TL;DR:
Emotional stability enables the ADC, jungle, and top lane roles the most. Neurotic people should play support or mid lane.
Openness enables junglers, mid laners, and to a lesser extent, supports. Pro mid laners and junglers should be high in openness as the role demands flexibility due to meta shifts.
Agreeableness is not that important for role selection — it just changes the way you play the role. Disagreeable people like carries and assassins; agreeable people like tanks and healers.
Extraversion doesn’t matter for role selection that much.
Conscientiousness is good for all roles, but probably enhances top lane and ADC performance the most.
Top lane leads can get very snowbally, so a player who is behind will need to play differently in order to stop feeding — a conscientious personality and the kind of person who would not choose to wirehead themselves. Ideally emotionally stable enough to not get tilted by snowballs or junglers. Top laners should ideally be more active, dominant, or extraverted as many top lane champions are also initiators.
Jungle is a tilting and confusing role to play. You will have to bear with the fact that you will be the most flamed person in the whole game, so emotional stability is a must. Due to the cognitively complex nature of the role, Both agreeable and disagreeable styles of jungling can work — agreeable people tilt towards enablers or gankers, disagreeable junglers go for carries.
Laning as an ADC can be frustrating and tense due to the presence of the support and that junglers/mid laners often choose to gank bot, so emotional stability is ideal. Openness/extraversion don’t matter, and neither does agreeableness, though I assume ADCs are low in agreeableness on average due to role selection. Conscentiousness would help with more rote stuff like positioning or not feeding. People with fixed or Black/White attitudes would probably benefit from palying a simple role.
Mid lane is to some extent a role you can paint with: a neurotic and introverted player can farm under turret while an agreeable and extraverted player could go for a roaming playstyle. In pro play, mid lane becomes more difficult as the meta changes require people to adapt to different playstyles, which makes it so that mid laners need to be highly open minded at that level.
Support is similar to mid insomuch as it is a role that can be played according to the player’s personality; disagreeable and emotionally stable supports can go for assassins or mages, agreeable and neurotic players can play healers or tanks.
After scrolling through 100 images of good trends maps, I was fully expecting a huge data set derived from surveys provided from reddit or something. "Damn, where does he keep getting this data from?"