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I just watched the Game of Thrones episode The Mountain and the Viper, and I'm curious about the realism of this fight (just curious: I’m not a critic, for me the fight rocks!)
1- Can a spear really pierce a body plate
as Oberyn pierced the Mountain? (We could say that the Mountain was not using a body plate, but I really don't think so.)
2- Can an extremely strong human (within the boundaries of realism) literally
smash a head only with his bare hands in a single crush?
As pointed out by Dima, Oberyn pierced Gregor in the gap underneath the arm:
Clegane lifted his own shield against the glare. Prince Oberyn’s spear flashed like lightning and found the gap in the heavy plate, the joint under the arm. The point punched through mail and boiled leather. Gregor gave a choked grunt as the Dornishman twisted his spear and yanked it free.
-A Song of Ice and Fire: A Storm of Swords, Part 2: Blood and Gold - Chapter 71 (Tyrion X).
Oberyn does later (at the end of the fight) pierce through Gregor's chest-plate armour, but he puts an incredible amount of force behind it:
Slowly, ponderously, he [Gregor] rolled onto his back.
The Dornishman flung away his ruined shield, grasped the spear in both hands, and sauntered away. Behind him the Mountain let out a groan, and pushed himself onto an elbow. Oberyn whirled cat-quick, and ran at his fallen foe. “EEEEELLLLLLIIIIIAAAAA!” he screamed, as he drove the spear down with the whole weight of his body behind it. The crack of the ashwood shaft snapping was almost as sweet a sound as Cersei’s wail of fury, ...
-A Song of Ice and Fire: A Storm of Swords, Part 2: Blood and Gold - Chapter 71 (Tyrion X).
Remember, this is not any ordinary old spear:
The spear was turned ash eight feet long, the shaft smooth, thick, and heavy. The last two feet of that was steel: a slender leaf-shaped spearhead narrowing to a wicked spike. The edges looked sharp enough to shave with.
...
“You will have no cause for complaint. Though Ser Gregor may. However thick his plate, there will be gaps at the joints. Inside the elbow and knee, beneath the arms... I will find a place to tickle him, I promise you.”
-A Song of Ice and Fire: A Storm of Swords, Part 2: Blood and Gold - Chapter 71 (Tyrion X).
As to the smashing of the face, Ser Gregor "The Mountain" Clegane was a humongous man, he has a tremendous body mass as well as strength:
Gregor Clegane is well known for his size, cruelty, and prowess in battle. Gregor is extremely tall (he is close to eight feet in height). He has "massive shoulders and arms thick as the trunk of small trees." Gregor weighs over thirty stone (420 lbs), nearly all of it muscle, making him near inhumanly strong. Gregor's strength allows him to wield a six-foot, two-handed greatsword with just one hand, giving him enormous reach while still wielding a shield. Such is the power of Gregor's strength that he has been known to hack men in half with just a single blow.1
Jaime says of Cregor's strength:
Robert had been stronger than him [Jaime], to be sure. The White Bull Gerold Hightower as well, in his heyday, and Ser Arthur Dayne. Amongst the living, Greatjon Umber was stronger, Strongboar of Crakehall most likely, both Cleganes for a certainty. The Mountain's strength was like nothing human.
-A Song of Ice and Fire: A Storm of Swords, Part 1 - Steel and Snow, Chapter 21 ([Jaime III][3]).
So when Gregor shoves his hands and the weight of his whole body onto a man's face, it is not implausible for him to do the damage that he did. Albeit there is slightly less of a demolition of Oberyn's entire head in the books, nevertheless the face was crushed:
He thrust his free hand into Oberyn’s unprotected face, pushing steel fingers into his eyes. “Then I raped her.” Clegane slammed his fist into the Dornishman’s mouth, making splinters of his teeth. “Then I smashed her fucking head in. Like this.” As he drew back his huge fist, the blood on his gauntlet seemed to smoke in the cold dawn air. There was a sickening crunch.
-A Song of Ice and Fire: A Storm of Swords, Part 2: Blood and Gold - Chapter 71 (Tyrion X).
[All emphases added by me]
1. http://awoiaf.westeros.org/index.php/Gregor_Clegane#Character_and_Appearance
According to two real life experts, 1 a bio-medical engineer and 1 a head injury expert, both say it isn't possible to crush a man's skull and make it explode.
Quote from Tobias Mattei, expert in how bike helmets protect head injuries:
“It would be impossible for even the strongest human to break the skull through compressive forces exerted by any means (either with their hands bilaterally or by stepping [on] it) in any portion of the skull,”
Quote from Cynthia Bir, a bio-medical engineer at the University of Southern California:
“knee jerk response is that there is no way to get the head to ‘explode’ by applying pressure from the eyes. You would need to create pressure inside the cranium. Even if you could generate pressure by squeezing the outside of the head, once the cranium is breached at the orifice where the eye nerves enter, this pressure would be greatly diminished.”
As for question one, there is even "canon" on that, so at least in universe its true. Ser Jorah tells ... some Dothraki, I think ... about armor and that the tip of swords is for piercing it. Dothreaki weapons are made for cutting and slicing which won't work against armor. Later on, I think even one or two episodes later, we get to see that in battle, where Jorah's opponent "hooks" him with his curved blade, cannot cut through his armor and Jorah just kills the man who wouldn't let go of his weapon. Don't ask me which concrete episodes though.
What I know from "real life" is, that steel is insanely heavy and consequently the plate used for armors were/are very thin. I'm very confident Ser Jorah's elaboration on piercing rather than slicing is true, not just in universe. I also know that arrows from relatively far distances were/are quite capable of piercing plated armor. I'm sure a trained main shoving a spear into a body has more momentum than an arrow at medium distances.
From everything I gathered during the guided tour through the museum where I got my knowledge from, I concluded, if I was ever sent back through time to fight in a medival battle, chain mails protect you much much better than any plated armor. At least that holds for plates with which you still want to be able to engage in a sword fight. The plated stuff is for looking rich.
