Thread: Optimizing Thief-based Xenon, interpreting calculations, & other questions

1. Optimizing Thief-based Xenon, interpreting calculations, & other questions

I've gained a better understanding of how %DMG, %PDR, and %ATT relate to one another, and how that relation will vary depending on one's own equipment+skills and the target mob that is being dealt with.

So I decided to create an Excel file that will take this step further by integrating all stats (STR/DEX/LUK) for the purpose of calculating clean & buffed ranges, displayed damage on all bosses, and every conceivable "ATT-to-%Stat, ATT-to-Stat (& vice-versa) relation" that is useful to me.

But there were some parts that I haven't been able to accurately test, or cultivate a coherent understanding for, so I was looking for some confirmation and/or clarification with some of the calculations I've made:

1. Is it correct to use following equalities to relate increases in ATT and some stat (i.e. STR, DEX, LUK, All Stats, %STR, %DEX, %LUK, %All Stats)?

For example:

1 ATT = ?%STR

1 ATT = ? DEX

4% All Stats = ? ATT

where x is what is being solved for, and where the prefixes are:
• b = base
• np = not affected by potential
• p = affected by potential

Because the damage formula (taken from here and here):

contains multiplicative components, I took the liberty of treating everything besides (STR+DEX+LUK) and ATT as constants, seeing they are irrelevant when equating the two %increases. Is this a logical method for calculating the desired unknown stat, x?

2. (This next part assumes that the methodology used above to compare relative %increases is correct.)

Does gaining more of one certain stat/%stat become less effective at a certain point (is it calculable?), and will the largest %increase point toward improving different stat(s)/%stat(s)? For example, if one improves his DEX stats, must he also improve his STR and LUK stats as collateral, or should he continue to improve DEX because it provides the largest increase for the same amount that could have been added to STR or LUK?

To approach this question in a different manner, I will change the focus from the generalized example above to one that is more relevant to my case. I currently have 1039 ATT (852 potential-dependent), 4296 STR (330 base, 1000 potential-dependent, 40 potential-independent), 4489 DEX (330 base, 1156 potential-dependent, 45 potential-independent), 7692 LUK (416 base, 1163 potential-dependent, 43 potential-independent), with 16% all stats from MW31 applied. This may seem awfully unbalanced, given that I am heavily %LUK-based since I essentially moved all my Dual Blade gears over to my Xenon).

With 22% ATT, 208% STR, 189% DEX, and 365% LUK, my calculations lead to this conclusion:

• 9% STR = 6.0484769 ATT
• 9% DEX = 6.8237752 ATT
• 9% LUK = 7.2889542 ATT

Putting aside the higher base LUK, the flat stat bonuses from my equipment/skills seem to be fairly consistent, so it seems that the imbalance can be attributed to the inflated %LUK.

But this is just looking at one piece of the big picture.

I'm not very sure how I should be interpreting this information, so I don't know how I should be upgrading my gear in the most optimal manner. It seems I'm limited to "guess-and-check" work where I plug-in hypothetical values of incremental %stat boosts, and in this case, I am simply looking at what %stat will provide me the greatest boost as it relates to ATT. I was thinking of dismantling my pure %LUK increases for some basic %all stat, or some combination of %all stat + another %stat, but I have a feeling that the "immediate largest increase" can be very misleading in the grand scheme of things.

If the idea of improving gear through flat increases of STR/DEX/LUK is ignored (for now), and only potential stats are to be modified, then it would seem initially that evenly balancing %STR/%DEX/%LUK (in a way such that any incremental increases in different %stats closely approach some uniform value of %all stats) is optimal. However, the results indicate that the increases are largely dependent on the current total stats I have, and that in almost all cases, %DEX and %LUK increases are the best. And even though I have less %DEX than %STR, does the slightly larger potential-dependent DEX have that much of an impact to supersede the effects of %STR?

Any clarification on this topic is very much appreciated.

3. Based on what has been said in this this thread and my own calculations for STR/DEX/LUK, the stats obtained from Inner Ability are not affected by potential. Does ATT from Inner Ability also follow this pattern? (For creating the equations in part 1. of my questions, I assumed that ATT from Inner Ability is not affected by potential either, but I don't have a way of testing this myself).

4. Do the critical numbers we see as damage follow a standard normal distribution, a skewed normal distribution, or neither?
This came to mind as I was reading this post, where he used the average of min/max-crit multipliers to establish a comparison. Are we allowed to just take the "average" of values?

I don't know how Maple "selects" numbers to choose from, but is it done in either of the following manners?:
• Choose a random value between min-crit multiplier & max-crit multiplier, choose a random value between min-"range" and max-"range", and then multiply the two random values together.
• Apply min-crit multiplier to min-"range", apply max-crit multiplier to max-"range", and then pull a random value between the lower and upper bounds.

I think from a programming perspective, the first method is simpler. But I wanted to know if the numbers are randomly generated and just naturally fall under a standard normal distribution, or if they're intentionally generated in a way such that the majority of them approach the average value.

5. Does anyone have an updated %PDR chart for the most prominent bosses? I've been using Maple Archive to look up Physical Reduction Rates, but it seems the database hasn't been updated since late June.
Also, does Mori Ranmaru actually have 0% PDR, or 55% PDR as this page indicates?

2. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

I skimmed over part 1 and didn't find anything wrong with those equalities. Should be fine.

For 4 the only time crit damage's distribution matters is if some of your hits hit damage cap. The mean is exactly the same for both of the distributions you suggested.

3. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

The math is pretty much accurate, I know what you are doing, and the answer isn't exactly most easily answered.

A good way to approach the problem is to first ask yourself whether you want to "shoot for the moon", or "take it step by step". The former is dead easy - aim for the best possible potentials (and stats, if you're into scrolling and stuff), then vary around a little to see what things, if compromised, doesn't change the final damage that much. 3 variables is a little annoying to handle but should be do-able.

The latter is just... see what can be improved right now to give the single-greatest increase, then move on from there. The assumption, of course, is that you're not walking into a damage valley. I always say "maximise the square" for this reason, and you must find out for yourself first how the path to the moon is like, then work from there step by step.

You will obviously know what variables are independent of what, blah blah. While equating %something to ATT gives a good idea of things, remember that all it tells you is the ATT-equivalence with that set of conditions. You can't see the rate of change of ATT-equivalence, and that is why I decided to stop trying to make a suitable graph/model because it is not easily understood nor visualised. What some people do, e.g. for molecular modelling, is to provide a set of boundary conditions. Say, consider this range of %this, %that blah blah, keep varying the numbers until the change in ATT-equivalence hits a minimum threshold.

Obviously, for Maplestory, when the boundary conditions are pretty fixed and you know the maximum and best possible potential lines to consider, given that our damage formula involves variables that are monotonically increasing, it's really not difficult to find the set of conditions that gives the maximum possible damage. Then ask yourself, is it worth spending so much effort like programming a code and considering so many differentials blah blah just to find the ceiling conditions? The global maximum is intuitively easy to consider and aim for, but mathematically difficult to show.

I can't offer much right now tbh. I dig the PDR values from extractions/SP database, and I don't know the method of number distribution. I've always used linear distribution (i.e. totally random) but it doesn't really matter in our case, for a long-run outcome without level-difference issues just involves the average value (if you cap only sometimes, then obviously you have a problem here).

4. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

First off, thank you guys, I appreciate your input.

I'm not hitting the damage cap quite yet with Snipe, so I guess it shouldn't matter how the numbers are distributed. The small observation came about as I was checking my theoretical numbers vs. actual numbers on mobs, when I noticed that my hits were falling most frequently within the middle portion of the lower and upper bounds; rarely did I ever hit within 500k-1m of the minimum and maximum values. This is what made me wonder how the numbers may actually be distributed.

It's likely that I will settle for the largest, most immediate changes first (such as cubing "uncubed" gear), and then move onto recubing pure %stat items (ex. 21% LUK) into a mix of %all stat and some other %stat (ex. 9% all stat + 9% STR, 12% DEX + 6% all stat, or some other variation), as opposed to discarding entire items for flat 18-21% all stat items (because that's.... very improbable, given my budget). I do seek to "shoot for the moon", but that will only be achieved gradually. So it's kind of like keeping some greater overarching goal in mind while taking minor detours?

And would bonus potential be a good example of "taking it step by step"? Given some scenario in which I am forced to decide between, say, 2% all stats or 10 ATT, and the numbers presently indicate that the ATT bonus is superior, I'd choose that to begin with; however, it's possible that I will have to revisit that potential again later on to see if its behavior has changed overtime, one that is indicative of a superior increase from %all stats (after receiving a very large bonus of ATT from enhancing tyrants, for example)?

Would this be one elementary example of showing the rate of change of ATT-equivalence (in terms of different increasing pure %stat values), given the restriction of 1-30% stat?

 %All Stats ATT %STR ATT %DEX ATT %LUK ATT 1% 2.01692573 1% 0.362956013 1% 0.46632912 1% 0.46632912 2% 4.394507197 2% 1.086567764 2% 1.241627425 2% 1.345000532 3% 6.72040211 3% 1.810179515 3% 2.01692573 3% 2.17198539 4% 9.097983578 4% 2.482104712 4% 2.843910588 4% 3.050656802 5% 11.42387849 5% 3.205716463 5% 3.619208892 5% 3.87764166 6% 13.80145996 6% 3.929328214 6% 4.44619375 6% 4.704626519 7% 16.17904143 7% 4.652939965 7% 5.221492055 7% 5.58329793 8% 18.50493634 8% 5.376551716 8% 5.99679036 8% 6.410282789 9% 20.88251781 9% 6.048476913 9% 6.823775218 9% 7.2889542 10% 23.20841272 10% 6.772088664 10% 7.599073522 10% 8.115939059 11% 25.63768074 11% 7.495700415 11% 8.42605838 11% 8.99461047 12% 27.96357565 12% 8.219312166 12% 9.201356685 12% 9.821595329 13% 30.34115712 13% 8.942923917 13% 9.97665499 13% 10.70026674 14% 32.71873859 14% 9.666535668 14% 10.80363985 14% 11.5272516 15% 35.0446335 15% 10.33846086 15% 11.57893815 15% 12.40592301 16% 37.37052842 16% 11.06207262 16% 12.35423646 16% 13.23290787 17% 39.74810988 17% 11.78568437 17% 13.18122131 17% 14.05989273 18% 42.12569135 18% 12.50929612 18% 13.95651962 18% 14.93856414 19% 44.50327282 19% 13.23290787 19% 14.78350448 19% 15.765549 20% 46.82916773 20% 13.90483307 20% 15.55880278 20% 16.64422041 21% 49.15506265 21% 14.62844482 21% 16.33410109 21% 17.47120527 - - 22% 15.35205657 22% 17.16108594 22% 18.34987668 - - 23% 16.07566832 23% 17.93638425 23% 19.17686154 - - 24% 16.79928007 24% 18.71168255 24% 20.05553295 - - 25% 17.52289182 25% 19.53866741 25% 20.88251781 - - 26% 18.19481702 26% 20.31396572 26% 21.70950266 - - 27% 18.91842877 27% 21.14095057 27% 22.58817408 - - 28% 19.64204052 28% 21.91624888 28% 23.41515893 - - 29% 20.36565227 29% 22.69154718 29% 24.29383035 - - 30% 21.08926402 30% 23.51853204 30% 25.1208152

Granted, this is only a small portion of the entire picture (that theoretically should include all possibilities, but rather difficult to visualize?), and definitely doesn't include all of the variations (mixes of pure %stats, mixes of pure %stats + %all stats, etc.).

As expected, the %All Stats function is the steepest, followed by %LUK, %DEX, and %STR. Although this may not be anywhere near to what you were referring to, I felt this was useful to me because it showed that while the idea that %STR, %DEX, and %LUK are weighted equally is true, it may not be covering the full story. (ex. 6% all stats could actually be worse than two 9% LUK lines, even though they both add up to "18% stats").

5. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

My point is that your graph, for example, shows you the equivalence to ATT at that set of conditions (presumably 0% something?). After you put in, say, 3% stat, that table needs to be re-crunched. So comparing it to a car, do you want a steeper acceleration for now, or just move in the direction of the highest possible speed, even if that path doesn't give you the greatest acceleration (which may or may not give you a larger speed with that set of conditions).

So leading on from the previous point, "shooting for the moon" would be something like "I will cube equipment A until it gets 27% ALL" or something like that (idk abt potential pools so idk what the highest really is). What you described is pretty much "going step by step to the end in mind". And here I leave you to decide if you want e
g. your bonus pot to be 10ATT giving a larger gain in damage for now but outcome-unoptimal, or 2% ALLwhich might give less damage now but grows more later and is outcome-optimal (you do the numbers, this is just a scenario). Much like choosing between 3% Stat and 6ATT at a lower level (of funding) and at a higher level ().

6. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

If you start increasing %dex, the boosts you get from %dex/luk/str/all will all remain constant. Nothing will change for those comparisons if you were looking at %dex vs %str or %dex vs %all.

The boosts you get from +dex/all will increase though, so if you were looking at +dex vs %dex or +dex vs +luk things will change.

7. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

I understand the car analogy and what you meant by "shooting for the moon" or "taking it step by step" now. But I don't understand your presumption of 0% stats as the standard set of conditions (for that graph in particular). Perhaps the graph is misleading because the x-axis "%Stats" should actually be renamed "+%Stats"; the numbers in the table/graph were calculated with my present stats (written in my original post; 1039 ATT, 208% STR, 189% DEX, and 365% LUK) in mind. Because my equipment potential stats are unchanging, why must the table be rewritten if the new %stat increases from 1-21% and 1-30% are already displayed?

Or, I'm misunderstanding you entirely, lol.

Yes, you are definitely correct. I calculated 1% STR to be equal to 0.85696% DEX, and even after varying all my present %STR/%DEX stats, it remained constant.

I think the mistake in my own train of thought came from my belief that varying one or two unrelated sources of %stat will affect the third %stat when its ATT-equivalence is found. At the moment, 5% STR = 3.2057165 ATT, but an increase of 9% LUK for example, will change the relation to 5% STR = 3.1739677 ATT; this observation made me believe that perhaps %STR/%DEX/%LUK are actually interdependent, and increasing/decreasing one would invariably affect another.

So, while +%stat boosts are independent of one another, flat +stat boosts are not... I'm still trying to grasp this concept.

Perhaps I'm not fully understanding the mathematical concept behind making changes to the equations...?

8. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

Your graph is not wrong. From what I see, it tells you how much ATT the next +%something provides in relation to ATT. The thing is, is this information valuable? Does it really help you? If your aim is to keep having the greatest increase in damage, then this graph provides little information.

Think of it this way. You want to find the highest point in the mountain in the shortest time. How do you do it? Find the steepest path and follow it. Your graph shows you the slope where you are right now, but 2 steps later the slope would have changed. The challenge is to find a way to visualise it, be it in a graph or an equation (which also becomes a graph I guess). So, for example, are you going to keep doing that graph everytime your potentials change/get better?

First, figure out what you want, then ask the right questions to guide you to what you want, then find the most efficient answers to those question.

9. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

Well that was only for the case where you change %stats and nothing else.
If you change +stat and nothing else, you get the opposite effect. All +stat boosts will remain the same and some of the %stat boosts will change.

10. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

Yeah, it will entirely depend on what I want at that moment in time. If I wanted to take the most likely route of upgrading by taking it "step-by-step", then I believe what can be inferred by the information presented in the graph above can be useful, to a certain extent. While it does not provide much information, I feel that it is sufficient to give me a general sense of "what's better than what".

For instance, if I need a new ring and I have the option to pick one of two:
• Ring A: 12% STR, 9% DEX, 9% DEX
• Ring B: 6% All Stats, 6% DEX, 6% LUK
The graph allows for an analysis of the rings in terms of ATT by simplifying and converting the potentials:
• Ring A: 12% STR, 18% DEX -> 6% STR, 6% DEX (3.929328214 ATT + 4.44619375 ATT)
• Ring B: 6% STR, 12% DEX, 12% LUK -> 12% LUK (9.821595329 ATT)
Conclusion: I would choose Ring B over Ring A because the ATT-equivalence of its %stats is greater.

In my opinion, a graph like this is useful to me because it provides an intuitive means to compare items with similar stats when the conclusion is not so obvious at first glance. Granted, this method of analysis becomes rather... pointless if I have the tooltips in front of me that tell me exactly the +range increase of each item, or if I perform before & after calculations of ranges and compare their differences.

The idea of comparing relative increases seemed like an effective indicator for which items to pick and choose from (especially when considering the limited stock of certain %items and their wildly divergent prices), which I believe is most important. Although this method fulfills its purpose in the example above, would it not be safe to analogously interpret my findings in this manner? Maybe it's because I consider "%stats-to-ATT" to be synonymous to "%stats-to-actual damage"; can this way of seeing things lead to a misleading conclusion?

If I were to make something truly "useful" in all aspects, then would I have to create a generalized equation of 8 variables?: (%ATT [which should be constant for the most part, but must be included if there are sources of ATT that are not affected by potential], ATT, %STR, STR, %DEX, DEX, %LUK, LUK)... I imagine it is very difficult to visualize/conceptualize given the amount of variables.

For this reason, I settled with providing just one seemingly useful example of the dozens of tables/graphs that could be written to get a better view of the larger picture. Is this method of analysis by looking at each of the comparisons individually not recommended?

I wasn't sure if you were hinting at the amount of labor needed to produce these graphs, but the only numbers that I will have to manually enter are the ever-changing stats/%stats on my equipment. Since the Excel file automatically configures the rest of the calculations for me, it's not too much work.
But yes, it would be my intention to keep myself updated with the graphs as I modify/replace gears.

11. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

%stat:atk should lead you to the same conclusions that %stat:dmg does.

But if you want to compare things directly to damage, the equations might end up looking something like...

Amount needed to double damage

Attack: TotalAtk / %Atk
Atk%: TotalAtk / pAtk
All%: (TotalStr+TotalDex+TotalLuk) / (pStr+pDex+pLuk)
Stat%: (TotalStr+TotalDex+TotalLuk) / (pStat)
All: (TotalStr+TotalDex+TotalLuk) / (3+%Str+%Dex+%Luk)
Stat: (TotalStr+TotalDex+TotalLuk) / (1+%Stat)
bStat: (TotalStr+TotalDex+TotalLuk) / (1+%Stat) / MW
Boss%: (1+%Total+%Boss)

And after that you can divide them by each other to figure out everything you could possibly want to know, since all of those will lead to damage doubling.

12. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

In general, comparing to ATT and comparing to DMG gives the same conclusion. It does tell me e.g. Y%something gives me X attack, which is more than what the same-tier ATT potential line provides. The rest are then just comparing equivalents of ATT, thus giving the same conclusion. It is also very good for comparing equipment-to-equipment change (theoretical one, that is, if you can't get hold of the tooltip!).

The downside is: it cannot be generalised, because it is dependent on your current ATT, whereas things like %stat are effectively independent of ATT. So comparing a variable with another variable is taking a roundabout when instead you should be relating it to the independent variable i.e. your (fractional) DPS increase. I know it can be difficult to handle sub-decimal place values e.g. 0.012XXX, so comparing it to ATT e.g. 3%stat == 6.12ATT becomes much more reader-friendly. Use whatever you are comfortable with.

At the hyper-funded regime, you will have so much ATT/STAT that are subject to potential that it is virtually pointless to consider lines that provide ATT/STAT. You are therefore reduced to only %ATT, %DMG, %Boss, %IgnorePDR, %ALL and %STAT. I would find the global maximum, let's say it is 21%ALL and 70%Boss and 40%IgnorePDR and 12%ATT. I would cube my equipment until I reach that global maximum, so my task now is to decide what equipment's lines to cube away. THEN in this case your ATT-equivalence chart becomes useful because it provides a common basis of comparison - oh this line has the least ATT-worth so I should junk this first.

Using the generalised equation is helpful to plot your shortest path to the global maximum, but is difficult to use because graphs become multi-dimensional. It's akin to using Lagrange multipliers method in math, except that for us we go "from point to point" because we aren't actually tracing a curve.

I ain't trying to say which method is right or wrong. It's just that some methods are more efficient than others, and some are easier than others while having suitable approximations and assumptions.

13. Re: Optimizing Thief-based Xenon, interpreting calculations, & other questions

Well if anyone wanted a general equation that only uses the following: Current Average Damage, Change in Variable, Expected Increase From Change in Variable, it's not pretty.

dMEANDMG = MEANDMG*{[(1+ATK)(1+ATK%)+NPATK] * (1+BOSSTOTAL) * (1+CRIT%) * (1+CRITDMG%) * [(1+STR)(1+STR%)+(1+DEX)(1+DEX%)+(1+LUK)(1+LUK%)+NP STR+NPDEX+NPLUK-2] - 1}

Plug in something like V1 = ChangeV1 * IncreaseV1 / MEANDMG for all the variables up there.

When changing 0 variables, everything cancels and the change is 0.

With 1 variable changed it just becomes /* dMEANDMG = ChangeV1 * IncreaseV1 */

2 variables becomes

if they interact

if they don't interact

And there's a crazy amount of double and triple and higher order interactions for higher numbers of variables.

When expanding things you will find that...

NPATK does not interact with ATK or ATK%
STR and STR% do not interact with DEX, DEX%, LUK, and LUK%.
DEX and DEX% do not interact with LUK and LUK%.
NPSTR, NPDEX, and NPLUK do not interact with each other and do not interact with STR, STR%, DEX, DEX%, LUK, LUK%.
Everything else interacts.

It's simpler to just do NewDamage = DamageWithNewStats and Change = NewDamage - OldDamage though. Idk why anyone would do all of this.

They're of course interchangeable. The get to the thing above just factor out OldDamage
Change = OldDamage * (NewDamage/OldDamage - 1)

then convert NewStat to OldStat+Change for everything in NewDamage.
Change = OldDamage * (PolynomialBlob1/OldDamage - 1)

and then I'm too lazy to explain how that turns into this. Various components of the denominator get factored out into different places.
Change = OldDamage * (PolynomialBlob2 - 1)

idk I was bored

Also solving for V1 = ChangeV1 * IncreaseV1 / MEANDMG gives the following.

Spoiler

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