Taken at Face Value

The phrase “quadratic wizard and linear fighter” refers to the power level between the two classes, most commonly in Pathfinder and 3rd Edition D&D but also often in 1st and 2nd Edition D&D. The phrase means that the fighter’s combat power increases linearly, at a steady pace as they increase in level. In contrast, the wizard increases more slowly at first but then suddenly increases in power, passing then eclipsing the fighter in potency.

Some of this certainly has to do with realism in the game. Fighters always tend to be bound by the realm of possibility; while warriors can increasingly push the limits of human potential, surpassing even Olympic athletes, they still can never do anything improbable. Meanwhile, wizards laugh at improbably halfway through level five.

It’s a tricky line for a game system, because the fighter should still be a fighter and not suddenly gain magic for no particular reason, especially as the class is somewhat defined by being the mundane class that does not have any magical tricks or talent. Like Batman. Batman is defined by not having any super powers or abilities beyond a peak human. If Batman suddenly gained the ability to fly or benchpress a truck because he was fighting a cosmic villain like Darkseid it would seem like a dodge.