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Kazuo Ishiguro
House of Marbles
Posted - 2007.04.19 10:49:00 - [1]
 

Edited by: Kazuo Ishiguro on 22/04/2007 23:10:23
These seem to be the most under-rated of the pirate implant sets, so I thought I'd have a go at quantifying their effects. Entity's guide to pirate implants is a good starting point, but actually working out how much less damage you stand to take as a result of your reduced signature radius is not trivial.

For missiles, the damage formula is quite simple; a 1% reduction in your sig radius gives a 1% reduction in damage (assuming that your ship has a smaller sig radius than the missile explosion radius).

For turrets, the effects are wildly variable, depending on your choice of ship and the weapons used by the pilots attacking you. The turret chance to hit formula looks something like this:

P = 2^-((AB)^2 + C)

where A is transversal / (tracking * range), B is turret sig. res. / target sig. radius, and C is related to falloff.

Now suppose you, the target, plug in a set of assorted Halo implants, multiplying your ship's sig radius by r, where 0.79 < r < 1. Then the new chance to hit will be

P(r) = 2^-((AB/r)^2 + C)

Divide this by the original chance to hit:

P(r)/P = 2^(-[(AB/r)^2 + C] + [(AB)^2 + C]) = 2^[(AB)^2*(1-r^-2)] (the Cs cancel)

Making the assumption that signature radius does not significantly affect the hit type (excellent, wrecking, ... , etc), this figure is a good estimate for the % of the original amount of damage that will get through once the implants are plugged in.

Against turrets, the effects can be amazing- under the right circumstances a Halo set can halve people's chance to hit you, effectively doubling your tank.

I've created a small spreadsheet for people to experiment with:

http://dl.eve-files.com/media/corp/KzIg/Halo.zip


J'Mkarr Soban
Posted - 2007.04.19 12:21:00 - [2]
 

I thought sig radius determined if they hit you or not, not how much damage was done? For turrets at least.

The way it was explained to me many, many moons ago was the bigger the sig radius, the larger the target, so you could hit it easier. So if a frig laser has a sig thing (the thing gauging the targets sig - can you tell I'm not a turret boy? Very Happy) that is smaller than the targets sig, they will always hit.

Raivi
Sniggerdly
Pandemic Legion
Posted - 2007.04.19 12:28:00 - [3]
 

Yup, but lowered chance to hit means less damage taken over time on average. Nice calculations, this could come in handy.

Akita T
Caldari Navy Volunteer Task Force
Posted - 2007.04.19 12:32:00 - [4]
 

Edited by: Akita T on 19/04/2007 12:33:34

So if you deal an average of 10 actual damage per shot but hit 80% of the time, how is that radically different in the long run from dealing 20 actual damage per shot but only hitting 40% of the time ? Answer is, it's not that much of a difference. Doubled "evasion" counts as a doubled tank potential no matter how you put it.

And no, a small gun will NOT always hit a big target, it will only make it more likely to hit while inside optimal. You can still have small blasters missing battleships if you orbit too fast and too close.
As for how turrets work, it's completely FUBAR due to oversimplified server-side calculations.
If anything, the turret "to hit" formula and "damage dealt" formula need a serious, long look and subsequent upgrade to a much more intuitive (one could even say "realistic") style... with the first change being to STOP using "absolute transversal velocity" and distance as base and start using "relative angular velocity" instead.

Actual "to hit" formula:
hit chance = ((1/2)^((((Transv/(Range*Tracking))*(Sig_Res/Sig_Rad))^2) +((max(0,Range-Optimal))/Falloff)^2))

Also, quality of hit SEEMS to be influenced (albeit to a much lesser degree) by (some? all of?) the same factors as "to hit" formula... so Halo implants might be even better as you thought.

dalman
TunDraGon
Pandemic Legion
Posted - 2007.04.19 12:45:00 - [5]
 

Edited by: dalman on 19/04/2007 12:43:30
1.
Concerning the discussion here:
It has been shown by extensive testing, that hit chance does not only have an effect on how often you hit, but also on the quality of the hits.

As in, say your hit chance is 20%, and you fire 1000 shots and get 200 hits. Out of these 200 hits, there will hardly be a single "well aimed" etc - it will only be "barely scratches" etc.

While if your hitchance is 99%, you fire 202 shot and get 200 hits, you'll then find plenty of good hits and hardly no bad hits among them.


2.
Yes, as you show, Vs turrets the damage reduction of halo implants depends on the other variables in the equation. In some cases, the halos will hardly have any effect at all, while in others the damage reduction may be huge.

Kazuo Ishiguro
House of Marbles
Posted - 2007.04.19 12:48:00 - [6]
 

Edited by: Kazuo Ishiguro on 19/04/2007 12:49:03
In situations where the base chance to hit is near zero due to high transversal, I've noticed that the effect of a Halo set becomes very large and confuses Excel. This is correct, I think, but the chances are that you'd pretty much never be hit even without the implants in those situations.

So far so good- at least one person with extensive experience in this area seems to agree with what I've found Razz

What research have people done on hit type distribution at constant hit probabilities? Ideally, I'd like to see some logs with about 1000 shots from the same weapon, where tracking, transversal, range, and sig radius were all constant. This would then need to be explored for various hit probabilities (preferably by changing only one variable at a time to begin with).

Tactus
Mob Thought
The Gurlstas Associates
Posted - 2007.04.19 15:01:00 - [7]
 

nice clean sheet.

i've been using my own tool to do the same calcs... thanks for saving me the time to tidy it up! *grin*

hit probablity datasets are sorely lacking. i'd look first at the tracking guide and try to milk that as much as possible, before i spent hours ocr-ing screen caps from sisi.

Kazuo Ishiguro
House of Marbles
Posted - 2007.04.19 15:33:00 - [8]
 

There's a 'save logs to file' option under the logs screen in game - it's just a matter of a lot of text editing to extract the actual numbers from these logs. I might have a go on TQ with a destroyer, come to think of it...

J'Mkarr Soban
Posted - 2007.04.19 16:37:00 - [9]
 

AFAIK, QF can analyse logs.

And if anyone wants a willing victim to sit still whilst being shot at, I'm up for it, though my tank might not be heh Very Happy

Sonorra Baki
Interstellar eXodus
BricK sQuAD.
Posted - 2007.04.19 18:17:00 - [10]
 

EvE combat log analyzer

This tool does all that for you

Jei'son Bladesmith
The Storm Knights
The Cool Kids Club
Posted - 2007.04.19 19:09:00 - [11]
 

Originally by: Sonorra Baki
EvE combat log analyzer

This tool does all that for you


oooooooo Shocked pretty. Gonna have to play with that! Very Happy

Kazuo Ishiguro
House of Marbles
Posted - 2007.04.19 20:03:00 - [12]
 

Edited by: Kazuo Ishiguro on 19/04/2007 21:46:21
Thanks for the link. I'm testing using a Catalyst for now. I'll make the data available once it's in a useful form.

//edit:

So far I've got 4 sets of 1280 shots - they take about half an hour each to do. For the time being I'm experimenting with different ranges, keeping the ship and the target stationary. So far, it seems that at 40% chance to hit or lower, one only does about 80% of the damage obtained from the hit type distribution experienced under perfect conditions.

In theory, one would always do 3/102 = 2.94 % of damage under ideal conditions, due to the way that wrecking hits are imposed - it seems that under any conditions, one always gets about 1% wrecking hits

I've been using a Catalyst with 8x 125mm Railgun II (and a mag. stab. to up the rate of fire a bit). The damage mod was copied from ingame but I can give people all the numbers if requested.

http://dl.eve-files.com/media/corp/KzIg/turret_data.zip

Phish1
Sebiestor Tribe
Posted - 2007.04.19 22:13:00 - [13]
 

close range ranis setup i used on sisi with halos in:

3 neuts, nos
web, 7.5k scram, tracking disruptor
sar, DC, rep

think that fitted, may have been smaller guns, but meh

very small sig, rediculously small, good dps, tracking disruptor ment that allmost all targets coulnt hit me missiles (except t2 precision, and rockets) did **** all dmg to me

worked well, but i cant see it being too biable as the lack of mwd hinders it, was sonsidering a close range stiletto, but the dmg output is laughable on it.

James Lyrus
Lyrus Associates
The Star Fraction
Posted - 2007.04.19 22:21:00 - [14]
 

Originally by: Akita T


Also, quality of hit SEEMS to be influenced (albeit to a much lesser degree) by (some? all of?) the same factors as "to hit" formula... so Halo implants might be even better as you thought.


You are correct. There was a discussion about that ... oh ages ago, but basically, yes, worse tracking = worse hits even on a 0 transverse target.

Nyveg
Hyperborea Re
Posted - 2007.04.20 11:11:00 - [15]
 

You should calculate using areas, as I thought damage dealing works via overlay of a ships sig-circle vs. the sig-circle of a missle or circle of the gun-resolution.

Using Pi*r^2 lowering your sig-radius would therefore reduce damage / hit-propability by the power of 2.

So lowering Sig-radius by 20% (full set?) would lower area by 44% (divide by 1.2^2). Roughly 40% damage reduction against equally sized weapons, plus longer locking. Could someone add a full skirmish gangbonus?

Halo > it's reputation, Cartel ftw

Akita T
Caldari Navy Volunteer Task Force
Posted - 2007.04.20 11:34:00 - [16]
 

Edited by: Akita T on 20/04/2007 11:34:01
Originally by: Distrans
You should calculate using areas, as I thought damage dealing works via overlay of a ships sig-circle vs. the sig-circle of a missle or circle of the gun-resolution.

That's what the turret/tracking guide MISLEADS you to believe, and then the end page gives you the actual (NOT adjusted for hit quality) actual DPS. In fact, things couldn't be more different.
Actual "to hit" formula is the one listed above (simplified for "within optimal" to 0.5^(constant*Angular^2/TargetSig^2), and the "hit quality" formula is still (publicly) an unknown one.
So, for a base 50% chance to hit, making your target sig *2 (while keeping everyting else identical) would only increases chance to hit to 84% (roughly +68% overall DPS, quality of hit notwithstanding, that has to be added in later), while lowering your sig to *1/2 decreases chance to hit to a mere 6% (a -88% overall DPS, again quality of hit notwithstanding, for even more of a damage reduction).

Basically, the harder you are to hit normally, the more you benefit from halo implants (up to the point of practical near-immunity).
The easier you are to hit normally, the less advantage you get from halos (even NO advantage at all in some cases).
Halo implants are for small sig, fast craft users, there they really shine.

Kazuo Ishiguro
House of Marbles
Posted - 2007.04.21 15:13:00 - [17]
 

Edited by: Kazuo Ishiguro on 21/04/2007 15:34:59
I've actually found a use for the Coercer - it fits 8 gatling pulse lasers and 4 heat sinks quite comfortably, and more importantly it requires no ammo whatsoever, allowing it to be left afk while racking up thousands of shots. These weapons have a very low range & falloff, meaning most observations can be done at < 10km range, where distances are displayed ~1000 times more accurately.

Let Y be the observed damage output of a weapon. Let X be the expected damage of a certain weapon. X = base ammo damage * chance to hit * damage mod of weapon. In sub-ideal conditions, Y = k * X, where 0 < k < 1 over a suitably large sample. What I would like to find is a formula for k that looks at the same variables as the chance to hit formula.

So far, I'm just looking at falloff- the target is a giant secure container (sig radius 3000m) and I'm orbiting it at < 10m/s, virtually eliminating the effects of tracking and signature radius. I wonder whether k might be discrete, since data sets at 50%, 40% and 20% chance to hit (via falloff) all put k at about 0.81, whereas at 90% k = 1 ; I intend to find the cut-off point...

Edit: I think expected damage might be slightly different from what I said above. Assuming that each shot has a 1% chance of being a wrecking shot for 3x base damage (and thus not affected by the chance to hit), it might be more like this:

X = (0.01*3 + 0.99*chance to hit) * base damage * damage mod

This gives k = 0.80 at 50% chance to hit or less, and k = ~ 0.90 at 80% chance to hit.

Nyabinghi
Minmatar
Re-Awakened Technologies Inc
Posted - 2007.04.21 16:27:00 - [18]
 

Any calculations on locking time per sig radius?


Kazuo Ishiguro
House of Marbles
Posted - 2007.04.21 17:18:00 - [19]
 

Edited by: Kazuo Ishiguro on 21/04/2007 17:17:08
It's towards the bottom of the spreadsheet I linked to in my first post in this thread:
http://dl.eve-files.com/media/corp/KzIg/Halo.zip

I'm re-doing the tests at 20%, 40% and 90% chance to hit with the coercer, since I'm not sure how accurate the distances were in the earlier tests and the results are a bit out of line.

Also, for the time being, I think it's probably best to look at data from non-wrecking hits separately. Wrecking hits are, frankly, boring, and they mess up the sample averages if I leave them in with the others.

Fresh data will follow shortly...

major lulz
Posted - 2007.04.21 17:39:00 - [20]
 

One other point to take account of is that halo implants will not decrease your own accuracy like snakes do.

However I decided a long time ago (after doing something similar to you), that the benefits are too variable and that being able to travel about 1.4x faster than the opposition is too much of an advantage to leave (too cheap for full high grade snake).

Tista
Posted - 2007.04.21 17:44:00 - [21]
 

this is why using smaller ships such as the enyo and astarte is quite often better than using large like megathron or armageddon

Kazuo Ishiguro
House of Marbles
Posted - 2007.04.21 20:14:00 - [22]
 

Edited by: Kazuo Ishiguro on 22/04/2007 17:04:04
More data acquired - lots of it. There are runs of 1500-2000 shots at 10% increments of chance to hit, each on its own sheet within the workbook:

http://dl.eve-files.com/media/corp/KzIg/turret_data.zip

I invite all those interested to have a look for themselves and see what sense they can make of it. k, defined as above, to a good approximation, when dealing with non-wrecking hits, is something like

(Chance to hit + 1)/2

As the chance to hit tends to zero k curves away slightly, towards a limit somewhere between 0.5 and 0.6. It might be that k is a simple function related to falloff (the only hit chance factor active in this data), but I haven't looked into that just yet.

//edit: Breakthrough! The answer seems to lie in the distribution of shot damage expressed as a % of the expected damage for a single shot (ignoring wrecking hits). There is a very simple relationship:

Let x = damage mod * base damage

Max damage per non-wrecking hit) = (150% - {1 - chance to hit}) * x

Minimum damage per non-wrecking hit = 50% * x

Distribution over this range (within shots that hit) seems to be uniform, and the chance of a wrecking hit is a constant 1%.

This leads to the following estimate for expected damage output, X:

X = x * [1%*3 + 99% * (chance to hit) * (150% - {1 - chance to hit} + 50%)/2 ]
= x * [1%*3 + 99% * (chance to hit) * (chance to hit + 1)/2 ]

This matches the data very neatly (and supports the guess above). There are no counter-examples to the range formula above.

I'll be in touch with Naughty boy...



//Edit again: this rather old post by TomB supports what I've found:
http://myeve.eve-online.com/ingameboard.asp?a=topic&threadID=89658&page=4#113

The link doesn't seem to be working properly for me - the post in question is about halfway down that page (#113).

Kazuo Ishiguro
House of Marbles
Posted - 2007.04.21 22:50:00 - [23]
 

Addendum: how this affects Halo implants...

The chance to hit part of the calculation is unaffected by the result found above. The only difference is that if we want to work out the tanking bonus granted by the implants, we need to look at expected damage rather than just the chance to hit. The idea is the same - just consider the new expected damage received divided by the old. With various things defined as above:

Old expected damage = x * [99% * P * (1+P)/2 + 1%*3]
New expected damage = x * [99% * P(r) * (1 + P(r))/2 + 1%*3]

x cancels out, but this time, because of the nature of wrecking hits, we get a rather ugly fraction and the falloff term no longer cancels:

[99% * P(r) * (1 + P(r))/2 + 1%*3]
----------------------------------
[99% * P * (1+P)/2 + 1%*3]

I've added this to the new version of the Halo implants spreadsheet, along with a nice graph:

http://dl.eve-files.com/media/corp/KzIg/Halo.zip

Generally speaking, I'd say they're good for any ship against a ship of the same class (or larger) using turrets, but otherwise they're probably not worth having.



easei
Havoc Violence and Chaos
Merciless.
Posted - 2007.04.21 23:14:00 - [24]
 

Couldn't you have a like 6% sig radius size with a full halo +titan + claymore?

Aggressive Salesman
Caldari
Posted - 2007.04.21 23:32:00 - [25]
 

Wow, if this is accurate then Halos are pretty much worthless. Only interceptors can manage to get any realistic use out of it. If you fight against a ship with bigger guns, as long as you maintain any kind of decent transversal they can barely hit you already. Also the bigger the ship you fly, the more worthless these implants become because the harder it gets to go fast and the harder it gets for your guns to track the opponent.

Essentially we'd be paying 1 billion so that when you solo some guy in a bigger ship, instead of having a 10% chance of hitting you he has 4%. Even the new lock time isn't bigger than a few decimals most of the time. Nice deal Rolling Eyes

Summary: spare your cash and get yourself a nice Crystal or Snake set that works Cool

dalman
TunDraGon
Pandemic Legion
Posted - 2007.04.21 23:41:00 - [26]
 

Edited by: dalman on 21/04/2007 23:44:25
As this topic came up again, which is good, I decided to post what I've always thought since it was found that quality was affected by hit chance.
http://myeve.eve-online.com/ingameboard.asp?a=topic&threadID=257236&page=3#84

Looking at your numbers here, it looks like I am correct
Originally by: Kazuo Ishiguro
http://dl.eve-files.com/media/corp/KzIg/turret_data.zip

So thanks for that test.
I'm expecting some small errors in your test, as you're doing it with transversal. That makes it hard to get an exact test environment (easier to know that the game will actually have your calculated hit chance in a test in falloffrange with 2 stationary ships/objects).

Your work on "average" damage dealt gives the same result as my theory.

Your test series is better than the "lacking ones" I based my thoughts on... There's no hits occuring that shouldn't be there.
Two thumbs up.


*edit* fixed link

Kazuo Ishiguro
House of Marbles
Posted - 2007.04.22 00:12:00 - [27]
 

Originally by: easei
Couldn't you have a like 6% sig radius size with a full halo +titan + claymore?


I've updated the spreadsheet to include optional gang bonuses, taken into account whether or not implants are used. Use the link in my sig - it's a double redirect, but it seems to work.

Dalman : The transversal in these tests was as close to 0 as I could get it - for some reason the game won't let you keep a container at range, so I had to orbit it. Only the range was varied. The effect of sig radius was equally minute- frig sized guns against a 3000m radius container (Mothership = ~1300m)

dalman
TunDraGon
Pandemic Legion
Posted - 2007.04.22 00:58:00 - [28]
 

You could have just stopped your ship (Ctrl + space) Wink

Kazuo Ishiguro
House of Marbles
Posted - 2007.04.22 07:20:00 - [29]
 

In practice, I think it's easier to set an orbit, as it's very fiddly trying to stop within 1m of the desired distance, even if you're going at 2m/s. But be my guest if you want a Coercer parking competition YARRRR!!

Akita T
Caldari Navy Volunteer Task Force
Posted - 2007.04.22 11:00:00 - [30]
 

Originally by: easei
Couldn't you have a like 6% sig radius size with a full halo +titan + claymore?

Just a note, the Minmatar titan effect is mutually exclusive with the claymore link effect... the higher one is applied, they're not compounded.


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