Damage Caps, Rollovers, and other #'s ---edit 9.03.09

[Myhrginoc]

Keep in mind data width caps will affect every step of a calculation. Even the order in which something is calculated can have impact. Almost every calculation in D2 uses integer math at the CPU level, so the maximum data width is 32 bits. If you multiply two N-bit numbers together, the result can be 2*N bits wide. So A times B divided by C is not necessarily the same as A divided by C times B, if A times B yields more bits than your data type allows. But if A divided by C is less than 1 then you get an underflow that yields 0 when multipled with B in the second ordering. Life, mana and stamina are shifted eight bits to allow higher precision (in 256ths), so the discernable range is restricted to ±8.8 million. So by the time you factor in all the combat modifiers you have a lot of opportunities for A * B / C calculations to exceed 8.8 million. Blizzard's low numbers never did, but guess what many modmakers changed? Patch 1.10 rearranged the calculation orders to get the higher caps.

[seth_southerland]

exactly how does a person know how much damage they are doing? all i have to look at is a range of numbers.

[Myhrginoc]

You don't know how much, the range shows a band of possible random outcomes. The displayed range is buggy anyway, to add to the fun. Besides, during gameplay would you want to see a (probably wrong) number pop up every time you hit something? Would get annoying real fast...

[Hans]

Plugy can show the different damage types in the character screen. The damage may not be correct. I do not know if the version that Zy-El uses can display the damage.

[KseAli]

[quote=Hans";p="393941"]
Plugy can show the different damage types in the character screen. The damage may not be correct. I do not know if the version that Zy-El uses can display the damage.
[/quote]

I don't know about 44c, but first version of Zy-El with Plugy didn't display damage. From that time I'm using my own statinterface.txt corrected for Lod109d and can see separately values for each type of elemental damage.

[Al-T]

...and you are still left wondering...."well that's the damage that my character does but what about negation from monsters resistances and absorptions which are never seen"?

Just hit till you kill

[Claws]

I just have to notice this once:

The damage cap ist not at 87040. Also the (2^10+2^12+2^14+2^16) or 1024*85 = 87040 calculation makes no sense.
Capping occurs already at 84k. Necrolis had a much better explanation for calculating the cap and it corresponds with the real capping in the game:

[quote=Necrolis";p="399565"]If one uses simple math we can work out accurate values. Damage is signed, so it has 2 ^ 31 - 1 as a max value, next blizzard uses 8 bit precision for life mana and damage, leaving 2 ^ 23 - 1, next we get to the main cause of the roll, blizzards percentage function, this multiplies by the percent base first, which is 100, this leaves 2 ^ 23 - 1 / 100 as the cap. The rollover occurs when the signed bit is overwritten making the value negative, this happens every ((2 ^ 23) - 1) / 100 damage, so every even multiple of that value is negative. Though it is possible to roll multiple times when you start hitting excessive damage (2 ^ 23 as a base damage value)[/quote]

Thus the cap is at ((2 ^ 23) - 1) / 100 = 83886. And it rolls over at 167772.

I don't understand how the wrong value could have been reapeatingly posted from 2003 on in this forum and nobody verified (or ameneded) it. (I saw that Myhrginoc calls it 83k which is quite the correct value).

I would apreciate if the first posting in this thread and the Wiki could be edited.

[Al-T]

I am editing the Wiki at the time of writing this. I don't know why I put those values there as I know 83886 is the correct value .

As for this thread, a lot of the posts do talk about monster resistances so mentioning 87K in those circumstances is not incorrect due to the order of the damage calculations (and like I mentioned in my previous post here, we have no idea if Kato has given monsters absorb values which would also have to be factored in).

GhOsT(Eth)'s original post was from Wed Feb 19, 2003 12:32 pm and if you read the entire Sticky carefully enough you will see that the values in the very first post have been corrected several times by other posters.

Probably the best example was given by Kurse on Page 4 of this thread. Also, that's what a continuing thread is for....posts don't get deleted but "new knowledge" or "adjustments" are made in the most recent posts.

Thanks for pointing out that I had it wrong on the Wiki. The Wiki has now been updated to show the correct values

[Dapaba]

Having a lot of problems with caps and finding it hard to do calculations without some basic info, so here goes:

How is the cap/rollover calculated when you have a damage range? For example, my Pal's weapon has about 2k difference between minimum and maximum which translates into about a 300k gap when using Zeal + Fanatism. I'd assumed the cap follow the max damage, but that doesn't seem to be the case.

Thanks for any help.

[Hans]

Dapaba that is a good question.

I will see if I can get find info on how the damage is calculated in 1.09. I believe it is the same formula that is for 1.11 and 1.12.

[Metropolis Man]

I will see if I can get find info on how the damage is calculated in 1.09. I believe it is the same formula that is for 1.11 and 1.12.

Is this the reason there are no damage caps in ES — because it's based on 1.10?

[Necrolis]

I will see if I can get find info on how the damage is calculated in 1.09. I believe it is the same formula that is for 1.11 and 1.12.

Is this the reason there are no damage caps in ES — because it's based on 1.10?

1.10 has a cap, its just not reachable, 1.10 changed around the main math calc that was responsable for rollovers(the percaentaging func), and basically increased the cap in that area by 100 times(8.3 milion as opposed to 83k)

[Dapaba]

Dapaba that is a good question.

I will see if I can get find info on how the damage is calculated in 1.09. I believe it is the same formula that is for 1.11 and 1.12.

How is the formula calculated for 1.11/1.12? Or better yet, do you have a link that I could check out? This will be a problem for as long as I play Zy-El, so better to learn this stuff. Al-T's method of just adding damage until you kill again is good, but not very....precise.

[Necrolis]

Didn't notice dapaba's question... The game rolls a random between min and max(all damage%, +damage, source damage etc is applied before this), then things like critical/deadly are applied, then we do absorbs, reductions and resists, then the final amount is summed and applied(all damage types are summed up into one variable before application), there are multiple points where this can roll, when the damage% is applied to min and max, when resists, or percentage absorb/reduction is applied etc, but those depend on the value generated by the random between min and max damage(for each element). Just note that with zeal and any other weapon damage based skill, the percentage base is 128, meaning the roll over point is 2 ^ 18 - 1 or 65k in certain parts

[Hans]

I am having problems on finding the exact formula.

Thanks Necrolis for the post.

I just want to clear the process on the checks done

1 first check to see if rollover when the check is done on Damage %
2. When the check is made to find the actual damage done (resists and the absorbs) and weapons based skill and auras.

Correct me if I am wrong Necrolis.

I would like to add an easy explanation on how damage is calculated in 1.09 so it will be easier for players to figure out to avoid a roll over or much they need to get to the next cap.

[Dapaba]

Thanks Necrolis.

So, as Al-T has noted time and again, don't worry about the caps/rollovers, just add more damage when you stop killing...or use a weapon with min/max damage close together.

Hans, I think I'm catching on...with so many levels in Zy-El, and so many variables that can cap/rollover a person's damage, probably only spell damage is possible to regulate on a regular basis. Physical damage changes to rapidly in Zy-El to keep to a certain damage area?

[Hans]

On the physical damage side I only focus on keeping the minimum below the cap.

[czg]

Are there any caps to IAS / FRW / MF / Balance etc.?

[gogodanny]

the cap to ias doesn't really exist as characters just won't swing any faster than given breakpoints. There r some charts around although I don't have the URL handy.

FRW dito, there's no rollover that I know of.

MF simply has returning values. Imagine it like a curve that approaches a certain value but never touches it, even in infinity :-)

fhr should be the same as with fr and ias, fcr etc ...

[czg]

Are there any caps to IAS / FRW / MF / Balance etc.?

Of course what I meant to ask about was GF, not MF (which is covered above)

There r some charts around although I don't have the URL handy.

Does anybody have the url? Some of my items are fast approaching 1000% for several stats so if, for example, FCR is limited to 255% on a pair of gloves then I'll need to do some reducing.

[Hyabusa1239]

I have a question about rollovers.
From the wiki:

Damage Cap : 100
You have : 275
Damage starts over at : 200 (this is the rollover point)
Your actual damage : 75
In the example above you do damage from 1-100, no damage from 101-200, damage from 201-next cap and so on.

Rollover: Your damage displays back at 0 after this amount, but still includes the amount after the rollover e.g.

Rollover : 200
You have : 450
Actual Damage : 50

What I am not understanding is in the case of example 1, it says your actual damage is 75...so with the rollover wouldn't it make sense to "stop" at 199 to get the best possible damage?

Will we ever do more than that 199 damage? Or is that the best possible outcome?

If someone could help me understand this it would be greatly appreciated.

Thanks!

[Necrolis]

You'll want to stop at 99, because from 100 to 200 damage becomes negative(in the example)

[Hellwolf_36]

100 is the highest positive value in damage you can have. At 101, you will do nothing until you reroll your damage to 200. In the example, he is doing 275 so only 75 of the damage will actually take life away.

[Hyabusa1239]

Ok I think I get it now, thanks for the responses!

[Clersius]

This would fall under the "and other #'s" section of the subject line. I was recently fiddling around with a spreadsheet, trying to find the ideal combination of amounts of life and %max life jewels for my merc that would scale from her current level through around level 4000. What kept coming up for all levels between 500 and 4000 was the necessity for a jewel with 29 mega-loads of 150% max life, or 4350% total.

So, intent on my purpose, I set out with gusto to create this wonderful and amazing jewel. 10 applications, huzzah! 15 applications, tremendous, a thing of beauty! 20 applications and my mouth was watering, my heartrate was increasing... this was going to be legendary! (At least in my world... ) All of a sudden, BAM! Head, meet brick wall.

The point of all this rambling is that, on the 21st application of 150% max life to a jewel, you only get 71% of the total 150%, giving a cap of 3071% max life to any one jewel. Hopefully this information will help someone down the line keep from wasting a Zy-El Scroll on that 21st mega-load.

Happy roads!