Is it a myth that level affects the chances of successfully running away?

[froggyfrogsock]

filler

 

[SadisticMystic]

Speed affects your chances of running away, and more levels means higher speed.

 

[RichestAirPirate]

Yes and no.
Okay, so, in simple terms, it isn't level that determines your run away success, its speed. The faster you are than your opponent/the slower your opponent is compared to you, the easier it is to run from a wild Pokémon. And vice versa, the slower you are than your opponent/the faster your opponent is compared to you, the harder it is to run.

The illusion of level determining your flee success rate is because leveling up tends to also increase your speed stat.