The socks are for the 13 yr old grandson who has big feet (size 10 men's) and skinny legs so don't know if they will stay up or not.
I'm assuming you wouldn't have mentioned this except that it's important to you. Are you working with his actual measurements - foot length, circumference of foot at its widest, instep measurement taken on the diagonal from the back of the heel and around the foot, and his ankle circumference? With those measurements you can make a sock that fits his foot specifically and is sized to fit his ankle and whatever part of the leg it covers. My DD just got the measurements of my SIL's foot so that I can make his to custom fit him.