Why are we even having this discussion? Everything in life is a matter of probabilities, there will always be those 0.001% cases that you can point to saying it's possible, that doesn't mean it's likely enough to make it relevant.
How many people were incapacitated from a bullet than went through their skulls and how many weren't incapacitated? I'd wager the ratio would make your case insignificant.
Even if you think an arrow going through someone's head shouldn't kill all the time, can't we at least agree that it should kill MOST of the time? I mean, what do you think are the chances that you'd keep fighting like nothing happened after an arrow breaks your skull, cuts parts of your brain and creates internal bleeding in it? I'm not a doctor but I'd bet... not many.
Both you and the other person arguing against my original statement are wrong. Yes, it will kill you. Yes, it will incapacitate you. However, anyone who has been in combat or worked in the emergency medical field can tell you that almost no one dies/becomes incapacitated immediately. When you sustain such an injury your body going into "flight or fight" mode. Meaning a few things. One, most people [censored] themselves. Two, the body will lose fine motor control, but continue on with improved functions related to "fighting" or "fleeing."
Your statement of probabilities is true, however it actually goes in the opposite direction in this instance. Yes, bullets will likely tear enough brain matter that almost all functions shut down in a matter of seconds. This highly depends on the type of gun/bullet used though. An arrow in particular in a low velocity projectilve. Meaning it ONLY damages that eye, a very small portion of the brain, and the back of the skull (if it even makes it through all that).
Finally, there is also a huge difference between "fat white kid" (you guys) getting hit in the head with an arrow and a battle-hardened bandit living by the blade and a bit of fur armor.
I don't care to get super specific, especially considering the sources of "not a doctor" and "troll." However, feel free to read "On Killing" and "On Combat" by LT. Col Grossman if you would like to be educated on the physical and mental affects of high stress situations. Also, feel fre to look up any number of case studies involving head injuries and low velocity trauma.