In Florida there's a long tradition of shooting deer in the head with rimfires and .223s, sometimes for poaching purposes, sometimes for legitimate hunting (.223 only, rimfires are prohibited for legal deer harvest). I am aware of instances where deer have had their jaws blown off with high-powered rifles where the brain was missed, resulting in a messily wounded deer. I've also seen where head-shot deer will put the deer down, but not kill it, and result in having to cut the deer's throat to finish it off. I even saw that once on what superficially looked like a perfect brain shot. Its darn hard to tell exactly at what angle a deer is holding its head in the twilight. Also, a deer's brain is flat from the side, making it a narrow target. From head on the brain is a larger target, but the head has some dramatic angles head-on that can lead to deflection.
The lungs are a larger target than the brain, and the head of a whitetail is constantly jinking and bobbing. It makes it a tricky target. A good lung hit that tears a large-enough hole usually dispatches a deer within 20 seconds, about what you see in this video, except that most of the time with arrows or firearms the deer runs full blast until collapsing into death throws. It seems that a common reaction from airguns is that deer don't feel the need to run off full blast.
I also recently did the math on a deer's reaction speed to a .30 pellet. It would take a deer about .136 of a second to hear the noise of the gun firing. It takes .192 for the pellet to reach the deer at 50 yards at a 860fps muzzle velocity and accounting for deceleration with the pellet's BC. A deer's reaction time is around .15 of a second as a maximum. Some deer test faster. The time for the deer to react is .056 on this setup. Wherefore the pellet should theoretically hit the deer's head before it can react to the shot sound. But that's 50 yards. At 75 yards, the deer's reaction time is .097. Still maybe ok. But beyond that, you're cutting it close as to whether the deer can be starting to move its head towards the shot noise.
