User:Raine Valen/Musings/Game Theory

=The Resources= Let's start with something relatively basic. In Guild Wars, as in everything, every action has a cost and must draw from a resource in order to be carried out. These costs differ from action to action, with many actions requiring several resources.

1: Time
Time is the basic resource, the platform upon which everything else is built. While some uses of Time are very tangible and concrete, such as casting time and the time remaining in a match, there are other, more subtle applications of the Time resource, such as the time required to kite or weapon swap. All other resources replenish with the passage of Time (either directly or indirectly), and as most actions require Time to execute, other resources are absolutely useless without Time to spend them. It should also be noted that Time is constant - every player and NPC gains Time at the same rate. The ultimate goal of any team is to exhaust the Time of their opponent. When a team requires more Time than they have, they begin to lose. Whether they need Time for Energy to regenerate, Time to save a teammate from a spike, or Time to move to an objective, creating a need for Time greater than Time's constant inflow is the only way - the only way - to win.

2: Health
Health is a simpler resource than it is often made out to be; it is largely a rough measure of Time and Energy. However, Health usage has one serious ramification that no other resource matches: when you run out of Health, you die. While running out of Energy or having all of your Skills on recharge is bad, being dead has its own implications. Namely, a dead character cannot use Time at all, meaning that Time is wasting away on teams with dead players.

3: Energy
Energy is a very straightforward resource. Most Skills require energy to activate, which makes Energy a very valuable commodity. Energy replenishes automatically with the passage of Time under normal circumstances, and can be used to alter other resources, such as by replenishing the Health of allies or decreasing that of foes. Though Energy constantly replenishes with Time, there are caps in the amount of Energy that any one player can hold at a time. Because of this, a character who cannot hold more Energy is, in effect, wasting Energy at a rate equal to their inflow of Energy due to Time.

4: Adrenaline
Adrenaline is very similar to Energy in application. The main difference is that Adrenaline does not replenish itself automatically with Time, but instead is replenished as a character attacks or takes damage. It also differs in that skills within a player's skill bar each store Adrenaline independently of one another, while Energy-requiring actions all draw from the same pool.

5: Skills
The Skills on a player's skill bar are a resource. Many, when used, are disabled for a period of time, meaning that the player cannot draw on the same resource again for that period. This resource is closely related to Time, Energy, and Adrenaline.

6: Position
Position is a resource that is often overlooked. Though independent of Health, Energy, or Adrenaline, Position is very much related to Time due to the simple fact that moving takes time. It is for this reason that a kiting Monk pressures the opposing team's Time by wasting the Time of the melee character attacking them. The simple quantification of Position as a resource is "distance to objective location". A Warrior standing adjacent to a Mesmer in the direction in which the Mesmer would like to go to reach their objective location is pressuring the Mesmer's Position while maintaining a very good Position, themself, with no other factors considered. A Monk with Mending Touch in touch range of three allies has more Position resource than a Monk with Mending Touch in range of one ally, with no other factors considered. Position does not replenish automatically with Time, but does take Time to recover.

=Pressure and Resource Exchange= Pressure is, basically, the depletion of one team's resources by the efforts of other team. Every action taken in competitive play is taken with the goal of pressuring the other team - warriors hit casters to pressure their health, eles blind and snare warriors to pressure their position, rangers interrupt to pressure casters' time and energy, monks prot to pressure warriors' time. It should be noted that, in order to consume the resources of another, one must spend their own resources. However - and this is important - the rate of exchange is not always equivalent. I will repeat and boldicize this because it is so important: the rate of exchange is not always equivalent. In fact, a player's skill can be quantified as the amount of resource they are able to consume, on average or in a specific situation, with a set unit of their own resource.

An Example:
To help us understand that the rate of exchange is not constant, let us look at a simplistic example. Obviously, in actual play, there will be many more factors to consider; this is just for the purposes of comparison. Example 1:
 * A monk on a four-man team is being trained by an axe warrior. The warrior builds adrenaline and spikes with Eviscerate, Executioner's Strike, and Agonizing Chop.  Panicked by the sudden drop in their health, the monk casts Return on a nearby ally, then casts Mending Touch and Word of Healing on themself, returning their Health to 90%.  The warrior catches up to the monk and continues to attack them, but the monk casts Patient Spirit on themself as their health begins to drop, which returns their health to 100% when it ends.  This occurs over six seconds, and the warrior is ready to spike again in four seconds.

Example 2:
 * A monk on a four-man team is being trained by an axe warrior. The monk counts the warrior's adrenaline, and, immediately upon the warrior landing Eviscerate, the monk casts Mending Touch to remove their Deep Wound, then casts Return on a distant ally after Executioner's Strike and Agonizing Chop hit.  They then cast Word of Healing, returning their health to 90%, and maintain a safe distance as the rest of their health regenerates.  This occurs over five seconds, and the warrior won't be able to spike again for another ten seconds.

Example 3:
 * A monk on a four-man team is being trained by an axe warrior. The monk counts the warrior's adrenaline, and, as the warrior reaches 7 adrenaline, the monk casts Return on a distant ally, then casts Spirit Bond on the ally nearest the warrior.  The warrior, having lost their target, changes to the nearby target, and spikes with Eviscerate, Executioner's Strike, and Agonizing Chop - Spirit Bond negates almost all of the damage, and the spike target remains at 90% health.  As the warrior continues to attack the kiting target, Spirit Bond triggers repeatedly, refilling the target's health.  Meanwhile, the monk casts Patient Spirit on themself to return their health to safe zones.  The warrior continues to build adrenaline, then spikes the target again; Spirit Bond, again, negates the damage.  This occurs over twenty-two seconds, and the warrior is ready to spike again in ten seconds.

In which situation did the monk perform best? Well, let's look at their resource consumption: It should be fairly obvious that the monk performed abysmally in the first scenario; they had to eat a huge amount of energy, their health dropped to critical levels, they sent many important skills into recharge, and they only bought ten seconds. The second monk performed better, experiencing no net energy loss, keeping their health at safe levels, and buying themself a better position. However, the monk in the third scenario performed best, using less energy than they gained over the period, experiencing almost no health loss, and putting almost no pressure on their skill bar.
 * The monk spends 20 Energy (in ten seconds) in the first, 15 (in fifteen seconds) in the second, and 25 (in thirty-two seconds) in the third.
 * In the first example, the monk's Health drops to critical levels; in the second, the monk's Health drops, though not quite as far; and in the third, the warrior only deals some auto-attack damage on the monk and almost none to their second target.
 * In the first and second, the warrior only burns half as much adrenaline as in the third.
 * In the first example, the monk burns Mending Touch, Word of Healing, and Return - all skills that have powerful effects and are frequently necessary, which leaves them in a temporarily vulnerable state. In the second, the monk uses Mending Touch (earlier - this increases the likelihood that it will be recharged when it is needed - but still sending it into recharge), Return, and Word of Healing.  In the third scenario, the monk uses Return early (giving them an advantage on its long recharge), then uses Spirit Bond (a skill with a relatively short recharge and that is used relatively infrequently), Mend Condition (which has a fairly negligible recharge), and Patient Spirit.
 * In the first scenario, the monk ends up with the same Position in which they started - with an axe warrior training them. In the second and third, the monk ends up with a better Position - they gained Position as the scenario played out.