Does this take into consideration installation of:First, congrats on winning a free gear swap! That's one helluva prize!
Second, I agree with Roy - 4.56 is the sweet spot for 37s and your intended uses.
I've done quite a bit of research on gear/tire combos for the diesel. Hope it helps...
I'll start with just the drive ratio numbers. Not taking into consideration additional rolling mass, increased wind resistance, etc. Just "gearing math".
OEM = 32.7" on 3.73 gears.
37s on 4.10 = 2.27% loss in torque, reduced RPM, increased MPG. For 37" tires specifically, 4.10 gears are numerically the "closest" to OEM tire/gear combo. ("Closest" = absolute value; i.e., least amount of loss or gain.)
37s on 4.56 = 8.05% increased torque, higher RPM, decreased MPG. 8% is a noticeable jump (whether it's a gain or a loss, 8% is quite a chunk)
Interestingly, 40s on 4.56 = 0.57% increased torque, higher RPM, decreased MPG. Mathematically speaking, 40" tires on 4.56 gears are the closest gear/tire combo that match OEM gear/tire. The next closest is 37s on 4.10 at 2.27%, as stated above.
Now, inject some reality into the nerdery. Tire mass matters. Wind resistance matters. I guess one last thing to ask yourself... You're running 37s on the OEM 3.73 gears now, right? What has your experience been? If it's miserably underpowered, then go with lower (numerically higher) gears - 4.56. But if you barely noticed, then probably 4.10s would work. If you plan on towing, the 4.56 will help you avoid "lugging" the engine (struggling at low RPMs). Plus, 4.56 is better for the rocks, which you said you do quite a bit of.
I also agree with what Roy said that anything above 4.56 would be overkill. If we were talking about a gas engine, then 4.88s would be appropriate. But you simply don't need the additional torque, and you really need to avoid the higher RPMs on the diesel.
Bottom line: for the use cases you described, I think 4.56 is the sweet spot.
A. Steel skid plates
C. Rock sliders
D. Recovery gear, compressor, etc.
Thankfully I don’t have over landing gear or a fridge, etc.
Am kinda sad the ecodiesel doesn’t have the 4.10 as an option.