Damage Per Second - DPS Formula / Attack Chains

DPS Formula / Attack Chains

There are certain aspects of the actual attacks a player must know in order to calculate a DPS Attack Chain. The following three attributes are generally regarded as universal throughout the MMO community:

• Base Damage: The damage an attack does regardless of equipped gear or outside enhancements.
• Base Recharge/Cool down: The time it takes for the attack to be used again.
• Activation Time: The time it takes for an attack to animate.

Tying these together is the simple formula of: Damage / (Activation Time + Recharge) = Damage per Second

As an example, if a player has an attack that does 75 damage, with an activation time of .25 seconds and a recharge of .75 seconds, the DPS is calculated as:

Using this attack, the character can apply 75 damage every second indefinitely, barring game restrictions such as energy or ammunition, to their target. However, most of the time one attack simply is not enough to yield significant DPS to bring down a tough foe. For this, it is necessary to calculate the DPS of a series of attacks. To do so, the calculation is performed disregarding the recharge.

What this means is that the original attack has the potential to do 300 damage in a second, as with only its activation time as a limit for how often the base damage can be applied within the time period. An attack's DPA is more important than its individual DPS, as by the time the player activates another attack, their first attack may be recharged already, making the recharge part of the equation redundant.

Adding a second attack to a character, such as a slower but more damaging attack: 100 damage, activation time of .50 seconds and a recharge of .75 seconds.

The fact that an attack does more base damage does not necessarily mean that it would be good for an attack chain, which varies per chain. As for making the chain, it's convenient to use small intervals in time like .25 seconds (the greatest common divisor of the activation and recharge times) and put them in a table: (let's assume we start with attack 1)

Where A denotes an Activation interval and R a Recharge interval. Notice that there is a returning pattern called a cycle, with length 5 short intervals of 0.25. In such a cycle there are 3 intervals occupied with Activation and two empty intervals (see also Get a filler attack).

With this starting point, we can now figure out the "long-term DPS" of these attacks. For convenience, they both have a recharge of .75 seconds. Why recharge is important again is due to the player wanting to recycle the first attack, as it has the high DPA number needed to get high DPS. We'll now calculate the DPS for such a cycle:

From this point the first attack will have recharged, and the cycle is essentially complete, giving us 140 DPS overall. To increase DPS, and avoid the down time created by the recharge times, one can do two things:

• Get a filler attack: A “filler” is an attack which can be inserted into a string that may have non-optimal DPA, but its recharge and activation times may be just enough to prevent the gap seen above as the character waits for one of its two attacks to recharge. This keeps the character continuously dealing damage and as a result deals higher DPS.
• Reduce the Recharge/Increase the Damage: A second option available for all characters in an MMO is to “buff” their attacks (granted they lack a filler) via equipping certain gear, items or by casting certain spells on themselves for a time. By increasing the damage, or decreasing the recharge time (optimally both), a player can attain much higher DPS as their best chain now does more damage without pauses.

To fit these examples into our chain, say there was an attack that perfectly fit the recharge “gap” created by our first two attacks, and did 50 damage. Our chain would now follow a repeating 1-2-3 pattern, and have a sustained 180 DPS, which is a nice improvement to the old chain. If the damage and recharge times of the two attacks were to each be buffed by say, 25% (x 1.25 for damage, / 1.25 for recharge), they would have the following attributes: 93.75 and 125 damage, .6 seconds recharge.

Recalculating the chain, we get 218.75 damage in a cycle of length 1.10, resulting in 198.86 DPS compared to 140, also an interesting boost. Notice that there still is a 'hole' of 0.35 seconds of free time in the enhanced cycle, so combining the right enhancements with a (buffed) filler attack will give an even greater DPS.