In all seriousness, I strong suspect that the .416 would be massively disappointing..... Very effective (with a expanding bullet) but likely often not the hammer of Thor kills one would expect. Most 416 bullets aren't going to be dialed in for great expansion on little itty bitty deer.... Just my educated guess on that....
Yes, its a really big magnum cartridge, with really impressive numbers. However, most of that energy and mayhem are going to take place in the hillside beyond the deer, not "in" it. The velocities are actually pretty moderate. 2300-2400 is slow by modern standards. And the bullet is fairly tough. I'd expect a decent sized entry hole, and a fairly narrow through-and-through wound channel, with a similar exit. Basically, think of a 1" hole, drilled cleanly through said deer. You could probably shoot the deer facing dead on. Still going to be a 1" hole, front to rear, through the whole damned deer. This will be dependent entirely on the BULLET used...
A buddy routinely uses .375 H&H on deer. His experience? It's really just a glorified 30-06. Very similar wounding. All the extra penetration doesn't matter on a target that is still generally 16-20" deep.
I popped a decent buck with a 225 grain Nosler Partition at 30 yards out of a .350 Rem Mag, with muzzle velocities of 2675 fps. Actually a disappointing kill. As with 375, there was very little difference between this shot and a similar shot with my normal 308 Win.... In actuality, my 308 Win load with Nosler Ballistic Tips drops them far faster than that 350 does. Its because of the different bullet construction. Velocities are very very similar....
If you expect massive tissue damage and "OMG!" carnage, what you need is speed. Flat out velocity. And softer bullets.... My last coyote kill was a 160 Nosler Partition out of a 280 Ackley Improved at an honest average muzzle velocity of 3003 fps. You could have dropped a tennis ball through him, side to side, and barely touched the hole....
Any cartridge that runs 2300-2400 and uses a "normal" isn't going to be dramatic. Think in terms of a 45-70. Lots of power, but plodding along. And penetrate measured in feet, not inches. Step it up to anything over 3000 fps and wounding generally becomes very dramatic, but with much shallower wounds. Big, explosive penetration that doesn't go overly deep. Different projectiles can modify this....