Solving the Evade Equation

[dockside]

You're wrong

Amazing what some drugs can do isn't it

[Tradersoft]

Amazing what some drugs can do isn't it

Now that's original <3

[intelknight]

replaced the data with an updated version, which is further down this page.

[mr_road]

snip

fantastic data collection...

if we take defense rating to be dodge ranged + AAD and we plot (attack rating / defense rating) to % chance to hit you get:

for AR/DR < 2: a linear relationship (appears to be linear)
for AR/DR > 2: a flat line... ie. AR/DR >2 doesn't lead to a change in chance to hit

AR/AD = 1 gives 66% (or close to it)

to further investigate, we'd need more data (of course).

the same data set but with the defender at varying agg/def slider positions. 50%, 88% and 100% could be used to calc the effect of the slider.

i'd also be interested in:
- what the percentages look like when DR is a lot greater than AR
- what the crit rate is for different values of AR and DR
- what the percentages look like for the same DR but with varying amount of evades and AAD

[Threezey]

Hi, I'm back =D Even if it's just for a short while [who knows].

Just want to say I check in on this thread now and then [at points i was dying to resubscribe just to reply, hehe] and find it interesting how it is playing out.

Anyway... nice to see people taking initiative

[gergiskoo]

Personally, intelknight, I'd like to see that hole from 10 to 35 AAD filled with some data. I ran it all through Excel and found that it was just too hard to fit a curve to it accurately (thus, too hard to linearize, etc.) with that big statistical gap there.

[intelknight]

Personally, intelknight, I'd like to see that hole from 10 to 35 AAD filled with some data. ...

Uhm, I just realized I did not use auno right when I was looking for items that buff AAD.
Let's see if I missed anything that a lowbie agent can wear:
- Jobe bracers - got them
- Vagabond cloak - got it
- Symbs - from Nasc
- Ring of luck - defensive. gotta buy it.
- Jobe clusters
- Agent OFAB ring
- Gold Filigree Ring set with a Black opal
- AI armor, (CM, CC, Strong). Can I even find it in low QL's?

[gergiskoo]

Clan pads from the newbie isle give 5 each. No playshift reqs.

[intelknight]

Clan pads from the newbie isle give 5 each. No playshift reqs.

ahh right, i fergot they are not nondrop.

Guess I'll have to go clan for a bit ... guess it will make the tests a bit less boring - having an omni beat on a helpless clan.

Edit: You will need to have atleast one faction point with Clan Devoted and Clan Conservers. Side change denied. Your form has been destroyed.

[Hacre]

Has anyone rechecked their numbers and formulas since the 3% base chance to miss/hit was removed?

Checking because there was a formula earlier in the thread that someone claimed was 2.5% inaccurate. Well that's pretty close to 3%..

[intelknight]

Has anyone rechecked their numbers and formulas since the 3% base chance to miss/hit was removed?

Was that done in 17.10.2?
I indeed noticed a 100% hit chance when I tried to re-check one of the 97% numbers.

[Hacre]

Was that done in 17.10.2?
I indeed noticed a 100% hit chance when I tried to re-check one of the 97% numbers.

Was done in one of the 17.10.x patches. No more fumbles either \o/

[Josephina]

Has anyone rechecked their numbers and formulas since the 3% base chance to miss/hit was removed?

Checking because there was a formula earlier in the thread that someone claimed was 2.5% inaccurate. Well that's pretty close to 3%..

If you're talking about my formula, it had an average error of 2.5% for Threeze's data, not a systematic error, so the removal of 3% won't suddenly make it spot on.

Because of several reasons it would be very hard to get accurate data and you will always get an error between calcs and measurements. Possible reasons that I can think:
* You only have a finite number of datasamples
* The unknown way in which AOs random number generator works (it probably rolls random numbers between 0 and 100, rescaling those to the AR and DMS values).
* the agg/def bar works with a limited amount of intervals (probably 8 or 10)
* The AR vs DMS formula was thought up by FC, and with FC you can usually expect the worst as soon as any kind of math or think-process is involved.


My best guess for an approximative formula is still the same:
chance_to_hit == 0.75* AR / [(150 - slider)/100 *evades + 4/3 AAD]
With slider between 0 for fulldef and 100 for fullagg.

With Intelknight (1 to 24 on X-axis), Threeze's (25 to 40 on X-axis) and Lupus' (41 to 47 on X-axis) data, that formula gives the following graph (chance-to-hit on Y-axis, yellow is the measured hit%, blue the calculated hit%): http://img136.imageshack.us/my.php?i...degraphpm3.jpg

The displayed data was corrected to take into account a standard 1% chance to hit and miss:
corrected_hit_rate = (measured_hit_rate - 0.01) /0.98

Still obviously wrong (10%+ off in several places), but better than the other formulas I've seen so far.

[mr_road]

My best guess for an approximative formula is still the same:
chance_to_hit == 0.75* AR / [(150 - slider)/100 *evades + 4/3 AAD]
With slider between 0 for fulldef and 100 for fullagg.

i calculated the percentage chance to hit for goyo's and intelknight's data. intelknight's data consists of two line segments which appear to join at the point where AR / (AAD + evade) = 2, so i've only looked where this fraction is < 2. for >2 the chance to hit is flat ~97%.

if you graph the observed chance to hit vs equation chance to hit you get two reasonably straight lines.
if the equation was an accurate prediction of the chance to hit, the lines should be on the line (0,0) to (1,1). however, this doesn't appear to be the case. intelknight's data has increasing error for decreasing chances to hit. goyo's data has increasing error for increasing chances to hit.

what this suggests to me is that the form of the formula is correct, but the factors associated with AR, evades and AAD are incorrect. the other option might be another part of the equation based on player level... which has been mentioned before.

[intelknight]

97% was the 3% cap (really a bottom) on chance to miss.
They removed it few weeks ago in 17.10.2 patch.
I've been doing more tests to reduce errors (gotta post the data :-), and I got full 100% after 100's of hits.

I agree that my data look linear in AAD and AR (aside from the 97% cap).
Problem is, Josephina's and Pomidor's formula are not linear since both have AR divided by some function of Evade and AAD.
The thing is, the combination of limited range of AR & AAD and large errors make it hard to distinguish between linear and non-linear formula.

I am working to get wider range of AR's and lower errors.


I suspect goyo's data might follow a different formula since he has stats above 1,000 or even 2,000. Otherwise, thanks everybody for contributions and let's keep this rolling.

[mr_road]

I agree that my data look linear in AAD and AR (aside from the 97% cap).

Problem is, Josephina's and Pomidor's formula are not linear since both have AR divided by some function of Evade and AAD.
The thing is, the combination of limited range of AR & AAD and large errors make it hard to distinguish between linear and non-linear formula.

I am working to get wider range of AR's and lower errors.

I suspect goyo's data might follow a different formula since he has stats above 1,000 or even 2,000. Otherwise, thanks everybody for contributions and let's keep this rolling.

your data looks linear in (AR/(Evade + AAD)) vs Probability to hit

so does Goyo's. its just a different 'line'. which has very low AR to high DEF values.

the formula's aren't linear in relation to evade or AAD, but it is linear in relation to the ratio of AR/defense rating. the problem being, we aren't too sure about what the defense rating is.

[intelknight]

Improved the accuracy, and added some new experiments

 Obs   WS   AAO  AR  DEF AAD   % hit    Hits   Error
    1     39   1  40 100%   0  88.73%    2671    1.2%
    2     39   1  40 100%   5  80.48%    2669    1.5%
    3     39   1  40 100%  10  75.86%    2552    1.7%
    4     39   1  40 100%  35  53.67%    2286    2.1%
    5     39   1  40 100%  40  51.54%    2111    2.2%
    6     39   1  40 100%  45  49.62%    2100    2.2%
    7     49   1  50 100%   0  97.26%*    583    1.4%
    8     49   1  50 100%   5  88.76%     534    2.7%
    9     49   1  50 100%  10  83.92%     846    2.5%
   10     49   1  50 100%  35  60.47%     936    3.2%
   11     49   1  50 100%  40  59.47%     940    3.2%
   12     49   1  50 100%  45  54.29%     945    3.2%
   13     59   1  60 100%   0 100.00%    2011      0%
   14     59   1  60 100%   5 100.00%     408     0%
   15     59   1  60 100%  10  97.58%    2068    1.6%
   16     59   1  60 100%  35  69.13%    2838    1.7%
   17     59   1  60 100%  40  65.10%    2842    1.8%
   18     59   1  60 100%  45  60.08%    8891    1.0%
   19     69   1  70 100%   0  97.32%*    820    1.1%
   20     69   1  70 100%   5  98.14%*    808    0.9%
   21     69   1  70 100%  10  97.52%*    807    1.1%
   22     69   1  70 100%  35  74.29%    1622    2.2%
   23     69   1  70 100%  40  70.54%    1619    2.3%
   24     69   1  70 100%  45  67.82%    1641    2.3%
   25     59   1  60   0%  45  77.64%    1825    2.0%
   26     59   1  60  50%  45  70.04%    2233    1.9%
   27     59   1  60  25%  45  74.07%    2125    1.9%
   28     59   1  60  75%  45  67.36%    2362    1.9%
   29     14   0  14 100%   0  58.08%    1911    2.3%
   30     14   0  14 100%   5  54.94%    2255    2.1%  
   31     14   0  14 100%  10  49.62%    2088    2.2%
   32     14   0  14 100%  35  35.31%    2642    1.9%
   33     14   0  14 100%  40  32.87%    2093    2.1%
   34     14   0  14 100%  45  31.63%    1334    2.5%
   35     79   1  80 100%   0 100.00%     368      0%
   36     79   1  80 100%   5 100.00%       assumed
   37     79   1  80 100%  10 100.00%     467      0%
   38     79   1  80 100%  35  85.83%    2392    1.4%
   39     79   1  80 100%  40  81.48%    2252    1.6%
   40     79   1  80 100%  45  75.83%    2929    1.6%
   41     14  10  24 100%  10  58.83%    2604    1.9%
   42     14   0  14 100%  10  60.08%    3552    1.7%

* Test was done before 17.10.2 patch which removed the cap on chance to hit, so the value might be 100.00% as in Obs.13, which was done after the patch.

Attacker: lv.12 agent, froob, 100% Attack,
Target: lv.15 agent, LE, 22 Dodge Rng

AAO AR DEF AAD % hit Hits Error
Obs = Observation number for easy reference
WS = weaponskill of the attacker
WS = 13 means weapon was a QL1 pistol
all other values - Crescent Zapper rifle (upgraded starter)
AAO = Add All Offense of the attacker
AR = WS+AAO Attack rating of the attacker

AAD = Add All Defense of the target
DEF = Position of defense slider (100% = full DEF, 0% =full AGG)
DodgeRng is always 22

% hit = hits landed (including crits) / total hits
Hits = total hits
Error = 2*sqrt[ %hit*(1-%hit) / Hits ], a 95% confidence interval
I.e. there is 1 in 20 chance that true chance to hit differs from "% hit" by more than error.
Multiply it by 1.5 to get 1 in 100 chance.


If anybody wants to get serious with it, try regressions:
- In Excel, go to Tools / Add-Ins, make sure 'Analysis Toolpack' is on. You might need the CD to get it on.
- Go to menu Data/ Analysis, select Regression
- Enter Y (one column of data) and X (one or several columns). More on that below
- Set output range and hit OK
- It will give you coefficients for a linear function of X, i.e. Y = c0 + c1*X1 + c2*X2 + ...
- you want low p-values (below 5%) and R Squared close to 1.0
- experiment with X and Y
Several ideas to get you started.
Y= % hit, X = all the rest
Y=log(%hit/AR), X = AAD & DEF -- this is equivalent to %hit = AR/ [c0 + c1*AAD + c2*DEF]
or X = AAD & DEF*AAD & "Constant is zero", which is equivalent to %hit = AR/ [(c1 + c2/c1*AAD)*DEF]
I did something like that for Goyo's data, but I do not have time now.
And yes, I do this kind of thing for a living.

[Manaas]

any conclusion yet?

[mr_road]

any conclusion yet?

42, i think.







sorry. couldn't help it.

[intelknight]

any conclusion yet?

Generated some more data (still have to update the table above), and found a formula that approximates the 100% DEF data with chance to hit below 95%. Formula stays within 3.5% of my data, and generally within the error bounds.

hit % = (33.75 + AR) / (83.33 + 1.5 AAD)

Notice that you can multiply top and bottom of the fraction by the same amount, and you will get same hit %. I chose to scale things up so that AR is multiplied by 1.

The number added to AR has to be there. Formula does not work at all without it.
It might not been obvious in data from high levels because it was getting dwarfed by AR.

There are few mighty good questions remaining
- How does Dodge of 22 enter this. I would assume it's in 83.33 somewhere
- is 1.5 the DEF coefficient instead of the rumored 1.3?
I think I am gonna experiment with DEF next
- where do the rest of the numbers come from. Maybe level difference (12 attacking 15)