But we know Blizzard's 1% is wrong. Their entire data doesn't reflect what we're seeing, thats the entire point of this thread. At 68% of max resist you no longer take 0% resist hits on elemental melee.

Their values might fit for PvP or things that are fully resistable.

What equation allows for an exponential concave up slope to stop, absolutely, at 0%, without passing below it? Keep in mind, its going to fit inside a computer code on probably 1 line. The simple one I gave fits all the datapoints.

Y=150*x*x-250*x+100

As for totaling 100%, we don't know the relationship between the equations, only the slopes and the general quadratic and cubic relationships if they turn out to remain accurate with further testing.

The way things are binned on overlap and such is open to debate, but as a programmer, your chance of 0% resist at 80% max is negative, but who cares, thats fine. Your dice roll is 1-100, and negatives aren't going to hit on that.

As for spillage, it all depends on the relationship between equations. They need not total 100% absolutely either. You're trying to make it far more difficult than it need be, when you put the constraints of reality and coding into the foray.

I mean seriously, how do we not know that 75% resist = 100-Y(50%)-Y(25%)-Y(0%)? Pretty simple way to tidy up your bins without getting fancy. Thats how I'd do it at least. This assumes If Y < 0 then Y=0.

The curves fit quite nicely, but they can't really be valid since they don't always add up to 100%...

Again, just remove the 75% equation, and make that equal to 100% minus the others. Pretty much the only way you're ever going to fit quadratics and cubics into a nice binned area.

Here, I made a graph for everyone:

What if I have under 350 defense? The graph doesn't say anything about that! Will mobs always crit me?

Its different, though, because where the points lie on the graph don't affect some overall property of several graphs combined - such as the average reduction (supposedly) needing to be linear with your resistance score.

HOWEVER, the difference is minor at best. I'd laugh at the guy that went to all the bother of trying to get the curves to match up perfectly. I'd have spent my time more wisely.

Results with new data which pretty much refute any higher order polynomial without using piecewise functions. (Though if someone tries tell me how high does your order need to be to get the curves to go through the data for 25%)





BTW the Equations from the previous data points on no resists for the fitting were

y=-2.2436x + 1.0092
y=-0.7153x + 0.4859

The new equations are

y=-2.2229x + 09891
y=-0.726x+0.4924

This little amount of change suggests that the basics of these linear equations are correct. As well it should be easy to remove a portion of the data and the graph should still fit the same.

Can you give us your new data Cryect?

Oh forgot to say I updated the excel spreadsheet same location as before.

http://acm.jhu.edu/~cryect/resistance.xls

@Cryect: you put way too much faith in your data.

E.g your last data pint as absolute bogus. You have less avg resistance than on your semilast data point.

Since no one was interested in my suggestion of bernstein polynoms (which just for your information come straight out of real use in probabilty theory where they were created for just such purposes), i made a graph.

B03: (1-t)³
B13: 3t(1-t)²
B23: 3t²(1-t)
B33: t³

where 0<=t<=1 (which can be identified to your normalized resistance to a given mob)
denote the basis consisting of 4 bernstein polynoms of 3rd degree.

When you identify B01 as the probability curve for resisting 0%, B13 resisting 25%, B23 resisting 50% and B33 resisting 75%, you can state the following:

1) Every Bi3 (i=0,1,2,3) is <=1 and >=0 for every t.
2) The sum of all 4 Bernstein Polynomials is always 1.
3) The avg predicted Resistance (as given by AvgPredictedRes=B03*0+B13*0.25+B23*0.5+B33*0.75) is linear in t (=your resistance) and starts with 0 and ends at 0.75 when you are resistance capped.

If you want to consider full resists too, you would just have to go to the base of 5 Bernstein Polynomials of 4th degree Bi4.

As you can see these would fit the Blizzard description perfectly.

They do not fit your data perfectly. But as pointed out above, its the question how much faith you give to that.

Here's a graph.



P.S Im not saying that some observations Cryect made are not spot on. E.g he predicts a cutoff of 0% resistance at a certain point, whereas htese functions would not cover that. I'm just saying that its moot to discuss which piecewise linear function is used ... whatever function was originally the base for the mechanic, Im pretty sure it is all done in a huge look up table.

Resize the picture to 650 pixels wide and itll look way way better.

Also, I think data does ultimately trump attempts to prove a hypothesis... it appears as if there is no trivial way to describe the 25% resist data without getting absurd. Maybe its a Fourier transform! Lets get some inverse space matrices going here kids.

Anyway, Kudos Cryect... I'm not sure sui should give up though

Shrug, a single data point might be off but the combination of them should give us the correct trends. The last data point has a .7% difference from the previous point which seems well within error range. They both in theory should be exactly 69% above the cap one of the data points above the cap is .07% below the cap and the other is .63% above the cap what do you see wrong in this? If you want to call a data point bogus you better back it up with a good reason besides saying that data points with higher resistance level should always have average resistance.

If they trend to linear piecewise functions without any curvature I don't see how you would think they are not linear? Are you trying to claim over 45k hits they trended to linear equations but are really some more complex curve that doesn't fit?

You could achieve complex graphs if they're filling in the bins as they go for the cubic functions, but what basis they would have for that would be up in the air as there would be 2 bins to fill in, not just 1. The 25% doesn't fit, and the 50% is so sharp I'm not even going to bother trying, cause I know its not within 1%. The quadratics are within 1% however, but that becomes meaningless... although maybe its quadratic, linear, linear, quadratic... still, doubtful.

Did we just argue all day about this?

Heh, I'm curious to see what he comes up with and I could see the arguments against the original data set calling it linear. I had some hestitations myself but I like going with my gut (I'm an engineer in my thinking and had a minor in Applied Math and not Math in college for good reason :p).

The more data I gather the more I feel sure. I need to fix up a few things in my recap then upload that and some others can go gather some data as well.

Heh, more fun than arguing about hypothetical DPS improvements for rogues that blizzard has already decided on.

It was pretty awesome.

Time to "fit" the data to some nice, round numbers.

At the end of the day it is good science anyway. Still though, dragons, seriously... Don't drop below the origin lest you be eaten.

Riide inntoooo the Danger ZooARRRGGHH!!

Sui, I think you are grossly missreading him if you think your contribution is in any way unwanted. If anything, you should expand your idea as much as possible... isn't that what you should do to help prove your hypothesis?

Back when I was tanking twin emps I logged all the damage I took trying to work out how much sta/resist to wear for the fight. In the process I learned that Blizzard's table for 'non-binary spell' resists is incorrect.

http://worldofwarcraft.com/info/basics/resistances.html

The column under Resistance Score '250' should read:

Chance to Resist 100% Damage : 0
Chance to Resist 75% Damge : 80%
Chance to Resist 50% Damage : 16%
Chance to Resist 25% Danage : 3%
Chance to Take Full Damage : 1%


In order for magic mitigation to be capped at '75%' when your resistance is maxed out, they have to have you fully resist 25% of the incoming damage and have a tiered set of occurences for 100%, 75%, 50% and 25% damage received. However the chance for 100% mitigation does not happen. Instead you take 25% damage instead of 0 damage. Which is an increase of 6.25% more damage than 75%, making maximum mitigation only 68.75%.

Also testable in duels with rank 1 shadowbolts etc.


So when figuring out how the curve from 0 to 25 to 50 to 75 to 100 resist occurences works, this needs to be thought about, at least the the extreme end. Its pretty significant since 75% mitigation is 25% better than 68.75%.

What I don't like about sui's graph is the end of it. We know for sure that no matter how much resist gear you have, you won't see 75% reduced on every hit. Can the Berstein polynomials be manipulated to be assymetrical? Its a nice fit, but its too neat at the top end.

What is there to expand?

On one hand we have some plausible assumption which ALL probability functions should meet. That is:
semi positive definite (always >=0)
total probability is always strict 1
avg resisted damage is strictly linear in resistance level

And on the other hand we have data which
do not meet the curves as suggested by blizzards page
is not always plausible (I pointed one significant aberration ... just look at your graph ans say that the last sample does not look gravely out of place)
suggests *significant* different behaviour (a cutoff of 0% resists at a certain point e.g.)

There is no more to say. In the end I'm only interested in the practical use of such observations.

It does not really matter if the mechanic was defined as pecewise linear or some other functions, because in the end you can bet money on it there are no single calculations going on (keep in mind that evaluating piecewise lienar functions is not the optimal way to do it) and all is done in one huge look up table.

I just want to know If the cutoff Cryect has observed will be verified by others or not.
The rest is of no importance.

Yes, that data did bother me but there seemed to be no evident reasoning for it. :-/

Its not actually the 75% being so high so much as the 50% being so low (2% change over a 16% value is a much larger difference than a 2% change over a 80% change).

Another data point that bugs me is at resistance of 7 I get 0 75% resist but at a resistance of 17 I get 27 and can't understand if it is linear piecewise why you would have it setup like that. Maybe the probability is so low that the chances of none appearing at 7 resist isn't that odd but it feels odd and I'm a touchy feely person when it comes to working with data sets (it has its issues and bias's I know but works well when reverse engineering file formats and other man made model generators).

Natural systems yeah I would question piecewise functions (those points in equations that would seem to break under common sense are almost always the most important parts of the equations which show the important data).

And sorry about my tone, I am taking any criticism seriously and looking at other suggestions and quite open to changes in data gathering.

edit: Also I think we are all pretty much in agreement on its a lookup table of some sort and curious so what happened to complete resists if it doesn't exists for spells either.

with all this discussion about the data, would it be beneficial to setup a standardized testing method and have lots of people go out and collect data to be compiled together? surely if many different people were out gathering data, we'd have a higher resolution on the X-axis of Cyrect's plots, and we'd also reduce the influence of random errors.

an increase in resolution on the X-axis would also make piecewise linear behavior much easier to spot, wouldn't it?

EDIT: to clarify, the X-axis resolution of this data is limited by the gearset available to any given person testing it. Cyrect can sit there and get 5000 data points for each level of resist he can achieve, but if only one person is testing it, we'll have only his series of x-values, and there's no way for him to fill in the gaps without acquiring more resist gear. with a variety of people collecting data, we'd have a variety of gearsets and possible resist-level values to work with.