Weapon damage distribution (as promised)

[Doer]

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.



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. [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.



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.

[Hally]

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]

Originally Posted by Hally

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

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.

[Doer]

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]

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]

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]

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


Click to enlarge

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

[KapokWu]

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]

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. 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?

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.

[Witte]

Originally Posted by Doer

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. 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?

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