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Wild Fox
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Posted - 2010.01.14 19:20:00 -
[1]
I looked for and couldn't find a proper formula to calculate the turret DPS. There was enough data, but no final formula. So here's my stab at making one. Note: this is theorycraft based on posts here and elsewhere -- I did not run any tests (so far).
Let's assume that we know the turret's base DPS (e.g. from EFT). We'll call it BaseDPS.
Let's also assume that we know the chance to hit. There is a formula (http://wiki.eve-id.net/Tracking) which has been confirmed and which seems to work well. We'll call our chance to hit Phit.
And finally (to simplify calculations but without loss of generality) let's assume that our Phit is greater than 1%. In the case that it's less than 1% everything is easy since all hits will be wrecking hits, they will all have the hit quality (which we'll call Qhit) of 3 and the DPS calculations are trivial in this case.
So we have BaseDPS and Phit. First thing we need to do is to calculate the expected quality of hit, E(Qhit).
Let's consider only landed hits, that is ones which did NOT miss.
The probability of having a landed hit be wrecking is (0.01 / Phit) and in that case our Qhit is 3. So the first part of E(Qhit) for landed hits is just
(0.01 / Phit) * 3
The probability of having a landed hit be NOT wrecking is, accordingly, ((Phit - 0.01) / Phit). The expected Qhit for a landed, non-wrecking hit should be the average, that is, (((Phit - 0.01) / 2) + 0.5). Thus the second part of E(Qhit) for landed hits is
((Phit - 0.01) / Phit) * (((Phit - 0.01) / 2) + 0.5)
And the total formula for the expected quality of hit for landed hits is
E(Qhit) = [(0.01 / Phit) * 3] + [((Phit - 0.01) / Phit) * (((Phit - 0.01) / 2) + 0.5)]
Doing standard algebra simplifications we get
E(Qhit) = (Phit^2 + 0.98 * Phit + 0.0501) / (2 * Phit)
The rest is easy. Expected DPS is just base DPS times the probability to hit times the expected quality of hit. So
E(DPS) = BaseDPS * Phit * (Phit^2 + 0.98 * Phit + 0.0501) / (2 * Phit)
Simplifying
E(DPS) = BaseDPS * (Phit^2 + 0.98 * Phit + 0.0501) / 2
And that is the final formula for the expected turret DPS.
Note that the BaseDPS is effective base DPS -- after all the bonuses from skills, equipment, etc. Also note that this is the formula for when the chance to hit is greater than 1%. When that formula makes it into a spreadsheet or an online calculator, it would be simple to add the special case of the chance to hit being less than 1%.
So, how much did I screw up..? :D
Fox
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Kalnov
Gallente Problematique Inc.
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Posted - 2010.01.14 21:51:00 -
[2]
Edited by: Kalnov on 14/01/2010 21:51:17 http://web.archive.org/web/20071223162431/www.eve-online.com/guide/en/g25.asp
This helps too.
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Saietor Blackgreen
Crimson Star Empire Symbiogenesis
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Posted - 2010.01.15 08:23:00 -
[3]
Originally by: Wild Fox I wonder why they call it a "simplified" formula..? It should be exact.
It is simplified because below 1% hit chance it doesnt calculate your damage right, because it simplifies the way wrecking hits are calculated.
In normal conditions, wrecking occurs, basically, if you have "hit roll" = 100/100, so every 100 shots. Because hit quality is dependent on your hit roll, you cant get "wrecking when missed" - you nly get it when hit, so 1/100 shots wrecking occurrency is preserved.
However, if your overall hit chance is less than 1%, you wont be getting a wrecking every hundred shots - simply because you hit less frequently than that. Every hit will be wrecking, but you will hit less than 1% of a time too.
So, second set of formulas (simplified ones) doesnt take this into account - it has separate formulas for above and below 1%.
Also, they call it simplified, because it is LESS COMPLICATED, not less precise really :)
--- EvE online. New game every 6 months. |
Ki Tarra
Ki Tech Industries
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Posted - 2010.01.15 17:13:00 -
[4]
Originally by: Wild Fox I looked for and couldn't find a proper formula to calculate the turret DPS.
Did you try the obvious: Turret Damage. Originally by: Wild Fox So, how much did I screw up..?
Not at all, but there is an easier way to reach the same conclusion.
Start by ignoring including wrecking hits.
Minimum damage is 0.5, maximum damage is Phit + 0.5. Giving the average hit a damage of ((0.5) + (Phit + 0.5))/2 = (Phit + 1)/2
Factor in the frequency of hits: Phit * ((Phit + 1)/2) = (Phit ^ 2 + Phit) / 2
Next calculate the damage that would come from the worst 1% of hits. (0.01 ^ 2 + 0.01)/2 = 0.00505.
Subtract the damage that would have come from the worst 1% of hits and add the damage that comes from wrecking hits: (Phit ^ 2 + Phit) / 2 - 0.00505 + .03 = (Phit ^ 2 + Phit) / 2 + 0.02495.
Then simplify the appearance of the equation: (Phit ^ 2 + Phit) / 2 + 0.02495 = (Phit ^ 2 + Phit + 0.0499) / 2
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pittom
Gallente Life Immortal
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Posted - 2010.01.16 08:35:00 -
[5]
My equation:
you + time - Life = OP
Try something like:
You + Life + Hooker + Beer + Smoke - Crazy calculations = Groovy
Cmon dude seriously!!
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Hugo Lordmagnus
Caldari Vexillari
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Posted - 2010.01.16 20:14:00 -
[6]
"Oho!' said the pot to the kettle...
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Wild Fox
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Posted - 2010.01.19 20:28:00 -
[7]
Originally by: pittom
Try something like:
You + Life + Hooker + Beer + Smoke - Crazy calculations = Groovy
Cmon dude seriously!!
That looks like a failfit to me :D
I prefer something like:
Me + Life + Sex for free + Good Wine + Other psychoactives + A variety of crazy stuff *including* calculations = Fun
Kaa
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