Just remember that Jax is the OG cocky and arrogant boi™ of League
and 
are mere imitations of his might. let it be known
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ASol > Jax > Draven
: "What is the definition of underwhelming? Oh, right! You."
Jax is cocky and had every right to be, because in his old lore he was literally the best. He'd just win every fight he was in. The old Institute of War had to give him a limited choice of weapons to give others a chance, and he chose a lamp post just to brag as he still won everytime.
I remember reading the questions and answers for Draven when he first came out and when someone asked which champions Draven would have the most respect for they said Jax and Twisted Fate. A Sol also comments on what a fine dragon Draven would make. It’s funny how they would like each other.