I was considering travel rules, the appointment of a quartermaster and of a navigator. An adventuring party is probably made up of young people that overestimates their abilities, else they would rate going on an adventure as suicide and choose less risky paths.
Considering a classical game with STR, CON, DEX, INT, WIS, and CHA. Could Hubris be expressed as
Hubris ← INT + CHA - WIS ?
Hubris ← INT + CHA - WIS - (age / 10) ?
The player would roll a d20 under Hubris (or over 21 - Hubris), a failure would mean that the DCs (difficulty class) exposed to them would always be lower than they really are. Not very immersive.
Could a failure compel a character to request responsibilities above their competence level? Wouldn't that be forcing something on the player?
The referee could instead present the context from the point of view of hubristic characters to the players and let them get hurt by the real context later on.
Could the prod toward hubris be less radical? Could the referee simply talk the characters toward their hubris? Could that be done through a follower or some other NPC? "Yes, I am sure you can do it, you are exceptional!"
But I have the impression that such Potemkin scaffolding or manipulation can't go beyond the first step of a campaign. And it's probable that seasoned players will not fall for it.
Could the players' disregard for consequences stand in for character hubris? The players would gamble their characters for the fun of it.