Weapon damage distribution (as promised)

Doer

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A while back i mentioned that i'd tediously recorded over 1k results of the damage done with a maxed out M2100 (tt) pistol in a hunt. The intent was to see what kind of distribution the damage falls into, and also to compare with a follow-up in a year or so should i become less n00ber by then. n.b. Misses were not tallied.

I finally plotted the distribution, and present it here for your perusal. Nothing too surprising: the distribution is purely "random", with an equal probability of any damage value between 0.5 max and max.
200602statsplot1.png

200602statsplot2.png


Mean damage = 75.005% max
Mean damage, including crits = 77.270% max

Some comments, given the above conclusion:

  • if a weapon without maxed stats (ie minimum damage lower than 1/2 maximum damage), follows a similar distribution, it will seriously impact your damage efficiency, whereas if the distribution were a modified normal distribution, un-maxed stats wouldn't have as much effect
  • there's not really anywhere to go from here--the average damage is exactly 0.75 max, and i don't think that will change no matter how many more skills i gain
  • crits can make a nice improvement on overall efficiency when your crit hit ability is maxed

Discuss amongst yourselves.

PS This posting brought to you by Comcast Broadband, which is incredibly accurate at reporting adverse weather conditions--it just fails leaving me connection-less. The ugly pixelation artifacts of the plots due to the transparency are because i'm too lazy to re-upload without a transparent color. ;)

Edit: update May 2006

My thanks to my friend for lending me a nice weapon for hunting this weekend, which also prompted me to collect data for a non-SLB (skill learning bonus) weapon. Here's the plot with a red line added to indicate what the distribution approaches as skills (damage) are maxed. Kill strike and wounding are unlocked at the two positions marked.

There are a lot of bogus ideas about how damage is done with low skills. This test proves (well to my satisfaction anyway) that damage is always random within the range of min to max as described in the weapon stats. The minimum varies with skills, which is where the inefficiency arises with lower skills. It starts at 25% of the max and can increase up to 50% of the max (which is commonly seen in the opalo maxed stats, for example). This one single phenomenon is the reason the opalo is a dream weapon far superior to almost all others until one has very high skills as far as damage/pec economy is concerned. [Ed: this was before the amp system was changed to limit it to 50% of the gun damage; the opalo is still a very good weapon for beginners with an a101 amp but is no longer the economical wonder it was when it could be used with a huge amp; however, the many new (L) weapons with SIB have taken up the slack.] I don't think hit ability really affects economy that much, as i don't notice myself missing much more often at 2.2 Hit Ability than with the amped opalo. Of course it does make a difference, but it seems that the damage interval makes a bigger one. Subjectively. :D [Ed: i have used weapons without SIB more extensively now and it is clear that a low HA makes a large difference in effective economy. See the weapon tool in Entropia Tools for a handy calculator that takes into account hit ability as well as min damage.]

The one wildcard i still don't have good data for is how crit frequency is connected to crit hit ability and other skills. Regular crit hits raise economy significantly as seen in the data from the maxed wallgun up above.

200605statsplot1.png


Edit: update January 2007

This question comes up again and again so i hope for greater awareness of this kind of study. For those who are interested to know how to increase their minimum damage i recommend this post with the breakdown of skills that affect mindmg. The conjecture in that post that killstrike is at least part of the missing 12% contribution to mindmg is indeed correct. Whether it represents all 12% i don't know.
 
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Hally

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very nice a good sound proof maybe u care to do the exact same with a noob with no skills and possibly both again with another weapon ?
 

Doer

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Hally said:
very nice a good sound proof maybe u care to do the exact same with a noob with no skills and possibly both again with another weapon ?

Not a chance :laugh:

Someone else is welcome to repeat it though. Just requires lots of pauses and/or screenies, and lots of away-from-PE time to collate the data.

As i said, i'll be repeating it in a while when i've unlocked a couple skills to see if there are any changes, but the results this time leave little room for change, really. Only thing i think could change is the impact of crit hits on the overall damage percentage, if skills like RDA and such increase crit hit frequency at all. However, it will be hard to show statistically that the mean damage percentage is increasing, as there were only 32 crits in the data.
 
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Doer

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Myth busting

I updated the original post with data for a non-slb weapon (without maxed stats). Hopefully this reduces the confusion out there about how low skills affect weapon effectiveness and efficiency.

cheers
 

Gargamel

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Great work :)

While making the weapon tool I wondered if higher skills affect damage after weapon minimum damage is maxed out. This research shows I that I don't need to adjust the tool in that section

Now if only someone studied the effects of hit ability and critical hit ability ...
 

Witte

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Great work :)

I will bookmark this post, so that when anyone comes with one of those bullsh*t makeup stories, and claims based on thin air, I can show them reality (which on their turn, wont understand, deny or ignore ;))

ps, another test that proves the same:

http://deltaforcesoc.info/viewtopic.php?t=943
 

IvoL

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Nice job!
I reformatted my graph and plotted the data in the same format as you did, so they can be compared better.

[br]Click to enlarge[/br]

As you can see the graph is pretty linear as well, the minimal dmg being 28% of the max, the critical hits have been discarded from this plot leaving 530 measurements. This was done with my Thorifoid battle mace with the help of some friendly Argonauts :cool:
 

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Nice job and a quick +rep.

The official name is the Uniform Probability Distribution (being
the same everywhere on the interval).

You don't need so tantilising test series though, a nice
200 samples is enough to verify the type of the distribution.
The standard courses usually assume this or that distribution
and there is seldom actual tests for verifying the type of
the distribution
.

If someone wants to test the critical hit probability and
its dependence on the CritHit ratio shown on the gun,
then he should collect data like this:


1.2 5
1.4 8
1.2 4
....


where the first number is the CritHit ratio of a particular
player, and the next one is the observed number of
the crit hits (for example 300 shots/slashes). The sample
needs not to be big, since you get several test persons
per each CritHit level, and also many levels. It is faster
to use many persons than trying to inch up from 1.0 to 5.0
for example. It may take a year. ;)

Good luck for the researchers! It is better to see the plot
form the above outlined study before starting to formulate
the relation...

Edit: It might be better to use always the same mob in these
tests, just in case.
 

Doer

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Thanks for your comments everyone. With IvoL's contribution i think it's safe to say that melee damage follows the same Uniform Probability Distribution. Thanks KapokWu for the lesson in statistics. I thought i'd be able to avoid ever having a class in that. :mad: I considered looking up the name of the distribution, but figured layman's terms had a better chance of getting through to those who cling to the notion that these kind of things are unknowable without being an MA employee (i had a long and aggravating conversation with two better-known players about a similar subject in Atlas the other day. Well actually it was a short conversation with many repetitive verses, with a chorus of "I don't believe the charts, unless MA employees made them". Perhaps EU is just full of a lot of agnostics for some reason? :confused:

Unfortunately due to the pseudo-random origin of the numbers and the cyclic dynamic nature of so many things in EU, many people arrive at pet theories that can be "proven" to their satisfaction through a few coincidental grouped low damage hits, skill gains, lack of skill gains, etc. People love to see patterns and i'm sure someone will be claiming to see the Virgin Mary in the skillgain distribution next week. (No disrespect to religion, just to those nuts that think a deformed doughnut should become a sacred relic.) In the end i suspect most of the urban legends implying some pattern will be chocked up to this tendency.

As far as resolving the crit hit issue, we do know that the numbers (the scale from 0-10) are not a percentage because it says so. It could still be linear as you suggest, of course (eg a percentage multiplied by some factor). The main problem is that the frequency is low enough and with enough tendency to be grouped (again, the pseudo random numbers and cycles) that it does take a lot of samples to get an accurate indication. For example, there were only 7 crits in the 632 shots i recorded, and all of them fell in the first 2/3 of the shots chronologically.

Some other notes about this test:
  • Average damage: 0.67 max
  • Average damage w/ crits: 0.68 max
  • A beacin scope and abrer laser were attached to the carbine at all times
  • The first 457 shots were done at CP on aurli and kreltins, the remainder on bristles. The average damage for the two groups differs by less than 0.005 max damage, so if you think the mob difficulty makes any difference on damage done, again that's a myth.
  • Observant souls will note that a min damage of 0.32 max gives an mean of 0.66 max, not 0.67. I am attributing this both to experimental error and the fact that my listed damage percentage became 0.33 max shortly after the end of the hunt, which is a mean of 0.665 max.

At this point i think it's pretty safe to say that anyone who plans to hunt with nothing but amped wallguns their whole time in EU may freely sell off rifle/handgun/aim/etc without hurting their hunting ability (as long as you keep enough to max your opalo stats), except where the skill gives hitpoints.
 
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Witte

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Doer said:
Thanks for your comments everyone. With IvoL's contribution i think it's safe to say that melee damage follows the same Uniform Probability Distribution. Thanks KapokWu for the lesson in statistics. I thought i'd be able to avoid ever having a class in that. :mad: I considered looking up the name of the distribution, but figured layman's terms had a better chance of getting through to those who cling to the notion that these kind of things are unknowable without being an MA employee (i had a long and aggravating conversation with two better-known players about a similar subject in Atlas the other day. Well actually it was a short conversation with many repetitive verses, with a chorus of "I don't believe the charts, unless MA employees made them". Perhaps EU is just full of a lot of agnostics for some reason? :confused:

I would rather call them religious, with EU being their religion and Mindark being their god ;)

Unfortunately due to the pseudo-random origin of the numbers and the cyclic dynamic nature of so many things in EU, many people arrive at pet theories that can be "proven" to their satisfaction through a few coincidental grouped low damage hits, skill gains, lack of skill gains, etc. People love to see patterns and i'm sure someone will be claiming to see the Virgin Mary in the skillgain distribution next week. (No disrespect to religion, just to those nuts that think a deformed doughnut should become a sacred relic.) In the end i suspect most of the urban legends implying some pattern will be chocked up to this tendency.

Thats silly, it by no chance looks like Virgin Mary. It looks like Elvis!

As far as resolving the crit hit issue, we do know that the numbers (the scale from 0-10) are not a percentage because it says so. It could still be linear as you suggest, of course (eg a percentage multiplied by some factor). The main problem is that the frequency is low enough and with enough tendency to be grouped (again, the pseudo random numbers and cycles) that it does take a lot of samples to get an accurate indication. For example, there were only 7 crits in the 632 shots i recorded, and all of them fell in the first 2/3 of the shots chronologically.

I am more interested in what impact HA has. Although, I think the only safe way to test that is using a melee weapon. I will do a testrun later on. My suggestion is to take a melee weapon, and do 100 hits, then count the misses. To be sure you did 100 uses, the decay need to be calculated. Will post results as soon I have them
 

Witte

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It ended up being more work then I thought so I didnt count the total hits I did.

Anyway, using a full TT blade I had:

45 misses
8 critical hits

A full tt blade should give: repairs/decay = 13.1/2.79 = 469 hits

Misschance = ~9.6%
CHchance = ~1.7%


Opalo 300 shots:

32 misses
4 critical hits

Misschance = ~10.7%
CHchance = ~1.3%


So, it looks like it that misschance is about 10% and CH chance about 1.5% For both weapons I have all stats maxed out.
 
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Vagrant

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call me stupid if you want..but i see some lines with some numbers i probably missed something..
 

goldpython

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Vagrant said:
call me stupid if you want..but i see some lines with some numbers i probably missed something..
Nah, that stuff can be that way if you're not used to looking at it.

Look at Doer's first graph like this:

Look at the axes. In english they describe what is shown about like this: This is a graph that shows how often I get a certain percentage of the max damage that the weapon will do.

So, the first point is at Frequency about 3.2%, damage about .5. Since the chart is of an M2100 that has max damage of 4, this means that about 32 shots out of 1000, I'll get a damage that is about half of max, that is, 2 for the M2100.

Take the 6th point in: It's at Frequency around 4.9% maybe, damage is at .64 or so. So for 49 shots out of 1000, he gets somewhere around 2.5 damage.

The n=1405 means Doer collected this data, and as he states in the first paragraph, threw out the misses, and had 1405 shots with information collected.

The main point of the graph is that those dots lie roughly off of a horizontal line. What that means is that you're just as likely to get damage of 2 as 3 or 4. The chances are all the same from half of max up to max. If the line was slanted, the chances are better where the line is higher, worse where lower.

On the second graph, it's a bit different presentation of that same data that makes what I said above easier to see, but the main fact is still the same.

The third graph is very interesting and illustrates how Hit Ability plays into it. A lower hit ability moves the minimum damage lower, so the line shifts to the left, but notice the right hand end of the line. It's in the same place. Also, it's key that both lines are still straight, meaning again, that your chances of making a high damage hit are no different than your chances of making a low damage hit. It's the minimum damage due to low skills that changes things.

Hope that helps. :)
 

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Nice work, especially the graphical representation. Did something like this myself recently (https://www.planetcalypsoforum.com/forums/showthread.php?p=277133) but not with as many data points. Nice to see that it really amounts to a uniform distribution (i.e. flat between the borders), when n gets bigger. You will find miss and critical hit rates in my post as well, look very similar.
 

Doer

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Bump for results that people are still asking about.
 
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Great job! Now let me spread some +reps...
 

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Great job. Next time when we go to kill chompers, I will sak my girlfriend to write down all my hit's, Ch and misses, so we will have alot of daa for concludent tests. CH and minimum damage are the 2 things that afect the most the economy. But there is one more important than all... missed shots.
 

Doer

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Apparently the first post is too old to edit. :confused:

Anyway, still nothing new to report, damage still appears to be a uniform distribution.

20080203-EU-Damagedistribution.gif
 

Jeffe

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Very nice work and info, +rep
 

Legion

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fyi, Comcast is one of the worst isp's one can have and they are even up in the thingy in the us cause they shut of users from their connections when using torrents.

Thingy = some dude in the us government or something looking into them of if it was the court.. dunno
 

Immortal

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Question: (using as much jargon as poss.)

when amped is it rand(a+b) or rand(a)+rand(b)?
 

Jimmy B

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Question: (using as much jargon as poss.)

when amped is it rand(a+b) or rand(a)+rand(b)?

afaik, putting an amp on a gun effectively causes the min and max damage of the gun which otherwise behaves the same as before. So I'd guess rand(a+b), although I'm having a little mental difficulty in convincing myself that's any different to rand(a)+rand(b) right now :D
 

Witte

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afaik, putting an amp on a gun effectively causes the min and max damage of the gun which otherwise behaves the same as before. So I'd guess rand(a+b), although I'm having a little mental difficulty in convincing myself that's any different to rand(a)+rand(b) right now :D

With rand(a)+rand(b), I think the distribution will looks something like a trapezium :scratch2:. Although avarage damage would remain the same.
 

Jimmy B

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With rand(a)+rand(b), I think the distribution will looks something like a trapezium :scratch2:. Although avarage damage would remain the same.

Couldn't be bothered to label the axes right but just to satisfy my curiosity:

rnd.jpg
 

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And here's the companion graph for Jimmy's data. rand(a) + rand(b) seems to be triangular.

randarandb.GIF
 

Witte

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And here's the companion graph for Jimmy's data. rand(a) + rand(b) seems to be triangular.

randarandb.GIF

I think its only triangular when max(a) = max(b). Thats why I suggested the trapezium ;)
 

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I think its only triangular when max(a) = max(b). Thats why I suggested the trapezium ;)

You are right, of course. Here is rand(1)+rand(2).
randarandb_171644.GIF

Should have seen that with the linearity in the middle of Jimmy's graph.
Well, at least I got another post out of the deal, learned how to upload and reference EF images, and re-proved my ability to make mistakes and learn from them. Onward to 10 posts!

Noodles
 

Jimmy B

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Nice random math moment hehe :D
 

Doer

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From February this year in response to someone questioning whether dmg was really still a uniform distribution, i posted this in the thread on the effect of attachments:
I looked at the damage distribution from the first part of the hunt (before changing amps). The average fraction of max damage done was 0.696. 0.692 is what is predicted by taking the mean of min and max.

20080203-EU-Damagedistribution.gif


Still looks like a uniform distribution to me.

It belongs in this thread, as someone is again questioning it and i pointed them here.
 
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