Armor, How Does It Work?

[Jonneh 82]

Came across this topic recently: http://forum.wurmonl...rotection-info/

There was some interesting discussion going on in there about the effectiveness of different armor types. As the test server gives exact number which is useful from a statistical view I decided to figure out a formula to determine the effectiveness of armor.

A line on the combat tab on the test server looks something like this:

[12:14:57] Damage=2043.4200261523176*0.30655867=626.4281226352826 crit=false

where the bold part is the armor "multiplier". The damage done on any hit is the damage it would be without armor * the armor multiplier.

I started of by testing the multipliers at varying QL for drake armor:

QL(x)...Multiplier(y)
01......0.9175
25......0.665625
50......0.4625
75......0.340625
90......0.3065

Putting those numbers into formulize and giving it a few minutes spat out this equation:

y = 0.9291 + 4.813e-5*x^2 + 5.214e-9*x^4 - 0.01165*x - 2.687e-7*x^3 - 2.066e-13*x^6

I then tested it with scale armor:

QL(x)...Multiplier(y)
01......0.915
25......0.64374995
50......0.425
75......0.2938025
90......0.257

Putting those into formulize gave this equation:

y = 0.9271 + 2.101e-5*x^2 + 5.796e-7*x^3 + 4.38e-11*x^5 - 0.01217*x - 2.32e-13*x^6 - 4.623e-9*x^4

Both these equations look incredibly over complicated for what they do, and probably are ridiculous compared to what Rolf uses in the server code, but they are very accurate given the data supplied (Less than 0.0000000000000002 maximum error).

Having different equations for every armor type would be redundant, so I assumed that they used the same equation and had a separate modifier applied either to the QL before putting it through the equation or to the multiplier given by the equation.

A quick division of the two equations can help out here:

y = (0.9271 + 2.101e-5*x^2 + 5.796e-7*x^3 + 4.38e-11*x^5 - 0.01217*x - 2.32e-13*x^6 - 4.623e-9*x^4)/(0.9291 + 4.813e-5*x^2 + 5.214e-9*x^4 - 0.01165*x - 2.687e-7*x^3 - 2.066e-13*x^6)

Plotting that on a graph gives this:

Ignore the 90+ area, I don't have data for that so it does crazy things.

From this graph you can see that the damage reduction does differ between the two sets at different qualities, but not by much. A 1ql drake set is very similar to a 1ql scale set, a 90ql drake set it roughly 85% as good as a 90ql scale set.

The multipliers for each armor type at QL 1 are as follows:

cloth: 0.9325
leather: 0.93
studded: 0.9275
chain: 0.925
plate: 0.9175
drake: 0.9175
scale: 0.915

I might look into glance rates too, but that is probably dependent on many more variables such as weapon QL, weapon skill, fighting skill etc...

Edit: fixed graph, wasn't straight line, ignore what I said previously about that...

Edited December 5, 2012 by Jonneh

[Sklo:D 2,210]

Studied that months before, but never wrote it down.

Anyways, nice work.

[Fractal618 22]

Very interesting I took the Drake and Scale data, plus the "1 Quality" modifiers, and just extrapolated each point. although using my method means that Drake and Plate would have the same exact curve, since they both start at the same quality 1 modifier. I have no idea if this chart is accurate xD *runs to the field for experiments*

https://dl.dropbox.c.../wurm armor.xls

edit: I have a hunch that the Plate modifier is actually closer to 0.9 at quality 1.... It looks like all of the other curves are spaced pretty evenly.

edit: just realized that the y-axis on the graph is incorrectly titled. "unblocked damage" would have been more appropriate.

Edited December 6, 2012 by Fractal618

[Jonneh 82]

Very interesting I took the Drake and Scale data, plus the "1 Quality" modifiers, and just extrapolated each point. although using my method means that Drake and Plate would have the same exact curve, since they both start at the same quality 1 modifier. I have no idea if this chart is accurate xD *runs to the field for experiments*

https://dl.dropbox.c.../wurm armor.xls

edit: I have a hunch that the Plate modifier is actually closer to 0.9 at quality 1.... It looks like all of the other curves are spaced pretty evenly.

I used your data to come up with equations for the other armor types, I collected more data from cloth earlier (1-90ql with 10ql increments) and it fits pretty well.

Cloth:

y = 0.9378 + 2.502e-6*x^3 + 1.049e-10*x^5 - 0.005022*x - 7.134e-5*x^2 - 2.664e-8*x^4

Leather:

y = 0.9369 + 1.009e-5*x^2 + 3.372e-7*x^3 - 0.006918*x - 1.338e-9*x^4

Studded:

y = 0.9353 + 1.089e-5*x^2 + 3.9e-7*x^3 - 0.007778*x - 1.574e-9*x^4

Chain:

y = 0.9336 + 1.09e-5*x^2 + 4.539e-7*x^3 - 0.008619*x - 1.861e-9*x^4