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(DPS) vs (Accuracy - Deflection). Here's the maths. Enjoy.

DPS Accuracy Attack Deflection Attack Resolution Combat Calculation Minmax

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#81
Azrael Ultima

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My problem with this is that the Might / Weapon Damage curve is linear, whether or not Might gives a mix of penalties and bonuses or bonuses only. It needs to be changed to a curve that's steep at the beginning and gives diminishing returns, otherwise min-maxing will always remain the king.

 

In other words: every point spent on a stat should always give a slightly smaller bonus than the previous one.

 

The increase to base damage is linear. The increase to your final damage, however, is not. You're forgetting that you will generally already have some Might when considering whether to add more.

 

Not sure what you mean by "min-maxing will always remain king". MinMaxing is an approach to building your character, not a certain technique.



#82
Matt516

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The Might bonuses are always multipliers, so if it feels like a particular ability or set of abilities does too much damage even when the Might is set very low, the problem is likely with the base damage values on those abilities.

I think we're dealing with a psychological effect here at least partly. It just feels "wrong" that dumped stats still give bonuses, even if they're small. I have a feeling that if you set the zero point to 10 and applied the adjustments as negatives below and positives above, a lot of people would be happier even if it ended up in the same place.

(I do think the abilities ought to have more impact in absolute terms as well; I don't really feel I'm missing much from my dump stats or gaining much by pumping them. I would like it to sting if I dumped something to 3 so I'd have to adjust my tactics accordingly.)
I agree - however it's important to remember that due to how the math works, you couldn't actually preserve the same percentage range AND absolute range simply by changing the zero point. In fact, the higher the zero point is (going up to 10 from the current 0 for example), the smaller the percentages needed to yield the same absolute range. Which means that if they raise the zero point but keep the same absolute range, people will potentially complain even more about stats not having an impact (even though the actual impact would be the same).

Edited by Matt516, 25 August 2014 - 02:45 PM.

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#83
Matt516

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Still working on the next revision of the spreadsheet.

 

Currently able to calculate true DPS based on the following factors:

 

Crit Damage

MIG % Damage Bonus/Point

MIG % Damage @ 0

DEX Accuracy/point

Might

Dexterity

Base Accuracy (from class)

Bonus Accuracy (abilities etc)

Weapon Base Damage (avg)

Attacks/Second

Target Deflection

Target DT

DT Effectiveness

 

Any requests for other parameters to include in the calculation? I honestly can't think of anything else that affects dps (that is general).. maybe add in weapon damage from enchantments, etc? I haven't included it currently because between weapons and spells you can have all kinds of extra damage types added into the mix that then have to have their own DT effectiveness factored in, which isn't at all complicated to calculate but it really clutters the table. Plus I wanted to keep this as more of a general thing for aiding in the tuning of MIG/DEX/Crit variables. Thoughts?


Edited by Matt516, 25 August 2014 - 04:32 PM.


#84
Yonjuro

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Still working on the next revision of the spreadsheet.

 

Currently able to calculate true DPS based on the following factors:

 

Crit Damage

MIG % Damage Bonus/Point

MIG % Damage @ 0

DEX Accuracy/point

Might

Dexterity

Base Accuracy (from class)

Bonus Accuracy (abilities etc)

Weapon Base Damage (avg)

Attacks/Second

Target Deflection

Target DT

DT Effectiveness

 

Any requests for other parameters to include in the calculation? I honestly can't think of anything else that affects dps (that is general).. maybe add in weapon damage from enchantments, etc? I haven't included it currently because between weapons and spells you can have all kinds of extra damage types added into the mix that then have to have their own DT effectiveness factored in, which isn't at all complicated to calculate but it really clutters the table. Plus I wanted to keep this as more of a general thing for aiding in the tuning of MIG/DEX/Crit variables. Thoughts?

 

  It might be beyond  the scope of what you want to model here, but how about interrupts/resolve?



#85
Matt516

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Still working on the next revision of the spreadsheet.

 

Currently able to calculate true DPS based on the following factors:

 

Crit Damage

MIG % Damage Bonus/Point

MIG % Damage @ 0

DEX Accuracy/point

Might

Dexterity

Base Accuracy (from class)

Bonus Accuracy (abilities etc)

Weapon Base Damage (avg)

Attacks/Second

Target Deflection

Target DT

DT Effectiveness

 

Any requests for other parameters to include in the calculation? I honestly can't think of anything else that affects dps (that is general).. maybe add in weapon damage from enchantments, etc? I haven't included it currently because between weapons and spells you can have all kinds of extra damage types added into the mix that then have to have their own DT effectiveness factored in, which isn't at all complicated to calculate but it really clutters the table. Plus I wanted to keep this as more of a general thing for aiding in the tuning of MIG/DEX/Crit variables. Thoughts?

 

  It might be beyond  the scope of what you want to model here, but how about interrupts/resolve?

 

 

While I might be interested in adding that capability at some point, 2 things keep me from doing it right now:

 

1) My primary motivation for the spreadsheet is to provide a tool that allows people to easily iterate through multiple tweaks in order to see how various tuning tweaks affect the damage curves - in particular, tweaks to MIG, DEX, and Crit Damage (which I think will be the key 3 parameters to tweak in order to get the balance figured out). It's really easy to compare the effects of different damage-affecting stats and attributes because the utility curve for damage is very simple: bigger is better. Determining whether or not two dps builds are to equally viable and balanced (for example, a MIG build with slow weapons, and a DEX build with fast weapons) is really really easy - do they do the same damage?

 

Interrupts, while certainly an important part of combat, aren't as easy to model because while dps is just a number, where higher is better, the impact of interrupts is pretty much impossible to compare directly to damage. Interrupts are more of a tactical tool than a direct power boost, so while I could see myself adding some interrupt calculations in a separate sheet just for fun, I don't think it would be at all useful for the primary purpose of the spreadsheet.

 

It should also be mentioned (and I'll be sure to mention it when I post the spreadsheet) that even MIG and DEX are tactical attributes in some ways as well. MIG gives Fort and Healing, and DEX gives Reflex and Spell Duration (when you crit with spells). Neither of those things are directly comparable to each other either - which is wonderful, by the way. I wouldn't want a system in which two different attributes only affect effective damage - there'd be no point in having two different attributes. 

 

So even though the dps aspect of both those attributes is a very important part, even then it doesn't tell the whole story. Which is why I'm trying to be very conscientious about the narrow focus of my current efforts - to let people rapidly tweak and tune different damage-related parameters to better understand the system and suggest improvements.

 

2) I don't know how the math on interrupts works. Not sure if the Concentration bonus is subtracted from the interrupt chance, or multiplied by it, etc. Also not sure what reasonable values of interrupt chance even are - I haven't played a lot of the Beta because I don't enjoy the combat right now and would rather focus on theorycrafting and giving general feedback until the major bugs and combat issues are fixed. Are interrupt values even given in weapon and spell descriptions? I've never seen them, but that doesn't mean they're not there.

 

#2 is also the same reason I haven't implemented recovery time and weapon attack animation speed, btw - the math isn't entirely clear as to how recovery time is calculated (lighter armors have a higher number, so I'm not sure how to translate to actual numbers) and I've never seen an attack animation speed value in a weapon description. Much easier just to put "attacks/second" in and then update if we get more information.


Edited by Matt516, 25 August 2014 - 05:08 PM.


#86
Yonjuro

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1) My primary motivation for the spreadsheet is to provide a tool that allows people to easily iterate through multiple tweaks in order to see how various tuning tweaks affect the damage curves...

 

 Sorry, I wasn't clear. I meant the impact of a character's Resolve on the damage curve of that character.

 

 Your attacks can get interrupted which would impact your DPS because you need to start the attack/reload/spell or whatever over again. 

 

 Resolve makes it happen less often.



#87
Matt516

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1) My primary motivation for the spreadsheet is to provide a tool that allows people to easily iterate through multiple tweaks in order to see how various tuning tweaks affect the damage curves...

 

 Sorry, I wasn't clear. I meant the impact of a character's Resolve on the damage curve of that character.

 

 Your attacks can get interrupted which would impact your DPS because you need to start the attack/reload/spell or whatever over again. 

 

 Resolve makes it happen less often.

 

 

Hmm, very good point. That does take care of the motivation/justification aspect. Unfortunately, implementing that would still require having a reasonable way to model a few things we don't really know much about at the moment:

  • Detailed math behind interrupts and concentration (see #2 of my last post)
  • More information on exactly how recovery time interacts with interrupts

Additionally, the enemy interrupt frequency would depend on their attack speed and interrupt chance, which are both variables that could potentially affect the final answer a lot and also vary quite a bit between enemies, leaving no clear general effect of RES on dps. Somewhat similar to how the effect of DEX depends greatly on enemy DEF, but (I predict) worse.

 

Also, because rounds are asynchronous (as far as I know), the phase difference between two characters' individual rounds would matter quite a bit. If the individual attack patterns of the two characters are lined up such that the enemy always hits right before you hit, you're going to get interrupted a lot more than if it's the other way around. Additionally, the difference between the overall attack speeds would cause the attack patterns to go in and out of phase, which would make things even wonkier.

 

And worst of all... the effect of an interrupt on your dps depends on at what point in your attack animation you are interrupted. The later in your attack animation, the worse your dps gets. But there aren't any stats or attributes that affect this - it's only dependent on the relative attack speeds of the combatants and how far in or out of phase their attack patterns are. So you would see huge variations in the dps impact from something you can't control at all.

 

Basically, taking Interrupt into account would be more akin to writing a combat simulation than simple algebra. Not something that's undoable, but somewhat nontrivial to do it right (as far as I can tell). I'm not certain it could be boiled down to a simple multiplier of overall dps like MIG and DEX can - though I could be wrong. It'd certainly be very nice if it could.

 

So the answer is still... maybe in the future? This'll be a much more feasible thing to do when combat is cleaned up so we know more about the intricacies of the system.  :)

Sorry - I only have a limited amount of time haha...

 

PS - I'm not a huge fan of interrupt as a mechanic, to be honest. Not as something that can happen from any attack. Interrupting just spells - fine. Interrupting attacks, but with a spell or ability - fine. But this whole "anything can interrupt anything" mechanic I am not at all fond of. It adds RNG, but in a really unpredictable way that is hard to anticipate. Making an intelligent decision about whether to put points in RES or something else is thus really difficult. Boo interrupt. :p


Edited by Matt516, 25 August 2014 - 05:37 PM.


#88
Caerdon

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How are you taking DT into account? You can't just calculate average damage and subtract DT from that. Grazes and weapons' damage ranges make the calculations pretty ugly...

#89
Matt516

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How are you taking DT into account? You can't just calculate average damage and subtract DT from that. Grazes and weapons' damage ranges make the calculations pretty ugly...

 

I thought that at first as well, and it certainly seems that it would be that way. But because your damage loss from DT on any given hit is additive (subtractive I guess), not multiplicative, it comes out of the dps calculation as a separate subtracted quantity. This means that average weapon damage is actually completely fine to use, as long as the weapon has an equal probability of all damage rolls in the damage range. The dps you lose from DT is (mostly*) only dependent on your attack speed, not the damage you were going to do.

 

Here's the equations:

 

Attached File  Capture.JPG   38.12KB   0 downloads

 

*Ok, so this isn't strictly true in all cases. If any given strike has its damage reduced to 0 by DT, then some of the DT may actually be wasted on that hit. The presence of Grazes and Misses (Hits and Crits as well on really high DT enemies) can therefore cause the impact of DT on dps to be overestimated a bit. So I'll admit that the attached equations are only correct if Grazes still pass some damage through DT, and that they don't really account for the presence of Misses. Unfortunately this can't really be fixed algebraically because there's no tidy algebraic way to express the logic "If x < 0, x = 0, If x > 0, x = x". I'd welcome suggestions for fixing it though (aside from just implementing logic, which is certainly doable in Excel and might just have to happen now that you've pointed it out :p).

 

 

TL;DR - Weapon damage range isn't a problem at all. You can just use the average. Grazes and Misses (any attack resolution in which not all of the DT is used) can be a problem in certain situations, causing an overestimation of the dps loss due to DT.


Edited by Matt516, 25 August 2014 - 06:30 PM.


#90
Yonjuro

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Also, because rounds are asynchronous (as far as I know), the phase difference between two characters' individual rounds would matter quite a bit. If the individual attack patterns of the two characters are lined up such that the enemy always hits right before you hit, you're going to get interrupted a lot more than if it's the other way around. Additionally, the difference between the overall attack speeds would cause the attack patterns to go in and out of phase, which would make things even wonkier.

 

And worst of all... the effect of an interrupt on your dps depends on at what point in your attack animation you are interrupted. The later in your attack animation, the worse your dps gets. But there aren't any stats or attributes that affect this - it's only dependent on the relative attack speeds of the combatants and how far in or out of phase their attack patterns are. So you would see huge variations in the dps impact from something you can't control at all.

 

Basically, taking Interrupt into account would be more akin to writing a combat simulation than simple algebra. Not something that's undoable, but somewhat nontrivial to do it right (as far as I can tell). I'm not certain it could be boiled down to a simple multiplier of overall dps like MIG and DEX can - though I could be wrong. It'd certainly be very nice if it could.

 

 

 I think the above can be simplified by treating interrupt as a random variable and assuming for the DPS calculation that it hits in the exact middle of any attack. It's exactly how you would handle rotational latency for a disk access calculation, if you know what I mean - half of attack time is the average if you are equally likely to get interrupted any time during the attack.

 

The result would be, for a given set of stats, a curve of DPS values that varies over interrupt probability (which itself would depend on the number of enemies, their attack speeds and their perception scores but the magic of the random variable glosses over all of that, hopefully leaving behind a clear signal about the Resolve stat).


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#91
Matt516

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My problem with this is that the Might / Weapon Damage curve is linear, whether or not Might gives a mix of penalties and bonuses or bonuses only. It needs to be changed to a curve that's steep at the beginning and gives diminishing returns, otherwise min-maxing will always remain the king.

 

In other words: every point spent on a stat should always give a slightly smaller bonus than the previous one.

 

The increase to base damage is linear. The increase to your final damage, however, is not. You're forgetting that you will generally already have some Might when considering whether to add more.

 

Not sure what you mean by "min-maxing will always remain king". MinMaxing is an approach to building your character, not a certain technique.

 

 

The increase to final damage actually is linear if the only thing you're varying is MIG. The only thing that changes the marginal value of one more point in MIG is changing the Accuracy multiplier or the Base Damage.

 

See these again:

Capture.JPG


#92
Bester

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Is MIG responsible for how much a character gets healing from a healing spell or the reverse?

 

Also, could you perhaps make an excel file where one can input their stats and see the resulting DPS?



#93
Matt516

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Also, could you perhaps make an excel file where one can input their stats and see the resulting DPS?

 

That's exactly what I'm working on. :)

 

Should have it up by Wednesday night at the latest (I'll make a new post). It'll include the ability to vary everything I listed in my post higher up on this page.


Edited by Matt516, 25 August 2014 - 07:23 PM.

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#94
Sensuki

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You need the math for two weapon fighting, which we don't have.

I know the animation speed and recovery times for everything else.
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#95
Matt516

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You need the math for two weapon fighting, which we don't have.

I know the animation speed and recovery times for everything else.

 

Sweet. PM me and I can add them to the spreadsheet. The calculation of attack speed from animation speed/recovery times should be fairly straightforward.

 

How does one get from the recovery values given in the armor description (increases with lower recovery time) to recovery time? Do you know the formula, or have you just timed it?



#96
Matt516

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Also, because rounds are asynchronous (as far as I know), the phase difference between two characters' individual rounds would matter quite a bit. If the individual attack patterns of the two characters are lined up such that the enemy always hits right before you hit, you're going to get interrupted a lot more than if it's the other way around. Additionally, the difference between the overall attack speeds would cause the attack patterns to go in and out of phase, which would make things even wonkier.

 

And worst of all... the effect of an interrupt on your dps depends on at what point in your attack animation you are interrupted. The later in your attack animation, the worse your dps gets. But there aren't any stats or attributes that affect this - it's only dependent on the relative attack speeds of the combatants and how far in or out of phase their attack patterns are. So you would see huge variations in the dps impact from something you can't control at all.

 

Basically, taking Interrupt into account would be more akin to writing a combat simulation than simple algebra. Not something that's undoable, but somewhat nontrivial to do it right (as far as I can tell). I'm not certain it could be boiled down to a simple multiplier of overall dps like MIG and DEX can - though I could be wrong. It'd certainly be very nice if it could.

 

 

 I think the above can be simplified by treating interrupt as a random variable and assuming for the DPS calculation that it hits in the exact middle of any attack. It's exactly how you would handle rotational latency for a disk access calculation, if you know what I mean - half of attack time is the average if you are equally likely to get interrupted any time during the attack.

 

The result would be, for a given set of stats, a curve of DPS values that varies over interrupt probability (which itself would depend on the number of enemies, their attack speeds and their perception scores but the magic of the random variable glosses over all of that, hopefully leaving behind a clear signal about the Resolve stat).

 

 

I'm reasonably sure I know what you mean, but if you wouldn't mind PM-ing me with more information it certainly wouldn't hurt. :)



#97
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Also, because rounds are asynchronous (as far as I know), the phase difference between two characters' individual rounds would matter quite a bit. If the individual attack patterns of the two characters are lined up such that the enemy always hits right before you hit, you're going to get interrupted a lot more than if it's the other way around. Additionally, the difference between the overall attack speeds would cause the attack patterns to go in and out of phase, which would make things even wonkier.

 

And worst of all... the effect of an interrupt on your dps depends on at what point in your attack animation you are interrupted. The later in your attack animation, the worse your dps gets. But there aren't any stats or attributes that affect this - it's only dependent on the relative attack speeds of the combatants and how far in or out of phase their attack patterns are. So you would see huge variations in the dps impact from something you can't control at all.

 

Basically, taking Interrupt into account would be more akin to writing a combat simulation than simple algebra. Not something that's undoable, but somewhat nontrivial to do it right (as far as I can tell). I'm not certain it could be boiled down to a simple multiplier of overall dps like MIG and DEX can - though I could be wrong. It'd certainly be very nice if it could.

 

 

 I think the above can be simplified by treating interrupt as a random variable and assuming for the DPS calculation that it hits in the exact middle of any attack. It's exactly how you would handle rotational latency for a disk access calculation, if you know what I mean - half of attack time is the average if you are equally likely to get interrupted any time during the attack.

 

The result would be, for a given set of stats, a curve of DPS values that varies over interrupt probability (which itself would depend on the number of enemies, their attack speeds and their perception scores but the magic of the random variable glosses over all of that, hopefully leaving behind a clear signal about the Resolve stat).

 

 

I'm reasonably sure I know what you mean, but if you wouldn't mind PM-ing me with more information it certainly wouldn't hurt. :)

 

 

 

Sent.


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#98
sophismata

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What about the inverse issue? That is, that a character with 3 Might does too much damage?

 

The Might bonuses are always multipliers, so if it feels like a particular ability or set of abilities does too much damage even when the Might is set very low, the problem is likely with the base damage values on those abilities.

 

I think Infinitron was referring more to the fact that people expect a low attribute to create an incompetency rather than a reduced competency. While I understand you are protecting people from themselves with the current attribute system, there is something to be said for genuine character flaws.

 

As long as the impacts of player decisions are clearly advertised, you can afford to be a little harsher with boni / malus distribution. However, it could just be that people are remembering their 18/00 fighter a tad too fondly, given how much of an outlier ogre strength is in AD&D 2E.


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#99
Matt516

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http://img2.wikia.no...ewsEveryone.jpg

 

Good news everyone! Version 2 of the spreadsheet is ready to roll. I'll be putting the link up tomorrow in a new post (I am way too tired to write the post tonight).

 

Why am I tired, you ask? Because I programmed a calculation that takes every single possible damage roll, every single possible attack resolution, calculates how much DT reduces your damage for each, then weighs it by probabilities of occurrence to get the true mathematical effect of DT on your damage (accounting for misses, grazes, any attack resolution where the DT blocks your damage entirely and some DT is therefore wasted). That's kind of a bitch to do in Excel. :p

 

Also calculated the tradeoffs between MIG and DEX in terms of dps multiplier (correctly this time, thanks Azrael). The jist of it is that DEX is more valuable if you're fighting enemies with higher Deflection than your Accuracy, and MIG is more valuable if you're fighting enemies with lower Deflection than your accuracy. 

 

But what I'm most excited about is "the tuner" - it's a page that allows you to test up to 20 different combinations of every stat I could think of (not to mention base game values like crit damage, etc) to get the final dps. So you can make your own graphs, share new insights about balance with the community, etc.

 

Looking forward to sharing it with you tomorrow! :)


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#100
Matt516

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Here's a permalink to that post (and site of continuing discussion re: dps, stat balance, spreadsheets, etc): http://forums.obsidi...ited/?p=1496416







Also tagged with one or more of these keywords: DPS, Accuracy, Attack, Deflection, Attack Resolution, Combat, Calculation, Minmax

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