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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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#41
Doppelschwert

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I thought critical damage is already 2x the normal damage?



#42
Matt516

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Love that suggestion! Thanks for making use of the spreadsheet to test and suggest tweaks - that's why I made it public. :)

Also re: stats impact - I've done some thought about it and I think I've changed my mind. The numerical values for the stats do need to be tweaked in the upwards direction.

Though I do wish people would stop making the framing error where they think that (for example) -15%-15% is fundamentally different from 0%-30%... it isn't. Not if the base values of whatever the stat in question that is affected by that attribute (damage, health, etc) are adjusted accordingly. The important thing is the difference between the lowest and the highest bonus, not whatever arbitrary reference point is attached to it.

That said, (as I mentioned) I do think those bonuses differences should be considerably higher. If MIG is tied to damage, 3 MIG should have much less damage than 18 MIG. I'd venture to guess the sweet spot would be around 75% difference in damage between the two.

That said, you couldn't use the same treatment for all the attributes. Each would have to be looked at on its own, and perhaps a few altered in more than just numerical ways.

#43
sophismata

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Comparing base damage alone is misleading, it is very important to compare progressive, relative damage values.

 

The framing / reference error is annoying, but ultimately meaningless. Doesn't really affect game-play.



#44
Matt516

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Something to take into account is that the actuall bonus damage increase of raising Might by 1 point isn't actually 2% of your current damage, but 2% of base damage, so if you're at Might 15 rasing to 16 its only a (132/130=1,0154) 1,54% actual damage increase. So it's possible the current balance between Dex and Might is actually fine. (Though I still think all attributes could stant to have a lot more impact).


Is that correct though? That would be an awfully complicated way of applying the bonus. Any reason it wouldn't just be the much simpler 1.30 * base damage ---> 1.32 * base damage? (for 15 MIG to 16 MIG)

EDIT: I might understand what you're saying - you're calculating the percentage damage increase an additional point of MIG gives you from your previous MIG-adjusted damage. Fair enough. But the same thing would apply to the increases in damage from DEX/Accuracy (I'm pretty sure) so I don't think it makes a difference. The values I've calculated for Accuracy dps increase are relative to base, as is the 2% value for MIG. So MIG is still 2X the damage increase of DEX at the 5-45 point disparity mark and 1.33X the damage increase of DEX at the <5 point disparity mark.
Actually, it's far more important than you realise. At Acc = Def, increasing Acc by 1 point is a 76.5%/75% = 2% gain.
Sound familiar?

Again though, that's not a fair comparison. If your current value is 75 of base and you increase it by 1.5 of base, of course that will be larger relative to your current value than increasing something that's already 130 of base by 2 of base will be. But that doesn't matter. The actual damage increase in terms of real damage numbers (i.e. actual dps) is based off of your base damage, which means the only fair way to compare the bonuses from dexterity and might is to compare the bonuses based on base damage. Which is conveniently how they are already expressed in my calc and in the rules. There's no need to try and get super clever with this - the math for comparing the two bonuses (boni) isn't complicated. :p

#45
NeV3rKilL

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I thought critical damage is already 2x the normal damage?

 

Crits are x1.5 damage. You can find it here:

http://forums.obsidi...-and-a-tileset/



#46
Azrael Ultima

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Again though, that's not a fair comparison. If your current value is 75 of base and you increase it by 1.5 of base, of course that will be larger relative to your current value than increasing something that's already 130 of base by 2 of base will be. But that doesn't matter. The actual damage increase in terms of real damage numbers (i.e. actual dps) is based off of your base damage, which means the only fair way to compare the bonuses from dexterity and might is to compare the bonuses based on base damage. Which is conveniently how they are already expressed in my calc and in the rules. There's no need to try and get super clever with this - the math for comparing the two bonuses (boni) isn't complicated. :p
That would only be correct if (1)Total Damage = Base_Damage*(1+Might*2%) + Base_Damage*Acc_Modifier or some variation thereof.
(yes, this would result in double base damage, but this is merely for illustration, i'm only interested in the damage differences when changing stats)
 
For (2)Total Damage = Base_Damage*(1+Might*2%)*Acc_Modifier it's the other way around.
 
Don't get to stuck up on the absolute values.
 
For an example: 100 DPS base, 0 Might, Acc = Def
(1) base: 100*1 + 100*0.75 = 175
(1) Might +1: 100*1.02 + 100*0.75 = 177, 2 damage increase
(1) Dex +1: 100*1.02 + 100*0.765 = 176.5, 1.5 damage increase
 
(2) base: 100*1*0.75 = 75
(2) Might +1: 100*1.02*0.75 = 76.5, 1.5 damage increase
(2) Dex +1: 100*1*0.765 = 76.5, 1.5 damage increase
 
Despite the gain from Dex being seemingly lower, the actual damage increase is identical. On a high evasion enemy, increasing Dex is likely much more valuable than increasing Might. What your diagram is missing is a graph showing the actual damage gain from the Dex increase.
 
In other words, it's quite likely people are currently heavily underestimating the value of Dex.

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#47
Matt516

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I think you are right, though I'm not sure if your conclusions are entirely correct. I'll elaborate in a bit, but basically, I don't think DEX bonuses (boni) are always stronger than MIG bonuses (boni). Will elaborate in below paragraphs, but first a few words about how I messed up and how you caught it. :p

I certainly intended the calculation to be done as per "2)", because "1)" is just nonsense to any sensible way of calculating the damage. I think I screwed up in some of my later assertions and calculations - though I believe the accuracy of my initial plot is unaffected by this. My statements on comparing MIG and DEX are affected, however. I'll have to look over the math again tomorrow night when I have the chance (on mobile until then, so not ideal) and adjust if necessary.

It looks like because the bonuses (boni) from DEX and MIG are multiplied together, the marginal benefit of an increase in one attribute (in terms of true damage) ACTUALLY depends on the value of the OTHER bonus. Fascinating.

Try your example again with the base bonus from MIG already at 1.2, for example. In that case, the true damage increase (numberswise) from a 1.5% increase in DEX is actually MORE than the increase from a 2% increase in MIG. Or if you try it with the base bonus from MIG at 1, but the base bonus from DEX at 0.85, the same 2% and 1.5% increases yield a higher true damage increase for the 2% MIG increase.

These trends continue and are very clear: the value (in real damage) of a marginal % damage increase from one attribute is directly (and linearly, I *think*) dependent on the magnitude of the % damage multiplier from the other attribute. Very, very nice catch - thanks.

Long and the short of it is - my plot and table are still right as far as your expected dps from DEX (well, accuracy minus deflection technically) goes, but I was completely incorrect about being able to then compare those bonuses (boni) from MIG and DEX in a vacuum. The actual value of a marginal increase in one depends on what the already existing value of the other one is - the higher the other bonus is, the more valuable a marginal increase in the first bonus will be.

Edited by Matt516, 23 August 2014 - 09:14 PM.

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#48
Caerdon

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Interesting discussion, guys. I think I've made some errors as well when calculating the effects of DEX, so I'll have to take another look at things later.

 

Though I do wish people would stop making the framing error where they think that (for example) -15%-15% is fundamentally different from 0%-30%... it isn't. Not if the base values of whatever the stat in question that is affected by that attribute (damage, health, etc) are adjusted accordingly. The important thing is the difference between the lowest and the highest bonus, not whatever arbitrary reference point is attached to it.

 

Uhh... that's not right. Going from +0% to +30% is a 30% increase (Duh!) but going from -15% to +15% is roughly a 35% increase. The change may be the same in absolute terms, but it makes a bigger difference in the latter case. Can't adjust for that.


Edited by Caerdon, 23 August 2014 - 09:27 PM.


#49
Azrael Ultima

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Long and the short of it is - my plot and table are still right as far as your expected dps from DEX (well, accuracy minus deflection technically) goes, but I was completely incorrect about being able to then compare those bonuses (boni) from MIG and DEX in a vacuum. The actual value of a marginal increase in one depends on what the already existing value of the other one is - the higher the other bonus is, the more valuable a marginal increase in the first bonus will be.

That was basically the point.

 

It just so happens that that increase is exactly the relative damage gain from the attribute, precisely because they are multiplied.

To be specific, it is due to multiplication of real numbers being commutative. It doesn't matter which part of the calculation sees a relative x% increase, it will increase the result by x%.

 

I think the high gain range for Dex could stand to be a little larger, but it is by far not as weak as it looks at first.

 

Your calculations weren't wrong, as such, just incomplete.



#50
Matt516

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Interesting discussion, guys. I think I've made some errors as well when calculating the effects of DEX, so I'll have to take another look at things later.


Though I do wish people would stop making the framing error where they think that (for example) -15%-15% is fundamentally different from 0%-30%... it isn't. Not if the base values of whatever the stat in question that is affected by that attribute (damage, health, etc) are adjusted accordingly. The important thing is the difference between the lowest and the highest bonus, not whatever arbitrary reference point is attached to it.


Uhh... that's not right. Going from +0% to +30% is a 30% increase (Duh!) but going from -15% to +15% is roughly a 35% increase. The change may be the same in absolute terms, but it makes a bigger difference in the latter case. Can't adjust for that.

Can you provide an example calculation? I don't think you're correct: I'm pretty sure the difference between 0.85x and 1.15x will be exactly the same as the difference between 1x and 1.3x.

#51
Caerdon

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Interesting discussion, guys. I think I've made some errors as well when calculating the effects of DEX, so I'll have to take another look at things later.

Though I do wish people would stop making the framing error where they think that (for example) -15%-15% is fundamentally different from 0%-30%... it isn't. Not if the base values of whatever the stat in question that is affected by that attribute (damage, health, etc) are adjusted accordingly. The important thing is the difference between the lowest and the highest bonus, not whatever arbitrary reference point is attached to it.


Uhh... that's not right. Going from +0% to +30% is a 30% increase (Duh!) but going from -15% to +15% is roughly a 35% increase. The change may be the same in absolute terms, but it makes a bigger difference in the latter case. Can't adjust for that.

 


Can you provide an example calculation? I don't think you're correct: I'm pretty sure the difference between 0.85x and 1.15x will be exactly the same as the difference between 1x and 1.3x.

 

 

The difference is the same in absolute terms, but relatively it's different, and you can't just compensate for that by adjusting the base stats.

 

Let's assume the base health for a character is 100, 3 CON gives +0% health and 18 CON gives +30% health. Raising CON from 3 to 18 would raise the health from 100 to 130. That's a 30% increase, right?

 

So what if 3 CON meant -15% health and 18 CON +15% instead? At 3 CON the health would be 85 and raising CON to 18 would raise health to 115. That's the same 30 point increase in absolute terms, but it's also relative 35.3% increase ((115 - 85) / 85 = 0.353).

 

Now, we could compensate by upping base health to 118 instead of 100. Then 3 CON (-15%) would give the same 100 starting health as before, but now 18 CON (+15%) would give 136, which is more than 130.

 

So no, going from -15% to +15% is not the same as going from +0% to +30%.


Edited by Caerdon, 24 August 2014 - 07:45 AM.

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#52
Matt516

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Interesting discussion, guys. I think I've made some errors as well when calculating the effects of DEX, so I'll have to take another look at things later.

Though I do wish people would stop making the framing error where they think that (for example) -15%-15% is fundamentally different from 0%-30%... it isn't. Not if the base values of whatever the stat in question that is affected by that attribute (damage, health, etc) are adjusted accordingly. The important thing is the difference between the lowest and the highest bonus, not whatever arbitrary reference point is attached to it.


Uhh... that's not right. Going from +0% to +30% is a 30% increase (Duh!) but going from -15% to +15% is roughly a 35% increase. The change may be the same in absolute terms, but it makes a bigger difference in the latter case. Can't adjust for that.

 


Can you provide an example calculation? I don't think you're correct: I'm pretty sure the difference between 0.85x and 1.15x will be exactly the same as the difference between 1x and 1.3x.

 

 

The difference is the same in absolute terms, but relatively it's different, and you can't just compensate for that by adjusting the base stats.

 

Let's assume the base health for a character is 100, 3 CON gives +0% health and 18 CON gives +30% health. Raising CON from 3 to 18 would raise the health from 100 to 130. That's a 30% increase, right?

 

So what if 3 CON meant -15% health and 18 CON +15% instead? At 3 CON the health would be 85 and raising CON to 18 would raise health to 115. That's the same 30 point increase in absolute terms, but it's also relative 35.3% increase ((115 - 85) / 85 = 0.353).

 

Now, we could compensate by upping base health to 118 instead of 100. Then 3 CON (-15%) would give the same 100 starting health as before, but now 18 CON (+15%) would give 136, which is more than 130.

 

So no, going from -15% to +15% is not the same as going from +0% to +30%.

 

 

My bad - you are 100% correct that because changing base health would be required to get the same starting or ending point (when adjusting the bonus frame), and because the bonuses (boni) then depend on the new base health, it is indeed impossible to change the framing of the % difference between small and large stats while still preserving both the same absolute ranges and the same % bonus difference. Good catch. I really do need to stop making statements based on nebulous half-math done in my head. :p

 

My mistake was due (once again, actually) to a failure to take the principal being multiplied by the percentage into account when accounting for differences between percentages. Pesky algebra.

 

That said. I do think that most people who are asking for the stats to be framed as going from negative to positive modifiers (instead of constantly growing modifiers) aren't generally doing so because they have thought the math through - they are wanting it because that's how D&D did it. At least that's the impression I've gotten, because I've never seen anyone say "such-and-such would be better because then if you had a base of X and bonuses (boni) of Y and Z, you'd have values of A and B instead of C and D." That's why I've kind of been knee-jerking every time someone suggests it - because I would prefer that suggestions about mechanical changes be based on wishes about the mechanics, not general random preferences. 

 

Of course, there is certainly something to be said about how the framing affects the player's experience. It may be that for many people, a -/+ system just feels subjectively better than a +/++ system - even when the numbers are the same in the end. Which is certainly something to take into account when designing something that is ultimately designed to provide the player with a rewarding experience.

 

However. There is a potential pitfall with that approach. Say OE did want to go to a -/+ system instead of a +/++ system for the stat bonuses. Let's use the same base=100, boni=0-30% as our example. If they wanted to preserve the number range (100-130) while making the bonus system -/+, they'd have to change the base to 115 and the boni to -/+13%. This is interesting, because although the number range is still 100-130 (so nothing has changed from a mechanical standpoint), the subjective values of the boni have decreased. In fact, it follows fairly easily once you're thinking about it correctly (thanks again, Caerdon) that if you want the maximum subjective values for the boni with a given target number range, the best way to do that is with the +/++ system. What is one thing people have been complaining about endlessly (in regards to the stats)? That the boni are too small. Could it be that OE prefers the +/++ system specifically because it yields larger subjective values for the boni, thereby making people feel better about their stats? Hmm..


Edited by Matt516, 24 August 2014 - 03:50 PM.


#53
Matt516

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By the way - new and improved DPS calculation post is in the works. Will take DT into account, include many more plots, and also address the concerns and errata people have mentioned thus far. I'm hoping that this new and improved calculation post can be used as a quick reference to help steer conversations about mechanics and stats (as they affect damage) in a more factually and mathematically grounded direction. I (like everyone in this forum) want the game to be as great as can be - and our feedback about mechanics and stats is only as valuable as our understanding of how they actually affect our gameplay. At least, that's my $0.02. :)

 

EDIT: This probably won't be coming for a few days. Will take some time to get right. Is there interest in something like this though? Have y'all enjoyed having this first set of calculations as a reference and would you enjoy having a more comprehensive set?


Edited by Matt516, 24 August 2014 - 04:14 PM.

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#54
DrBrian

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There a few points in favor of dexterity these maths can't take into account.

 

On-hit status effects: Stunned or dazed for example. I'm expecting most of these to not be directly associated to the damages inflicted. The more often you will hit the enemies, the more often they will be afflicted by the debuff.

 

Avoiding overkill: assuming you have the options to have 50% chances to hit for 100 damages or 100% chances to hit for 50 damages a 101 hp enemy, on average the second option is more effective. Of course it also requires to take damage threshold and penetration into account complicating further the calculations.

 

Crit multiplier variables: it is likely some percs and weapons will increase this, making critical hits and consequently dex more valuable.



#55
Bester

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By the way - new and improved DPS calculation post is in the works. Will take DT into account, include many more plots, and also address the concerns and errata people have mentioned thus far. I'm hoping that this new and improved calculation post can be used as a quick reference to help steer conversations about mechanics and stats (as they affect damage) in a more factually and mathematically grounded direction. I (like everyone in this forum) want the game to be as great as can be - and our feedback about mechanics and stats is only as valuable as our understanding of how they actually affect our gameplay. At least, that's my $0.02. :)

 

EDIT: This probably won't be coming for a few days. Will take some time to get right. Is there interest in something like this though? Have y'all enjoyed having this first set of calculations as a reference and would you enjoy having a more comprehensive set?

 

Yes. Do it.



#56
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Yup, I am on the edge of my seat.  Definitely get another post started when you can.



#57
Stun

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EDIT: This probably won't be coming for a few days. Will take some time to get right. Is there interest in something like this though? Have y'all enjoyed having this first set of calculations as a reference and would you enjoy having a more comprehensive set?

Considering all the likes and commentary you received from your initial graphical analysis, I'd say absolutely.

Plus, it's why we're here. When discussing the function of the Beta, Josh Sawyer instructed us to "throttle the mechanics". Well, what's what you're doing. So keep doing it.

#58
Helm

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Thanks for this.

 

It shows that the system is a bunch of overly complex horse****. Who thought it would be a good idea to combine crits, hits, missing and grazing into one stat? they might as well have just made it a simple damage modifer like might.

 

That stats have two simple damage modifiers and everybody can use every weapon. Great.

 

Deprecate it.


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#59
Answermancer

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Thanks for this.

 

It shows that the system is a bunch of overly complex horse****. Who thought it would be a good idea to combine crits, hits, missing and grazing into one stat? they might as well have just made it a simple damage modifer like might.

 

That stats have two simple damage modifiers and everybody can use every weapon. Great.

 

Deprecate it.

 

 

It's really not that complicated and I think Accuracy is one of the better stats in the game. I agree that others need work but Accuracy work really well in my opinion.



#60
Matt516

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Thanks for this.

 

It shows that the system is a bunch of overly complex horse****. Who thought it would be a good idea to combine crits, hits, missing and grazing into one stat? they might as well have just made it a simple damage modifer like might.

 

That stats have two simple damage modifiers and everybody can use every weapon. Great.

 

Deprecate it.

 

 

To be honest, I don't mind this system at all. You could make a similar plot for any similar system in an RPG - THAC0, for example. The only major difference is that this system includes a 4th category - "graze" - in addition to the traditional "hit/miss/crit". There's really nothing particularly odd about this system lol - and it's not super complex.

 

As for making Accuracy a simple damage modifier, that wouldn't really be the same thing (and wouldn't be nearly as interesting). It is still an individual roll for every attack, which means that on the small scale (i.e. individual battles) you'll still see things like lucky crits, unlucky misses, all the things we love (and sometimes hate) about any general RPG "roll-to-hit" system. What my plot does is weigh the different possible outcomes by probability to obtain an equivalent simple damage modifier that will hold when you average a lot of attacks together. So you see - making it a simple damage modifier (a suggestion that could be applied to literally any game that includes a "roll-to-hit" system btw) wouldn't really be the same thing. Rolling to hit and miss adds more of a simulation aspect, as well as some RNG. I like having the flavor of simple damage modifiers and modifiers "to-hit" as well.

 

You had similar complaints in a few of the other threads as well, if I recall correctly. I'm gonna give you the benefit of the doubt and assume that you're (generally) so negative on these forums because you really really want the game to be good (as opposed to just trolling). If that's true, then we share a common interest - to make the game as good as can be. In the interest of helping the game be better and in fostering productive discussion that can actually potentially change the game for the better - please don't let this thread descend into another negative spiral of arguing and complaining. I've presented the math here and you don't like how they've done it. Fair enough. Do you have any suggestions for how they could improve it?


Edited by Matt516, 24 August 2014 - 09:50 PM.

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

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