FrogReaver
As long as i get to be the frog
Overkill Damage is often brought up in DPR discussions as a theoretical offset to the damage that characters with fewer harder hitting attacks are doing. The basic concept seems reasonable on the surface but what never gets accounted for is that a character with a single attack can kill enemies faster on average than a character with 2 attacks even when they do the same DPR.
Proof:
Enemy has 5 hp
PC1: 60% chance to hit. 8 Damage (no variation). 1 Attack
PC2: 60% chance to hit. 4 Damage (no variation). 2 Attacks
PC 1:
PC 2
As you can clearly see above, the Character that makes a single attack actually kills the 5 hp enemy faster on average than the PC making 2 attacks. (In the example provided both PC's have the same overkill damage whenever this particular enemy dies). So why is PC 1 killing this enemy faster? Because the chance to kill on rounds X distribution.
Why do we consider PC 1's overkill damage to be higher than PC 2's (given that it was the same in the example provided)? Because the other half of enemies PC 1 fights will leave him doing more overkill damage. Thus, on average PC 1 does more overkill damage than PC 2
On the enemies where PC 1's overkill damage is higher, what causes that? Basically it happens because the hp value fell is such a place that PC 1 needed X hits to kill it on average but PC 2 only needed 2X-1 attacks. This occurs any time an enemies hp divided by 4 is an even number. When the enemies hp divided by 4 is an odd number PC 2 needs 2X attacks.
Why do I discount overkill damage? Because, the most important factor is how fast the enemy dies. If the enemy dies faster then you get to start applying your damage to the next enemy that much faster. Since equal DPR characters kill different enemies faster or slower on average (and their chance to kill an enemy on round X distributions are never the same) then looking at overkill ignores the most important factor. In fact, that's why I call overkill damage a fallacy. It's a nearly meaningless stat in the grand scheme of things that some individuals regard as providing a significant insight in analysis. It can't do what they want it to do because equal DPR characters don't kill enemies at the same rates. Oftentimes the fewer attacking higher damage character will on average kill enemies faster.
What more work needs done in this area?
Adjust the results for different chances to hit. Different numbers of attacks. Probably most importantly would be to adjust for variable damage dice as opposed to a specific damage value for every hit. It would also be helpful to compare a few enemies that PC 1 kills faster and some PC 2 kills faster and see if the magnitudes and relative values of such faster average kills are much different.
Proof:
Enemy has 5 hp
PC1: 60% chance to hit. 8 Damage (no variation). 1 Attack
PC2: 60% chance to hit. 4 Damage (no variation). 2 Attacks
PC 1:
PC 2
As you can clearly see above, the Character that makes a single attack actually kills the 5 hp enemy faster on average than the PC making 2 attacks. (In the example provided both PC's have the same overkill damage whenever this particular enemy dies). So why is PC 1 killing this enemy faster? Because the chance to kill on rounds X distribution.
Why do we consider PC 1's overkill damage to be higher than PC 2's (given that it was the same in the example provided)? Because the other half of enemies PC 1 fights will leave him doing more overkill damage. Thus, on average PC 1 does more overkill damage than PC 2
On the enemies where PC 1's overkill damage is higher, what causes that? Basically it happens because the hp value fell is such a place that PC 1 needed X hits to kill it on average but PC 2 only needed 2X-1 attacks. This occurs any time an enemies hp divided by 4 is an even number. When the enemies hp divided by 4 is an odd number PC 2 needs 2X attacks.
Why do I discount overkill damage? Because, the most important factor is how fast the enemy dies. If the enemy dies faster then you get to start applying your damage to the next enemy that much faster. Since equal DPR characters kill different enemies faster or slower on average (and their chance to kill an enemy on round X distributions are never the same) then looking at overkill ignores the most important factor. In fact, that's why I call overkill damage a fallacy. It's a nearly meaningless stat in the grand scheme of things that some individuals regard as providing a significant insight in analysis. It can't do what they want it to do because equal DPR characters don't kill enemies at the same rates. Oftentimes the fewer attacking higher damage character will on average kill enemies faster.
What more work needs done in this area?
Adjust the results for different chances to hit. Different numbers of attacks. Probably most importantly would be to adjust for variable damage dice as opposed to a specific damage value for every hit. It would also be helpful to compare a few enemies that PC 1 kills faster and some PC 2 kills faster and see if the magnitudes and relative values of such faster average kills are much different.
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