Thursday, April 24, 2014

Effectiveness curves


A few years ago, I took a game design course as a non-major-specific elective.  Many different "curves" were discussed throughout the class: difficulty curves, learning curves, effectiveness curves.  Each of these curves is a theoretical function with arbitrary units which is given a whole lot of thought, despite being unmeasurable.  Weighing my compulsion to quantify things against the difficulty of trying to measure the skill levels of a sufficiently large number of players, I've decided not to get too number-y here.


What is a skill cap?

Skill cap has adopted two meanings in the gaming community.  Depending on whom you ask, "skill cap" means either the level of skill required to play at the highest possible level, or the potential effectiveness of playing at that level.  Technically, the former definition is correct.  According to the latter, Noxxic's DPS rankings should be an indication of skill cap for each spec.

So skill cap is, basically, how hard it is to reach a spec's full potential.

Potential is the highest effectiveness a spec can reach.

Skill floor is, in short, always zero.  It's the amount of skill you play with when you have no experience.  Many times, when players discuss the "skill floor", they really mean the effectiveness at or near the skill floor.  Classes with pets have a high effectiveness near the skill floor because pets do some of the work with no user input.

Because learning and effectiveness curves generally take the form of Sigmoid functions (bounded, monotonically increasing functions like the CDF and hyperbolic tangent), it is impossible to assign a single value to the skill cap - effectiveness increases with skill at an increasingly decreasing rate.  Instead, we should look at the skill required to reach specific proportions of the potential effectiveness: How much skill does it take to play at 50% effectiveness?  How about 99%?

Discontinuity

Effectiveness curves are not always smooth functions.  For example, the point at which a melee DPS realizes he/she is supposed to stand behind the target causes a jump discontinuity.  By loosening the restrictions on positioning, players on the lower end of the skill spectrum perform better, while neither the skill cap nor potential are changed.



AddOns

Addons tend to complicate things.  For example, the fire mage spell Combustion used to combine the effects of three different DoT's.  Having to keep track of all those effects gave fire mages a very high skill cap, despite having an otherwise simple rotation.  Accordingly, they also had a high potential.  The addon CombustionHelper trivialized tracking those DoT's by displaying their values in a window and lighting up when Combustion was off cooldown and the DoT's had reached certain values.



In this visual, the lower red curve represents fire mage effectiveness without using addons.  The upper pink curve represents fire mage effectiveness with CombustionHelper.  Notice that the potential effectiveness does not change; however, the addon drastically decreases the level of skill required to reach high levels of effectiveness.

The addon SpellFlash allows a player to reach ~80-90% effectiveness with little skill (aside from good reaction time) by highlighting an optimized rotation.  Because of addons and class guides, the lower end of the effectiveness curve is largely irrelevant.