“Catastrophic failure [of the unhelmeted skull] during testing…experiencing a maximum load of 520 pounds of force,” says the Journal of Neurosurgery: Pediatrics.

According to NASA, the average push strength of an adult male is about 220 lbs of force, with a standard deviation of 68 lbs. If Gregor Clegane were three standard deviations from the mean (the top 0.1%), he would be able to produce about 424 lbs of force, which is not quite enough. He would need to be about 4.5 standard deviations above average to crush a skull with his bare hands.

This is pretty extreme, but if strength is normally distributed in Westeros, Gregor would only be about 1 in 147,160. Another way of saying this is that if one baby were born every day, a man as strong as this would come around about every 403 years. Since birth rates are much higher than that, it’s not impossible.

This is also consistent with what we know about Gregor in general. He’s described as being nearly eight feet tall, or 96 inches. The average height of men in the United States is about 70 inches, with a standard deviation of 4 inches. This means that Gregor is about 6.5 standard deviations taller than average. It seems likely that he would be similarly above average in terms of his strength.

Verdict – it is statistically possible that someone strong enough to crush a skull with their hands exists in Westeros, and Ser Gregor is a good candidate for the role.