Monday, November 21, 2016

RPG Design: Linear Fighters, Quadratic Wizards

This week, I'd like to take a look at another infamous design issue that haunts Dungeons & Dragons and similar games: Linear Fighters, Quadratic Wizards.



Linear Fighters, Quadratic Wizards refers to the fact that, in D&D, Fighters' skills and abilities improve at a largely linear rate, whereas Wizards improve much faster.  The reason for the latter is because Wizards' powers (as primarily encapsulated by their spells) increase simultaneously along multiple axes: not only to they get more spells but also the effectiveness of any given spell (e.g., damage output, range, etc.) tends to also increase as the Wizard levels up.

For example, let's take a look at a common Level 1 spell in AD&D:

Magic Missile (Evocation)
Level: 1     Components: V, S    Range: 6" + 1"/level     Casting Time: 1 segment    Duration: Special     Saving Throw: None    Area of Effect: One or more creatures in a 10 square foot area 
Explanation/Description: Use of the Magic Missile spell creates one or more magical missiles which dart forth from the magic-user's fingertip and unerringly strike their target. Each missile does 2 to 5 hit points (d4+1) of damage. If the magic-user has multiple missile capability, he or she can have them strike a single target creature or several creatures, as desired. For each level of experience of the magic-user, the range of his or her Magic Missile extends 1" beyond the 6" base range. For every 2 levels of experience, the magic-user gains an additional missile, i.e. 2 at 3rd level, 3 at 5th level, 4 at 7th level, etc.

So, a 5th level Magic-User casting Magic Missile has a tripled damage output and a range that's nearly doubled compared to a 1st level Magic-User, not to mention that he can cast Magic Missile four times per day compared to a 1st level Magic-User's one time.

Meanwhile, the AD&D Fighter has also improved over four levels (e.g., THAC0, weapon proficiencies, etc.) but not to the same extent (i.e., he isn't hitting three times as hard or making four attacks per round).  And difference between the two classes only becomes more pronounced over time as each spell continues to become more powerful and as the Wizard picks up more spell slots.

Furthermore, the spells themselves are unbalanced in the spell levels.  For example, Wish (a 9th level) is far more than nine times more powerful than any 1st level spell.

The net effect is that the Wizard will pass the Fighter in mid-level play and far outstrip the latter in high-level play.



Linear Fighters, Quadratic Wizards is an issue specific to Dungeons & Dragons because of the magic system, most notably because of casting speed and versatility of spells (i.e., D&D Wizards are quick casting generalists).  For example, if spells took hours to cast or if Wizards needed to choose between limited selections of spells, their power would be sharply scaled backward.

In addition, 3e exacerbated the issue by changing the assumed default play style: in older editions, it is assumed that once PCs reach name level (usually around 9th level), play will shift to domain management (i.e., the PCs will transition from itinerant adventurers to rulers).  Thus, the ever more powerful spells of magic-users will be balanced by the fighter's ever larger armies.


In terms of Sorcery & Steel, my rules set, I've taken a two fold approach to Linear Fighters, Quadratic Wizards:

  • Remove gamist restrictions on magic items

Just like I removed the gamist restrictions on weapons and armor, all classes can use all magic items.  Thus, in actual play, it matters less that the Wizard can cast Lightning Bolt if the Fighter has a Wand of  Lightning Bolts.

  • Turn wizards into glass cannons

By giving wizards a clear Achilles' heel, namely significantly less hit points than in standard AD&D, the two classes remain relatively balanced since the Wizard never outgrows a dependence upon the Fighter as a meat shield.


Finally, I would be remiss without including this notable (and hilarious) example of the trope:


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