PlanetSide Universe - View Single Post - A quick bit of math
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Old 2013-06-28, 08:32 PM   [Ignore Me] #16
Artalion
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Re: A quick bit of math


Also, straight DPS is not the correct way to compare weapons. The best is TTK, accounting for the fact that the firing sequence starts with a bullet and not with the intervals between bullets (when you click your mouse, you instantly fire a bullet, you don't have to wait a 60/RoF interval of time before the bullet fires). So, comparing starting weapons

1. Guass SAW -- Five bullets to kill, four intervals/gaps between bullets to kill (the actual 60/RoF firing time), takes 4*60/500 to kill = 0.48 seconds.

2. Orion -- Seven bullets to kill, six intervals/gaps between bullets to kill, takes 6*60/750 = 0.48 seconds

3. T9 Carv -- same as Orion

So the true TTK is identical between all three of them.

Now if you want to calculate how quickly you can kill multiple people in a row without letting go of the trigger, or how quickly you can kill a MAX with an LMG, then yeah, Gauss SAW is probably going to fall behind because the benefit of having that high-damage starting bullet goes away the longer you fire. It makes up for this with the huge 100-round clip size.
Time to Kill is a very useful statistic, but it is also deceptive. It makes certain assumptions, the biggest is that the shots you are firing will hit. But as is often the case, recoil can radically reduce the accuracy of your shots. In close quarters combat, when both players are moving around, accuracy is further reduced.

So the TTK statistic also needs to take into account the average number of shots fired per kill.

For each shot you miss, you will have to add a time break for the missed shot. This would be about .12 seconds for each NC miss, and .8 for each TR/VS miss. When you start to take misses into account, DPS matters.

Now let's look at the TTK statistic, assuming that each opponent has missed exactly one shot.

NC: 5 breaks * 60/500 = .6
TR/VS: 7 breaks * 60/750 = .56

At the end of short battles, I often find that I've expelled about ten rounds. So let's measure that period of time, shall we?

My TTK is 1.08 s (9*60/500) while my opponent would be .88 s (11*60/750).

The bottom line here is that the TTK statistic is misleading and that his assertion that NC weapons are at a disadvantage against their competitors is plausible. VS weapons have no recoil, which translates to higher accuracy. TR weapons do have recoil, which reduces their accuracy, but the effect is much less pronounced because their weapon is more forgiving, that is, a miss with a TR weapon is the same as a miss with a VS weapon.

But NC weapons have heavier recoil and a slower rate of fire, which means that their miss penalty is 50% more than their competitors. In fact, we can show that their time to kill is only identical when every shot hits, and that they are always at a disadvantage with each miss.

But why not make things more interesting. Let's assume that two heavies are dueling with overshields activated. This brings their health to 1700 as health. The numbers come out to this.

NC: Nine shots kill. That comes out to .96 seconds. (8*60/500)
VS/TR: Twelve shots kill. That comes out to .88 seconds (11*60/750)

Assuming perfect accuracy (HA!) the NC are at a clear disadvantage. And as I have already shown, when accuracy is equal (HA!) the disadvantage become even more amplified. Therefore, the default NC weapon at 10 meter engagements are weaker or equal to their enemies.

All this information was assuming an engagement at ten meters, which isn't unusual. But perhaps they are having a ranged engagement. Let's see if the NC prevail at range.

At range, assuming perfect accuracy the numbers give us this:

NC: Six shots to kill.
VS: Eight shots to kill.
TR: Nine shots to kill.

NC TTK: (5 shots+(shots missed=0))*60/500= .6 seconds.
VS TTK: (7 shots+(shots missed=0))*60/750= .56 seconds.
TR TTK: (8 shots+(shots missed =0))*60/750 = .64 seconds.

For a moment, it looks like the NC have something to celebrate. They can claim that their weapon is better than the TR at range.

But then we take inaccuracy into account and things go downhill for the NC very quickly.

Let shots missed= 1.

Then the following numbers occur:

NC TTK: .72
VS TTK: .64
TR TTK: .72

Equality is reached within one missed shot, and by two missed shots, you get:

NC TTK: = .84
VS TTK: .68
TR TTK: .76

Now comparing heavies with overshields at range and perfect accuracy.

NC: Eleven shots to kill.
VS: Fourteen shots to kill.
TR: Fifteen shots to kill.

NC TTK: 1.2 seconds.
VS TTK: 1.04 seconds.
TR TTK: 1.12 seconds.

TL;DR

VS heavies have an absolute advantage over all other factions, and places first close up and at ranged combat. They are able to kill the heavies of the other factions faster at range and up close.

TR heavies come in second, they are plausibly equivalent to VS at close range, but recoil makes equal accuracy unlikely, giving the advantage to Vanu. TR are at a clear disadvantage at range. This disadvantage is amplified by the reduced accuracy of the TR due to recoil. They are able to kill NC heavies at range.

NC heavies have the worst guns of the three factions. They are dominated by the TR and VS at close range. They have a plausible advantage over the TR, but that advantage only exists when accuracy is perfect. If one shot is missed, it is equal to a TR weapon, and for misses greater than one, NC returns to third place. They will lose to the heavies of both factions, even with perfect accuracy.
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