aggdef bar, def rating and everything

[Mr_Stabby]

Time to lay out another theory - today just toying around i noticed a few things:
1 - the difference of XXX less ar vs evade is much more effective at low skill levels then in high so for example a player with 1 ar will have much more trouble hitting a player with 200 evades then a player with 200 ar hitting a player with 400 evades - this strongly suggests that some kind of division occours between def and off skills
2 - this continues into negative numbers - means the formula must not break down when going into negative

this suggests 3 possible formulas for hit/miss calculation structure:
1 - there are 3 different calculations (for positive vs positive, pos vs neg and neg vs neg) for it, imo very unlikely
2 - 0 AR isnt really 0 and is infact base ar+ar divided by base def+def somehow, might be it might not.. the good news is its testable because according to my quick calcs it has to be roughly within the range of 1k so if negative cap can be achieved i would call it evidence! (ill test it as soon as i get the nessecary ppl which might take a while but if you got nothing to do feel free to do it for me)
3 - def is through some formula substracted from off, the remaining number is then divided (somehow) by the average of def and off skill and makes up the hit/miss percentage, also a likely scenario however i really hope its not because the details of this structure would be the hardest to work out

[Kaylinne]

Originally Posted by Mr_Stabby a player with 1 ar will have much more trouble hitting a player with 200 evades then a player with 200 ar hitting a player with 400 evades

That just makes no sense to me.

[Mr_Stabby]

punctuation is for sissys

if u have 1 ar and try to hit something with 200 evades your chances to hit are much lower then if you had 200 ar and tried to hit something with 400 evades

[gergiskoo]

That is, the relationship between AR and evades isn't linear.

I have a theory that may work with this, where AR only checks AAD, which, in turn, is related somehow to evades.

In other words, the actual check occurs between AR and AAD, and AAD changes based on how much skill you have in the appropriate evade. It may be 1 evade = 1 AAD, or it may not be. And it also may be that 1 AR and 1 AAD balance each other out (as in a 100% def check), or the relationship may be different. This would also explain why FC is so reluctant to let us see our actual AAD, because it would allow players to figure out the actual mathematical AAD function.

In math form:

D = AAD
E = Evade
F = AAD bonus from items, etc
ΣD = D(E) + F, where D(E) is an unknown, possibly linear function, hopefully D(E) = E.

and

A = AR
W = Weapon skill
O = AAO bonus from items, etc
ΣA = W + O

and

H = % chance to hit. Most people assume that this is 100% (that is, 1.00), as would be the case with a 100% def check. According to Stabby's theory, this isn't 1 and it's not even a constant, it's a function that relates A and D.
X = Attacker's position on the Agg-Def slider
Y = Defender's position on the Agg-Def slider
R = unknown function
S = unknown function
R(X) * A = H * S(Y) * D

Note that this may not make much sense since it's 2 AM and I'm barely awake. Does this sound logical to anyone else?

[Kaylinne]

I said nothing about punctuations, the idea that player with more AR can hit less player with less evades than vice versa makes no sense to me.
If I have 1k AR I should be able to hit someone with 200 evades more than if I had 200. 200 against 400 shouldnt be able to hit at all.

[navycut]

Originally Posted by Kaylinne I said nothing about punctuations, the idea that player with more AR can hit less player with less evades than vice versa makes no sense to me. If I have 1k AR I should be able to hit someone with 200 evades more than if I had 200. 200 against 400 shouldnt be able to hit at all.

erm lol he didnt say 1k AR he said 1 AR dunno where u saw that 1k.

[Kaylinne]

Originally Posted by navycut erm lol he didnt say 1k AR he said 1 AR dunno where u saw that 1k.

My bad, wtb better glasses

[Mr_Stabby]

Oki back from testing, apparently there is no negative cap for evades or AR and i got lineral results from going to as low as -3k, i had another idea later to try non-100% ar/def check perks in negative numbers to finally crush the hidden basenumber idea but thats gonna have to wait for now :/

as for now im leaning towards option 3 sadly which could be like what gergiskoo said or could not be anyway as of now im trying to think of more tests to see some kind of limits or lineral progressing of the formula to give me hints.

Kaylinne: u still didnt get me what im saying is
ChancetohittargetA = 1 AR vs 200 evade
ChancetohittargetB = 201 ar vs 400 evade

now even tho the difference of both of them is the same and by no means have they got a good chance to hit we can still say that
ChancetohittargetB > ChancetohittargetA

[gergiskoo]

Originally Posted by Mr_Stabby Kaylinne: u still didnt get me what im saying is ChancetohittargetA = 1 AR vs 200 evade ChancetohittargetB = 201 ar vs 400 evade

To put this into slightly clearer terms, the chance to hit is not based on the actual difference between evade and AR (that would be H = |E − A|), but on some other relationship (such as H = A ÷ E, or something totally different and possibly more complicated), with the result that stabby found.

The next step is to get more precise results from the test. That entails strictly controlled equipment and IP setups, and of course lots and lots of datapoints.

[Ixiaan]

Originally Posted by gergiskoo D = AAD E = Evade F = AAD bonus from items, etc ΣD = D(E) + F, where D(E) is an unknown, possibly linear function, hopefully D(E) = E.

I don't see what the difference between D and F is. Also it is not clear what the ΣD notation implies. (ΣD = defensive rating? i.e. the defensive counterpart to attack rating)

Originally Posted by gergiskoo A = AR W = Weapon skill O = AAO bonus from items, etc ΣA = W + O

Again it is not clear what the meaning of ΣA is.

Originally Posted by gergiskoo H = % chance to hit. Most people assume that this is 100% (that is, 1.00), as would be the case with a 100% def check. According to Stabby's theory, this isn't 1 and it's not even a constant, it's a function that relates A and D. X = Attacker's position on the Agg-Def slider Y = Defender's position on the Agg-Def slider R = unknown function S = unknown function R(X) * A = H * S(Y) * D

This assumes S^-1 is invertible which is not necessarily true. It also assumes that R and S are separable which also may not be true.

It would be more general to say there exists a map H from (A,X,D,Y) to the interval [0,1]. More precisely we could say there exists a measure H over the sample space {a,x,d,y} where a, x, d, y are the sets of possible A, X, D, Y values. (I think the first definition is sufficient for our purposes as long as H is properly normalized.)

Originally Posted by gergiskoo Note that this may not make much sense since it's 2 AM and I'm barely awake. Does this sound logical to anyone else?

Use LaTeX code next time!

[Ixiaan]

Originally Posted by Mr_Stabby as for now im leaning towards option 3 sadly which could be like what gergiskoo said or could not be anyway as of now im trying to think of more tests to see some kind of limits or lineral progressing of the formula to give me hints.

It would be nice if you posed some of your data.

[gergiskoo]

@ ixiaan: ΣD is total D (like a ghetto summation or something... i'd been using it in physics). That is, base defense Defense Rating + AAD. So yes, ΣD is your total defense rating. Again, it was 2 AM, it made sense at the time

Also you made some good points, I'm no math major or anything. But I doubt the functions involved would be too complicated, since the game has to compute them constantly and near-instantly.

[Threezey]

I wish it didn't take so long to collect accurate data. ;/

[gergiskoo]

If anyone wants to coordinate it, I'd be willing to spend a bit of time on testlive to work some of this data out.

[msbish]

Originally Posted by Mr_Stabby punctuation is for sissys if u have 1 ar and try to hit something with 200 evades your chances to hit are much lower then if you had 200 ar and tried to hit something with 400 evades

well if u got 1 AR vs 200 defense..u got 199% more defense than attackrating

if u got 200 attack rating and 400 defense rating, u got 100 % more defense than attack rating. so ofc u wil hit more with second alternative

so i think ure completely wrong, and it should be 100 AR vs 200 evades or 200 AR vs 400 evade would give same % of misses

[Doctorhyde]

Originally Posted by msbish so i think ure completely wrong, and it should be 100 AR vs 200 evades or 200 AR vs 400 evade would give same % of misses

The bigger question for me, and I think most people at this point, isn't if the %miss is linear that way but rather the relationship about whether 100AR vs 200 evades has more misses when compared to 100AR vs 200 AAD.

The case I really want to know:

% misses on 2000AR vs 2000 evades
% misses on 2000AR vs 2000 AAD
% misses on 2000AR vs 1000 evade + 1000 AAD

(at each major AGG/DEF bar setting to see if the equation changes in favor of evades or AAD depending on AGG/DEF settings ... my feeling is that AAD is more effective if you can go full DEF and evades are more effective if you can't ... but that's a gut feeling and not something I've tried to prove).

IF things do scale linear (and I agree with Msbish that 100 vs 200 compared to 200 vs 400 is the "right" comparison, not 1 to 100) then 100 vs 100 would work ... and you're on your way to proving that portion of it. But all that really does is make it easier to do the final comparisons in a controlled environment.

In the end all we really need to know is whether Evades, AAD, or a combination is better at various AGG/DEF settings. More defense and AR will always be the goal ... the question is which -type- of defense is more effective in various circumstances. I know that you're hoping to find it out ... I'm just not sure you're asking the question in a way that will get you there.

This is important to both my Fixer and my Doc, in different scenarios, because one uses full DEF and the other uses around 50%. Both have higher AAD than evades. I could easily believe that in one case I might do better with replacing AAD with evades (for PvM ... I think in PvP versus perks that AAD has serious bonuses even if a few more regular hits come through).

Good luck Mean that truly, not a troll/sarcasm.

[msbish]

mhm i get ure point, i also think it escalates with level, but stil linear and prosent based

like i think a dude with 70 AR hitting a char with 100 defense wil miss as mutch as
a agent with 700 AR hitting on 1000 defense becuse the % AR against def is the same

i also think 1 aad can count as 1 defense point on all 4 defensive skill NR/duck/evade/dodge

just as AR calculates 1 aao as 1 Attack rating

[Doctorhyde]

Originally Posted by msbish i also think 1 aad can count as 1 defense point on all 4 defensive skill NR/duck/evade/dodge

The answer is still out as to whether 1 AAD = 1 duck/evade/dodge ... but ... AAD definitely doesn't have a 1pt AAD = 1pt NR relationship. If it did Fixers would be the overlords of any nanocasting profession. It -may- affect NR at some level, but I'm pretty certain it doesn't.

[defender4]

<< math major here

I've had some statistics courses, so I do know a little about playing with probability distributions and hypothesis testing.

I'd be interested in testing some of this out.

Maybe we could roll some lvl 10 toons on test live and get some data, then setup some excel spreadsheets or open office spreadsheets to do some number crunching.

I really think that 1 aod is not the same as 1 evade. This was something I noticed on an ma round lvl 50.

We should definitely not forget to consider possible level and prof effects. Note that many nanos have level checks and so may weapons. Nobody has mentioned it, but profs could potentially effect the equation.

The best way to approach this would be to:

1) Roll two characters that are the same level and profession
2) Set them up with the same skills and same weapons (including same quality)
3) One character takes around 100 shots at the other (haven't done the math to guess what this number should be, but it needs to be high, since we will assume it to be a bernoilli random variable)
4) Adjust one and only one variable to 20 different settings, and fire 100 shots at each of these settings (see comment above)

This will give us enough data to plot the effect of a single variable and make some estimations. To see the effects of other variables, this process must be repeated. Once all variables have been plotted, then we must determine how they effect each other. This is the hard part and requires a large amount of effort.

I think that writing some programs may be necessary here, due to the large quantity of data needed to make some good estimations. Fortunately, AO's chat logs are not too difficult to parse. (I don't trust existing dd programs here, I've experienced a number of bugs with them.)

One last note. Remember that PvM damage is different than PvP damage, this may also be true of hit ratios. In fact, such an effect could potentially cause the affor mentioned effect.

Anyway hit me up on Masta4/Merlin4/Defender4/Gangsta4 on RK1 if you wanna play with it.

PS: Maybe rolling some froobs on RK2 would be better, cus we could get more toons involved and thus decrease the time needed for the measurements.

[gergiskoo]

I personally like the idea of doing it on Testlive because it's easier to level and acquire gear there, so you can run tests more efficiently.

And let's just get the variables plotted before we worry about parsing data and whatever. Hopefully everything will come out clean, so we can get nice and neat equations for the curves without crazy decimal coefficients and enormous degrees and such.