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Wisdom - is it worth the skill points? #40784
19/03/03 06:31 AM
19/03/03 06:31 AM
Joined: Mar 2003
Posts: 27,492
Canada
Raze Offline OP

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Raze  Offline OP

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Joined: Mar 2003
Posts: 27,492
Canada
I've heard opinions either way, but for some masochistic reason decided to ferret out the cold hard facts.

Warning - the following post contains math.

Wisdom levels
1 ) 2% experience bonus, clvl 6
2 ) 4% experience bonus, clvl 12
3 ) 6% experience bonus, clvl 18
4 ) 8% experience bonus, clvl 24
5 ) 10% experience bonus, clvl 30

From this web page on Divine Divinity's site, the experience required for each level is;

E = 1000*(level^3 - level)/3


If you put a point into Wisdom at level 6 (70k exp), you will get a 2% bonus. To get to level 12 you need (572k - 70k) = 502k experience, but due to the bonus, you only have to earn an additional (502k / 1.02) = 492.16k. This means you would reach level 12 after earning (492.16k + 70k) = 562.16k experience points.
In this context, earned experience means experience not counting any Wisdom bonus.

Doing the same for each Wisdom skill level, you can calculate the required earned experience to reach a specific experience value with Wisdom bonus. If you graph the results of experience with Wisdom (Ew) versus earned experience (E), you would end up with a set of 5 connected line segments with slopes of 1.02, 1.04, 1.06, 1.08 and 1.1 (excluding experience for character levels less than 6, which would just be a line segment of slope 1.0).

The appropriate values are (in thousands of experience points);

Level (Ew)

E

Ew

6

70.00

70

12

562.16

572

18

1875.62

1938

24

4386.94

4600

30

8451.75

8990

** E0, Ew0

30 (E)

8990.00

9582.07


The first line is at the start of level 6, before Wisdom comes into play. The next 4 lines show how much experience must be earned in order for that value plus the Wisdom bonus to bring you to levels 12,18,24 and 30. The last line indicates that if you earn enough experience to get to level 30, the Wisdom bonus will not be enough to get to the next level (9920k). That fact is used implicitly in the next calculation.


When does the Wisdom skill actually pay off?

Let's say you have earned E experience, which is dE more experience than you had earned at level 30 (call this E0, the value in the line above with the '**' ).

dE = E - E0

with the Wisdom bonus, this increase in earned experience results in an additional

dEw = 1.1 * dE = 1.1 * (E - E0) = Ew - Ew0

of experience points.


At some point the earned experience points E will correspond to a character level L.

E = 1000*(L^3 - L)/3

Assume that the experience bonus from Wisdom is enough to bring you up k number of levels, to L+k, where L and k are both integers.

Ew = 1000*[ (L+k)^3 - (L+k) ]/3

If you substitute these equations into the two above, you get an equation in terms of L and k, which can be solved numerically.


When do you get one extra level?
with k = 1, L = 37.41

If you earn enough experience to reach level 38, the Wisdom skill results in an a bit more than one extra level.


When do you get two extra levels?
with k = 2, L = 64.14

If you earn enough experience to reach level 65, the Wisdom skill gives you a tad more than two extra levels.


Conclusion;

Unless you go completely insane using resurrect on the dragon riders at the end of the game, maxing Wisdom will only result in one extra level. It takes 5 skill points, and gives back one skill point and 5 stat points. Leveling up will be a little faster, though.

If you have nothing better to put skill points in, this is a fair trade. When I started, I kind of assumed Wisdom would eventually have a better pay off, but with so many spare skill points, I can hardly complain that it was a huge mistake. At the end of the game I had 10 un-used skill points, even after maxing one skill I didn't use and topping off a few I didn't need. If you would use those 4 skill points (net) elsewhere, don't bother with Wisdom. Most of the posts I recall seeing from people who have finished the game, though, have mentioned having skill points left over. They would be better used in Wisdom than not at all.

Any points in Wisdom will help, it just may not result in a full level increase. Each level you go up would come a little bit earlier in the game than it would otherwise, which could potentially come at an opportune moment. Also, if you find something with wisdom on it, you don't have to trade a skill point for the bonus experience. A low level of Wisdom might not be enough to result in a full extra character level, but it could get you a level higher than you would have been. For example, if you earn enough experience to get to level 49 and just a hair more than two thirds of the way to level 50, Wisdom level 1 would be enough to get you up to level 50. Not a huge difference, but it could help out a bit at the end of the game.

BTW, if you ignore Wisdom until level 30 then max it, earning enough experience to get to level 45 will be enough to get an extra level. With the 5 level jump on becoming the Divine One, that is not vastly different than level 38 (from always increasing Wisdom when available).
If you missed putting a point in Wisdom right away when leveling up, there is no need to kick yourself over the 'lost' bonus experience.


one more thing...
4 skill points (net loss) could be considered a lot to give up.

Do you need to max Wisdom to get any benefit?

The great thing about graphics calculators is that you can change a couple constants to variables, and solve the equation above for L and k assuming any level of Wisdom.

If you put skill points in Wisdom up to a certain level, then stop, when will it be enough to gain an extra level (k=1)?

Wisdom Level 1, L = 151.01
Wisdom Level 2, L = 76.16
Wisdom Level 3, L = 51.91
Wisdom Level 4, L = 41.44
Wisdom Level 5, L = 37.41 (to re-cap)

With Wisdom at level 3, you need to earn enough experience to reach level 52 for it to result in an extra level. This would put it very close to the end of the game, or past it, for most people. Level 3 looks like a waste of skill points.

With Wisdom at level 4, you need to earn enough experience to reach level 42 for it to result in an extra level. This is a little later than level 38 (for a maxed Wisdom), but certainly early enough to be useful. You may not get much benefit clearing out the Dark Forest, but you would by the time you become the Divine One.

At level 4, you would have a net loss of only 3 skill points, and an extra 5 stat points. This could be considered the sweet spot, depending on how many extra skill points you have; almost the same benefit as maxing Wisdom, but costing one less skill point.

Re: Wisdom - is it worth the skill points? #40785
19/03/03 12:59 PM
19/03/03 12:59 PM
Joined: Mar 2003
Posts: 62
Belgium
Purple_Heart Offline
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Belgium
Nice Raze!
Good job. I am glad to get some stats on it, i had the feeling that indeed it was not really a good skill unless you had left-overs.

Thanks again for confirming.


.
Re: Wisdom - is it worth the skill points? #40786
19/03/03 02:16 PM
19/03/03 02:16 PM
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Venom Offline
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I've read this post on the old forum, and as a math student I must say i enjoyed it thoroughly !

Keep up the good work... (btw u a student 2? )

Re: Wisdom - is it worth the skill points? #40787
19/03/03 03:56 PM
19/03/03 03:56 PM
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Posts: 1,943
Misty (smoggy) Mountains
NeroJB Offline
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NeroJB  Offline
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Yeah that is kinda freakishly over analyzed...wow

Re: Wisdom - is it worth the skill points? #40788
19/03/03 07:32 PM
19/03/03 07:32 PM
Joined: Mar 2003
Posts: 60
Washington DC USA
Tiffin Offline
journeyman
Tiffin  Offline
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Washington DC USA
Elegant!


Tiffin
Re: Wisdom - is it worth the skill points? #40789
19/03/03 07:50 PM
19/03/03 07:50 PM
Joined: Mar 2003
Posts: 1,943
Misty (smoggy) Mountains
NeroJB Offline
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that is another way to put it

Re: Wisdom - is it worth the skill points? #40790
19/03/03 11:49 PM
19/03/03 11:49 PM
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Posts: 161
Middle Earth
Gandalf Offline
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Middle Earth
Whlie Raze was figuring all that out, I completed the game and played it a second time! j/k
Great post, Raze!



Re: Wisdom - is it worth the skill points? #40791
26/03/03 04:29 PM
26/03/03 04:29 PM
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Buddah Offline
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Great analysis, but you forgot to factor in that as you go up levels the amount of experience you gain for killing monsters goes down. I don't know what the formula is, but I notice that after leveling up the amount I get for killing a common monster often goes down. That means that going up levels faster will decrease the total experience you get in the game, which makes wisdom worth even less.

Re: Wisdom - is it worth the skill points? #40792
26/03/03 05:00 PM
26/03/03 05:00 PM
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R
Reptile Offline
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Reptile  Offline
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Definitely worth it. I did level faster. Did not see any decrease in xp for
critters. I would not play the game without taking the skill personally, but
that is just my preference.

Re: Wisdom - is it worth the skill points? #40793
26/03/03 05:03 PM
26/03/03 05:03 PM
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Posts: 2,548
Belgium
joliekiller Offline
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joliekiller  Offline
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experience goes down.... when i was about lvl30, killing orcs dindt give me experience anymore


Joliekiller, paladin on a crusade against (almost) all evil.
Re: Wisdom - is it worth the skill points? #40794
26/03/03 06:11 PM
26/03/03 06:11 PM
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Posts: 7,702
Germany
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kiya Offline
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kiya  Offline
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Going down with XP pts is due to game balance - the higher your level and the lower the enemie's lvl is the less skill pts you get. At lvl 34/35 I only got XP from Giant elite orcs.
That's why I killed every monster in Rivertown before entering the Castle - and did the Dark Forest afterwards (stronger enemies, higher lvls). And had end lvl 52 at the end of the game (maxed out wisdom, too).
Kiya

Re: Wisdom - is it worth the skill points? #40795
26/03/03 08:01 PM
26/03/03 08:01 PM
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Posts: 244
kathythekrazykat Offline
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Did you use the resserect thing?


well...so long and thanks for all the info
Re: Wisdom - is it worth the skill points? #40796
26/03/03 08:07 PM
26/03/03 08:07 PM
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Germany
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kiya Offline
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Nope, that's cheating in my way to play.
Kiya

Re: Wisdom - is it worth the skill points? #40797
15/04/03 05:15 AM
15/04/03 05:15 AM
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Melbourne, Australia
HandEFood Offline
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Post note:

Even if you find a magical glorious artifact with Wisdom (5) on it at the beginning of the game, you will still only gain about 1 level by the end.

Re: Wisdom - is it worth the skill points? #40798
15/04/03 12:36 PM
15/04/03 12:36 PM
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HelasYmanube Offline
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I think we've reached that "Stuff it, do whatever you fancy" moment on this question. Personally I shove 3-4 points in and look for items that grant the other two (they can benefit you earlier than spending a skill point would otherwise allow).

I like the idea of levelling faster. And one can't argue against that fact.

Still, it may be that you'd rather spend the points elsewhere, but choosing wisdom is better than leaving them spare, as has already been mentioned.

Raze : *hommage* for the math


"Are you looking at me?"
Re: Wisdom - is it worth the skill points? #40799
04/05/03 09:58 AM
04/05/03 09:58 AM
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Australia
Krezack Offline
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Krezack  Offline
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Australia
Holy crap, Wisdom sucks more crap than I first gave it credit.


Nordom: "A question, Morte: how do you stay aloft?" Morte: "Flatulence, you stupid polygon."
Re: Wisdom - is it worth the skill points? #40800
05/09/06 07:19 PM
05/09/06 07:19 PM
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mosthated Offline
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Hey Raze...if you could run a little hypothetical for me on this it would be greatly appreciated.

At level 8, I found a +1 wisdom item. I wrote it at level 8, and added a point to wisdom at level 9. At level 12 I put another point into Wisdom, giving me 3 wisdom. At level 15 I found a second +1 wisdom istem, so I put it on and used it, giving me 4 wisdom. Then at level 18 I put a final point into Wisdom and I have had 5 wisdom ever since. So what will my bonus be at the end? SHould I continue to use/wear the items?

So here is my breakdown.
Level 8 - Wisdom Level 1
Levels 9-11 - Wisdom Level 2
Levels 12-15 - Wisdom level 3
Levels 16-17 - Wisdom level 4
Level 18+ - Wisdom Level 5

How long, if at all, should I continue to use the items?

I don't have a problem with them becoming outdated as they are both equipped with some decent charms and both have a free charm slot for the next decent "very large" charms I will find.

What do you think?



1!2@3#4$5%6^7&8*9(0)-_=+[{]};:'"\|,,.>/?`~
Re: Wisdom - is it worth the skill points? #40801
06/09/06 06:17 AM
06/09/06 06:17 AM
Joined: Mar 2003
Posts: 27,492
Canada
Raze Offline OP

Larian Studios
Raze  Offline OP

Larian Studios

Joined: Mar 2003
Posts: 27,492
Canada
I'll have to redo the above, since I had to reset my programmable calculator's memory awhile ago, and don't still have the original written derivations. I will edit this post tomorrow (hopefully) and PM you when it is done.

Re: Wisdom - is it worth the skill points? #40802
08/09/06 01:15 AM
08/09/06 01:15 AM
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Posts: 14
mosthated Offline
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Hey right on man but if its a crapload of work font worry about it. Thanks either way.


1!2@3#4$5%6^7&8*9(0)-_=+[{]};:'"\|,,.>/?`~
Re: Wisdom - is it worth the skill points? #40803
08/09/06 07:24 AM
08/09/06 07:24 AM
Joined: Mar 2003
Posts: 27,492
Canada
Raze Offline OP

Larian Studios
Raze  Offline OP

Larian Studios

Joined: Mar 2003
Posts: 27,492
Canada
It wasn't that much work, but yesterday I was too tired to do math when I had some free time, and today I had company over.


As a limiting case, if you start the game by finding 5 items with a Wisdom bonus, you would have to earn enough experience to reach level 31 before the bonus would give you a full level, and 62 before it would result in 2 bonus levels.


With your values, by the time you earn enough experience to reach just over level 33, the Wisdom bonus will have given you an extra level. You would not be able to get a full 2 level bonus until you had earned enough experience points to reach just over level 62.5.
How long you continue to wear the items with a Wisdom bonus is up to you. At least after you hit level 34 the bonus is less significant, though it will help you level a little faster.

EDIT: Lets' say at level 25 you decide to replace one or both of the pieces of equipment with a Wisdom bonus. Dropping down to level 4 Wisdom would increase the amount of experience you would have to learn to just over level 38, while level 3 Wisdom would make it character level 48.6. You wouldn't be delayed terribly much by removing one of the pieces of equipment (an extra 5 levels), but both would put achieving the bonus level fairly late in the game.


Calc, the spreadsheet program in OpenOffice, contains an equation solving function which is good enough for this application. I did a couple test cases on my calculator, and then did up a spreadsheet in Calc, which anyone can use to check various scenarios. Since the experience required to reach a given level is proportional to the cube of the level, though, you are probably not going to get significantly different results than the cases discussed above.

Wisdom spreadsheet (11KB) - ods file, OpenOffice Calc v2.0.3

Note: There are columns in the spreadsheet for experience, which will not match the numerical values in the original post. I dropped the (1000/3) term, since it cancels out anyway, so you would have to divide the displayed value by 3 to get a result in thousands of experience points.

EDIT: I have updated the spreadsheet to be able to handle the removal of equipment with a Wisdom bonus, though have not done extensive testing. This can allow you to determine what effect changing equipment might have on the Wisdom bonus.

Last edited by Raze; 10/09/06 07:17 AM.
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