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Forums: Index > Watercooler > DPS calculation corrected

$\text{A} = \text {Accuaracy}$
$\text{D} = \text {Damage}$
$\text{DPS} = \text {DamagePerSecounds}$
$\text{FR} = \text {FireRate}$
$\text{M} = \text {Magazine}$
$\text{RC} = \text {Recoil}$
$\text{RL} = \text {Reload}$

$\text{RL} = \frac{ 2 }{ 1 + \text{ReloadModifier} }$

$\text{RC} = 0{,}1 \cdot \left( 1 - \text{RecoilModifier} \right)$

$\text{DPS} = \frac{ \text{D} \cdot \left( \text{A} / 100 - \text{RC} \right) }{ \frac{ 1 }{ \text{FR} } + \frac{ \text{RL} }{ \text{M} } } \underbrace{ + \frac{ \text{D} \cdot \text{RC} }{ \frac{ \text{M} }{ \text{FR} } + \text{RL} } }_{ \text{no RC at 1st Shot} }$

old formula on Weapons-Page:

$\text{DPS}_{\text{wrong}} = \text{D} \cdot \text{A} / 100 + \frac{ \text{D} \cdot \left( \text{A} / 100 - \text{RC} \right) }{ \frac{ 1 }{ \text{FR} } + \frac{ \text{RL} }{ \text{M} - 1 } }$

The kirsch 03:59, January 15, 2012

Welcome, new user, and thanks for taking the time to improve this formula, not to mention your pretty TeX markup. I moved this to the Forum because I thought that it needed discussion. Perhaps I should have moved it to a sandbox under your userspace instead... anyway, it seems to have settled down.

I hate having that DPS calculation on the Weapons page at all. It's not a part of the game itself, just a way that some players have of assessing a weapon's deadliness. And trying to include recoil and accuracy as if they were scalars is bogus. Leaves out critical hits, the effects of aiming.... DPS is a valuable tool, but it doesn't belong on a heavily trafficked front page like Weapons.

I'm trying to think of a better place to put this. Maybe DPS needs a page all to itself. Dämmerung 22:10, January 17, 2012 (UTC)

Righto. As part of cleaning up Weapons, I moved the old DPS into a subpage. The better to hide that mess. Dämmerung 01:15, January 18, 2012 (UTC)

Calculation without Accuaracy and Recoil effects:

$\text{DPS} = \text{D} \cdot \text{FR} \cdot \frac{ \frac{ \text{M} }{ \text{FR} } }{ \frac{ \text{M} }{ \text{FR} } + \text{RL} } = \frac{ \text{D} }{ \frac{ 1 }{ \text{FR} } + \frac{ \text{RL} }{ \text{M} } }$

The kirsch 06:37, January 18, 2012 (UTC)

hands The_kirsch chalk, invites him to the front of the lecture hall
Please justify or otherwise explain how you have derived these figures. For example, you define a sub-term RL as

$\text{RL} = \frac{ 2 }{ 1 + \text{ReloadModifier} }$

While I see what you want that to denote, how you have derived this particular definition is not obvious to me. I'm not asking you to remove that or any other factor from your calculations, I'm asking you to submit a proof. Dämmerung 14:44, January 18, 2012 (UTC)

The normal Reload time is 2 seconds

some Weapons have a positiv or an negativ Reload Modification calld "Reload Speed"

Sample:

Reload speed is "+46%" => 146% of normal speed

Reload time is = 2 seconds / ( 1 + 0.46 ) = 2 seconds / 1.46 = 1.37 seconds

other samples

The kirsch 15:35, January 18, 2012 (UTC)

The common Borderlands k/(1+v) stat modifier relationship. Klar. Let me recapitulate and see if I have this correct.

Let $\text{D}$ be the damage per shot, i.e. the gun card Damage statistic.

Let $\text{FR}$ be the number of shots per second from a loaded magazine, i.e. the gun card Rate of Fire statistic.

Let $\text{M}$ be the number of shots in a magazine, i.e. the gun card statistic.

Let $\text{RL}$ be the reload modifier, i.e. the gun card Reload Speed stat modifier, if present. If absent, defaults to 0.

Let $\text{t}_\text{reload}$ be the number of seconds required to reload a magazine.

$\text{t}_\text{reload} = \frac{2}{1 + \text{RL}}$

Let $\text{t}_\text{mag}$ be the number of seconds required to empty a fully loaded magazine.

$\text{t}_\text{mag} = \frac{\text{M}}{\text{FR}}$

Then $\text{k}_\text{RL}$ is a coefficient reflecting the relative overhead of reloading

$\text{k}_\text{RL} = \frac{\text{t}_\text{mag}}{\text{t}_\text{mag} + \text{t}_\text{reload}}$

And $\text{FR}_\text{adj}$ is the aggregate rate of fire, including reload time in the net rate.

$\text{FR}_\text{adj} = \text{FR} \cdot \text{k}_\text{RL}$

Therefore

$\text{DPS} = \text{D} \cdot \text{FR}_\text{adj}$

which, algebraically expanded into its original terms, becomes

$\text{DPS} = \frac{\text{D}}{\frac{1}{\text{FR}} + \frac{\text{RL}}{\text{M}}}$

The preceding ignores factors of accuracy, recoil, and critical hits. Dämmerung 16:59, January 18, 2012 (UTC)

Note that RL isn't always apparent from the gun card. Your sample weapon is by Tediore, a manufacturer who usually presents the Reload Speed stat modifier on the card, allowing for the weapon's stock, magazine, and material. In the general case, however, one needs to analyze all the parts and materials to know the RL. Dämmerung 17:16, January 18, 2012 (UTC)

Correcting the calculation of treload. The only class of weapon that has a base reload time of 2 seconds is Repeaters. For all other weapons, the base times are as follows (excluding factors of manufacturer, material grade, stock, and magazine, all of which will affect the time):

Weaponseconds
Repeater 2
Patrol SMG 2.2
Machine Pistol 2.25
Combat Rifle 2.4
Revolver 2.5
Support Machine Gun 3
Assault Shotgun 3.5
Rocket Launcher 3.5
Semi-auto Sniper Rifle 3.5
Combat Shotgun 4
Manual-action Sniper Rifle 4

The reload speed on the ZPR21-B Hunter's Shotgun cited above is 2.79 seconds without bonuses from proficiency or class skills. That includes a substantial bonus from Tediore material 3 and mag1, but a penalty from stock2. Dämmerung 00:29, January 21, 2012 (UTC)

I have updated the DPS page. Dämmerung 23:59, January 30, 2012 (UTC)