Re: Unit Cost Equation
 

Scott, I can't use magic path cost. (I am interested anyway, if you have a
formula for it.) What I need is the path levels in different columns -- 13
different columns if you have columns for elemental random, sorcery
random, and full random and you include holy and unholy. For example, a
F2E1 mage would have 2,0,0,1,0,0,0,0,0,0,0,0,0. If you don't have
information in that format already, please don't enter it by hand. When I have
time, I will use search and replace in a text editor to reformat the Magic
column into something I can use.

Re: Unit Cost Equation
 

Ah. Mm, okay. I can probably do that.

Re: Unit Cost Equation
 

OK, here's an "update" to Edi's Unit_DB (its actually a spreadsheet). Another tab has been added to include a column for almost everything. If anyone feels like parsing all 198 special abilities!!! Go for it!

Dom2_Unit_DB_Sorttable.xls

Sushi, this should give you more to work with than you need.

Re: Unit Cost Equation
 

EvilDave, here is the output with p-values for the mage commander equation.
As I have alluded to before, I am using a stepwise procedure. I first include all
the predictors I have available at the moment. Then I remove one predictor at
a time, starting from the highest p-values, until all remaining predictors have
p-values less than .10.

<font class="small">Code:</font><hr /><pre>
Coeff. Std. Error Std. Coeff. t-Value P-Value
Intercept -232.976 63.326 -232.976 -3.679 .0004
Morale 7.680 3.028 .155 2.537 .0127
MagicRes 16.015 3.847 .281 4.163 &lt;.0001
Defense 11.466 2.624 .397 4.369 &lt;.0001
ldr_norm .882 .314 .181 2.805 .0060
ldr_undead 1.142 .313 .178 3.643 .0004
ldr_mag 3.476 .466 .440 7.463 &lt;.0001
Strength 4.118 1.608 .137 2.561 .0119
Attack -10.712 3.643 -.225 -2.940 .0041
Precision -5.653 3.108 -.112 -1.819 .0719</pre><hr />

Re: Unit Cost Equation
 

Sushi: From this,I assume that a mage's HPs do not correlate well (or they are not well-predicted) by the gold cost of that mage?

This seems... weird. Very weird.

Re: Unit Cost Equation
 

That makes sense to me. Most national mages have about the same hp: between 10 and 20. It is the increased magic that bumps the price up. I think only jotun and pan have really high hps mages. I may have missed some, but the majority do not. So the difference in hp is a wash compared to other attributes.

Re: Unit Cost Equation
 

Perhaps, but the main reason that the Pan (to take an example) costs so much is not his magic, but his other abilities (HPs, Str, etc.).

I mean, if I tried to use this to make a mage, I could conceivably give them 1000 HPs, and have it cost no more than a mage with 10.

It's an interesting piece of math, but as a way to cost things, I'm not sure how useful it is.

Is there any way to get simple correlative data?

Re: Unit Cost Equation
 

Another explanation is that hp and strength (or some other attribute) are not independant: every high hp mage also has high strength, and the so the curve happens to fit well enough by just using one of the attributes.

Hence the dangers of using interpolation for extrapolation http://forum.shrapnelgames.com/images/smilies/happy.gif

Then again, one could argue that your 1000hp mage with 5str doesn't fit well with dominions.


p.s. I'm not a math genius. I might have it all wrong.

Re: Unit Cost Equation
 

Oh, I think I have a decent enough grasp of the math to agree with you that high-HPs and high-Str correlate to the point that one might overshadow the other in this equation.

However, for the purposes of uncovering a unit cost equation, the correlations need to be explicit.

What I mean is, if you tell me 'HP base is 2/3 Str, with a direct proportion after that', that is a lot more helpful as a gauge of making units. If that is what is necessary to make the equation truly useful, then I'd really like to have that. http://forum.shrapnelgames.com/images/smilies/happy.gif

Re: Unit Cost Equation
 

This equation is meant to give you a guideline for developing or repricing units. If you want to min/max your units you CAN, but it doesn't follow the spirit of the game. For instance, any size 2 unit with more than 17 hps better have a good explanation (like the fact that its a lich).

Re: Unit Cost Equation
 

All you really need to have is the ranges the equation came from, OR just make units that look similar to already existing ones. This equation was never meant to make units significantly more powerful than those that exist. Only to explain the price of the units that DO exist. So, the more your units look like those the more likely they are to be well priced.

To find out how much huge HP amounts are worth, you need to study powerful summoned monsters. . .

Re: Unit Cost Equation
 

However, if I wanted to make oddball units (and, really, modders generally want to make those, not 'more of the same'), this won't help as much.

Re: Unit Cost Equation
 

Thats why I reccomend doing a similar study of the summonables. With their higher skill levels, natural protection, hp, etc. they would show a clearer picture of what these very desiravle characteristics cost. ALSO, we know the approximate gold value of 3 types of gems (death, fire, and earth). Sushi is skilled enough to make non-linear guesses, as is likely important to describe the costs of some units like the iron dragon and tarasque. He probably does not have the time to do everything at once though.

Besides, most modders make new normal units, and as long as their units aren't significantly BETTER than say Vans, there shouldn't be a problem. Vans are pretty tough, if you want to make a unit significantly more powerful you will need another method. But consider the balance of such a race. The race would probably have crappy priests and expensive mages, with no research mage, or something like that. Typical power nerfs appear to be:

-weak priests
-slow "best" national research mage
-crappy national mages
-extra expensive mages
-crappy sacred units
-"capitol only" good units and other units that suck or are extra expensive
-crappy stealth units (no spy, assasin, or stealth commander)
-lack of random path mages
etc.

Anyone else have a good nerfing rule?

Re: Unit Cost Equation
 

OK, here is a new mage formula, with magic paths added. I also made some
procedural changes with modders in mind. Below the main formula are the
composite formulae I created in order to deal with the problem of coefficients
that should not be negative in the context of utility in the game.

Mage Commander (Adjusted R-squared = .95)

Cost = (4.2 * MagicRes) + (.3 * TacMove) + (34.3 * FullRand) +
(34.7 * ElemRand) + (27.1 * SorcRand) + (37.3 * Blood) + (27.5 * Death) +
(28.0 * Earth) + (29.5 * Fire) + (35.1 * Nature) + (32.7 * Astral) +
(34.5 * Water) + (15.2 * Holy) + (25.6 * Unholy) + (11.6 * Air_Prec) +
(2.9 * Att_Def) + (8.5 * Mor_RegLdr) + (6.6 * HP_Str_Prot)

Air_Prec = ((Air - .3) / .8) + ((Prec - 10.6) / 1.9)

Att_Def = ((Att - 9.4) / 2.1) + ((Def - 9.6) / 3.1)

Mor_RegLdr = ((Morale - 11.8) / 1.9) + ((RegLdr - 22.0) / 18.8)

HP_Str_Prot = ((HP - 12.7) / 8.1) + ((Str - 10.5) / 3.2) + ((Prot - 2.9) / 4.9)


Attached is some statistical output for math jocks.

Re: Unit Cost Equation
 

The most recent formula above provides an excellent fit to the data. However,
it may be interesting to see where the formula and the real price in the game
are very different. According to the formula, below are the top ten bargains
and ten worst buys for mages. What do you think?

<font class="small">Code:</font><hr /><pre>
Mage Real_Price Formula

Asmeg Jarl 160 249
Troll King 150 225
Centaur Hierophant 80 153
Sidhe Champion 140 210
Theurg 150 218
Sidhe Lord 280 348
Circle Master 100 164
Master 5 Elem. 190 252
Grand Master 270 330
Garnet Priestess 100 158

Pan 350 283
Arch Theurg 380 300
Niefel Jarl 500 419
Navigator 180 86
Capricorn 350 255
Lizard King 280 183
Hangadrott 400 282
High Priest of Sun 390 264
Anathemant Dragon 360 230
Alchemist 300 106</pre><hr />

Re: Unit Cost Equation
 

Alchemist, Anathemant Dragon, Hangadrott and Navigator have special abilities that are not counted in: alchemy bonus, fire immunity and heat, glamour, and sailing. And as Pan, Niefel Jarl, Carpicorn and Hangadrott are all physically powerful and undercosted, it seems this new formula doesn't take physical stats into account to the same extent than Illwinter does.
Also, is seems that priestly magic should rise exponentially (or at least in a rising curve, if that makes sense) so that Holy 4 is much better than twice Holy 2.

For the cheap ones, it seems part of the problem is that capital-onlyness does not reduce the price. Circle Master is the most cost-effective mage in the game before your modifications, so that might not be as bad as it looks.

Also, quite a many of them have priestly magic. I think 13 of these 20 units have priestly magic. Asmeg Jarl might have some, but Troll King, Circle Master, Pan, Navigator, Capricorn and Alchemist do not. Others do have atleast some, IIRC. You might want to check out holy magic again.

Re: Unit Cost Equation
 

Some of the units that your formula report as overpriced are intentionally overpriced for thematic reasons, such as the Lizard King. I imagine people still buy him occasionally just for the fanaticism. Others, as Endoperez pointed out have special abilitites, Pan has autosummon, Niefel Jarl Cold Aura etc. Among the underpriced some are cheaper because they are rare independents, such as the circle master.

If one were to put any stock into your formula the most conspicous offender is probably the Sidhe champion, since he besides being underpriced has a few extra abilities. On the other hand he is home site only.

Re: Unit Cost Equation
 

Sacred troops and priests have 1/2 upkeep and are generally given costs 25-50% higher. This might explain some of the worst buys.

Sidhe Lord and Sidhe Champ seems to be way overpriced with your formula. Why is the sidhe lord more expensive than the hangadrott? The hangadrott is better in every way except that he can't wear shoes IIRC.

Re: Unit Cost Equation
 

I don't think a mage formula is any more relevant to Niefel Jarls as to Ice Devils. They aren't mages so much as supercombattants with free magic paths... that can go underwater...

Jarls and Ice Devils are similar, but nobody thinks of Ice Devils as mages.

Re: Unit Cost Equation
 

There are some database errors in the magic paths. Oops! http://forum.shrapnelgames.com/image...es/redface.gif The errors are
sporadic, so I doubt that the formula will change much. I will repost after I
correct the problem.

Re: Unit Cost Equation
 

Here is the corrected version.

Cost = (2.7 * MagicRes) + (.6 * TacMove) + (.7 * RegLdr) +
(29.4 * FullRand) + (37.2 * ElemRand) + (26.9 * SorcRand) + (37.5 * Blood) +
(30.6 * Death) + (32.8 * Earth) + (33.2 * Fire) + (37.8 * Nature) +
(31.8 * Astral) + (33.2 * Water) + (16.3 * Holy) + (30.8 * Unholy) +
(2.5 * Att_Def) + (12.9 * Air_Prec) + (11.0 * HP_Str)

Att_Def = ((Att - 9.4) / 2.1) + ((Def - 9.5) / 3.2)

Air_Prec = ((Air - .3) / .7) + ((Prec - 10.6) / 1.9)

HP_Str = ((HP - 12.8) / 8.1) + ((Str - 10.5) / 3.2)


Here are the mismatch lists. The lists changed a little, so I also include the
ones that dropped off.

<font class="small">Code:</font><hr /><pre>Mage Real_Price Formula

Starspawn 150 294
Sorceress 110 200
Centaur Hierophant 80 166
Asmeg Jarl 160 241
Troll King 150 229
Master 5 Elem 190 269
Witch Doctor 80 144
Sidhe Champion 140 203
Amber Clan Mage 160 220
Circle Master 100 160

Garnet Priestess 100 153
Theurg 150 210
*Sidhe Lord 280 274
Grand Master 270 317


Warrior Mage 200 142
Pan 350 290
Hydromancer 180 117
Starspawn 280 216
Navigator 180 102
High Priest of Sun 390 306
Lizard King 280 179
Capricorn 350 247
Anathemant Dragon 360 232
Alchemist 300 122

*Arch Theurg 380 339
Niefel Jarl 500 443
*Hangadrott 400 361


* These had database errors earlier.</pre><hr />

Re: Unit Cost Equation
 

Since there is a Starspawn in both lists, maybe it would be better for you to make sure which one is which... I haven't played R'lyeh in a long time, and can't remember which one is cheaper. Also, which Sorceress is that on the upper list?

Re: Unit Cost Equation
 

Endoperez, your hunch was right. The starspawns got switched somehow, so
the more expensive one matches well. Same problem with the sorceresses. http://forum.shrapnelgames.com/images/smilies/frown.gif
Oh, well, maybe next weekend.

Re: Unit Cost Equation
 

Wow, I hadn't thought of THAT! I just didn't know which one was which. Well, it's nice to be of help, even when I don't realize I'm helping... http://forum.shrapnelgames.com/images/smilies/laugh.gif

Re: Unit Cost Equation
 

Sushi!
Sorry about the errors in the database (hope I didn't cost you more time than I saved). Great work!
I agree, after Sushi's equation contains all the variables he's prepared to list, the next step is to remove those units whos cost is thematically altered. They aren't representative of the truest cost equation, because they are altered.
The cost should be accounted for by the fact that they have holy magic (for the mages only).

Anyway ATTACHMENT

Attached is the updated costing spreadsheet. I'll make it cleaner whenever I know the equation is as complete as its going to get. . .

Re: Unit Cost Equation
 

As much as I hate to disagree with one of the game developers...

Using your own formulae, Sacred Commanders and Holy Priests have no extra gold cost.

At a guess, because the Sidhe Lord has Air and Nature magic. The IW formula assumes equal paths have equal costs. Sushi's doesn't.

As for my own thoughts, most of these have small path levels. If I read the formula correctly, the path costs do not follow IW's formula, which reduces multiple paths at low levels.

The Circle Master can be removed, as it is not an offender. He should cost about 160; in fact, at 100 he is the most under-costed mage in the game, on a percentage basis.

The Master of the 5 Elements is the most obvious mage that I base my comments on.

Re: Unit Cost Equation
 

Again, Sushi, the issue that I'm seeing with your cost analysis is that higher path levels aren't being given their properly higher costs. According to IW, magic paths have progressively increasing costs, and you have a simpler 'cost-per-level' scale.

If you go by IW costing, 2 in a single path is worth almost twice that of 1 in 2 paths.

About the only other concern I have is: where does the High Seraph fall?

Re: Unit Cost Equation
 

The High Seraph comes out costing 210 with Sushi's equation. If you download the spreadsheet I posted you can check for yourself.

I agree, that ideally his equation would price the lvl 2 paths seperately from lvl 3 paths.

Re: Unit Cost Equation
 

210? Nah, too low. As far as d/ling stuff goes, I'm not on my own computer right now, so it's not possible.

Re: Unit Cost Equation
 

There isn't an IW formula to speak of. If you are referring to the mod guidelines they are intended to be rough guidelines not a formula to follow slavishly. Kristoffer wrote both the guidelines and put the price tag on 90% of the units. Most units are priced according to 'what do comparable previously existing units cost' 'is there some specific thematic reason why their price should differ from X Y or Z' etc. Holy units are usually priced higher whether it is mentioned in the modding guidelines or not.

Re: Unit Cost Equation
 

Holy units, yes. I have never argued this point.

Holy commanders, no. You can show that, using the modding guidelines, Holy commanders don't cost any more than non-Holy commanders.

Now, Sacred commanders that are not priests (like the Shaman) generally do cost more.

As for there not being an IW formula, there are the modding guidelines. And if we are not to follow those in any more than the most general way, why have them? And to ask for a more-or-less accurate formula to follow when costing units is not 'slavish'. It's a way to ensure that units are equitable on a given scale.

Several of us are trying to establish a formula that will horizontally balance the commanders in the game. Are you saying that we should not?

I mean, if I followed the mod guidelines to the letter, a Holy-2 priest that are 50g come out to be 75g (50g, plus a 50% increase incost for being Sacred). A Daughter of Avalon, made using those mod guidelines, cost 180g (90g for magic + 30g for commander + 50% for being Sacred).

To finish, not a single commander that is a Priest, and several commanders that are sacred, has a cost that can be computed from the current mod guidelines. As such, if you insist that such a price increase is necessary, I hereby ask for better guidelines so that modding can be done better and more properly in the future.

Re: Unit Cost Equation
 

Use common sense, extrapolate from other units etc. I am a little sceptical to if you are liable to arrive at better or more balanced costs by assigning them from a formula. In order for the formula to be 'shown' to be balanced you have do one of two things
1. compare the prices the formula gives to preexisting prices
2. scrap the previous prices and experiment with the formula until you think that it results in reasonable prices.

In the first case you are accepting previously made judgements based on rough estimate and a certain amount of arbitrariness, in the second case you are comparing the newly derived formula based values to your own rough estimate of the relative worth of the respective units. In either case you are making estimates based on your intuitions. You can't escape making judgement calls, either you do it in when you induvidually assign prices to units or you do it when you check your to see if you formula produces reasonable costs. Add to this that it is a tall order for any formula to take in account the very variable effects of the various abilities in dominions and the synergies that might or might not develop and I think you will have serious practical problems in defining a formula that even begins to approach what you seem to be aiming for.

My personal experience from board games PnPRPG and CRPG is that the kind of possibilities present when you mod a nation in dominions is very hard to manage according to a set formula. I think rough guidelines and common sense, while not perfect or infallible, are preferable, in part because they do not impart the false promise of impartiality.


Edited for clarity

Re: Unit Cost Equation
 

Scott,

The method Sushi is using is pretty sophisiticated. His model is not as sophisticated as it could be. To help him make his model better, you could take his copy of my adapted edi's Unit_DB.xls, and parse out all of the special abilities. That would help a LOT.

I assure you that unless you make a unit that is more like a summonable (with crazy special powers) than a normal unit, you should get a pretty good result.

IF I where doing the model, and I'm not, I would use the columns in the database marked E1, E2, E3 to figure out magic path costs, because they would be more accurate. That would add some 20-30 equations to his model, however, and that would take time. Also, he needs to remove thematically prices units.

Finally, the ONLY way anyone will ever get an equation for the relative cost of very powerful units, is to somehow normalize the costs of the summonables. I can give you a few tips, Scott, if you'de like, but I'm not gonna teach you to use regression software (most people take a 3 hour college course to learn...).

I would say, that this is the best method currently available. Using it and the IW guidelines should give you some idea of how to price your units.

Re: Unit Cost Equation
 

The_Tauren13,

What method did you use to get to your equation?

Re: Unit Cost Equation
 

The one at the beggining of this thread? Well, I just quicklky slapped it together in the format (offensiveness*defensiveness)^(1/2)*other because if there were only 2 stats in the game, HP and damage, a very good cost formula would be (HP*damage)^(1/2).
I had hoped to mold it into something that could take a unit with just about any stats and give a reasonable cost for it by asking a series of simple questions: 'what attack value is worth twice 10 attack?', 'what defense value is worth twice 10 defense?', etc. and then modifying the equation as nescesarry.
However, Anime Girl was the only one who seemed interested in it, and then scott hijacked the thread to talk about commander costs again, so I just dropped it.