Why Melee Damage is so low (and 0 damage hits)

Now those are some hits I can get behind! What I don't understand is how you pulled 40 AR out of a standard store bought leather suit, but whatever.

Whoops, thanks for catching that! It was only 13 AR in the PreAOS tests

There is officially way too much math in this thread for me now.

Bottom line I think warriors need a boost.

I think the fact this is so difficult to understand and discuss means it's f'd up.

I don't think history or the way it was designed should over-ride changing it in a way that makes sense.

So this got me interested in figuring out the distributions at work here. I have majored in CS and mathematics, including statistics and probability, so this is not just coming out of no where. Lets just hope I don't embarrass myself here (I'm a bit rusty).

There is a problem when assuming damage mitigation is not random, when in fact its generated randomly much like damage.

Let X1 be a random variable having a uniform distribution of possible damage values on a Katana (5 - 26 damage)


Let X2 be a random variable having a uniform distribution of possible absorption of armor with AR 13 (lets round to 7 - 13 for simplicity)


Since X1 and X2 are independent and follow the same distribution, the Central Limit Theorem states X1, X2, .., Xn will follow a Normal Distribution as n approaches infinity. X1 has an approximate mean of 16 and standard deviation of 6. X2 has a mean of 11 and standard deviation of 2

Since X2 is not additive, the mean(X1 + X2) is 5 with a standard deviation of 6 which gives the following distribution for n = 2:

Figure 1


So in fact, the damages are following a normal distribution, (albeit not a strong one) that is just centered too far in to the negatives.

This shows that about 25% of each hit will have damage < 0

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Solution? Consider the fix of Armor Rating being a function of body location

Histogram of body location scaling on a Player


Again, Let X1 be a random variable having a uniform distribution of possible damage values on a Katana (5 - 26 damage)


Again, Let X2 be a random variable having a uniform distribution of possible absorption of armor with AR 13 (lets round to 7 - 13 for simplicity)
Let X3 be the uniform distribution seen above representing body location scaling on a Player

X3 and X2 will give us a conditional probability mass function which can be calculated for a particular x, but the graph is complex to show so and doesn't give much insight so I'm skipping it. However, it is a uniform distribution for a given x, bringing our n = 3 and X1,X2,X3 will give us a stronger normal shape.

So I can take the test data to see what the normal looks like. I purposefully did 20 (I think I only got 19, stupid excel!) repetitions during my test to get a 95% 19/20 confidence interval on the normal.

Figure 2


The values are much more ideal. With less than 5% of damage being < 0

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Just for fun, lets see what the normal looks like for my test data on the broken RunUO code and see how it stacks up to Figure 1



Whew, they look very similar!

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I hope this proves that damage here does follow a normal distribution, and that scaling by body position is indeed the solution to this! (Which I believe is how it truly is supposed to be given how not only does it normalize the values properly, but fighting an NPC also follow the same damage curve in Figure 2)

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1) The experimental values and the theoretical curves match. The mean and deviation doesn't have to be exact when it's an estimation! What matters is the distribution and correlation!

2) That fact any negative gets rounded to 0? That's negligible. The function is still a normal distribution when the mean is far away from 0. You're arguing the Central Limit Theorem?

3) Utility.RandomDouble();



4) I'm not trying to force anything. It makes sense. Armor scaling acts as a normalizer to extremely high AR values which don't make sense with weapon damage values. Huh, that's probably what the UO devs intended. Also attacking an NPC banker follows that curve. Players and Bankers don't need separate curves.

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40 AR test (Exceptional Barded Leather)





I can do a test to see how Invulnerability armor stacks up

Full Invulnerable Plate (77AR) vs Regular Katana

Note that all values below 0 will be rounded to 1. It is still a normal curve before rounding occurs. Notice how as weapon damage and armor value diverge, the curve shifts more and more to 0 and the correlation to a normal distribution becomes weaker. At this point, we can safely say it is not a normal distribution. But then again, this is the upper limit of armor rating.

The invulnerable platemail is certainly living up to it's name here.

Lets try Invulnerable vs. Vanq Katana

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Full Invulnerable Plate (77AR) vs Vanq Katana


The Invulnerable Platemail has met it's match.

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Exceptional Barbed Leather (40AR) vs Vanq Katana

I'm no statistician but Nightwolf's numbers do tend to reflect how melee damage SHOULD look in comparison to how it is calculated on this server. Especially in regards to armor mitigation and hit placement variables.

NPC bankers should follow the same armor rules as players, being humanoids who can wear pieces of clothing and armor.

You are most certainly forcing the solution that you think was intended. I mean, all of your tests here are demonstrating that less armor makes weapons hit harder. Congrats, great insight. There are a million ways to give players less effective armor.

Gideon is right, functions that get truncated on one side (and thus do not approach zero frequency on that side) are not normal distributions.

And the idea that you think there is ONE solution to the problem is the entire reason I get fired up when reading this thread. Even beyond the fact that your pet solution is based on either a complete lack of reading comprehension, or just deluding yourself, there are a million ways to make armor block less damage. The idea that scaling by body position is THE solution is ridiculously self-centered, and also nonsensical, since body position has its very own dedicated portion in the combat steps already.

I acknowledged the truncation in a post above which you have failed to read. As the curve shifts more and more to 0 the correlation to a normal distribution becomes weaker. Up to the point where it's no longer normal. But there are armor/weapon combinations that are very far from 0 and have a strong normal curve.

You are just as stuck in your point of view as I am in mine. One solution is usually the best answer (especially if this is a bug in RunUO which I will leave up someone else to decide). I'm providing evidence, proofs, and experiments. I'm not sure what you've provided other than a link to Stractics and personal attacks on my character.

But they aren't here! Thats the whole friggin point. You just acknowledged there is a bug, the same one I am describing.

You are bringing this topic down, to the point where I'm becoming exhausted, I have no more further to say on this subject and this will be my last post.

You provided evidence, proof, and experiments to show that making armor less effective results in more damage. I don't see how this moves the discussion forward at all, since every single person here seems to agree with that.

You tested one weapon that virtually no one uses, against a suit of armor that virtually no one uses, to prove that less armor effectiveness makes for more damage. Go re-run this with a +25 Vanq Halberd and tell me if you think your solution still makes sense. You can't test a solution that will apply to a range of weapons by just testing it for the one weapon on the furthest end of one spectrum.

Oh maybe you missed my posts then. In no particular order:

- the basic reading comprehension that what Stratics says directly contradicts your assertion about this "bug" that exists in RunUO.
- the rationale for why monster AR would be handled differently than player AR
- the rationale for why body position does not need to play a part in damage reduction (since it is already taken into account elsewhere in the combat system)
- the actual bleeping UO Demo code which directly invalidates your assertion.

Let me sum up your position. You had a theory that player AR calculations should follow monster AR calculations, because that's how it worked back in the day. This theory requires all of the following things to be true. I'll order them from "maybe" to "no way":

1) The body location to which a hit is made is taken into account in its very own step in the combat system, and then again in another step where it drastically alters the protection provided by armor.
2) Each piece of armor has its own "actual AR" figure, which means absolutely nothing, but is published by OSI and Stratics and such. Counterintuitively, "Displayed AR" is also actual AR, but they just want to call it "displayed".
3) the implementation of this system in RunUO was an insane fabrication by RunUO devs, who accidentally designed a crazy intricate system of armor effectiveness when they simply could have made things work like the 10-line monster AR code.
4) Stratics is wrong in its explanation of how combat works (they had direct access to UO devs for many articles and guides and tables, FWIW)
5) The actual UO code, per the Demo, was incorrectly implemented, and never publicly changed during the entire time this combat system was used (i.e. until AOS)


Let's contrast this to what my theory of "it's right" requires to be correct:

1) the body location to which a hit is made is taken into account in its own step. The Displayed AR figure is an approximation to give players a quick sense of their armor level across a complex system.
2) "Actual AR" is the actual AR of an armor piece.
3) The RunUO devs went through the effort of implementing this complex humanoid AR system because that's what they needed to do to mimick classic UO functionality.
4) Stratics page about combat, which they never changed in 5 years, is correct in how combat works.
5) The actual UO game code in the demo is the actual UO game code.

You are twisting my words, and I will take this last opportunity to clarify.

I am claiming player AR calculations should be based on Displayed AR not the AR of the material. I am also claiming there is NPC code (not only for monsters, but for Humanoids you keep bringing up) that asserts this.

Regardless of how the issue gets "fixed", we can all agree that the current system does not work correctly.

If we are all in agreement on this, as many on this server seem to be, then my question is why hasn't it been addressed yet?

We all know barbed leather should not be preventing as much damage as it does (I mean I've tested it with a supremely accurate katana of vanquishing and when I wasn't whiffing vs. my GM wrestling mage, the weapon is doing 1, 3, 4 points of damage on a VERY consistent basis)

This simply is not working correctly, I think we can all agree on that point. So why hasn't this issue been addressed?

This is semantics, but I'll bite.

This claim requires all of the following things to be true:

1) a woeful misunderstanding and misuse of the words "displayed" and "actual", on the part of the UO Devs
2) the RunUO devs were foolishly swayed by the actual meaning of the words, and because of this they crafted a complex simulation of what UO would have been like if the UO devs understood what the words "displayed" and "actual" meant.
3) Stratics was off by a factor of as much as FOURTEEN in showing how effective some pieces of armor were. No player noticed this discrepancy from 1998 to 2003, nor did any UO dev care to correct it.
4) OSI copy/pasted the actual UO code into the Demo, verbatim, except for this one specific armor calculation part, where they fabricated a more complex system than actually existed in the game, but never actually used said system.

You keep talking about being a developer yourself. Go find the demo code. Like 2 pages ago, you said you would. I'll no sooner spend the time looking for this than I would looking up and regurgitating Copernicus' proof that the earth revolves around the sun.

It can be addressed in many ways, but IMO the way to address it should have more going for it than simply being a band-aid. So that's why I, and Nightwolf and Gideon, are making proposals that have some other basis as well. I.E. Nightwolf wanting it to work like monster AR for simplicity and because he thinks that's how it actually worked, or Gideon wanting it based on a percentage so as to have a similar bell curve to most other games of the current day, or my wanting it to be based on players having to make strategic choices between different armor types, and not just having one choice be super obvious and required.

All points considered, I beleive we all see the need to have the current system "fixed", hopefully staff will address this one day.

Edit: I'll let off my claim that this is a bug for now. Instead just call it a purposed solution. One of many possible solutions.