Linear Warriors, Quadratic Wizards

Do note that this graph only shows progression up to Level 5

Linear Warriors, Quadratic Wizards is a /tg/-related trope that was popularized, if not created, by Dungeons & Dragons. It has its roots in Vancian Casting, and in particular the contrast between the Fighter and the Wizard (or, really, any martial character vs. any spellcaster, but we'll stick with the originals), and is a huge source of skub.

In a nutshell, LWQW refers to the disparity between fighters and wizards caused by the differing returns received as they level up. Fighters advance in a linear fashion; their skills improve, their attacking accuracy increases, and their attacks per round slowly increase. However, wizards advance in a quadratic fashion; they can cast more spells per day, they can cast more potent kinds of spells, and all of their lower-level spells increase in potency passively as well.

The end result? The high level fighter is clearly better than he was when he started... but the equally high-level wizard outclasses him in terms of potency and options.

This is a problem that has been around since Advanced Dungeons & Dragons; one of the key reasons that the gish concept through multiclassing took off so much was because it combined the fighter's low-level survivability with the wizard's high-level potency. It only got worse in Dungeons & Dragons 3rd Edition; the new multiclassing mechanics, combined with the scourge of "Ivory Tower Design" (aka, some choices are deliberately designed to be inferior to others) and the Fighter's front-loaded class design meant it was far more optimal to make it your "dip class" and focus your leveling on a more potent class.

Ways This Was Addressed

Due to the very diverse world of RPGs, there are no doubt multiple examples that show the issues being addressed in multiple ways. Some were viewed far more favorably than others.

• Dungeons & Dragons:
  • Advanced Dungeons & Dragons - While still an issue at this point, Dungeon Magazine has many warnings that spellcasters can render an adventure's challenge trivial, it wasn't too horrible and showed why this happened in the first place: Casters had to sacrifice initiative and spend several actions in order to cast their spells and if they were hit, that spell could potentially be wasted. In addition, their spell slots were restricted to the point that physical combat was a necessity.
  • Dungeons & Dragons 3rd Edition (and Pathfinder) - The first case of this being shown. All casters benefited from their casting stats contributing to how many times they could cast in a day, all spells scaled with the caster's level, and spells were so potent that you could actually cast them during a turn without risk of losing it while prepping it. Also present is metamagic, which allows a caster to add extra effects to a spell for the cost of a higher spellslot than intended.
    • Book of Nine Swords - Attempted to address this by giving martials a system of slots similar to casters. They now gained a system of attacks, boosts, and stances (collectively called "maneuvers") grouped by differing disciplines that worked like spells with an exception: these resources always regenerated after every fight (and somewhat during a fight), enabling a practitioner to fight constantly, even when the casters wasted their last spells.
    • Pathfinder did pretty much jack to fix this, and continued that way for a large chunk of its life. Toward the end it settled on two solutions 1: It's a world where even the illiterate plebs in a backwards village know perfectly well magic is real, anyone who isn't a total idiot is at least a partial caster or otherwise supernatural. A lot of the later classes are based around all being partial casters 2: Fighters eventually got the ability to trade their advanced weapon and armor training for truly extraordinary abilities. This gave them exponential growth, but much less of one than the fighter got. Third parties have also ported the maneuver system mentioned above.
      • Starfinder continued along from Pathfinder, but with the few truly non-magical classes benefiting from science that's effectively indistinguishable from magic, like cloaking fields and cryo weaponry.
  • Dungeons & Dragons 4th Edition - Attempted to end this problem by inventing the AEDU System, which definitely worked, but was enormously skubby. Essentially, everyone was stuck to the same style of abilities, with some being less available during the day compared to others. These different abilities used a common "pool" of mechanics, with classes being distinguished quite heavily by what mechanics they tended to emphasize; they have a tendency to look similar, but they play very differently. Another major solution to the problem was the Rituals mechanic; in addition to nerfing many of the "instant win" wizard spells like Sleep, "utility overshadowing" spells like knock and invisibility, the kind of things that tended to make other classes feel superfluous, were removed from the combat spells. Instead, they required time and money to perform, so it was worthwhile to let the class specialized in that particular skill or challenge actually try their hand at it instead of just "cast a spell, move on".
  • Dungeons & Dragons 5th Edition - Also attempted to solve this problem with less overtly new mechanics. Their solution was, firstly, to remove the idea of spells automatically increasing in potency due to their caster's level except for cantrips; in this version, you have to sacrifice a spell-casting slot of higher level to increase the might of your spells. They also removed the "chain of buffs" approach that had been integral to CoDzilla; most buffs became "Concentration" Spells, preventing you from casting more than one and also making it riskier to go into battle whilst buffed yourself. Finally, "minion mastery" spells were heavily nerfed.
    Meanwhile, martials are fundamentally similar to their 3e counterparts but with major defensive buffs: fighters can replenish a chunk of HP in one turn and reroll saving throws, barbarians roll twice for dex saves and rage now halves damage from attacks, and rogues get the benefits of 3e Defensive Roll at level 5 but with unlimited uses and no save needed. Casters still have the edge in sheer versatility, but over time high-level martials can match their damage output and are much harder to kill.
• Warhammer Fantasy Roleplay and Dark Heresy - While magic was locked to a single stat and spells were bought with experience, the real balancing factor was the fact that casting was innately a very risky ordeal that involved opening a gateway to Hell itself and required concentration (Here exemplified by a Willpower check) to harness successfully. If improperly controlled, the caster could potentially summon some horrific daemon who would be all too happy to kill anyone, summoner or no, alongside other possibly horrific effects.
  • Navigators (As seen in the Rogue Trader RPG) were somewhat less dangerous. While their powers lacked any chance of opening gateways and at worst only dealt harm to the three-eyed caster, their repertoire of powers is significantly smaller.