Cogmind > Strategies

Coverage Vs Integrity Formula

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Kyzrati:

--- Quote from: SimonScience on December 13, 2018, 09:30:53 AM ---As a quick comparison tool though Coverage/Integrity seems to work fine  ;D .

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Heh, yeah that's all it's for anyway, just a general idea of what you might lose first. In other words, a quick way to get an at-a-glance view of what you really need to prepare to replace at a moment's notice :P

Valguris:
This

--- Quote from: SimonScience on December 13, 2018, 06:34:49 PM ---it calculates the chance of survival at a damage, then multiplies that by the chance of survival at the next damage and so on,

--- End quote ---
does not equal this

--- Quote from: SimonScience on December 13, 2018, 06:34:49 PM ---which gives you the chance of survival of those damages combined

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They would be equal, if the correspoding events were independent (https://en.wikipedia.org/wiki/Independence_(probability_theory)#Independent_random_variables). But they are not. It's like rolling a 6-sided die and saying that the probability of getting 4 or higher ( 50% ) equals the probability of not rolling a 1, multiplied by probability of not rolling a 2, multiplied by probability of not rolling a 3, which gives (5/6)^3.


--- Quote from: SimonScience on December 13, 2018, 06:34:49 PM ---The division is so that it calculates the Expected Value (https://en.wikipedia.org/wiki/Expected_value), which is given by finding the mean of each result

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That is also incorrect. You should calculate the mean by multiplying the numerical value of each result by the probability of its occurence. No need for further division. Take a 6-sided die roll as an example again. Expected value of the rolled number is

where p_i = 1/6 (probability of rolling i) for each i. There is no need to divide this again by the number of possible results -- the averaging was taken care of via weighting each result by its probability!


Ah, and since the expected lifetime of a part equals (Integrity/PartCoverage)*TotalCoverage, and all your parts share the same value of TotalCoverage, then to compare item's expected durability you only need to compare their Integrity/PartCoverage ratio! Kyzrati's way is the correct way -- now proven mathematically!
...With a caveat that we assume that each point of damage rolls independently for which part it hits. Which is not true, since damage comes in chunks (shots). The difference is the most noticeable for parts with current integrity so low as to be destroyed within 1 or 2 hits (math geeks playing boardgames are probably familiar with this phenomena, since those games work with much fewer rolls than video games). I will not provide mathematical proof for this, but give an example instead:
Consider a part with 10% coverage and only 10 integrity remaining. A single 10 damage shot has 10% chance to destroy it. If we split this damage into n chunks, then the chance for destroying this parts equals (1/10)^n, which is 1/100 for 2 shots of 5 damage, or an astronomically low 1/10000000000 for 10 shots of 1 damage each (this last way is how Integrity/PartCoverage bases off its estimate). This also shows that damage reduction (Force Field, Thermal Shield, etc.) might be better than coverage for protecting those low integrity items, for example 50% damage reduction more than doubles life expectancy of those parts; to accomplish similar effect you'd have to more than double your TotalCoverage.

Unfortunately, accounting for "chunked" nature of damage requires the knowledge of received hits distribution (i.e. which weapons and how often hit you across a floor/ across a run/ across the next encounter, etc..., which depend on your build (avoidance), tactics you employ (short-ranged vs long-ranged, stealth, running from slow enemies but not from swarmers...) and map generation (which enemies you encounter, how close you come up on them). So the Integrity/PartCoverage is probably the best we can ever have.

TLDR for those, who want to skip all this math:

* Integrity/PartCoverage is the best metric to compare durability of items that we can mathematically analyze
* Life expectancy of a part (expected amount of damage received by Cogmind before that part gets destroyed) is (Integrity/PartCoverage)*TotalCoverage
* The above two measures greatly overestimate life expectancy of parts with very low current integrity (those that will get destroyed in 1-2 shots), such as hackware

Kyzrati:

--- Quote from: Valguris on December 14, 2018, 05:47:25 AM ---Kyzrati's way is the correct way -- now proven mathematically!

--- End quote ---
Wow, I did a mathy thing and it came out right? Speechless. Locking thread. No more digging into this, nope that's the end of it ;)

zxc:
Interesting read, guys!

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