Is there a Database of Mobs' Defense? (or Evasion?)

[Shamaya]

I've been trying to do some mathematical comparisons recently between Thf/Nin and Thf/War to see which mathematically should produce more damage, but the deeper and deeper I get into it, the more and more circumstantial that I realize that the comparison is. For example, the exact % improvement on pDiff when using berserk is totally dependent on mob defense. +25% attack will not always = +x% in the pDiff. So if I really want precise, worthwhile conclusions/results on this comparison, I'm going to need a list of mob defenses. If there is no such database of mob defense, I'm going to have to go test it myself if I want my mathematical comparison to be good.

So my question is - is there a database of mob defense? I've heard it claimed before on various forums that there was, but people that claimed this never bothered to link it. I'm skeptical as to whether or not such a database actually exists. But if it does, it would be an incredibly good asset to melee DD's. If anyone knows of one, could you please link it here?

An unrelated question: Is there a database on monster evasion as well? If not, I could test it using:

Low Evasion

If a monster checks as low evasion, you have a greater than 80% chance to hit it.

If the monster is higher level than you, you may have have less than 80% Hit Rate
Mathematically, your accuracy ? Enemy Evasion + 10

That quote is from wiki. So a third question would be...: Say I determine the threshold where a mob goes from normal to low evasion. If I want to talk about its evasion, should I add up all of my combat skill, dex, and acc at the time that I used to get the comparison? For example, say that my acc total from combat skill, dex, and acc was 350, and this is the point at which the mob's /check transitioned from normal to low evasion. This would be enemy evasion +10...so should I say that this mobs "evasion is 340"? Would that be a sensible evasion rating?

[VZX]

-I think there was some post back before about mob VIT/defense... only some of them
-Old wiki has some mob defense/VIT listed (colibri and mamool)
-Studio gobli has generated partial list of mob VIT/DEF/INT http://f4.aaa.livedoor.jp/~rmkta/ws/enemy.html

I think Nagamaki posted the formula while back to calculate enemy's stat/defense, given their main/sub job and racial rank for the stats

P.S: Has anyone researched the new melee pDIF after the last patch?

[Amele]

I've been working on gathering as much information as possible to put into a game mechanics article on new wiki about mob stats - but the actual information is pretty slim (and some of it is even contested, as little as there is)

if you're looking for a 'baseline' to calculate with, iirc. the lowest defense in merit is about 320 (most are in the 350 range). with similar evasion numbers.

you actually can calculate the effect of berserk without knowing the mobs exact defense if you know your net ratio (or thereabout) you'll probably need the mob level and the mob vit unless you have enough strength (over 125+ for most weapons, not sure for thief) to guarantee you've capped fstr, in which case you have a known quantity for your base damage.

you can use your known base damage to back figure what your pDIF must be approximately and then from there what your cRatio (and ratio) must be; at which point you can apply your berserk and recalculate your damage.

VZX- I haven't yet. I do know that it isn't really behaving like the old formulas did (I'm doing more with my weaponskills than I was expecting; I haven't kept a very close eye on my regular melee hits lately though, was trying to resolve weaponskills first.)

if you want, I'll take a full log dump of my next exp party on my 66 samurai and I'll see how much information I can distill from it for you.

[Shamaya]

I think Nagamaki posted the formula while back to calculate enemy's stat/defense, given their main/sub job and racial rank for the stats

P.S: Has anyone researched the new melee pDIF after the last patch?

I'm actually looking at those formula verifications in Nagamaki's post right now. It's a bit confusing but I'm working on it. As for pDiff, I heard speculation that, but nothing conclusive, sry.

if you're looking for a 'baseline' to calculate with, iirc. the lowest defense in merit is about 320 (most are in the 350 range). with similar evasion numbers.

you actually can calculate the effect of berserk without knowing the mobs exact defense if you know your net ratio (or thereabout) you'll probably need the mob level and the mob vit unless you have enough strength (over 125+ for most weapons, not sure for thief) to guarantee you've capped fstr, in which case you have a known quantity for your base damage.

you can use your known base damage to back figure what your pDIF must be approximately and then from there what your cRatio (and ratio) must be; at which point you can apply your berserk and recalculate your damage.

Ugh, this gets more and more frustrating the more I did in and try to learn about the game mechanics. I have to admit, I like that the game has hidden stats. It makes it harder to learn and I suppose gives one a sense of accomplishment and an edge if they take the time to learn it. But I'm still very new to these formulas so it's a bit rough for me.

I understand some of what you mean, but not all of it. Basically, this is my task for figuring out berserk potency: 1.Know my attack and target's level and know/figure-out its def, 2.Use target's level to figure out cRatio, 3.Calculate Atk-Def, then apply cRatio, 4.From there, I should be able to see where my pDif floor and ceiling are at that adjusted Atk-Def value, and I can easily calculate the pDif average, 5.Write down that pDif average, 6.Apply attack after berserk, then figure new Atk-Def, then apply cRatio once again, 7.Find new pDif ceiling and floor for that range, and calculate average, 8.Divide berserked pDif avg by unberserked pDif avg, and this should tell me the raw% increase in damage that I am getting when using berserk.

Using this method should give me a "raw-damage-%-increase" number, but it won't tell me the damage difference in precise units unless, as you say, I know my adjusted base-WD after adjusted for fStr. Now I think I understand what you were trying to say. Basically, for me to gauge Thf/Nin vs Thf/War, I take fStr into account, because all I'm looking for is that raw% increase in damage (from no berserk to berserk). I see from wiki that pDiff is a straight multiplier at the end of the calculation, so I shouldn't need to do anything else to figure this out:

Calculating Physical Damage
Physical damage is calculated by multiplying your base damage with attack/defense function
Damage = Base Damage x pDIF

In any case, I'm very glad you brought up cRatio because I've encountered that term recently and was unfamiliar with it up until now. I just went and checked it out and see what it does and how to calculate it. Very aggravating--just another step in all these tons of calculations that I'm doing. You can see the comparison that I've made so far by going here:
http://ffxi.allakhazam.com/db/jobs.html ... =11;page=1
But right now it is a work in progress. I think that the comparison as it stands right now is somewhat close to the truth, but I have to account for a few more things now. People seem to want to know everything before its considered worthwhile. They're probably right to feel that way though.

Please, someone correct me if I'm wrong about finding out the exact raw% damage increase from going unberserked to berserked. I need to know.

[Shamaya]

Well I just talked to Aurik, and he said this method should work in order to find the numbers that I'm looking for.

[GSDragoon]

viewtopic.php?t=16214

There's some numbers here.

[Shamaya]

That is epic, thanks.

[Amele]

I understand some of what you mean, but not all of it. Basically, this is my task for figuring out berserk potency: 1.Know my attack and target's level and know/figure-out its def,

the easiest way to do this is to use lots of gear swaps and /c your target a bunch. when he goes from high def to neutral, that's exactly its defense. if you can't get it to be high def, then you can use neutral to low and divide by 1.25 to get its exact defense.

2.Use target's level to figure out cRatio, 3.Calculate Atk-Def, then apply cRatio,

pretty much right, except I wanted to clear something up. the level adjustment isn't cRatio. the final value of (ratio - 0.05*dlvl) is cRatio.

ratio is simple att/def. so yeah, calculate attack/def then apply cRatio*

incidentally, the level adjustment is one of the things that I'm not sure is still the same post patch. but I haven't had a chance to look into it in detail yet (damn full time job!)

4.From there, I should be able to see where my pDif floor and ceiling are at that adjusted Atk-Def value, and I can easily calculate the pDif average,

actually, no; you can't easily figure out the pdif average (except for certain ranges) because the function doesn't appear to be normally distributed. better to use the median or the mode (mode is typically 1.0 if you're near 1.0 cRatio) otherwise median is pdif_max - 0.4 if you're high*

*again this is all in flux until we nail down the new values; this is probably right for 1handers.

5.Write down that pDif average, 6.Apply attack after berserk, then figure new Atk-Def, then apply cRatio once again, 7.Find new pDif ceiling and floor for that range, and calculate average, 8.Divide berserked pDif avg by unberserked pDif avg, and this should tell me the raw% increase in damage that I am getting when using berserk.

if you're going to do all of this, it's generally easier to just compare pdif_max and pdif_min's before and after.

Using this method should give me a "raw-damage-%-increase" number, but it won't tell me the damage difference in precise units unless, as you say, I know my adjusted base-WD after adjusted for fStr. Now I think I understand what you were trying to say. Basically, for me to gauge Thf/Nin vs Thf/War, I take fStr into account, because all I'm looking for is that raw% increase in damage (from no berserk to berserk). I see from wiki that pDiff is a straight multiplier at the end of the calculation, so I shouldn't need to do anything else to figure this out:
[quote:3e002]Calculating Physical Damage
Physical damage is calculated by multiplying your base damage with attack/defense function
Damage = Base Damage x pDIF

[/quote:3e002]

basically. I was saying that, if you can guarantee you have enough strength to cap your weapon rank (base damage is "D+Fstr" where fstr has a max of wrank+8) then you can skip all that attack defense stuff. swing at the mob enough times that you have an idea of what your max hit must be - and calculate pDIF from there.


you actually got me fairly interested. so here's the comparison:

base damage * ((1.25 * attack)/defense - 0.05dlvl) / base damage * ((1.0 * attack)/defense - 0.05dlvl) = ?

((1.25 * attack/defense - 0.05dlvl) / (1.0 * attack/defense - 0.05dlvl)

(1.25 * attack - 0.05dlvl*defense / defense ) / (1.0 * attack - 0.05dlvl*defense / defense)

1.25 * attack - 0.05dlvl*defense / 1.0 * attack - 0.05dlvl*defense

you could probably reduce this further, but since 2 of the 3 variables left should be 'known' (your attack and dlvl - more or less) you can calculate for fictitious but reasonable defense values and get a range of bonus that berserk would give you.

[Shamaya]

Thank you for going over all of that in more detail. Two more things continue to perplex me:
1.Mob level. How is this determined? I know I can easily go out and find a mobs defense through simple swaps, but if one wants to put this knowledge to future use, they should know the level of the mob they were checking. And yet, mob level can differ by 2-3 or more within the same zone. So how does one know?

2.Berserk and raw% dmg increase. Regarding how pDiff calculations are distributed throughout the ceiling and floor gap, you said:

actually, no; you can't easily figure out the pdif average (except for certain ranges) because the function doesn't appear to be normally distributed. better to use the median or the mode (mode is typically 1.0 if you're near 1.0 cRatio) otherwise median is pdif_max - 0.4 if you're high*

A reliable source also told me the same thing, that basically in other words, if you were to chart the distribution of pDiff calculations between the floor and ceiling, the curve would not be linear. When you say "high," I believe that I know what you mean. Glancing at the pDiff chart, there are a few tiers. At the points in which the ceiling and floor are farthest apart, they differ by 0.8 pDiff. The smallest regions in the chart differ only by 0.5 pDiff in spread. So by high, I assume thta you mean the former (0.8 pDiff). You mention going with the median, which is 0.4 below the max, but that's also 0.4 above the min. When I say average, I mean precisely the median as well, for since there are only two values that would be averaged (the max and the min), the average can only ever be the median.

There are going to be times, however, where the corrected pDiff range will not lie in that region, so I'll always have to use the avg/median.

Now back to whats puzzling me: I did a simple math problem to see if I'd get a different value if I averaged the floor and ceiling values before factoring in the difference between berserked and unberserked. I got two different values. I know this sounds confusing, so here's what I mean:
Just to make the math easy, say that my pDiff unberserked has a max of 2 and min of 1. Berserked it has a max of 3 and min of 2. What I had done in my previous Thf/War vs Thf/Nin test was take the average pDiff unberserked and then berserked, and fidn the ratio between them. So unberserked avg 1.5, berserked is 2.5. 2.5/1.5 = 1.666 trailing.

If I use the different method, though, my ratio of ceiling berserked to unberserked is 1.5 (3/2) and it is 2.0 for floor (2/1). In order to compare the two subs, though, I need a single value. Two just won't do. So if I say, "ok, well surely the raw% increase in the damage that berserk gives you is the average between its improvement over floor and it's improvement over ceiling." So if I average the two numbers (1.5 and 2.0) I get 1.75. This is different than the number I got earlier, which was 1.666 trailing. Which is a more accurate representation of of a ratio of improvement?

I like the latter one because you can get at it without making the assumption that pDiff fluctuation is distributed linearly. I'm still a bit confused why the numbers that I got didn't match up either way...I'm certainly not a math major, so, lol.

[Amele]

Thank you for going over all of that in more detail. Two more things continue to perplex me:
1.Mob level.

kill it and use the exp you got to determine the level.

When you say "high," I believe that I know what you mean. Glancing at the pDiff chart, there are a few tiers. At the points in which the ceiling and floor are farthest apart, they differ by 0.8 pDiff. The smallest regions in the chart differ only by 0.5 pDiff in spread. So by high, I assume thta you mean the former (0.8 pDiff).

by high, I mean where your pdif_min is greater than 1.0 (so that 1.0 is not within the range of the pdif.) for clarification. which is where the range is ~0.8 min to max on the old pdif yes.

You mention going with the median, which is 0.4 below the max, but that's also 0.4 above the min. When I say average, I mean precisely the median as well, for since there are only two values that would be averaged (the max and the min), the average can only ever be the median.

ah. you're either confused about how pdif works or you're misapplying the term average. -> function_pdif(cRatio) is not a two result function: you get values other than max and min, distributed over the entire range of the pdif_min to pdif_max.

the return value of function_pdif is not provably normal. (in fact it almost definitely isn't normal). the exact nature of the distribution is largely unknown. as such, the 'average' is not easily calculated. (it is generally accepted that at cRatio cap, the average is approximately the median. but I haven't seen a conclusive test)


most of the rest of what you said isn't useful math because it makes assumptions about max and min that aren't true. throw out average basically, just look at max, min, and median.

[Shamaya]

(it is generally accepted that at cRatio cap, the average is approximately the median. but I haven't seen a conclusive test)

I'm new to being familiar with cRatio, but when you say that it has a "cap," I assume that you mean the following?:

The Level Correction function
The Level Correction function modifies your (ranged) attack / monster defense ratio before it is used in the pDIF function.
Let's say you have 400 attack / ranged attack and the monster has 400 defense. Your (r)atk/def ratio would then be 1.
If the monster has a higher level than you, then a level corrected ratio is needed before calculating the pDIF.
Otherwise, when fighting EM monsters or lower, your atk/def ratio will not be modified when used in the pDIF function. In other words, there is no level correction.

That is, if the mob is of equal level or lower than you, one might be able to consider cRatio in a sense "capped" since its value will be 1, no matter how much lower the mobs level is than yours. However, if you mean capped in a sense that applies to mobs of level 76+, I'm not sure what you mean.

function_pdif(cRatio) is not a two result function: you get values other than max and min, distributed over the entire range of the pdif_min to pdif_max.

the return value of function_pdif is not provably normal. (in fact it almost definitely isn't normal). the exact nature of the distribution is largely unknown. as such, the 'average' is not easily calculated...
...most of the rest of what you said isn't useful math because it makes assumptions about max and min that aren't true. throw out average basically, just look at max, min, and median.

http://images.wikia.com/ffxi/images/4/45/PDIF.gif
I think I know what you mean here by it not being a two-result function. But there are at least two clearly defined values which are calculated specifically when the game is calculating pDiff. These would be the max and min. If these two values were not specifically defined, then there would be no defined range. Now, when melee hits strike, the damage that they do is calculated by a function of a pDiff multiplier value, and that value will exist somewhere within the range designated by the max and min (at that designated cRatio adjusted Atk-Def). Hypothetically, the pDiff multiplier chosen could lie anywhere within this range. However, how do we know which value within the range will be chosen? Well, we can at least assume that it's true that there's some probability that each individual value within the designated range will be chosen. It'd be nice if the %chance probability that a value in the range would be used would be equal to that of any other value within the range, but as you mentioned, this is not so. This, I believe, is what you mean by "the return value of function_pdif is probably not normal." By normal, I think you mean linear. By linear, I mean that the probability is evenly distributed within the range. As you mentioned it, this may not be so.

If it were so though, we could calculate an average, and that average would be the very same thing as the median in this case. For example, say our range was from 0 to 100, and there was a 1% chance that any value along that range be chosen. Every second, a value is chosen at random from within that range and outputted. Over a good amount of time, if you were to add up the total values of all the outputs chosen, and divide by the number of iterations, you would get the number 50. This also happens to be the average of the values 0 and 100, and it is also the median between these values. Thus, if pDif output worked in the same way, then the average value of all of the pDif multiplier outputs would be equal to the midpoint between the max and min, which, again is the same as the value of the max and min value added together and then divided by two (the average).

We don't know if the distribution of pDif fluctuation is linear. It could also be parabolic:
http://geoff82.files.wordpress.com/2.../parabola1.gif
Take this image for example. Say that the min pDif value existed at the far left of that image, at the very left edge of the parabola. And say that the max existed at the far right. Take the y axis, and designate it as representing ratio's of probability. The higher up on the y axis, the higher the chance that the value would occur, and the lower down on the y axis,t he lower chance that the value would occur. Now look at the shape of the parabola. It would hold that for values closer to the max and the min, the chance of it being chosen as a random pDif output would be higher. And for values closer to the median, the chance of them being chosen would be lower and lower as you get closer and closer. Even if the way that pDif values were chosen worked in this way, than the average output value over time would still be equal to the value at the median (or, again, the average of the max and min values).

But pDif distribution might not be "linear" or "parabolic" in the ways that I mentioned. It might be exponential, curving in one direction either to the max or the min, or it might show a linear progression of higher probability going from max to min or vice versa (using linear in a different way), or there might be gaps in between the min and max that couldn't be chosen, or the curve could be completely arbitrarily irregular, or any number of scenarios.

However the curve is distributed, there will be an average value. It might not be the same value as the average of the max and min aka median or midpoint (though for it to be this way, the curve would have to be asymmetrical with respect to the midpoint--why would SE do that? ..though they could). Even if we can't be sure what this average is, it'd be nice to have one.

So instead, you're right...if calculating the potency of pDiff increase going from, say, unzerked to zerked, we can simply talk of the increase that it gives to the max and the min. Then if we want to know the net potency, we could average these two values we get together. That might be a safer route. I'm not sure why we'd need to consider a median value otherwise. If we look at the pDiff chart, or go to wiki, it shows us the max and the min but makes no mention of median. I'm not sure how it would help us to know the median, outside of the reasons I had gone over before, where when I talked of average I think I meant precisely the same thing that you mean by median.

And on a last note, if I try to average out the pDiff increase for max and the one for min for a single measure of potency increase, I could still be wrong here. For example, if our distribution curve for pDif was asymmetrical with respect to the median, and values, say, near the max had a much much higher chance to occur than those near the min, this measure of potency would be an incorrect measure. I'd like to hope that this wasn't the case, but I suppose that without tests we can't be sure. If anything, it's always going to be safe to go with averages in the event of unknowns. As an example, if I were to ask you whether you thought that the calendar year where the sun will expand violently into a red giant and engulf the earth were to be an even number or an odd number, or at least what the %chance of it being an even number vs an odd number, to the best of your knowledge, what would you say? In the event of complete unknowns, it's always best to assume that each value in a given range has the same %chance to occur as any other in the range. That is the most reasonable neutral position.

[Burginator]

Joey, you care too much.

And my WAR is better than before, I'll beat your THF by more now.

Sincerely, Burg.

[Amele]

(it is generally accepted that at cRatio cap, the average is approximately the median. but I haven't seen a conclusive test)

I'm new to being familiar with cRatio, but when you say that it has a "cap," I assume that you mean the following?:

._. cRatio is the adjusted ratio, not the adjustment. cRatio cap is approximately 2.0 for 1h and 2.5 for 2h. depending on the level of the mob, the 'raw' ratio for this value will be anywhere from 2.0/2.5 up to about 3.0/3.5 (0 to 20 level gap)*

function_pdif(cRatio) is not a two result function: you get values other than max and min, distributed over the entire range of the pdif_min to pdif_max.

the return value of function_pdif is not provably normal. (in fact it almost definitely isn't normal). the exact nature of the distribution is largely unknown. as such, the 'average' is not easily calculated...
...most of the rest of what you said isn't useful math because it makes assumptions about max and min that aren't true. throw out average basically, just look at max, min, and median.

old pdif image

I think I know what you mean here by it not being a two-result function. But there are at least two clearly defined values which are calculated specifically when the game is calculating pDiff. These would be the max and min. If these two values were not specifically defined, then there would be no defined range.[/quote]

the game doesn't necessarily explicitly calculate these, they're just the boundary values of the return.

in rand(0,1) 0 and 1 are boundary values. in rand (0,1)+rand(0,1) the boundary values are 0 and 2 BUT; we never explicitly calculated the upper bound - it's just a result of the equation.

Now, when melee hits strike, the damage that they do is calculated by a function of a pDiff multiplier value, and that value will exist somewhere within the range designated by the max and min (at that designated cRatio adjusted Atk-Def). Hypothetically, the pDiff multiplier chosen could lie anywhere within this range. However, how do we know which value within the range will be chosen? Well, we can at least assume that it's true that there's some probability that each individual value within the designated range will be chosen. It'd be nice if the %chance probability that a value in the range would be used would be equal to that of any other value within the range, but as you mentioned, this is not so. This, I believe, is what you mean by "the return value of function_pdif is probably not normal." By normal, I think you mean linear.

no, by normal I mean normal. If I meant linear I would've stated linear.

By linear, I mean that the probability is evenly distributed within the range. As you mentioned it, this may not be so.

there's a difference between even and equal distributions *shrugs* a linear distribution would be equal probability for any given value (which is another possible result but doesn't match observed behavior)

Thus, if pDif output worked in the same way, then the average value of all of the pDif multiplier outputs would be equal to the midpoint between the max and min, which, again is the same as the value of the max and min value added together and then divided by two (the average).

you've made too many assumptions at this point to claim this with any mathematical confidence.

However the curve is distributed, there will be an average value. It might not be the same value as the average of the max and min aka median or midpoint (though for it to be this way, the curve would have to be asymmetrical with respect to the midpoint--why would SE do that? ..though they could). Even if we can't be sure what this average is, it'd be nice to have one.

right. but you're forgetting that SE may not be actually explicitly calculating the min and max range (see rand discussion above) and we don't know what the actual calculations look like.

so we have no grounds to state (beyond aesthetic sense) that the median and average should be approximately equal.

but I can already point to an area of the equation where the midpoint of pdif_max and pdif_min and the average are -not- equal (see: cRatio domains where 1.0 pdif is within the pdif range).

So instead, you're right...if calculating the potency of pDiff increase going from, say, unzerked to zerked, we can simply talk of the increase that it gives to the max and the min. Then if we want to know the net potency, we could average these two values we get together. That might be a safer route.

right and wrong, respectively. you can average them together but you can get a misleading answer if you don't have a good guess at what weight to give them respectively. (fortunately in this particular case, if cRatio is high, pdif_min is the same as pdif_max minus a constant, so the absolute improvement from zerk should be identical across the range.) the relative % improvement is probably not, however.

I'm not sure why we'd need to consider a median value otherwise. If we look at the pDiff chart, or go to wiki, it shows us the max and the min but makes no mention of median. I'm not sure how it would help us to know the median, outside of the reasons I had gone over before, where when I talked of average I think I meant precisely the same thing that you mean by median.

I mean that you should calculate the median. I made an assumption (that the median would be symmetric) that may be wrong; but you can calculate the exact median by going out and hitting something til you get a 'dominant' value much faster than you'll get an average.

If anything, it's always going to be safe to go with averages in the event of unknowns.

statistically, medians are more accurate when the average isn't confident.

As an example, if I were to ask you whether you thought that the calendar year where the sun will expand violently into a red giant and engulf the earth were to be an even number or an odd number, or at least what the %chance of it being an even number vs an odd number, to the best of your knowledge, what would you say? In the event of complete unknowns, it's always best to assume that each value in a given range has the same %chance to occur as any other in the range. That is the most reasonable neutral position.

this is a false argument; provably, even and odd numbered years are exactly equal in our current calendar; so the relative ratio is exactly 0.5.

we know this about the calendar because we know the function of the entire domain of the calendar (0 + floor(days since start - (days since start/365 * .24)/365) ); we don't know the exact function for any domain of the pdif calculation.

since you're so interested, I have some tests you could run.

the first is pretty trivial; go out with your highest level 1h job and kill lvl 1 mobs in your gear (weapon neutral) and make 3000 swings.

then do the same with your highest level 2h job for 3000 swings. and report all the numbers to me; I'll run the analysis and tell you what the 'likelihood' that the function is normal is (as well as the likelihood that the function is linear. etc)

[Shamaya]

._. cRatio is the adjusted ratio, not the adjustment. cRatio cap is approximately 2.0 for 1h and 2.5 for 2h. depending on the level of the mob, the 'raw' ratio for this value will be anywhere from 2.0/2.5 up to about 3.0/3.5 (0 to 20 level gap)*

Oh, ok I see what you mean now. That would explain why monks were complaining that they would hit for less/capped damage on lower level mobs, and other 1h experienced the same thing?

no, by normal I mean normal. If I meant linear I would've stated linear.

Ahh, ok, I see what you mean again, lol. Because I'm not a math curve I'm not familiar with the term "normal distribution." I thought you were using the word normal, and then distribution, not using it as a single term. And by looking at the wiki I see that the that a normal distribution curve is also often called a bell curve. Since I'm kind of limited with math concepts, I referred to the curve as being "parabolic," which is similar to bell curve, but not the same. I see again what you mean now.

[quote:46d57] Thus, if pDif output worked in the same way, then the average value of all of the pDif multiplier outputs would be equal to the midpoint between the max and min, which, again is the same as the value of the max and min value added together and then divided by two (the average).

you've made too many assumptions at this point to claim this with any mathematical confidence.[/quote:46d57]
You're right. That is based on an assumption. That's why I used the terms if, then. Also, that really only depends on only one assumption I think, that assumption being that there is symmetry along the midpoint (the shape of the curve from min to mid being symmetrical to the shape of the curve from max to mid). But when I revise the comparison I was talking about, I've already decided to take your advice. I'm not going to assume that the distribution works this way or any other way. I'll compare the difference between max's and min's.

you can average them together but you can get a misleading answer if you don't have a good guess at what weight to give them respectively.

Ugh. Yeah, it's going to be impossible for me to go into an in-depth comparison without making some assumptions. This is becoming clearer and clearer, lol. Sux.

this is a false argument;

I didn't necessarily connect the sun example to the "we should think this about pDif," but if I did, you'd be right. To connect the two would not hold necessarily. What I had in mind was basically, that there appear to me to be three possibilities. At a specific Atk-Def (after adjusted for cRatio), either the curve is asymmetrical with higher probabilities in the region between the mid and max, or the curve is asymmetrical with higher probabilities in the region between the mid and min, or the curve is symmetrical. If we have absolutely no hint as to which of these is more likely to be the correct scenario, well, I think you know what I'm getting at. Of course, there are probably people who do have a good idea as to which of these scenarios is the more likely one, at every Atk-Def or at different Atk-Def's, but I for one have no idea.

rand(0,1)

I'm pretty sure I know what you're getting at, and I see your point. I don't know what 'rand' means, though.

the first is pretty trivial; go out with your highest level 1h job and kill lvl 1 mobs in your gear (weapon neutral) and make 3000 swings.
then do the same with your highest level 2h job for 3000 swings. and report all the numbers to me; I'll run the analysis and tell you what the 'likelihood' that the function is normal is (as well as the likelihood that the function is linear. etc)

If I didn't have anything to do other than play the game, I'd probably actually take you up on that *laugh*. Would doing a test like this make progress in peoples' understanding of the game?

I think you've made my understanding of the ways and possible ways that this game works a lot clearer, Amele.

Joey, you care too much.

And my WAR is better than before, I'll beat your THF by more now.

Sincerely, Burg.

If you're talking about me caring too much about Thf, nay. Other than being in it for friends and social, why do you think I play this game? If you're talking about the message I sent you in-game, then you should get your negro ass online, bish. And yeah, told ya I was going to put that /tell in my sig some day =P.

I haven't gotten better gear lately but I'm always improving in skill and swaps. I'll take you on burg, any time. ^_-

[VZX]

We don't know if the distribution of pDif fluctuation is linear. It could also be parabolic:
http://geoff82.files.wordpress.com/2.../parabola1.gif

Take this image for example. Say that the min pDif value existed at the far left of that image, at the very left edge of the parabola. And say that the max existed at the far right. Take the y axis, and designate it as representing ratio's of probability. The higher up on the y axis, the higher the chance that the value would occur, and the lower down on the y axis,t he lower chance that the value would occur. Now look at the shape of the parabola. It would hold that for values closer to the max and the min, the chance of it being chosen as a random pDif output would be higher. And for values closer to the median, the chance of them being chosen would be lower and lower as you get closer and closer. Even if the way that pDif values were chosen worked in this way, than the average output value over time would still be equal to the value at the median (or, again, the average of the max and min values).

But pDif distribution might not be "linear" or "parabolic" in the ways that I mentioned. It might be exponential, curving in one direction either to the max or the min, or it might show a linear progression of higher probability going from max to min or vice versa (using linear in a different way), or there might be gaps in between the min and max that couldn't be chosen, or the curve could be completely arbitrarily irregular, or any number of scenarios.

However the curve is distributed, there will be an average value. It might not be the same value as the average of the max and min aka median or midpoint (though for it to be this way, the curve would have to be asymmetrical with respect to the midpoint--why would SE do that? ..though they could). Even if we can't be sure what this average is, it'd be nice to have one.

You could draw better with y=-x^2 rather than y=x^2

And whether it's parabolic or linear it doesn't matter, as long as the parabolic graph is symmetric.
It only make the difference in standard deviation/variance, not average.

Average still concentrates on the center, as well as median.

[Shamaya]

I was looking for one that curved downwards but couldn't. Google image'd that, lol.

[Amele]

Since I'm kind of limited with math concepts, I referred to the curve as being "parabolic," which is similar to bell curve, but not the same. I see again what you mean now.

yeah, in some ways a parabolic curve is an inverted bell curve (but there's some significant ways in which they're quite different.) if it helps to think of it that way, it's probably an ok assumption for most things.

[quote:454d3]rand(0,1)

[/size]
I'm pretty sure I know what you're getting at, and I see your point. I don't know what 'rand' means, though.[/quote:454d3]

ah, shorthand pseudo-code: rand(a,b) means 'generate a random number greater than or equal to 'a' and less than or equal to 'b''. in this case (0,1) would mean a random number between 0 and 1 (so like, 0.232561 etc)

so rand(0,1)+rand(0,1) would generate two numbers between 0 and 1 and add them together.

If I didn't have anything to do other than play the game, I'd probably actually take you up on that *laugh*. Would doing a test like this make progress in peoples' understanding of the game?

yes, actually; the test I outlined would make significant progress in our understanding of the game. (not as significant as the second and third set of tests I have in mind for after those first ones are finished!)

[Shamaya]

I'd consider doing it if it was far less than 3000 swings. I know that divisortheory is either a statistics major or close, and I believe that in most of the tests he's done (although not the TH+1 one), he thought that he could safely draw conclusions from 'value pools,' for lack of a better term, of significantly less than 3000.

[Amele]

the more exact you want your information, the larger a sample. in this case, I'm interested in the exact distribution and not just the mean(average), mode, or median. so I need a larger sample.

depending on the coherency results, 3000 swings should give me a margin of error in the 1-5% range. less would be correspondingly more depending on how regular the data was.

[Shamaya]

Hmmm...Well even if I was crazy enough to attempt such a thing, my jobs are as thus:
75 Thf, 75 Brd, 67 Rng, 53 Nin, 46 Cor, 37 War, Whm 37. Everything else is below 10. I never bothered to unlock sam, drk, or drg (yes, I know, I'm a nab). My great axe skill is probably like...10 or something. I'm guessing that for this, I'd need capped Atk-Def. Even with cRatio taken into account, I'm guessing I'd still need more great axe skill than that to do a test on 2h.

I think I get your idea here. If, just for example's sake, I was hitting the mob for a range of 1-10dmg. Then the number of times I hit for each of those 10 numbers would reflect the shape of the curve. So if I hit for 5 by far the most often, and then 6 and 4 for a good portion of the time, and then 7 and 3 a little bit less than that, and so on, this would basically reflect the shape of a bell-curve. If I hit for each value 1-10 the same number of times each, then that would reflect a linear curve with a slope of 0 or infinity, depending on which axes were designated the values of '1-10 dmg/strike' and probability. The fluctuation should be much higher than just 10 possibilities, so I see why you'd need such a large sample. Hmm..