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Posted By: Kustos So how does Constitution/Vitality work? - 30/07/14 09:26 PM
I've tried searching these forums and any wikis that I can find, but I've yet to discover a conclusive formula for determining how much Vitality a character will have at any level with a given amount of Constitution (Difficulty and Talents aside).

Hopefully someone can shed some light on this issue. I realize that knowing the formula doesn't change the way the game plays, but I'm trying to determine the Action Point value of specific Attributes, Abilities, Traits and Talents.

Thanks in advance.

TL;DR - How does Constitution impact Vitality (without difficulty and trait changes)?
I assumed that each point of Constitution increased HP by a specific amount (eg, 100). Is that not the case?

Edit: doing some tests
On HARD difficulty, at level 21 (no picture of health, Glass Cannon, etc)
7 Con = 599 HP
8 Con = 690 HP (+91)
9 Con = 786 HP (+96)
10 Con = 890 HP (+104)
11 Con = 1001 HP (+111)
12 Con = 1119 HP (+118)
When you adjust for the -25% hp from hard, the gains are
7 Con = 798.66 HP
8 Con = 920 HP (+121.33)
9 Con = 1048 HP (+128)
10 Con = 1186.66 HP (+138.66)
11 Con = 1334.66 HP (+148)
12 Con = 1492 HP (+157.33)
Meaning that the differences between points of vitality are
6.66
10.66
9.33
9.33
I'm assuming that the up and down is the result of rounding. The average difference is 9 (8.995).
Meaning that the formula COULD be
Each point of Constitution is worth apprx 50 Vitality + (level of new Con * 9)

So your 1st point of Con should be worth +59 vit, your 6th point of Con should be worth +104 vitality, your 10th should be worth +149 vitality, and your 15th should be worth +185 vitality.

Starting with 200 vitality at Con 0 and proceeding along that sequence seems to yield more or less correct values (802 HP at 7 Con, versus the observed 798.66 Con at 7)

Edit2:
@eskuche I forgot to factor in increases from level. I should clarify that at level 21 (and only at level 21), the formula I posted seems generally correct.
Posted By: eskuche Re: So how does Constitution/Vitality work? - 30/07/14 09:56 PM
Did a quick check at level 1. 5, 6, 8, 10 constitution give +52, 62, 83, 107 vitality, respectively.

It looks like constitution gives slightly quadratic vitality at a given level.

Based on my first run-through, it seems that the vitality per constitution ALSO increases per level and also slightly quadratically. After this, add flat bonuses then a multiplicative effect for talents/difficulty.

My guess is a formula something like this (uppercase are constants, X is level, Y is constitution):

HP = {[(aX + bX^2)*(cY + dY^2)] + flat bonuses} * {talents +/- difficulty modifiers}
Posted By: eidolon Re: So how does Constitution/Vitality work? - 30/07/14 10:13 PM
The number of additional HP points per additional CON is a bit weird.
After a respec I got
+128
+136 (08 more than last time)
+146 (10 more than last time)
+155 (09 more than last time)
+166 (11 more than last time)
+178 (12 more than last time)
+190 (12 more than last time)
+217 (15 more than last time)

edit: for other effects the game seems to be rounding down.
Be sure that you post what difficulty you are checking on.
Normal gives a 15% bonus to vitality, while Hard gives a 25% penalty.
Posted By: eskuche Re: So how does Constitution/Vitality work? - 30/07/14 10:27 PM
Originally Posted by eidolon
The number of additional HP points per additional CON is a bit weird.
After a respec I got
+128
+136 (08 more than last time)
+146 (10 more than last time)
+155 (09 more than last time)
+166 (11 more than last time)
+178 (12 more than last time)
+190 (12 more than last time)
+217 (15 more than last time)

edit: for other effects the game seems to be rounding down.


What level is this at? My post, and I think eidolon's as well, was gotten by hovering over HP and seeing the contribution from constitution, excluding difficulty.
Posted By: Kustos Re: So how does Constitution/Vitality work? - 30/07/14 10:31 PM
Thank you all for such good responses.

I've been tinkering with it for the past 24 hours and gotten nowhere.

When I get home from work I'll try to fire back some conclusions from all this info.
Posted By: eidolon Re: So how does Constitution/Vitality work? - 30/07/14 10:32 PM
I can't check the variables, since the data is just taken from some old notes where I wanted to figure out the exact bonus myself.
Level 20, Vit bonus of +0% (Hard difficulty, Picture of Health, Man-at-Arms 5)
0 Con = 138 Vit
1 Con = 210 Vit (+72)
2 Con = 288 Vit (+78)
3 Con = 371 Vit (+83)
4 Con = 459 Vit (+88)
5 Con = 553 Vit (+94)
6 Con = 655 Vit (+102)
7 Con = 763 Vit (+108)
8 Con = 878 Vit (+115)
9 Con = 1001 Vit (+123)
10 Con = 1133 Vit (+132)
11 Con = 1274 Vit (+141)
12 Con = 1425 Vit (+151)
13 Con = 1586 Vit (+161)
14 Con = 1758 Vit (+172)
15 Con = 1942 Vit (+184)
16 Con = 2139 Vit (+197)
17 Con = 2349 Vit (+210)
Posted By: eskuche Re: So how does Constitution/Vitality work? - 31/07/14 12:11 AM
Originally Posted by ScrotieMcB
Level 20, Vit bonus of +0% (Hard difficulty, Picture of Health, Man-at-Arms 5)
0 Con = 138 Vit
1 Con = 210 Vit (+72)
2 Con = 288 Vit (+78)
3 Con = 371 Vit (+83)
4 Con = 459 Vit (+88)
5 Con = 553 Vit (+94)
6 Con = 655 Vit (+102)
7 Con = 763 Vit (+108)
8 Con = 878 Vit (+115)
9 Con = 1001 Vit (+123)
10 Con = 1133 Vit (+132)
11 Con = 1274 Vit (+141)
12 Con = 1425 Vit (+151)
13 Con = 1586 Vit (+161)
14 Con = 1758 Vit (+172)
15 Con = 1942 Vit (+184)
16 Con = 2139 Vit (+197)
17 Con = 2349 Vit (+210)


Thanks! But how did you get 0 constitution?

Edit: if we can get these values at another level between 0 and 20 I can get the formula out.
Originally Posted by eskuche
Thanks! But how did you get 0 constitution?
Infect (Ranger skill) gives -3 Con and can target party members. Cursing Arrow gives -2 to all Attributes and can target party members. I think you can also use Withering Arrow instead of Infect, but I didn't try that.
Posted By: Kustos Re: So how does Constitution/Vitality work? - 31/07/14 06:02 AM
Excellent info.

I wish I would have remembered more of Math from school.

Its been a while since the last "Learning how to derive formulas" class. :P

I'll see if I can fill in the blanks. Gotta find an infect skill book...

Thanks for the help!
Posted By: Kustos Re: So how does Constitution/Vitality work? - 01/08/14 02:50 AM
Con at level 19

0 Con = 131 Vit
1 Con = 200 Vit (+69)
2 Con = 274 Vit (+74)
3 Con = 353 Vit (+79)
4 Con = 437 Vit (+84)
5 Con = 527 Vit (+90)
6 Con = 623 Vit (+96)
7 Con = 726 Vit (+103)
8 Con = 836 Vit (+110)
9 Con = 954 Vit (+118)
10 Con = 1079 Vit (+125)
11 Con = 1214 Vit (+135)
12 Con = 1357 Vit (+143)
13 Con = 1510 Vit (+153)
14 Con = 1674 Vit (+164)
15 Con = 1850 Vit (+176)
16 Con = 2037 Vit (+187)
17 Con = 2237 Vit (+200)
18 Con = 2452 Vit (+215)
19 Con = 2681 Vit (+229)
20 Con = 2925 Vit (+244)
21 Con = 3187 Vit (+262)

Con at level 20

0 Con = 138 Vit
1 Con = 210 Vit (+72)
2 Con = 288 Vit (+78)
3 Con = 371 Vit (+83)
4 Con = 459 Vit (+88)
5 Con = 553 Vit (+94)
6 Con = 655 Vit (+102)
7 Con = 763 Vit (+108)
8 Con = 878 Vit (+115)
9 Con = 1001 Vit (+123)
10 Con = 1133 Vit (+132)
11 Con = 1274 Vit (+141)
12 Con = 1425 Vit (+151)
13 Con = 1586 Vit (+161)
14 Con = 1758 Vit (+172)
15 Con = 1942 Vit (+184)
16 Con = 2139 Vit (+197)
17 Con = 2349 Vit (+210)

I can provide it for level 21 as well if it would help.

Thanks for the help!
I wonder if 1 Con = (level+1)x10 Vitality.
If so, that might be a hint to the greater formula.
Posted By: Kustos Re: So how does Constitution/Vitality work? - 01/08/14 06:01 AM
I've tried a similar math, but it never seems to be consistent as you level up. I'm trying to compare the difference between the "Free Health" you get each level.
Posted By: Kustos Re: So how does Constitution/Vitality work? - 01/08/14 06:54 AM
Here are the numbers for 21:

0 Con = 145 Vit
1 Con = 221 Vit (+76)
2 Con = 302 Vit (+81)
3 Con = 388 Vit (+86)
4 Con = 481 Vit (+93)
5 Con = 580 Vit (+99)
6 Con = 686 Vit (+106)
7 Con = 799 Vit (+113)
8 Con = 920 Vit (+121)
9 Con = 1049 Vit (+129)
10 Con = 1187 Vit (+138)
11 Con = 1335 Vit (+148)
12 Con = 1493 Vit (+158)
13 Con = 1662 Vit (+169)
14 Con = 1842 Vit (+180)
15 Con = 2035 Vit (+193)
16 Con = 2241 Vit (+206)
17 Con = 2461 Vit (+220)
18 Con = 2697 Vit (+236)
19 Con = 2949 Vit (+252)
20 Con = 3218 Vit (+269)
21 Con = 3505 Vit (+287)
22 Con = 3813 Vit (+308)
23 Con = 4142 Vit (+329)
24 Con = 4493 Vit (+351)
Originally Posted by Kustos
1 Con = 221 Vit

D'oh! Off by one, Scrotie.
Posted By: Kustos Re: So how does Constitution/Vitality work? - 02/08/14 01:50 AM
Anyone able to figure this out yet? I've still not figured anything out that works across the board.
Posted By: eskuche Re: So how does Constitution/Vitality work? - 05/08/14 03:21 AM
I got it.

It's approximately this (since we can't see rounding):

HP = (Level + 1)/2 * (0.4267x^2 + 5.2194x + 13.1),

where x is constitution. This is followed by flat boni then modified by summed multiplicative bonuses (i.e., lone wolf, glass cannon, picture of health, etc.)

Bam.

Edit: noticed that the level 19 values were almost exactly 10x the level 1 values, then that the level 20 values were about 10.5x.
Hey all

First of all, I want to thank Kustos for providing excellent data. Also, a special thanks to eskuche for the great work on the formula. I continued this excellent work by correcting the HP-data from Kustos with the idea of starting the formula with (Level + 1)/2, and then ran trend analysis using Excel. This gave the following results.

ax^3 + bx^2 + cx + d type (seems accurate till 17 CON):

HP = (Level + 1)/2) x (0,0088 x CON^3 + 0,1772 x CON^2 + 6,8279 x CON + 13,08)

ax^4 + bx^3 + cx^2 + dx + e type (seems very accurate):

HP = ((Level + 1)/2) x (0,00019 x CON^4 + 0,00228 x CON^3 + 0,24781 x CON^2 + 6,57627 x CON + 13,23818)

I hope this helps,
Jesper
Posted By: eskuche Re: So how does Constitution/Vitality work? - 06/08/14 11:44 PM
Great job, just a few points.

I'm not sure you need a third degree polynomal. I'd be much more inclined to believe that rounding accounts for the weird numbers and that the fit is simpler. Finally, if someone could find the HP for a level 1 + 0 constitution that would help immensely with setting the intercept at baseline smile
There's got to be a simpler formula behind the scenes. Keep in mind, this was designed by a human.
Thanks.

I completely agree that there must be something that I/we are missing since it is necessary to go to a fourth degree polynomal to get the number right (+1/-1). Basically this tells me that the "(Level + 1)/2 x ..." is not the entire explanation which might be why it transtales into a crazy formula.

Problem is that I've tested the formula by eskuche and got HP 1.882 accumulated |ABS| error when calculating the theoretical versus actual HP values using the provided dataset from level 19, 20 and 21. However, although I calculated a 2 polynomal formula using trend analysis, the formula by eskuche is actually more accurate than mine, especially at 0 CON, so didn't post mine.

I've also tested the data using regression analysis, but this provided me with some wierd results that I didn't know how to interpret reasonably :-/
Posted By: iru Re: So how does Constitution/Vitality work? - 08/08/14 12:42 PM

Level...CON.....Health from CON.....CONHealth*1.15...Actual HP (Normal mode)
1.......5..........52................59,8..............59
1.......6..........62 (+10)..........71,3..............71
1.......7..........72 (+10)..........82,8..............82
1.......8..........83 (+11)..........95,45.............95
1.......9..........95 (+12).........109,25............109
1......10.........107 (+12).........123,05............123


Some level 1 data for your work. They seem to use an integer, no rounding just cutting the decimals away.
Posted By: Kustos Re: So how does Constitution/Vitality work? - 13/08/14 04:24 AM
Hey guys,

I thought this thread had gone dark after a few days of inactivity. I'm well pleased to see that progress is being made. Thank you so much for your efforts!

It would be nice if we could get a quick word on this from the Devs...?
Posted By: eskuche Re: So how does Constitution/Vitality work? - 14/08/14 04:47 AM
I'm gonna stick by my equations smile

If someone could test 0 CON at level 1 that would be great, though, since we could set the intercept for the equation. I just based my 13.1 off inference.
An alternative explanation can be base health = 7 x Level - 2, implying that level 1 with 0 con would be 5 health.
Hi,

Aren't you making a mistake: you are calculating how Constitution (an therefore, Vitality) changes when changing The Constitution points a Character has, but for ONE Single level. But Constitution grows with the character Level, so it would be more useful to have the formula for the constitution as a function of player level. I don't see how you can derive this by using a single character level in your calculations.

This page mentions the following about "Constitution" in Divinity: Original Sin Enhanced Edition
https://divinity.fandom.com/wiki/Attributes_(Divinity:_Original_Sin_Enhanced_Edition)
"
Constitution
1 Maximum Action Points per point
6.2 Vitality per point and level (+7.13 in normal difficulty due to the +15% bonus)
"
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