Zombie Hunter University, Fairview

There are three reasons weapons may not deliver their advertised Damage Per Second. The first two are obvious: Accuracy and Reloading. If a weapon pauses to reload or if it fails to hit its target, that mitigates DPS.

The third reason is Over-Damage, which is what happens when weapons inflict more damage than necessary to kill zombies. This problem is easier to grasp in visual form. The chart below depicts what might happen if an Uzi sub machine gun were firing at a group of five Normal Zombies: Dog Zombie, Female Zombie, Male Zombie, Fat Female, and Fat Male.

The chart shows how much is inflicted by each shot and keeps a running tally of the total inflicted on each zombie. For example, Shot #5 is a critical that inflicts 14 damage points, which when combined the previous non-criticals adds up to 25.2 (hence, 14/25.2).

Firing 8.57 rounds per second, the Uzi theoretically inflicts 45.6 damage points per second, which should be enough to kill a crowd of 30 Normal Zombies in just under 17 seconds.

(Assuming an even distribution of zombies, their total Health Points would be 774. 774 divided by 45.6 is equal to 16.97.)

The chart, however, reveals something different. It takes 30 shots to kill five zombies. This means it would take 150 shots to kill 30 zombies. 150 divided by 8.57 is equal to 21 - four seconds longer than anticipated.

What is happening? The Answer is Over-Damage.

The Uzi's base damage for a non-critical hit is 2.8 damage points; a critical hit inflicts 14 damage points. An optimized Uzi fires 20% critical hits - one out of every five shots. As the chart shows, the combination of non-criticals and criticals tends to waste damage:

1. Shots 1-5 inflict 25.2 damage points on the Dog Zombie, which has only 20 health points. 5.2 damage points are wasted.
2. Shots 6-10 inflict 25.2 damage points on the Female Zombie, which has only 21 health points. 4.2 damage points are wasted.
3. Shots 11-15 inflict 25.2 damage points on the Male Zombie, which has only 24 health points. 1.2 damage points are wasted.
4. Shots 16-22 inflict 30.8 damage points on the Fat Female, almost exactly the same as her 30 health points.
5. Shots 23-30 inflict 44.8 damage points on the Fat Male, who has 34 health points. 10.8 damage points are wasted.

That is a total of 22.2 wasted damage points. This is why the Uzi takes longer to kill a crowd of 30 than one would calculate based on the numbers.

In real world applications, the difference between killing 30 zombies in 17 seconds versus 21 seconds may not seem like much, but these small amounts multiply over time during prolonged agro situations. Students wondering why they are not racking up as many experience points as they expect during outpost attacks should invest more in Reloading and Accuracy.

Students should also take a close look at the actual Damage Per Hit Numbers for the grinding weapon and see how they add up against individuals, not just averages spread over crowds.

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But What if the Critical Hits Landed Differently?

Note: The above chart assumes that every shot hits a target and that each zombie is killed in sequence. It is possible to imagine different sequences which result in faster kill times, but the above scenario represents a decent middle-ground estimate. For a comparison, take a look at the next chart which shows the different possible combinations of critical hits and non critical hits from an Uzi that can add up to enough damage to kill a Fat Male Zombie with 34 health points.

As the chart clarifies, assuming that every sequences of five shots includes one critical hit and four non-critical hits, there are four possibilities. Two of them require nine shots for a kill; one requires eight, one requires seven, and one requires six.

Statistically, the least likely scenario is the final one, in which the first shot is a critical hit; this will happen 20% of the time. 80% of the time, one or more non-critical hits will land before a critical hit. Probability converges on the middle scenario, which is the one depicted in the previous chart.