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#66094 by Jpsi Mon Nov 28, 2016 6:34 pm

Here comes a long overdue summary of an analysis I did about our Astroflux arts, and how to compare them.

Or: here are some information you never wanted to know about arts, but then, there're there so why not :mrgreen:

Thanks to Will for sharing some useful data back in June to get me started on the multi-arts analysis !!

Let me start by the end: ... sp=sharing

See the explaination in my third post. Bassically gives you the power of one art, and allow you to compare several arts with multiple lines.

The total unit level tells you something about how good/bad one art is:
- <1 : entry level arts
- 1-2 : low level arts
- 2-3 : average level arts
- 3-4 : good arts
- >4 : very good arts
The purple column allows you to create your own units, if you want to fine tune your value.

How I use the spreadsheet: I usually put the spreadsheet open on the left of my screen, while having astroflux open on the right side. My mouse stay on astroflux without clicking on the windows, so I can stay typing the art value in the spreadsheet while seeing the popup thanks to my mouse. I can go quickly from one art to another by moving my mouse. That's the reason why in the spreadsheet you can type everything: you can fill without using your mouse, which stay on the astroflux windows to show the popup.

(nb this gives a more accurate information, but is less practical to really know which art will get you the best values in your gameplay) ... sp=sharing

In this link you may find a spreadsheet with the possibility to fill in your arts and see they level equivalent. This can be useful to quickly compare 2 or 3 arts.

You may use this spreadsheet and copy it if you want.

The idea behind it is simple: each line of an artifact can be converted to a individual art level. So if you do this for each single line, you can come back to individual art level equivalent, and calculate the total level of your art.

You just have to fill in:
- in yellow, the value of the line (ex = 60%, or 1600.0). Don't forget the % sign for pourcentage !!! It will not do it for you !
- in blue(ish), the type of the line. You have to fill in a number, like 1 for instance if you have a % health, or 25 if you have a % rof. The value of each stat can be found in the table on the right side.

Let see one example:

Imagine you have those 3 arts, and you want to compare them:
Example1_arts_small.jpg (26.08 KiB) Viewed 14343 times

Using the spreadsheet you can see this:
Example1_EQ1_small.jpg (52.97 KiB) Viewed 14343 times

The conclusion is that the first arts has a better level equivalent (163.9), and will give you more stats.
But the second has almost the same level (162.3). Which is better will depends on the stat you want to use, but you know that in term of optimization, if you are using every single line, both arts will be (almost) as effective.

However, in practice you may not need the extra % corro resist, so you can also compare those 3 like that:
Example1_EQ2_small.jpg (57.24 KiB) Viewed 14343 times

Which make the third arts better in term of efficiency (if you want some defense of course).

You end up with an artifact of level 163.9 (equivalent), 131.6, and 148.4. I hope this make sense :P

In the next 2 posts I will go more in details about how the table works, and some fact about arts value.

Enjoy !
Last edited by Jpsi on Mon Dec 05, 2016 8:01 pm, edited 12 times in total.

#66095 by Jpsi Mon Nov 28, 2016 6:35 pm
Reserved for mono-arts analysis
Data: ... C7/pubhtml

Let's start with the basis: the value of an art is directly linked to its level via a linear correlation. The higher its level is, the higher its value will be.

2 parameters can be described to described this correlation:
- the slope of the cuve "a", which gives the amount of value the artifact will gain per level.
- the intercept at level 0, often called "b".

The relation will then be: value = a x level + b

The value of those 2 parameters can be found in the previous spreadsheet or on the link below.

Upgrading a mono-type artifact, with 1 level, will always result in the addition of "a" to its value (the slope).

Multiple upgrades (let say n upgrade won) should result in a gain of multiple times a (n x a), but the upgrade is not always an integer, so one can gain n x a +/- a/2 ( you can gain in practice for instance 5.2 levels, and it will show 5 level upgrades - see discussion with theCen).

There is a small dispersion around this central tendancy. The dispersion stay within one "a" (so far I can see), which means that an artifact of level n will never have an higher value than the artifact level n+1.

The dispersion around the tendancy (where 0 is a perfect correlation) can be ploted like this:
Dispersion.jpg (23.97 KiB) Viewed 14346 times

This is the data for all 3 types of resist (corro/kin/energy), which share the exact same correlation coefficient. I used n=153 to plot this (using some data of Will), and I correct for the normal slope to only study the dispersion.

The slope is in that case 1.1%. As you can see, the value of the dispersion is exactly between -0.55% and 0.55%, and is relatively homogeneous. The two bar of the sides are at half value, as the histogram counts only the numbers between 0.5% and 0.55% (instead of an interval of 0.1%, you get an interval of 0.05%, which divide automatically the number of counts by 2).

This mean that the dispersion is not a random phenomenon: my guess is that the level is not discret like one can think, but continuous. It just shows up as 86 instead of 86.3 (or 85.8). Both will be displayed the same way, but will not have the same value, the first will be higher than the former. This is why 2 artifacts of the same apparent level can still have different values.

Some statistics, like % health and % shield, or the 3 resist, share the exact same curve. Which mean than a 200% HP mono-art will have the same level as a 200% shield art. This is the same for the 3 resists.

However, this is not always true for all type of damage. You can notice that the coefficient for corrossive is a little different from the kinetic and energy value (those 2 are the same): % corro damage have a coefficient of 0.92%, while the other 2 are at 0.90%. It also start at a lower value (4.5% instead of 5.4%), which mean that a % corro art will have a slightly lower value at low level, and above level 80, will have on average a higher value than both other type.

This is effect is even more prononced for flat damage, but in that case it's the energy which is off. In practice, this is only for normal arts (I don't have enough data for superior and exceptionnal to show that kind of effect), so it will not impact our gameplay, but you should keep that in mind :)

It this intended or not, I don't know, but this strange effect exists at the moment :p

Here is for instance the data for % corro arts:
Damage all.jpg
Damage all.jpg (38.62 KiB) Viewed 14346 times

On the opposite of what one could think, the effect of the art quality (superior / exceptionnal) is not a simple relation (like x2 or x3). It strongly depends on the kind of that we are looking at. See the data for more information.

Here is 2 examples, for flat kin damage and % rof.
ArtQuality.jpg (58.4 KiB) Viewed 14346 times

Some example are even more strange, like the cooldown optimizer for instance: apparently, a normal art above level 155 will have an higher value than the superior version :shock:

To calculate the equivalent level of multiple arts, I am using the superior value, as this seems to give the best results for our high level arts (I consider 80% rof should give something like 160% damage). The drawback is that it does not work well for low value, as this an approximation. I can also give the level equivalent for normal arts, but then the level is too high if you use exceptionnal version (as we all do).

Data (again, same link): ... C7/pubhtml
Last edited by Jpsi on Sun Dec 04, 2016 9:49 pm, edited 5 times in total.

#66096 by Jpsi Mon Nov 28, 2016 6:37 pm
Reserved for multi-arts analysis
Data: ... Se/pubhtml

Multi-arts can have different level per line. Most of the time, the first line will get the highest level, but it's not always the case, it can also be the second or third line. During upgrade, each line will be upgraded individually.

This post mainly concern un-upgraded artifacts: I did some test using upgraded artifacts, and the values I will provide seems consistent with the unupgraded version. It will need trementous effort to show the difference in distribution between ungraded and un-upgraded artifact, so I will not comment and that (see post of Magenta about multi-arts to read about what most people think - however we miss the data to support those claims).

If you consider each lines of an art as its equivalent level (using the spreadsheet of mono-arts previously calculated), one can calculate the relative % increase in level due to the muliple lines. There is a lot of variation between the arts, so ploting the distribution and the average value seems the appropriate way to go.

For 2 lines, here is the data that can be ploted (for 150 arts). I use for this analysis only % damage lines (I accept the small corro difference as part of the dispersion), % resist (all type), % HP & SH, % armor and % resist.
Histogram2liners.jpg (62.5 KiB) Viewed 14342 times

The total of both lines is between 100.4% and 135.7% (except a fwe outliners at low level that I removed from this analysis - the method is mostly develop for medium/high level artifact). The average value of this total is 119.7%.

The first line has on average 74% of the level of the artifact. The second line has on average 46%. You can see both distribution on the histogram: while the second line seems a gaussian-like shape around its average, the first line showns much more variations. Most of the time, a good arts will have a high first line, and a bad arts can have very low first line. It can maybe be compensated by upgrading the arts, but this has yet to be proven.

Here is small table to recap the important feature (see spreadsheet for more details):
- 2 liners: from ~100% to ~135% of base art level, average of ~120% (n=150)
- 3 liners: from ~120% to ~165% of base art level, average of ~140% (n=138)
- 4 liners: from ~130% to ~175% of base art level, average of ~155% (n=73)
- 5 liners: from ~133% to ~180% of base art level, average of ~157% (n=22)

The gain between 4 and 5 liners is quite small, mainly due to the high fluctuation in number for 5 liners. Also, I have less data, so it's possible the average value will be around 160%.

So basically, a 2 liners level 130 will be most probably similar to a mono-art level 156 (=130 * 1.2). And to a level 182 if it's a 3 liners (130 * 1.4), and to a level 201 if it's a 4 liners ( 130 * 1.55).

On a side note, it seems that the higher the level was, the less fluctuation there was, but the average value seems quite constant. See the graph:
GainInLevelVSLevel2liners.jpg (36.55 KiB) Viewed 14342 times

Data (again, same link): ... Se/pubhtml

I also wanted to finish with 3 methods to compare multiple line artifact:

1/ the first one is just to take your artifact, and multiply each line by the number of line. Compare each line to the mono-artifact value to see if it's above or below what you have. It's a simple and effective way to make correct approximation and see the keepers.

example: you have a 2 liners. Multiply each line by 2, and check if both line are correct regarding what you have with you other arts (best % damage you have for instance, and best % hp you have, if you have a combi art damage/hp). For a 3 liners, multiply each line by 3.

2/ Using a art unit equivalent system. While less precise than the third method, it has the advantage to allow for some quick decisions.

I use a unit that gives me a very good arts at 4 unit, and good arts at 3 units.
One unit depends on each stat:
- % damage: 50% = 1 unit
- % rof: 25% = 1 unit
- % HP/SH : 100% = 1 unit
- Convert: 80% = 1 unit
- % resist all: 40% = 1 unit
- % armor: 150% = 1 unit

In general, one unit should equal ~50 levels on the scale given by method 3, but the use of approximated values make it more straightforward to use. You can use the spreadsheet to calculate all the unit values if you want.

3/ Using the equivalent level of the spreadsheet.

Probably accurate, it take also the most time. Use it only if you want to clean your inventory and make hard choiuces. Also, you can use it to evaluate yourself by comparison of the best artifact of the game (see post of brian).

Here is a small table:
- <100 level equivalent: low artifact
- 100 -150 : average artifact
- 150 - 200 : good artifact
- >200 : very good artifact (> 250 = goldy arts)

I hope this can help a bit some who are puzzeling with their artifact, see you in game ;)
Last edited by Jpsi on Mon Nov 28, 2016 11:55 pm, edited 2 times in total.

#66137 by Lapalme Tue Nov 29, 2016 9:35 am
Yes it is brilliant work - finally an artifact analysis that must be used by all.

Now in order to avoid typing all your art info into the tools provided above - all we need is an export tool to be created by the AF developers.
#66184 by Will Wed Nov 30, 2016 2:09 am
Great work. Yes I agree we need to be able to export artifact data. We could do tons more work with this ability. The bottleneck right now is the data collection, which is tedious, long, and generally nauseating. Jpsi will know that better than me. ;)

Regarding the dispersion, Jpsi, you mentioned in your second post: Looks like a normal distribution around the mean. I don't think this is programmed by the developers per se, but it occurs naturally given the semi-random generation of the artifact attributes...based on level of course. Fun to think of a naturally occurring side effect in artificially generated data. One of those fun things you get to learn when you pay attention in statistics class. ;)

Single-line artifact level-attribute correlation, as I found and you reiterated here Jpsi, is linear and nearly perfect (R-squares 0.95-0.99 in my analysis). While this is expected and unremarkable, it might be useful knowledge going forward looking at multi-line artifacts more. We can accept it as true that this linear correlation exists on single liners, and this might have some relationship with multi-liners (i.e., devs might treat single-liners as a kind of basis for programming the random generation formulas for multi-liners).

The discrepancy between damage types and slope coefficients (that "a" value) is strange, but at this point might could be attributed to either simple discrepancy in the data (i.e., damage type doesn't effect the "a" value) or this could have arisen from the tweaks the devs make to artifacts from time to time in their balancing efforts, although that seems unnecessary to little-old-out-of-the-loop me. Still interesting.

Similarly, no surprise with superiors and exceptionals in regards to slope coefficients. Makes sense that the slope coefficient would increase from normal to superior to exceptional. Although the relationship between the three is unusual. The anomaly you mentioned with cooldown arts sounds very odd. Cooldown arts are weird even by observation. It doesn't surprise me that something nuts like what you described might be happening.

I might take the data for the multi-liners and run the regression analysis myself again. I think I came up with something like that 74% for the first line, but if I remember right the correlation was very suspect for the remaining lines (like r-squares 0.5 and varying...and while I realize this might not be important, it's interesting when compared to the r-square for the first line, which I believe was near 1, or near perfect correlation). I'll have to look at this again and think about the results.

Again, great work Jpsi!

I am the monster that breathing men would kill...

#66212 by Jpsi Wed Nov 30, 2016 11:04 am
Ah Will, thanks for the feedback.

I really believe the dispersion is not a normal distribution. But I haven't formally tested the normality, so feel free to jump in to prove it. By essence, if it's not normally distributed, it's not random noise on the value (= they don't add any random noise component to the mean value, because if they were doing this, we will most probably see a gaussian shape - except of course if the random factor is not "noise-like", they also just could add a factor which is homogeneous distributed within -a/2 and +a/2). It seems that the dispersion of the value is homogeneously distributed along the level as. In other words, I believe the level is not discret, and what we see is the closed round level. Artifact at level 16.3 will show up on the same way than artifact level 15.8. But 15.8 will have a lower value than 16.3. So what we see as a dispersion, is an homogeneous distribution from 15.5 until 16.499 (or something) : does this make sense ?

During an upgrade, most of the time your artifact will gain a discret level of 1. This means that a 16.4 will be 17.4 then 18.4 and so on (if the slope is 1): this arts will always stay above the mean line. I am not completely certain about multiple ugrades. I think they gain a non-discret number, above 1. Like they gain 5.3 levels, and it show a level 5 upgrade. I have few data about this, but it might also be a rounding problem during the calculations. It seems very close to the a discret multiple of the slope.

I am not sure about how the formula of multi-liner works, I think they first define randomly the first line, then the second line come into place, with the distribution I ploted. Second line seems a gaussian with a mean of 46% and a std of 13.5%. :shock: EDIT: the first line share the same kind of distribution, as the second line, as both are linked (see below). First line can also have very low values. However, it seems this can be compensated by upgrading the arts. I tested yesterday to upgade once 6 arts with very low first lines: they all gained multiple level, one was +4 levels, the other were between a 10 level gain and a 18 level gain. With tend to prove the practical observation of Magenta, but really proving this would require much more upgrades (and I am not going to do it :P )

But if you want to see the link between the first and the second line, I think you will like this: you can plot the value of the first line vs second line, it gets you this:
Level second vs first line.jpg
Level second vs first line.jpg (50.41 KiB) Viewed 14274 times

The meaning of this is that the lower the first line is, the highest the second line is. What is striking is that the correlation coefficient is not 1: if it would be 1, the total value of the art will be independent from the first line. In our case, it's not independent, because the value of the second line increase slower than the decrease of the first line. This mean the first line will have a direct impact on the total value of an art (again, maybe this can be compensate via upgrade, but I don't know).

So with no surprise form the last figure, if we plot the total value of the art vs the value of the first line, we get this:
Total level vs first line.jpg
Total level vs first line.jpg (63.08 KiB) Viewed 14274 times

Last comment about the single line and the discripencie between damage type: the most probable explanation I can think of is that the dev program this after a long party, and they messed up the numbers :mrgreen: Or it was just for fun. From the data on corro arts, you can see that I actually saw a corro art level 117 (=111.8%) having a higher value of a art level 118 energy (111.4%), which is according to my other observations not possible: it really have a different curve coefficient :)

Effect is even more prononced for flat arts, see this curve:
Flat damage all.jpg
Flat damage all.jpg (56.44 KiB) Viewed 14274 times

Maybe you want the link to the real spreadsheet, to see the formula and copy the data more easily (I also give the data for others, if some curious want to see how the formula works).
Mono arts: ... sp=sharing
Multi arts: ... sp=sharing
(ps: can you check if it's indeed read-only ?)
Last edited by Jpsi on Thu Dec 01, 2016 3:48 pm, edited 5 times in total.

#66249 by Jpsi Wed Nov 30, 2016 9:15 pm
Thanks :P

I did some simulation, and I believe that I know what is happening with the multi-arts. I did the simulation on 2-liners, but probably the principle is the same for more lines.

The total amount of the 2 liners is divided between your 2 lines.
I think (it's just an hypothesis, probably more way to achieve same kind of results) that line 2 can goes from 0% untill 95% of your art level (= equivalent art level as previously prevented). The first line has 1.5 x time this amount, so can goes up to 142.5%. They are both directly proportional to the art level.

Now, the ratio between line 1 and line 2 is random:
- From what I can see, I think line 1 get from 15% up to 85% the total amount of level (let's call this ratio r),
- Then line 2 gets the rest (so 1 - r).

The r value has a small gaussian distribution, which I believe (from simulation) is calculated using the average from 2 random number between 0% and 100%.

From this ratio r:
- line 1 gets 1.425 x the ratio in level,
- line 2 gets 0.95 x the ratio.

The value is then calculated directly from the mono-stat curve, depending on the type of stat this is.

Let's take an example:

If you have an art level 130, the ratio r is first calculated (between 15% and 85%). Let's say you get 60%:
- the first line will get 60% x 130 x 1.425 = 111.15 (equivalent level)
- the second line will get 40% x 130 x 0.95 = 49.4 (equivalent level)

Let's say this arts is a double % energy damage, you will end up with:
- line 1 = 105.5% energy damage (equivalent level 111.1)
- line 2 = 50 % energy damage (equivalent level 49.4)
- total art value = 155.5% energy damage
For this art level 130.

Most of the time the value of r will be 50% (so 50% first line, 50% second line). In that case, we will get:
- first line = 50% x 130 x 1.425 = 92.6 level equivalent = 88.8% energy damage
- second line = 50% x 130 x 0.95 = 61.75 level equivalent = 61.1% energy damage

The most probable outcome of a level 130 energy arts (% damage) will be 88.8 % + 61.1 % = 149.9 % energy damage

In the game, we also have a small dispersion, which I believe is due to rounding up of the level and of both stat values.

ps: in the multi-arts spreadsheet, I added the last sheet to show the simulation.

#66481 by TheCen Sat Dec 03, 2016 7:32 pm
Finally.. more analysis by other people about arts... :D

I have a few questions. When you were doing your analysis; were you tracking art upgrades.... were you following the complete upgrade or just going by the popups from each upgrade? I ask because I have warned players in the past that the popup is not always accurate and does lie. Also, when tracking upgrades I have noticed that sometimes upgrades don't actually hit their average or I should say fall well short of their normal upgrade. But, on the very next upgrade them seem to fix this error. Did you notice this as well?

#66484 by Jpsi Sat Dec 03, 2016 10:07 pm

About the upgrades, I can't really comment because I didn't have enough data. What I did see is that for the most probable upgrade, level 1, the gain was alway the slope (the art progress on 1 level in the curve). For multiple upgrade, we most of the time gain n time the slope, where n is the slope of the curve. The problem is, it's not exactly n time the slope, sometime it's a little bit below, sometime a bit above. I am unsure if this is due to rounding problem on my part, of the fact that the upgrade will gain 10.3 level (instead of 10) for instance. This can justify my rounding problem, but I am not certain about this.

Feel free to do your own upgrade analysis, and test your hypothesis. Using the mono-arts spreadsheet you can see if an art is above or below the mean. You can then follow it while it goes up in level. I have to say I am most of the time working on the art value, and not what is written on the pop-up (the spreadsheet calculates the gain per upgrade, depending on the level gain): I never checked what you saw.

For the multi-liner, studying the effect of the upgrade is more complicated: we need enough mutiliner upgrades that have the "correct" stat (only lines with % damage, % resist, % hp or % sh, % armor, or % shield regen - those are the one where I have the most data of, and we can't use lines that could be sup/exp, because we can't know if they are sup/exp). Then we can plot the distribution first line and second line, and compare it with unupgraded version. To validate Magenta theory, we should see less dispersion on the first line.

Just one last tip about using the spreadsheet: I usually put the spreadsheet open on the left of my screen, while having astroflux open on the right side. My mouse stay on astroflux without clicking on the windows, so I can stay typing the art value in the spreadsheet while seeing the popup thanks to my mouse. I can go quickly form one art to another by moving my mouse. That's the reason why in the spreadsheet you can type everything: you can fill without using your mouse, which stay on the astroflux windows to show the popup.

ps: I will probably provide an art equivalent unit spreadsheet, which is actually what I am using for my own arts. I'll share it as soon as possible. The other spreadsheet gives accurately the level of each line, but your real power is not directly dependent of the level of each line individually, but on the total of every line of one art.

#66486 by TheCen Sat Dec 03, 2016 10:39 pm
Oh I have done my fair share.

Here is my original post: viewtopic.php?f=13&t=6006&p=40167#p40167

I did update the 2 charts in the video that is attached to that post. But, they do not reflect the current Strength and Level designations... they still have the old Level and potential level designations. :?

In it I did provide a spreadsheet of all my art upgrades 45+ arts. But, over time the arts have been adjusted through updates.. and I never went back in and changed the formulas to reflect the new game. Quite frankly, I didn't see the point of doing that. I already gleamed the information I wanted from the original tracking of each upgrade.

Nonetheless, I am going to repeat to anyone here that is reading this... the popup that comes up after you upgrade arts lies to you. Do not believe every number on it. I'd suggest writing down your figures before and after an upgrade so you know exactly how much you gained. Then you can know what to expect for each upgrade after that.

#66504 by Jpsi Sun Dec 04, 2016 9:21 am
Oh I forgot about this video, but I can remember your spreadsheet ... ingle=true (I am more comfortable sitting in front of a list of data than in front of a video, even if your videos are always great): this was actually the main reason why I never tested the upgrade myself. You did a great job at it.

Well your data can give us the answer about the way the upgrade follow the slope during multiple level upgrade :P Can I have a link to the spreadsheet (read only), so that I can copy it ? The published page is not copiable, and for some reason (too big ?) it's very slow, I almost can't scroll in it.

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