# Skill progression formulaes

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At some point, I went ahead and sat myself down to find out what formulas Ascaron has given us for the Sacred 2 skill progressions.

Knowing that they have an affinity to fractions of the form a*(x+b)/(x+c), which flatten out to an upper bound 'a' for large x, made things a lot easier.

Although the form above does not apply to all progressions, it does to apply to most.

Concerning precision, the deviation is negligible and will only ever differ from the Wiki's chart value in the last relevant digit.

Not that it really matters. I assume most of us just play it by ear most of the time.

So what's precise and exact enough for me to not feel uneasy about posting it here, is probably precise and exact enough for anyone who will actively use these formulas.

And is definitely enough for those of us that just want a better picture of the capabilities of the skills they pick.

For most people, the formula itself is probably of little interest. The bounds, however, are plainly understandable and not nearly as exhausting to read through, which is why I have marked them bold. I find it interesting to know that it's impossible no matter how much +all skills I have, that the contribution of Combat Discipline to spell damage will never grow beyond 450%. Or that the regeneration time reduction you get from Concentration will never exceed 75%.

The values here are approximations, so if you do exceed these limits, then good for you, but you won't exceed them by much more than you already have. ^^

So far, I have the following formulas for the following skills:

Notation: (pre-mastery;mastery), unless marked with "(abs)" the bonus is percentual.

The following skills' progressions are identical up to a scaling of their upper bounds.

They take the form:

( A * (x + 1.5) / (x + 100) ; B * (x - 32.5) / (x + 66) )

where x is the skill level

Here, I will list only the limits A and B as (A,B)

(300;450)

Combat Discipline (CD): damage (to settle any confusion about the factor 10 and whether the bonus is % or absolute, see here)

Warding Energy Lore: shield energy

Damage Lore: damage/duration improvement -100

Speed Lore: attack/defense value (abs)

(200;300)

Ancient Magic: damage

Alchemy: potion effect bonus (displayed value ingame -100)

(400;600)

Tactics/Aspect Lore: damage

Armor Lore: armor

Shield Lore: defense

Spell Resistence: SR bonus

Enhanced Perception: MF bonus

~Weapons: attack value (abs)

(20;30)

Tactics/Aspect Lore: crit

Speed Lore: speed

(33.3(irrelevant);50)

Riding: speed

(500;750)

Riding: Combat Art bonus

(80;120)

Aspect Lore: exec. speed

~Weapons: att. speed

As this list of skills shares the exact same graph as Combat Discipline - up to rescaling - I think this progression merits a graph:

The following skills share the same progression as CD, but transformed (via x/(a+x) for some a>0) to be a probability or a reduction, taken to mean a number <100% (<1) :

( 66.6 * (x + 1.44) / (x + 34.3) ; 74.8 * (x - 33.2) / (x - 9.0) )

Concentration: reg. time reduction

Ancient Magic: opp. immunities reduction

( 80.0 * (x + 1.50) / (x + 21.25) ; 85.6 * (x - 32.9) / (x - 19.0) )

Combat Reflexes/Spell Resistance: crit reduction

Aspect Focus, Devine Devotion: reg. time reduction

Enhanced Perception: detection chance

Spell Resistence: 1 - damage reduction (meaning the SR table values for dam. red. and crit. red. add up to 1)

Blacksmith: smithing cost reduction

The following progressions were either partially or totally different from that of CD:

Bargaining: quality of wares = 0.1 * (x + 1)

Blacksmith: workable level = + x/3 (x/2 for Mastery) (abs)

Combat Reflexes: evade ( 57.0 * (x + 1.43) / (x + 43.5) ; 69.9 * (x - 19.1) / (x + 5.95) )

For all who don't know this: it pays to put that one more point into CR to get lvl75. Although the limits of pre-mastery and mastery are closer together than those of most other skills, the jump of 11.7% from 74 to 75 is like getting paid your evade chance retroactively.

Toughness: armor (abs) ( 204.2 * (x + 1.05) / (x + 103.1) ; 400 * (x - 32.5) / (x + 66) ) =Toughness: 10*(dam reduction)

With toughness' damage reduction, it's similar, but not as extreme: the jump is of only 3.5%, but when your increments per level are all downside of 0.1%, a jump of 35x that doesn't look too bad. Especially considering that all the skills like CD hardly jump at all: Toughness jumps 7x as strongly as CD skills, and CR almost 12x as strongly.

( UNSOLVED ; 60 * (x - 32.5) / (x + 66) )

Pacifism: damage red.

Shield Lore: block chance

Blacksmith: chance to remove

( UNSOLVED ; 30.7 * (x - 30.0) / (x + 63.0) )

Bargaining: chance for special offer

Warding Energy Lore: shield reg. ( mastery only ; 30.9 * (x - 32.8) / (x + 34.6) )

For the following progressions I couldn't find a similar formula:

~Weapons: chance for double hit

Damage Lore: effect chance =Warding Energy Lore: damage absorption

Constitution works a bit differently: The health-point bonus you get is linear in skill level, but depends (slightly) quadratically on the player level.

So far this is what I have:

Health bonus = ( 0.0005557*L² + 0.2438*L + 12.14) * x, (abs)

where L is char level and x is skill level.

The Vitality HP bonus, the Constitution HP bonus and the actual base HP (total -these two bonuses) are independant of eachother.

I have the coefficients fairly precisely, but they should be tested at higher CharLvls.

Lastly, I have also found a coefficient for the survival bonus increase dependant on what Sacred 2 calls "Alive Time" (total time in combat since last ressurection):

SB = T / (21600 + T), (another formula type Ascaron loves to death)

where T is the alive time.

By this idea, the (misleadingly named, but not wrongly) 'faster increase of survival bonus +p%' means that yor alive time is, in effect, magnified by p%.

Not only does this make your SB increase faster (hence the name), but it also increases your SB retroactively. I've verified this to be true.

To sum up what's missing:

Pre-mastery:

Pacifism: damage red.

Bargaining: chance for special offer

All:

~Weapons: chance for double hit (only mastery relevant)

Damage Lore: effect chance =Warding Energy Lore: damage absorption

Other:

Constitution: HP regeneration rate

or for that matter, the relation between HP and HPregen at all.

Other areas of possible interest:

Highest Combat Art Level Without Penalty

Attributes' contribution to the values they affect. E.g. Str, Dex, Int to weapon damage.

If anybody has any clues as to what the mechanics are behind these, I guess here would be a suitable place to share them.

Nathaniel

Edit: A similar thread has also been started in the SacredWiki general discussion area.

Since they discuss the same matter, I decided to link the thread here

Edited by gogoblender
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Wow, nice work there

Very interesting nokka, nice work.

lol!

The is fantastic and very detailed, I was with ya right up until:

So far, I have the following formulas for the following skills:

Help a poor fella with only a high school education please. can I kill more stuff with this! Just kiidding, it does look like you put some serious work into this. the more mathematically inclined are gonna love it. And your already got nods from Antitrust and Slevin. gtratz!

Nice work. Must have taken a fair bit of time to work all that out. Have a drink on me to cool off

lol!

The is fantastic and very detailed, I was with ya right up until:

So far, I have the following formulas for the following skills:

Help a poor fella with only a high school education please. can I kill more stuff with this! Just kiidding, it does look like you put some serious work into this. the more mathematically inclined are gonna love it. And your already got nods from Antitrust and Slevin. gtratz!

I haven't had a chance to really mull over it but I think it basically is saying that you can use these numbers to determine how high you could take a skill before it no longer gives you any benefit from that skill.

Armor Lore would be an easy one to use since the tooltip for Armor Lore shows you exactly what % it increases your armor. nokka's formula states that pre-mastery you can never achieve higher than +400% armor bonus and with mastery you can get no higher than +600% armor bonus. Determining what skill level that equates to is the real meat of these formulas, but only if you're interested in getting the absolute most value out of a certain skill.

Edit:

Using the formula for Concentration, with a skill level of 1000

74.8 * (1000-32.9)/(1000-19.0)

74.8 * (967.1)/(981)

74.8 * (.9857) = 73.7

Assuming I did that right then I don't think we have anything to worry about with Concentration...

Edited by Numerii

nokka you could please explain the formula for the damage mitigation provided by Toughness. From what I'm reading you only have it down as Toughness: 10* (damage reduction).

I'm really not following that line but this is the one formula that interests me the most since I will be shooting for an exact increase in damage reduction from this skill for a couple of builds of mine and knowing exactly what skill level I need to have to get that increase would be of great benefit to my planning.

nokka you could please explain the formula for the damage mitigation provided by Toughness. From what I'm reading you only have it down as Toughness: 10* (damage reduction).

I think it means that the % of damage reduction of toughness is 10 times lower than the additional armor. But calculating with the formula toughness skill level of my Temple Guardian I have other values as there are shown in the menu.

Yes. If you meant what it sounds like you meant, Slevin, then yes, that's what the formulation means

It's a bit odd that you have other values. But I'm not completely surprised that's the case:

I got my values for all the skills from the SacredWiki skill pages, not ingame. The same goes for Toughness.

Also, there's been an expansion and a patch since I did these calculations...

...

I've just checked ingame as well:

Indeed, Toughness' values ingame are not those of the Wiki chart.

I'll repeat that for anyone interested in updating the Wiki:

erherm-- INDEED, TOUGHNESS' VALUES INGAME ARE NOT THOSE OF THE WIKI CHART!

I basically get ingame values as 1/3 higher than the Wiki claims they are.

So, I think it's safe to assume that the maxima have been raised by 1/3 of what they used to be.

Instead of (153.15;300) take (204.2;400) and the values should be right.

I'll only edit the original after I get some confirmation from elsewhere.

Either that or the 4/3 factor is only for Shadow Warriors, which I doubt. ^^

I also checked to see if there was a CharLvl dependant factor (as with constitution), and there isn't, so no worries there.

Thank you for pointing that out, Slevin. I hate having mistakes in my work. ;P

Could you check with your Temple Guardian and verify or ..uh ..falsify^^ the numbers?

You don't have to plug in any numbers, just compare the Toughness page.

(side note: I just noticed the abbreviation for Temple Guardian auto-completes)

And thank you, Numerii, for asking the question in the first place.

My formulations sometimes get incomprehensible, so a number of people are bound to not understand right away.

The sooner someone asks, the better.

Also, good luck with your builds.

Also, Numerii, I just noticed that you mixed formulas on Concentration:

The maximum was right, but the fraction was different:

74.8 * (x - 33.2) / (x - 9.0)

You took the function from Combat Reflexes: (x - 32.9) / (x - 19.0)

Although at level 1000 it doesn't make much difference:

74.8 * (1000 - 33.2) / (1000 - 9.0) = 74.8 * 966.8 / 991 = 72.9

which differs from your value by 0.07sec on a 10sec regen time.

It always helps to double check. ^^

Could you check with your Temple Guardian and verify or ..uh ..falsify^^ the numbers?

With your new numbers the values do now agree with the toughness values of my Temple Guardian.

Btw did you check if any other values in Ice and Blood differ from the wiki charts?

Thank you for the confirmation

I've made the edit in my original post.

Although no, I have not checked any other skills for updates.

Is there anything in the changelog for sacred2 that would lighten the workload?

Like "Balanced the progression for 'Toughness', 'Blabla' and 'Blablabla'." that you've seen?

Is there anything in the changelog for sacred2 that would lighten the workload?

Like "Balanced the progression for 'Toughness', 'Blabla' and 'Blablabla'." that you've seen?

I never read in the game files because I'm a bit noobish in such things.^^

But I checked some of the skills and compared with the values of my toons and they seem to be correct.

Thank you for checking, Slevin.

It'd probably be easier and more practical just to wait until someone complains that my formula is wrong.

So I think I'll just do that.

After all, as you said, apart from Toughness, which has already been corrected, everything so far seems OK.

If something should come up, I'll edit.

If something should come up later...

Well, then I assume Gogo will be gracious enough to give me editing permission?

(200;300)

Ancient Magic: Damage

Alchemy: Potion effect Bonus

It seems to be Potion effect Bonus +100 of alchemy.

Bargaining: quality of wares = 0.1 * (charlvl + 1)

It seems to be half as high as your values.

Edited by Slevin
(200;300)

Ancient Magic: Damage

Alchemy: Potion effect Bonus

It seems to be Potion effect Bonus +100 of alchemy.

That's true, both ingame and in the Wiki. But the reason I wrote "Potion effect bonus" is because the actual bonus is the number you see -100.

The way they wrote it is misleading, as "+104.9%" means the affected value is more than doubled right from the start.

That's why I left off the +100.

But seeing as it can be confusing on my part and/or rubs people the wrong way, I'll make a note of it in the original post.

I found a similar thread in the SacredWiki area and decided to link it at the end of the original post.

Apparently, Numerii, you've also seen this thread ^^

PM Gogo or schot for editing permission on the wiki.

nokka, you may did not notice the edit of my last post.

But here I have some more questions.^^

Blacksmith: workable level = + L/3 (L/2 for Mastery) (abs)

Does that mean, that it doesn't depend on the level of the blacksmith skill?

Constitution works a bit differently: The health-point bonus you get is linear in skill level, but depends (slightly) quadratically on the player level.

So far this is what I have:

Health bonus = ( 0.0005557*L² + 0.2438*L + 12.14) * x, (abs)

where L is char level and x is skill level.

I have the coefficients fairly precisely, but the formula doesn't seem to work as well when calculated with vitality.

So it means the formula only works when vitality wouldn't exist as attribute?

Lastly, I have also found a coefficient for the survival bonus increase dependant on what Sacred 2 calls "Alive Time" (total time in combat since last ressurection):

SB = a * T / (10000 + a * T), (another formula type Ascaron loves to death)

where T is the alive time and a is, by my calculation, 4.61.

I want to think 'faster increase of survival bonus +p%' means that this 'a' is multiplied by 1+p% (e.g. p=5, a->1.05a).

The modifier "faster increse of SB" increases the SB and so the attributes immediately. I don't think that the SB increases faster in the time wearing an item with that mod. It should better mean "SB +xx%" whereas the SB is not increased by the shown percentage.

Have you tried playing with the balance.txt settings for SB? They might give you a hint on the multipliers involved.

Have you tried playing with the balance.txt settings for SB? They might give you a hint on the multipliers involved.

Sry I'm a bit noobish in such things. Thats why I'm very happy that there are people like you or nokka.:rolleyes: Btw I even don't know where to find the balance.txt.^^

Thank you, Slevin, for pointing out the mistakes/misunderstandings in Blacksmith, Bargaining and Constitution.

At the time, I used L to mean 'Level' which could be interpreted as both. I forgot to change the L in Blacksmith to an x, and I even wrote out the L in Bargaining as charlvl ...

As far as Constitution goes, that last sentence didn't make sense, so I replaced it with a different 'but' and added an explanation for vitality.

However, Bargaining's values seem to be right: I checked with my bargaining char, and she said level 198 has 19.8 which is the wiki table value.

I still don't get why I wrote charlvl... Sometimes people do stupid things...

Now, having looked at what I've only seen refered to as "a certain file" and would for this reason have called *******.txt,

I could only find 3 values possibly concerning Survival Bonus:

UBmean = 500,

UBpivot = 21600,

UBquot_attr = 3000

UB being Überlebensbonus in German. I haven't worked around with those values yet to see what they are, but I'm pretty sure of two things now:

1. UBquot_attr = 3000 is the attribute bonus (30%) when SB = 100% (so, never. ;P)

2. How the SB increase works. I'll be including this in an edit, but I'll say it here once as well:

Indeed, it is not as the modifier claims it is. It does in fact raise the SB immediately, which I failed to notice. Thank you, Slevin.

Here is how it works: (and how lots of other stuff works, by the way, which involve percentages exclusively <100%, e.g. Deathblow)

A number p < 1 (=100%) corresponds to a number x < infinity, by the function p = x/(1+x) or equivalently x = p/(1-p).

What Sacred needs to do a lot is to increase/decrease percentages by an absolute amount or a factor (relative amount). But it can't allow a 'p' to grow over 1, because >1 doesn't make sense in these cases. In these cases it does the following: It modifies x, and uses the p corresponding to the modified x.

In short
: (take x = p/(1-p), y = q/(1-q), and 'a' to be your multiplication factor)

: p "+" q = (x+y)/(1 + (x+y))

Multiplication
: a "*" p = (a*x)/(1 + (a*x))

So the idea in the original post wasn't wrong at all, as I just now realise. I just forgot to consider the alteration of 'a' raises your SB retroactively.

UBmean = 500,

UBpivot = 21600,

UBquot_attr = 3000

UB being Überlebensbonus in German. I haven't worked around with those values yet to see what they are, but I'm pretty sure of two things now:

1. UBquot_attr = 3000 is the attribute bonus (30%) when SB = 100% (so, never. ;P)

One of them is just a multiplier, it tells the game how high should the SB be for a given "alive time" as you call it. Probably the pivot one, it's been a while. Not sure what the other does.

Thank you, Antitrust!

That hint you gave me with what 'pivot' means made the formula exact!

I've made the changes in the original post.

What I figure it means, is that the SB at time UBpivot is UBmean. Here, after 21600sec Alive Time, your SB is 50%.

It makes me happy to have an exact formula in my post.

Thanks a lot.

Wow that's great Nice job

I'm having issues with the math though... If I reverse the SB = T / (21600 + T) to calculate the needed time to get 100% SB, I get 6 hours (100(21600 + T)=T)... What am I doing wrong?

I know the actual achievable SB is around 99% after about 833 hours, after calculating it crudely...

Woot, 600 posts Now that's something I can calculate properly...

Edited by Antitrust