The only difference is that you don't drive on your transmission. You actually need tires. And the size of those tires will affect you ratio on the pavement.
All that math only applies to the OEM tire size.
What is the number one reason we all want to regear everything on our rigs after we get bigger size tires?
Everything falls out of spec with 33", 35", 37" etc.
If everything stays the same, then how come there will always be a difference between 33's and 37's?
Yes the drivetrain will remain constant in it's ratios, but the tire sizes will affect everything in all gears 1 through 4, high or low.
There is a good reason people have installed 4.88 and 5.29 gears once they got a bump in the tire size.
Right but you will always have a 3.3:1 transfer throughput regardless of tire size. The math does not change based on the tire, in fact it is not even considered when deciding throughput ratio of the transfer case. Tires don't "theoretically" change the transmission ratio, transfer case ratio or axle ratio. They don't change.
Of course there will be a final ratio difference between 4.88 and 5.29, the math says so (trans 1st x t/c low x diff) and there will be a realized difference based on tire (2πr). But to say "you would only get that 3.3:1 ratio with 31" tires." isn't true. You get 3.3:1 out of your t-case with 21"
And yes, I can provide the math to support what I said, upon request.
Please do.