Damage calculations

[Wraith]

A friend and I were having a conversation about the calculations people use to determine melee and WS damage. He says that the equations can't be accurate because they don't take into account the language SE's programs use, and that the only way to be accurate is to actually see the source coding. I argued that people have been working on these equations for 6 years now, and using values they obtained from the game, so the programming language used to do calculations in the game shouldn't matter.

In the end, he gave the calculations about 90% accuracy, whereas I said they should be about 99% accurate. My question is how accurate would you all say the damage equations are? How certain can we be on how things like fSTR, pDIF, and the like are calculated?

He also claims that a better judge of which piece of gear gives better damage output is by parsing, while I say that there are just too many variables going on in a parse to give as accurate a readout as paper calculations. What do you all think on this topic?

[Faux]

Woozie would love this topic but I have not seen him browsing BG as of late.. I will point him to this topic and perhaps he will make a nice informative post for you if nobody has done so by then.

[ringthree]

A friend and I were having a conversation about the calculations people use to determine melee and WS damage. He says that the equations can't be accurate because they don't take into account the language SE's programs use, and that the only way to be accurate is to actually see the source coding. I argued that people have been working on these equations for 6 years now, and using values they obtained from the game, so the programming language used to do calculations in the game shouldn't matter.

In the end, he gave the calculations about 90% accuracy, whereas I said they should be about 99% accurate. My question is how accurate would you all say the damage equations are? How certain can we be on how things like fSTR, pDIF, and the like are calculated?

He also claims that a better judge of which piece of gear gives better damage output is by parsing, while I say that there are just too many variables going on in a parse to give as accurate a readout as paper calculations. What do you all think on this topic?

I am not a computer programmer, but a simple understanding of math and calculations would lead almost anyone to conclude that the language does not matter if the basic principles are understood. As long as the rounding is understood, the mathematic equation does not change if we have the assumptions of the equations correct. I think your friend may be confusing the variables within the equations for the equations themselves. We know (or at least theoretically know with the appropriate testing to back the theory) that the equations work, we do not know the way that SE derives the variables for the random factors in the equation. The only way we would know this is if we did have access to their random number generation algorithms. But the equations were derived from situations in which the variable part of the equation was stabilized. And the proof is in the pudding, the equations work. I have not seen an example for a place where they did not work. There might be places in which, in a certain variable range, there are certain factors that we do not know about, but as we do not know about them and for that there is no test, and that circumstance just becomes a Schrödinger's cat.

That all said, weren't the original equations from Studio Gobli given to them by SE?

As for parsers, they can lie just like any other measure of data that is variable and open for interpretation. There are many factors that apply to parsers that make them a good tool for general analysis but should not be taken as gospel. They are like any measure of a large system with multiple variables apply, in that they provide a representation of a larger whole, but individual variables act on other variables in a myriad of ways making them always at least partially indeterminate. This isn't necessarily bad, but this indeterminate factor increases as the change in inputs decrease making it increasingly difficult to determine differences between smaller variations in input (i.e. differences in stats on gear). This is not limited to in-game variables like level of mob versus variable in the weapon damage equation, but also things like when you weaponskill, how fast you engage, the amount of time it takes the bard to get songs up, or even when your mage casts Dia. Too often people treat parsers as iron law, instead of a guide for making informed decisions.

Ultimately, neither equations or parsing will give you a complete answer. I have already stated the problem with parsers but the damage equations do not factor in same things as the problems with parsing (e.g. weaponskills, engage time, bard delay, Dia casting) and they also do not factor in accuracy, which is a major indict.

You should use all means at your disposal to come to a conclusion on decisions like these. Just using one or the other limits the amount of information input into the decision-making criteria and can lead to incorrect or flawed conclusions.

[Kirschy]

There's an important thing to note. Since the 2H patch, calculations have changed somewhat(for 1H and 2H), and we are no longer able to deduce as much with extreme accuracy.

That being said, the older calculations were an extremely accurate model. The model explained virtualli every aspect of damage calculation. When a model is able to predict outcomes to such a precise degree, it's hard to argue it's accuracy. For example, with the introduction of gorgets, their damage increase in capped conditions were able to be deduced to 1/256th...

If your friend is arguing that using the damage calculations to deduce whether STR+X vs Attack+Y is better in a certain situations merit/HNM situations, then yes, there is some uncertainty. While the damage calculations still accurately model damage calculations in those situations, there are unknowns such as enemy defense, enemy VIT, or damage distribution in certain pdif ranges.

As for parsing being an accurate measure of how different equipment setups work, I agree to some extent. As long as you are parsing for appropriate numbers such as average melee hit, accuracy, or crit hit rate over a long period of time, it gives you a good idea. To declare it even close to the accuracy of older damage calculations is silly talk though.

[Woozie]

Our approach at understanding the damage calculation is comparable to a physicist approach at understanding nature.

We start with the system we want to describe. Obviously, we don't know the actual "language" behind the system, so we instead use our laws of mathematics to describe it the best way we can. We analyze our data and draw conclusions based on it. We test our conclusions.

Most of the damage equations have been tested to a large extent and it has been shown that our formula do in fact describe damage output to a very good accuracy. Of course, our formula may differ slightly from the way SE programmed it. I don't know, I know very little about programming.

I do know that from a statistical standpoint, our data correlates very closely to the predictions of our models. Thus, we assume it to be "correct", just as a physicist who's data correlates closely to mathematical models assumes the models to be "correct".

The point I'm trying to make is that the damage formula we have now are very good models for measuring our damage output, as shown by many tests. Your friend shouldn't argue that our damage formula are wrong solely due to the fact that we don't know the code. If he thinks they're wrong, he can only show this by doing a test showing descrepencies. At the present, most tests that I know of shows consistancy.

There's always the possibility that a few changes can be made to the formula to make them more accurate (e.g. there's always the possibility that the formula aren't exactly 100% accurate), but the fact is, they do serve as really good models for damage formula.

And where does he get this "90%" number from? Did he pull it out of his ass? And what exactly does he mean by them only being 90% correct? Does that mean we can always expect a 10% deviation from any testing we do? Or does it mean that of every 10 tests we do, 9 will be consistant and one will be completely wrong? Or does he mean that 10% of the formula we use are outright incorrect? In most cases, saying a model is "90% wrong" is meaningless. He has to be less vague.

[Woozie]

A parse is kind of like a scientific experiment. It's subject to systematic and random errors. Most people who parse a party do so without any effort to weed out or at least calculate such errors. There are lots of obvious ways that error occurs in these parses, but it's usually not worth trying to weed out, since you can get the general gist of what you were looking for through just a normal parse in most cases (i.e. was my acc good or was my acc bad? Did this person outdo me by a long shot? Did a change in my gear setup make a considerable difference).

Most people don't parse for the sake of "What was my pDIF? Exactly how many points of damage did this one little change make to my WS?" etc.

And yeah, I do still browse BG, Faux (it's my firefox homepage lol). It's just that I stay mostly in general now since I haven't played FFXI since September.

[Wraith]

I think by 90% he was meaning that there would be a 10% error on any calculation made with the equations.

One of the things we talked about was Myochin kote +1 and Chiv chain vs. Bandomusha kote and pcc. I calculated out his average melee hit damage against greater colibri, and found his str<=>atk ratio to be 1:2.55. So using that, I deduced that Myochin kote +1 and Chiv chain would have an effective attack of 25.5, with 10.25 acc. Bandomusha kote and pcc would have an attack of 22 with 10 acc. According to the damage calculations, AF+1 gloves with chiv chain should outparse bandomusha kote with pcc, but he claims that in his parses comparing the two sets he came to the opposite conclusion.

Which method would you say is more trustworthy in this instance.

[VZX]

I personally see parsing as how good you are, as a player, to maximize your gear setup.
Rather than arguing minuscule amount of difference from X STR vs Y atk, it's better for them to optimize their play style (no disengage between 1 mob to another, precision timing doing ranged attack in every single shot, etc). By doing that, they can see a noticeable increase in their parse result.

[Wraith]

Well, if the skill of the player didn't change from one parse to another, how can the discrepancy be accounted for? Would u say it's from error in the calculation, error in the parser, or some variable he didn't account for (i.e., the whm was only casting dia when he was testing H.kote, and wasn't when he was testing AF+1).

[VZX]

That's 1 example why parse can have high error margin. You don't isolate variables when you do parsing (i.e. you're doing practical battle).

Secondly, there always human errors. Say, today, out of 100 fights, I only disengage once on chan #80 with running distance from 1 monster to next ranging from 5.0 to 8.0. Tomorrow, the number will not always be the same.
I probably will have the distance changed to 6.4 - 9.0, disengaged 4 times on chain #40, chain #60, #70, and #92.
Even this kind of mistake can skew your parse result more than the discrepancy we have on pDIF.

There also thing such as "minuscule difference" one shouldn't care about when they make a judgment on a single slot (not as a whole). Say, from 1 testing, equipment A gives 80-100 damage range, equipment B gives 81-100 damage range in which, their average damage difference is roughly ~0.05 damage out of 100 landed hits. I wouldn't say "A is better than B" or vice versa. The difference is simply too small about to argue whether one is a better piece than another

[ringthree]

Well, if the skill of the player didn't change from one parse to another, how can the discrepancy be accounted for? Would u say it's from error in the calculation, error in the parser, or some variable he didn't account for (i.e., the whm was only casting dia when he was testing H.kote, and wasn't when he was testing AF+1).

There is no error if there is a difference in parses. It is the nature of variables in a large system. There are a myriad of factors that determine damage for each swing and the damage it inflicts. This is then multiplied by a huge number of swings, applied to a large number of mobs with more variation in their statistics. Even if the players was perfect and managed to perfectly replicate their performance from one xp party to the next, they could not account for the actions of the 5 other people in their party and how their actions interrelate with the parsing player.

A better question would be why are you operation from the assumption that a parser can ever give you exact results. It can not. It can only give you a snapshot of a very large and variable system. The idea that there is a comprehensive way to account for the discrepancies between parses misses the point. Discrepancies are observations outside of the norm which is not the case, the differences between parses are just the results of variables within a large system. Discrepancies would be damage results that did not follow the theoretical equations that we currently understand.

[Amele]

I think by 90% he was meaning that there would be a 10% error on any calculation made with the equations.

One of the things we talked about was Myochin kote +1 and Chiv chain vs. Bandomusha kote and pcc. I calculated out his average melee hit damage against greater colibri, and found his str<=>atk ratio to be 1:2.55. So using that, I deduced that Myochin kote +1 and Chiv chain would have an effective attack of 25.5, with 10.25 acc. Bandomusha kote and pcc would have an attack of 22 with 10 acc. According to the damage calculations, AF+1 gloves with chiv chain should outparse bandomusha kote with pcc, but he claims that in his parses comparing the two sets he came to the opposite conclusion.

Which method would you say is more trustworthy in this instance.

your calculation was flawed in this case. - his testing method was likely also flawed (since he just used straight exp parses?)

not sure what you mean by str<>att ratio of 1:2.55 -> I'll assume you mean he has a cRatio of 2.55 (this is .. very high by the way. we're talking like 1000+ attack here) so I'm probably assuming incorrectly. as such I'll use made up numbers and run with it.

I'll assume a str of about 100 and an attack of about 800 excluding the neck and hands slots. (good but not zomg numbers).

the equations you are comparing are all of the following form: (things in brackets are weaponskill only) Disclaimer: these are the old level adjustment formulas. I do not believe that level adjustment or fSTR was changed for 2H but it may have been.

f(d) * pdif() * {fTP} = damage. f(d) is D+f(fstr)+{WSC} ; pdif is f(Ratio - .05*dLevel)
this is all alot of text, I know.

basically, we know that greater colibri at level 81 are 322 defense. so your ratio with 800 attack is 2.48 (800/322) and your cRatio will be 2.18. (2.48 - .05*6)

assuming hagun f(d) will be 75+f(str) f(str) will be 9 of a possible 16 maximum (colibri have ~67 vit at level 81) so a total of 84. (f(str) for melee is (STR-VIT+4)/4)

this gives a max damage of about 220 per swing. adding 10 str will bring your cRatio up to 2.2~ and your fstr to 11, bringing your max damage up to about 227.

if you instead add 22 attack you bring your cRatio to 2.25~ and your max damage to about 226. (basically no difference) your accuracy increase is about 10 in both cases.


if your friend has much less attack (say in the 700's) then bando will perform better. if he has much more attack, then myo+1 will perform better. similar but reverse case for strength.


--
does that help you with how to walk through the equations?

[AoshiZ]

Regardless of whether you know programming or you can actually see the source code (and actually I am a programmer), there are values that are output. Like stated, the equations that may have been derived can possibly be different than the source code, but the result value is all that matters.

When you plot points on a graph from data, the first approach to understanding the data is to create a formula that plots a line which inlcludes all the points. Since the community generated formulas to plot damage values that are consistent with the damage output in the game, we can asses that the damage formulas are accurate (at least they used to before some recent patches, we gotta rework some stuff). Many people have tested various combinations and helped correct mistakes in the formulas. And the product is that we were able to achieve a model that is fairly accurate today.

Will the community derived formula cover things such as new items that push attack into levels that we could not reach before? Possibly not because that is out of our testable environment at the moment. However, I can assure you that people will correct formulas or extend formulas for different tiers to match any ranges when they appear in the future.

In a nutshell are the damage formulas accurate? yes they are. Will they be accurate in the future? maybe...

Edit:
Additional Comment: The damage formula calculates your damage range. A Parse (in the terms that you are using it), is a series of data collected to asses what your performance is in a specific environment and to possibly asses the environment. These two things go hand in hand. They are different yet they complement each other in terms of analysis. Our Damage formula require variables such as enemy defense and Vitality. These can be obtained by parses. Using these obtained values an individual can use the formulas to predict performance in other environments with similar variables.

Which is better? Use both of them they each have their advantages.
You want to estimate how you will do on a rare NM with known defense before you fight it? You won't get that with a parse.
You want to know how you perform on a new enemy? You wont get that with the damage formula.

[Wraith]

not sure what you mean by str<>att ratio of 1:2.55 -> I'll assume you mean he has a cRatio of 2.55 (this is .. very high by the way. we're talking like 1000+ attack here) so I'm probably assuming incorrectly. as such I'll use made up numbers and run with it.

No, I was talking about taking the damage equation with his current gear, removing a small amount of str (4), and seeing how much additional attack would be needed to have equivalent damage. With his gear on greater colibris, it came out to 1 str equaling roughly 2.55 attack. So then Af+1 gloves and chiv chain would be 10 str, or equivalent to 25.5 attack, where b.kote and pcc is 22 attack. I'm sure that in actual combat the difference here wouldn't even be noticeable, but with enough small tweaks like this in your gear you could improve your results. Also, the Af+1 gloves & chiv chain set are cheaper and relatively easier to obtain.

[Kirschy]

No, I was talking about taking the damage equation with his current gear, removing a small amount of str (4), and seeing how much additional attack would be needed to have equivalent damage. With his gear on greater colibris, it came out to 1 str equaling roughly 2.55 attack. So then Af+1 gloves and chiv chain would be 10 str, or equivalent to 25.5 attack, where b.kote and pcc is 22 attack. I'm sure that in actual combat the difference here wouldn't even be noticeable, but with enough small tweaks like this in your gear you could improve your results. Also, the Af+1 gloves & chiv chain set are cheaper and relatively easier to obtain.

It doesn't sound like you are using the damage equations properly. The coli vary in VIT, Defense, and level. You don't seem to be accounting for possible buffs(songs, berserk, whatever), debuffs(dia), or level correction either. :/ Your results might be based on the calculations, but they're far from precise on the actual performance changes.

[Amele]

not sure what you mean by str<>att ratio of 1:2.55 -> I'll assume you mean he has a cRatio of 2.55 (this is .. very high by the way. we're talking like 1000+ attack here) so I'm probably assuming incorrectly. as such I'll use made up numbers and run with it.

No, I was talking about taking the damage equation with his current gear, removing a small amount of str (4), and seeing how much additional attack would be needed to have equivalent damage. With his gear on greater colibris, it came out to 1 str equaling roughly 2.55 attack. So then Af+1 gloves and chiv chain would be 10 str, or equivalent to 25.5 attack, where b.kote and pcc is 22 attack. I'm sure that in actual combat the difference here wouldn't even be noticeable, but with enough small tweaks like this in your gear you could improve your results. Also, the Af+1 gloves & chiv chain set are cheaper and relatively easier to obtain.

that's.. weird experimental method, the equations aren't that straightforward (kirshy goes into why in her post). by equivalent damage, what are you talking about? single hits? double hits? you could be off by a large factor (as much as ~33% or more) depending on how you determined equivalency.

either way, the actual difference is so small as to be virtually non-existent at the values I suggested. if your friend -isn't- running 800+ attack or super low strength then it's even less likely that af+1 and chiv will outperform b.kote and pcc a meaningful amount.

[Aireiya]

While parse summaries can be open to too many variables to accurately interpret the differnence between two pieces of equip, for equips that deal with acc/str/attk exclusively there's a different, easier way to compare.

Have parses for each set of equip, and instead of looking at total damage, look at the avg melee damage per hit, including crit, and look at the acc.

Since it's just str and acc, it's easy to see which setup will have you hit harder and which setup will give you more acc. If the acc setup and damage setup are different, calculate effective damage while taking hit rate into consideration and it'lll give you the ideal setup.

[kareface]

Our approach at understanding the damage calculation is comparable to a physicist approach at understanding nature.

Probably not a great example seeing how no single physicist has been able to accurately and completely explain nature. Every working theory has major gaps, and no one can agree on a universal understanding of nature. It is one of the least understood and most controversial topic in science. The only thing everyone can agree upon is we know the "physical laws" we operate under today are wrong. But no one has yet to find the right answer.

[Nazrious]

has any one ever tried alternating parses?

where one fight in one gear set with the variable slot being say neck.

then every other fight swapping the neck out.

Rather then doing 200 fights in PCC then 200 fights in say a gorget or torque the people runnign the test will simply run 400 fights with a A-Set data and B-Set data. thus:

PCCfight> Gorgetfight> PCCFigt> Gorgetfight> PCCFigt> Gorgetfight> PCCFigt and so on and so on.

This at least will help to minimize the deviation of parse results, even though random variables will be apparent throughout any such kind of testing. Then you can even work in the deviation formula and get a more uniformed bell curve going on knock out the outliers. then you would have two much more uniformed sets of data with similar circumastance for both.

But then again I haven't taken math and such since first year of undergrad, which was a few years ago. but it was just a thought.

As far as the calculations go with every adjusment SE makes to damage calcualtions they become obsolete and must be reaffirmed and tweaked. So in long stretches of stability then tend to work very well, however right after a chance from SE they may be very flawed. or at least part of them may be flawed, it depends on what exactly and how much is changed.

~p~

[AoshiZ]

Our approach at understanding the damage calculation is comparable to a physicist approach at understanding nature.

Probably not a great example seeing how no single physicist has been able to accurately and completely explain nature. Every working theory has major gaps, and no one can agree on a universal understanding of nature. It is one of the least understood and most controversial topic in science. The only thing everyone can agree upon is we know the "physical laws" we operate under today are wrong. But no one has yet to find the right answer.

I actually think its a great example.

Since damage calculation's exact inner workings are based on our frame of reference and the data we are able to collect thus far. Similar to how we have formulas for gravity such as x = 1/2gt^2 that give us great results for our reference frame. Even though there are possibilites with darkmatter and newtons grav theory being wrong and all that.

has any one ever tried alternating parses?

where one fight in one gear set with the variable slot being say neck.

then every other fight swapping the neck out.

Rather then doing 200 fights in PCC then 200 fights in say a gorget or torque the people runnign the test will simply run 400 fights with a A-Set data and B-Set data. thus:

PCCfight> Gorgetfight> PCCFigt> Gorgetfight> PCCFigt> Gorgetfight> PCCFigt and so on and so on.

This at least will help to minimize the deviation of parse results, even though random variables will be apparent throughout any such kind of testing. Then you can even work in the deviation formula and get a more uniformed bell curve going on knock out the outliers. then you would have two much more uniformed sets of data with similar circumastance for both.

But then again I haven't taken math and such since first year of undergrad, which was a few years ago. but it was just a thought.

As far as the calculations go with every adjusment SE makes to damage calcualtions they become obsolete and must be reaffirmed and tweaked. So in long stretches of stability then tend to work very well, however right after a chance from SE they may be very flawed. or at least part of them may be flawed, it depends on what exactly and how much is changed.

~p~

Don't take this personally but your math makes no sense to me atm. Can you elaborate?

There is no difference between

"PCCfight> Gorgetfight> PCCFigt> Gorgetfight> PCCFigt> Gorgetfight> PCCFigt"

and

"200 fights in PCC then 200 fights in say a gorget or torque"

in data collection.

And as for the following statement:
"Then you can even work in the deviation formula and get a more uniformed bell curve going on knock out the outliers. then you would have two much more uniformed sets of data with similar circumastance for both."

They can cut out the standard deviation regardless of whether your alternating approach was used.

And as for making a more uniformed bell curve. This should be achieved by collecting a larger sample space. Is there some shortcut or new way of statistical analysis i'm not familiar with?