you this: I've only been stuck a couple of times (both in the same area), and it was in such harsh conditions that 4/5 trucks in our group got stuck and we had to spend the night on the spot.
I got stuck a lot the last time I went offroading, sometimes in small amounts of mud.. I was trying to keep up with some crazy Toyotas though with front and rear lockers, dual T-cases, 38''+ tires, etc.
Usually I judge by how much room between my center section and tire (so i see why you asked) but you can still plow through if youre bottoming out if you have enough traction. Open diff in the rear? gonna have issues going through much, LS? might help a bit, lockers? gonna have a hard time getting stuck
erm, yeah, Encho is right, far too many variables and unknowns to give you the slightest idea.. but a stock Bronco with 31s and a LS rearend can do more than most stock vehicles.
Encho is right... the question cannot be quantified. Too many variables. If you want to know approach, departure and break-over angles, you can measure them. But there is no accounting for the other variables especially driver talent.
There you go, all you had to do was try. He probably doesn't have enough torque to move those huge tyres, let alone swamped with mud. Also, fat tires = stuck in mud, the less resistance you offer to the mud the better you'll cut through it. Skinny, tall tyres with an aggressive pattern are the way to go.
Do you have any pictures? upload them!.
P.S.: Don't give your friend too hard of a time, it could be you in his place some other time and it's pretty annoying.