History Main / LinearWarriorsQuadraticWizards

** Replace "Wizard" and "Warrior" with "Anime Protagonist" and "[[MediaNotes/TheGoldenAgeOfAnimation Golden Age]] Cartoon", and you've got [[Recap/DeathBattleS08E16SaitamaVsPopeye Saitama VS Popeye]]. [[spoiler:Saitama is the WorldsStrongestMan and poster child for the ComedicInvincibleHero, but as an Anime Protagonist he's still somewhat bound by the laws of physics, while Popeye's ToonPhysics make him akin to a NighInvulnerable PhysicalGod, [[OutsideContextFoe unlike anything Saitama's ever faced before]] and on a completely different level to him. The fact that he even held his own in their fight proves Saitama's strength, but fighting him was ultimately [[ButForMeItWasATuseday another day at the races for Popeye]].]]

''Melee classes gain power at a linear rate as they level up. Magic users gain power quadratically as they level up.''

A quirk some VideoGame and especially TabletopRPG game systems share is that melee classes are more powerful, versatile or useful at lower levels than casters or magic-using classes. However, the trend reverses at higher levels, when the magic users gain a breadth of both versatility and pure power over simplistic hack and slash heroes.

Yet the trend reverses at higher levels. As the trope name says, the power of a warrior is linear. It grows at a steady pace whose increase can be predicted by simple arithmetic. But a wizard's power is quadratic or even [[ExponentialPotential exponential]]: as it grows, the rate of growth also multiplies. Learning something such as a spell leads to multiple, often unpredictable, varieties of more things to learn, in a manner similar to how a single infected person can infect multiple people unpredictably, or how a WikiWalk on [[JustForFun/TVTropesWillRuinYourLife TV Tropes]] or Website/TheOtherWiki forces you to follow more links which lead to discovery of more varieties of knowledge and tropes which have lots of interesting links themselves that lead to more countless instances of discovering tropes, and so on. Thus, in the end wizards must at some point become the more powerful class. For example, while warriors are still stuck at physical hacking and slashing, wizards have discovered how to [[RealityWarper warp reality itself]].

First off, the idea that warriors hit a development ceiling at some point. They hit the limits of human (or near-human) ability and can't bend physics any farther. Since warriors don't have magic, how is physical force supposed to beat, say, an intangible ghost or some supernatural baddie with the magical ability to ignore it? Basically, warriors can only be so fantastic, so even as they improve, those improvements mean less.

Secondly, in such a setting, there may be dozens if not hundreds of small-time mystic dabblers, but they quickly thin in numbers, only to resurface as potent adventuring wizards, culminating in the classic mystic powerhouse like [[Literature/TheLordOfTheRings Gandalf]] or [[TabletopGame/ForgottenRealms Elminster]], or the EvilSorcerer in the EvilTowerOfOminousness. Meanwhile, the [[Franchise/ConanTheBarbarian Conans]] and Literature/{{Beowulf}}s have the run of the place, being able to both solo and group. In essence, the mages study under the promise of a dull and complex path with great profits at the end.

Thirdly, there's more than a bit of WishFulfillment here. Gamers, and by extension game designers, tend to be nerds by definition. The notion that a wizard (generally something of a brainy bookworm) may start out weaker than the DumbMuscle, but surpass them entirely in the endgame, proving that knowledge is power that can modify the environment itself, thus making large muscles redundant in comparison? This account holds a lot of inherent appeal to them.

However, if this results from a development mistake, or enough complaints convince the author/programmer to change things, there are ways to limit the awesomeness of wizards. These include [[PowerAtAPrice restrictions on magic itself]], the two classic examples being the {{Mana}} mechanic or the even more restrictive VancianMagic. Both of these serve to cap how often a wizard can cast spells. [[ArmorAndMagicDontMix Preventing casting spells while wearing armour]] is another, though this is often partially countered by providing a range of protective magics that work much like normal armour ''only better'', but of course for a limited time. Other restrictions also exist; a common one is simply to make the wizard [[SquishyWizard Squishy]]. Others involve sanity and [[KarmaMeter corruption]] systems, or making the casting of a spell a tactically debilitating act.

Attempts to keep warriors' capabilities "normal" are far less prevalent in works of Eastern origin which are more likely to give their warriors CharlesAtlasSuperpower, and so the trope has weakened slightly in the minds of the younger generation. Other character types, such as the MagicKnight, the KungFuWizard, and practitioners of FullContactMagic, mingle both styles of fighting to their own advantage by either using magic to augment raw strength or training their physical abilities to "power up" their magical attacks.

* In ''VideoGame/{{Simutrans}}'', freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances, or docks and ships over water, you get the idea); however, you may soon be limited by bottlenecks in the production chain when storages run dry (e.g. that oil well may not be productive enough to feed your power station) or fill up (e.g. that gas station in that little town may not be able to move gasoline as quickly as you could ship to it). On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and tourist traps to your network, your ridership will increase dramatically, as people who couldn't get where they wanted to go (and thus won't use your system) before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In ''VideoGame/{{Simutrans}}'', freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances, or docks and ships over water, you get the idea); however, it is subject to bottlenecks in the production chain when storages run dry (e.g. that oil well may not be productive enough to feed your power station) or fill up (e.g. that gas station in that little town may not be able to move gasoline as quickly as you could ship to it). On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and tourist traps to your network, your ridership will increase dramatically, as people who couldn't get where they wanted to go (and thus won't use your system) before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In ''VideoGame/{{Simutrans}}'', freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances, or docks and ships over water, you get the idea); however, it is subject to bottlenecks in the production chain when storages fill up (e.g. that gas station in that little town may not be able to move gasoline as quickly as you could ship to it). On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and tourist traps to your network, your ridership will increase dramatically, as people who couldn't get where they wanted to go (and thus won't use your system) before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In ''VideoGame/{{Simutrans}}'', freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances, or docks and ships over water, you get the idea); however, it is subject to bottlenecks in the production chain when storages fill up (e.g. that gas station in that little town may not be able to move gasoline as quickly as you could ship to it). On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and tourist traps to your network, your ridership will increase dramatically, as people who couldn't get where they wanted to go before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In ''VideoGame/{{Simutrans}}'', freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances, or docks and ships over water, you get the idea); however, it is subject to bottlenecks in the production chain when storages fill up (e.g. that gas station in that little town may not be able to move gasoline as quickly as you could ship to it). On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and attractions to your network, your ridership will increase dramatically, as people who couldn't get where they wanted to go before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In ''VideoGame/{{Simutrans}}'', freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances), however, it is subject to bottlenecks in the production chain when storages fill up (e.g. that gas station in that little town may not be able to move gasoline as quickly as you could ship to it). On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and attractions to your network, your ridership will increase quickly, as people who couldn't get where they wanted to go before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In ''VideoGame/{{Simutrans}}'', freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances), however, it is subject to bottlenecks in the production chain when storages fill up. On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and attractions to your network, your ridership will increase quickly, as people who couldn't get where they wanted to go before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In ''VideoGame/Simutrans'', freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances), however, it is subject to bottlenecks in the production chain when storages fill up. On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and attractions to your network, your ridership will increase quickly, as people who couldn't get where they wanted to go before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In "VideoGame/Simutrans", freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances), however, it is subject to bottlenecks in the production chain when storages fill up. On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and attractions to your network, your ridership will increase quickly, as people who couldn't get where they wanted to go before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In VideoGame/Simutrans, freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances), however, it is subject to bottlenecks in the production chain when storages fill up. On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and attractions to your network, your ridership will increase quickly, as people who couldn't get where they wanted to go before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In "VideoGame/{{Simutrans}}", freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances), however, it is subject to bottlenecks in the production chain when storages fill up. On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and attractions to your network, your ridership will increase quickly, as people who couldn't get where they wanted to go before are now able to. As another advantage, having a good passenger network encourages city growth, which spawns more industries and increase production chain efficiency when you go back to freight.

* In "VideoGame/{{Simutrans}}", freight plays the "linear" role, while passengers and mail play the "quadratic" role. Moving freight is comparatively easy to start with and to make a profit on, as you simply connect point A to point B with rails and a suitable train (or road and trucks for shorter distances), however, it is subject to bottlenecks in the production chain when storages fill up. On the other hand, you'll struggle to make a profit when your passenger network is small, but as you connect more cities and attractions to your network, your ridership will increase quickly, as people who couldn't get where they wanted to go before are now able to.

** Building on its predecessor, ''VideoGame/DragonQuestIX'' inverts this trope. Low level attack spells don’t do considerably more damage than any properly equipped physical class, and it only gets worse from there—by the end of the game, a gladiator with an axe can do more damage to a single target ''or'' a group ''at no MP cost'' than an equivalent caster using expensive spells. The best strategy for most bosses looks like an episode of Anime/DragonBallZ[[note]]And since the artwork is all by Akira Toriyama, it really does look ''exactly'' like Dragon Ball Z...[[/note]], with physical characters boosting Tension for several turns then unleashing hell. (Oddly enough, the game gives your main character an exclusive skill that boosts another character’s Tension, meaning the best possible support character is you.) Multi-target attack spells can soften up multiple enemies, but that generally only saves you a turn or two, and your physical characters can get multi-hit weapons that do roughly the same amount of damage, though they better spend their time dropping one enemy per round each.

** ''[[TabletopGame/AdvancedDungeonsAndDragons2ndEdition Second Edition]]'' included many of the same balancing factors as the last one. Less powerful classes progressed through levels faster, and fighters enjoyed benefits such as Exceptional Strength, more hit points for high Constitution, and more followers at high levels, but still wind up getting seriously outpaced in power at higher levels. All of this depends on one's attributes, though: a fighter needs STR 18 and CON at least 17 in order to benefit from those specific perks. And even though wizards and clerics need high INT and WIS respectively to be able to utilize their best spells, they're still ''a lot'' better with their main stat being lower than 16.

** ''[[TabletopGame/DungeonsAndDragonsFifthEdition Fifth Edition]]'' took steps to get warriors and wizards closer in terms of combat ability. The edition raised the floor on wizards by adding cantrip spells, which wizards can cast as many times a day as they want. The Concentration mechanic also lowered the ceiling by preventing the most powerful spells from being used simultaneously, and forcing those spells end early if the wizard failed a saving throw after taking damage. Meanwhile, warriors got buffs to the number of attacks per round, made {{Critical Hit}}s easier and/or stronger, and let warriors bypass enemy resistances while also gaining some of their own. Finally, the advantage-disadvantage mechanic simplifies buffs quite a bit. Spells still allow for a greater deal of narrative agency, but stacking multiple area-of-effect spells and gigantic buffs on top of each other is no longer possible. So while this trope is still present in 5e, warriors and wizards are much closer in power than before.

** A preface to this: In many games in the series (''VideoGame/FinalFantasyV'', ''VideoGame/FinalFantasyTactics'', ''VideoGame/FinalFantasyV'', and ''VideoGame/FinalFantasyX'', to name just a few), any character can get more or less any ability, and the most powerful characters can [[MinMaxing cherry-pick a build]] from combat ''and'' magical skills.

* ''VideoGame/MightAndMagic 6'' & ''7'' plays with this trope. Warriors tend to be better in the beginning until the mages get access to their stronger spells and enough mana to be able to use it reliably0, at which point magic users outshines them. However at the end game you gain access to blasters which make both equals in damage dealing but the warriors come out on top again. Clerics and Sorcerers still have a fair few [[GameBreaker Game Breakers]], however.

** A preface to this: In many games in the series (''VideoGame/FinalFantasyV'', ''VideoGame/FinalFantasyTactics'', and ''VideoGame/FinalFantasyX'', to name three), any character can get more or less any ability, and the most powerful characters can [[MinMaxing cherry-pick a build]] from combat ''and'' magical skills.

*** If anything, the original ''Final Fantasy'' is Linear Fighter/Quadratic Black Belt. Black Belts start out substantially weaker than fighters, typically achieve parity somewhere around the volcano stage, and go on to become spicy kung-fu death on a stick in the endgame.

** A preface to this: In many games in the series (''VideoGame/FinalFantasyV'', ''VideoGame/FinalFantasyTactics'', and ''VideoGame/FinalFantasyX'', to name three), any character can get more or less any ability, and the most powerful characters can [[MinMaxing cherry-pick a build from combat ''and'' magical skills]].

*** If anything, the original Final Fantasy is Linear Fighter/Quadratic Black Belt. Black Belts start out substantially weaker than fighters, typically achieve parity somewhere around the volcano stage, and go on to become spicy kung-fu death on a stick in the endgame.

** In [[Recap/DeathBattleS08E02ShadowVsRyuko "Shadow VS Ryūko"]], [[spoiler:{{Franchise/S|onicTheHedgehog}}hadow is the Quadratic Wizard this time, to [[Anime/KillLaKill Ryūko Matoi's]] Linear Warrior: In their base forms, Ryūko was much physically stronger and tougher than Shadow, enough to potentially kill him in one hit. However, Shadow being much faster than Ryūko as well as being able to {{teleport|Spam}} as well as [[TimeMaster slow down and]] [[TimeStandsStill stop time with Chaos Control]] made landing that hit unlikely. Additionally, Shadow possessed far more destructive power with his Chaos abilities through removing his [[PowerLimiter Inhibitor Rings]] which, combined with the aforementioned speed and Chaos Control, meant that he could reliably damage Ryūko faster than her Life Fibers could {{heal|ingFactor}} her. What's more is that [[SuperMode Super Shadow]] was vastly faster and more powerful than Ryūko while in Senketsu-Kisaragi and has the benefit of NighInvulnerability.]]

* Similarly inverted in ''VideoGame/Lineage2''. The damage is linearly proportionate to Physical Attack stat for archers and warriors and proportionate to a square root of Magic Attack for wizards. As a result, while magic users can still provide a steady DPS during late game, they are overshadowed by top archers by a large margin.