How much should a Random-5 Mage cost?
 

Believe me, it's lower than you think.

Short answer: ~160g.

How did I come up with such an answer? Well, I took the modding guidelines from Illwinter's site, and figured out the probability of each type of mage you can get out of a random-5 mage. I then multiplied the cost of such a mage by the probability of it appearing. I then summed them together, and that should be the cost of the mage.

Assumptions made for calculating price:

For initial path above 3, I simply extrapolated the cost of a 4 path by adding 60 (the increment) to the 3 path, and I added 60 again for the cost of a mage with 5 in a path.

For additional paths over 3, I used the same path costs as the third path.

If either of these assumptions are incorrect, better data would be appreciated. The way I have calculated them, it would be easy to switch the costs of the different mage builds to get a different answer.

Other interesting data from this experiment:

Probability of getting a 5-random mage with at least a 3 in any one path: 11.99%.
Probability of not getting a 3 in any one path: 88.0%
Probability of not getting at least a 2 in any one path (all ones): 20.5%

(Note: This also assumes that the mage has 'typical' (i.e., bad) stats.)

The distribution looks like Chi-square, but I don't retain the statistical knowledge to make use of this. I took a rather 'brute force' approach to calculating the probabilities.

I'm now going to go through each mage in the game, and calculate their costs. Any discrepancies (positive or negative) will be reported. Further comments will NOT be made. That is, I am not going to tell the designers of the game that this needs to change, or that needs to change. I am simply going to observe the existence of discrepancies (as the designers have identified mage-cost mechanics).

I hope to have this done sometime before the weekend is over.

Re: How much should a Random-5 Mage cost?
 

The costs of national mages and troops are not solely based on stats. Overall balance of the nation(s) is more important, and thematic considerations play a part too.

*edit*

Or that's what I think anyway.

[ June 19, 2004, 19:58: Message edited by: Teraswaerto ]

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">I can tell you of one discrepancy that you will probably find right away. The nations that existed in Dominions 1 will tend to pay less for the same magical power than the themes and nations that were added in Dominions 2.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Well, I'm doing this mainly to help modders. For example, in just the relatively short time I've been doing this, I think I'm noticing a similar cost reduction for a capital-only vs. non-capital-only commander. Something of this nature would be VERY helpful for modders to know.

Something else I've noticed is that if you are a priest, the cost of being a priest subsumes/replaces the cost increase for being sacred. (Cf. Amazons)

However, one of the reasons I am not going to do much if any evaluation of the discrepancies found is precisely because stats don't paint the whole picture.

We'll see. This should be an interesting experiment, no matter the resulting data.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">While I don't doubt you, Graeme, I don't have any knowledge as to what was in Dom1 vs. Dom2 (though I believe themes were introduced in Dom2), and so unless someone tells me what nations were added, I won't know the difference. http://forum.shrapnelgames.com/images/icons/icon12.gif

Re: How much should a Random-5 Mage cost?
 

Oh, before I go any further, I'd like to thank whoever made the Unit_ID.xls file (I believe it was Maltrease..?), without which this project would be a lot more tedious and time-consuming.

Thanks! http://forum.shrapnelgames.com/images/icons/icon7.gif

Re: How much should a Random-5 Mage cost?
 

I'm not sure your method is "fair". I mean, having the average of the cost of an Abysian Blood mage, an Atlantian Water mage, and a Vanheim Smith is not a good estimate of a random mage, because variety/flexibility itself is a thing that should be paid and that noone in my 3 examples gets.

What is the nearest thing to a random-5 mages I think of is Arco Mystic, but he has only 3 random elements + 2 fixed Astral . He costs 180, and is usually considered rather underpriced.
I'm not sure a random-5 mage would fit thematically anywhere or be "balanced", but I suggest a cost of at least 240 gp.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Flexibility is not necessarily a good thing, however. The flip side of being flexible is not being reliable. This, to me, is at best a wash.

I don't know how else I could evaluate them. I honestly don't see how it _can't_ be fair to look at them strictly on the numbers. I'm not going to be making any qualitative judgements as to the various numbers I generate.

With the specific example of a 5-random mage, the most common occurrence is a 2/1/1/1 mage (with a 0.513 probability), and that has a price tag set by Illwinter at 160g. Again, if you think the 4th path's 1st level should cost more than the third path's first level, that's your opinion, but I have no rubric to deal with, so I'm trying to extrapolate from the current rubric.

Really, I'm not sure how I could calculate the price of mages with random picks aside from the method I'm using. Strict probability and a weighting of price based on those probabilities seems the 'fairest' way, to me. No, it doesn't take into account the other variables involved, but then the very lack of those other variables in the analysis may point to the way to quantify those variables.

<font size="2" face="sans-serif, arial, verdana">I don't know, personally. You can look at the Master of the Five Elements and the Celestial Master from Tien Chi to see the most likely costs. I haven't gotten to them in my analysis yet, but they're costed pretty well.

I think the main point I'm unfortunately failing to get across is how not-good the 'average' random-5 mage is. You have to buy on average 6 5-random mages before you get one that has a 3 in a single path. That is something that most if not all of your examples above have that the random-5 mage most likely does not, and that's a difference of 60g. There's a greater than 70% chance that the 5-random mage doesn't even have 2 paths at 2. All of these lower the price, believe it or not.

Unfortunately, by the way that Illwinter currently has their pricing scheme up, randomness is not valued as highly as specific picks, if those specific picks are at all concentrated.

I'll do the Master of the Five Elements right now to show you how I'm doing this.

Commander: 30g
Holy-2 Priest: 20g
The probability that the Master of the Five Elements is a 2/1/1/1/1 is 0.625. A 2/1/1/1/1 Magic Path is worth 140g. Multiply 140 by 0.625, and you get 87.5.
The probability that the Master of the Five Elements is a 1/1/1/1/1/1 is 0.375. That is worth 90g. Multiply 90 by 0.375, and you get 33.75.
Add these together, and the Master of the Five Elements should cost 171.25g. Its actual cost is 190g. This can lead to several conclusions, which I've said before I really won't go into at this point. I agree with Gandalf that interpretation of data is not as useful to IW as the data itself.

I will say that any mage that has only 1 random pick that I've done so far (mostly independent due to the structure of the .xls file) I've matched with Illwinter's costs about 90% of the time. I also calculated the cost of the Jade Sorceress as 182.25, which is quite close to IW's cost of 180.

In any event, I think I will continue on as I have until I receive a different method of evaluating the grey areas in the current rubric.

Re: How much should a Random-5 Mage cost?
 

Can anyone tell me if the picks of the Loremaster are indeed random? That's a 4-Random mage (with a large research bonus, IIRC) for 150g (calculated cost: 142.27).

Also, does anyone know of a large detriment to the Circle Master?

Also, I note that the Master of the 5 Elements Random is only in Elemental. This guarantees him to be a 2/1/1/1 mage. So:

Commander: 30
HH: 20
2/1/1/1 Magic: 130
That comes out to 180.

Almost finished with the stats. http://forum.shrapnelgames.com/images/icons/icon7.gif

[ June 20, 2004, 00:01: Message edited by: Scott Hebert ]

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Are you sure about that cost? The average cost for a mage with 1 magic skill and 2 holy magic is more around 80-90 gold.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Very likely. I've seen 1-1-1-1, 2-1-1, 2-2 and 3-1, although I'm not sure I've ever seen an all-elemental or an all-sorcery. So it's either 4 x 1? or 1Elem + 1Sorc + 2 x 1?.

<font size="2" face="sans-serif, arial, verdana">If you're looking for hidden weaknesses in the Circle Master that would explain his low cost, he hasn't any - at least, none I'm aware of.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">The way I calculated the cost for a 1/1/1/1/1/1 magic path was as follows:

First path, first level: 30 points.
Second path, first level: 20 points.
Third path, first level: 10 points.

These values are all from the Modding Guide on Illwinter's site. As stated in the original post, I am going to assume that further paths do _not_ depreciate like the first paths. From this:

Fourth path, first level: 10 points.
Fifth path, first level: 10 points.
Sixth path, first level: 10 points.

Add those all up, and you get 90g. Multiply this by the probability of getting a Master of the Five Elements with this (0.375), and you get 33.75. I then calculated the value of a 2/1/1/1/1 magic path, as follows:

First path, second level: 90 points.
Second path, first level: 20 points.
Third path, first level: 10 points.
Fourth path, first level: 10 points.
Fifth path, first level: 10 points.

This comes to 140 points. If you multiply this value by the probability of getting a Master of the Five Elements with those magic paths (0.625), you get 87.5.

Now, if we add together the 87.5 and the 33.75, we get a total of 121.25. This is the magic path cost for a mage with 5 paths at 1, plus 1 random pick. Add to this the cost for Holy-2 (20), and the base cost for the commander (30), and you will get the total calculated cost for a Master of the Five Elements.

121.25 + 20 + 30 = 171.25

This is not its actual cost (190). I'm not exactly sure what is causing the increase in cost, but I have my ideas.

I am sorry if what I posted before was confusing. I'm not that good at explaining myself. Of course, this is all academic if the Master of the Five Elements, as is listed in the unit spreadsheet can only get an Elemental pick.

Note that if the random is restricted to an Elemental pick, the cost of the magic path increases.

Are there any problems that people can point out with my math? As I said before, I'm doing this through a rather brute force approach to the probabilities, and since this is involving a lot of arithmetic, I may be making silly errors.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Thank you. http://forum.shrapnelgames.com/images/icons/icon7.gif This helps...

<font size="2" face="sans-serif, arial, verdana">All right... because it's shockingly low.

One other question. Can anyone confirm whether or not the Galderman's random picks can be the same? I know that when I've played Mitgard, I've never seen the Galderman get 2 in the same path for his randoms.

Re: How much should a Random-5 Mage cost?
 

The reason that the Circle Mage has such low cost for the paths is because it is a rare site that is hard to find.

You have to take that into account.

Look at Celestial Master's for a cost estimate of what you are doing for Randoms.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">I understand your methodology, but you should realize that it will fail on just about every mage that has only one point of magic. This is especially true for the holy-2 mages with one skill point. The theurg acolyte is a perfect example. He has 1 astral, two holy, and costs 90 gold. Some other examples are the Mictlan priest(BHH-80), the Serpent Acolyte(NHH-80), the Shaman(NS-110), the Master of the way (W?-100) and so on.

Re: How much should a Random-5 Mage cost?
 

Here is the list of those mages in the game whose calculated gold values are different than their actual gold values. Note this assumes a 30g base cost for the commander. For some commanders (Vanheim and Jotunheim in particular), this obviously will skew the data. For those whose actual cost is over their calculated cost, I will at some point make a list of how much the 'base' commander would cost, with no magic.

The following gives a ratio of how close the two values are to each other. If the value is under 1, the actual value is lower than the calculated value. If the value is over 1, the actual value is higher than the calculated value. If anyone is interested in the raw values, I can also post those.

If a Commander is not listed, that means either that their listed cost is equal to their calculated cost, or there was not sufficient information to make the determination.

Something else that has been ignored is factoring in Sacred. There are only two examples where the listed 50% increase would make the data make more sense, and there are numerous examples where the data makes much less sense if this is taken into account. When it is noted that the direction in the Modding Guidelines is for sacred _units_, not necessarily commanders, I believe that Sacred on a commander does not change its value.

Amber Clan Mage: 0.94
Amber Clan Priest: 0.9
Asmeg Jarl: 1.14
Dwarven Smith: 0.88
Jade Sorceress: 0.98
Shaman: 1.38
Troll King: 0.83
Vaetti Hag: 0.92
Adepts of any of the 3 Orders: 0.89
Alchemist: 3.33
Azure Mage: 0.83
Circle Master: 0.56
Conjurer: 0.75
Enchantress(N###): 1.19
Enchantress(NN##): 1.27
Fire Lord: 1.67
Gnome: 0.97
Ice Druid: 1.29
Illusionist: 0.92
Lore Master: 1.05
Navigator: 2.25
Sage: 1.33
Sea Father: 1.21
Shadow Seer: 0.88
Sorcerer(Indep): 1.03
Sorceress(FE): 1.04
Sorceress(AA): 0.89
Warrior Mage: 1.67
Witch: 0.83
Anathemant Dragon: 1.09
Anathemant Salamander: 1.18
Warlock: 1.01
Warlock Apprentice: 1.07
Newt: 1.13
Sanguine Acolyte: 1.25
Sanguine Anathemant: 1.16
Demonbred: 1.13
Mystic: 0.99
Astrologer: 0.88
Consort: 1.6
Coral Queen: 1.28
Deep Seer: 0.75
King of the Deep: 1.05
Empoisoner: 1.38
Hierodule: 0.8
High Priest of C'tis: 1.5
Lizard King: 1.56
Keeper of the Tombs: 1.1
Sauromancer(F): 0.82
Marshmaster: 1.03
Sauromancer(N): 0.82
Shaman: 1.38
Harab Elder: 0.9
High Seraph: 0.6
Seraph(non-RoR): 0.71
Seraphine: 1.13
Ermorian Cultist: 0.9
Grand Thaumaturg: 0.89
Jotun Gode: 2.5
Jotun Skratti: 1.08
Vaetti Hag: 0.92
Gygja: 1.38
Niefel Jarl: 1.72
Norna: 1.16
Black Sorcerer: 1.17
Ear of the Lord: 1.4
Sorcerer: 1.09
Sorceress: 1.22
Witch Doctor: 0.89
Voice of the Lord: 1.13
Bard: 1.25
Monk: 0.6
Sidhe Champion: 1.4
Sidhe Lord: 1.47
Tuatha: 1.05
Crone of Avalon: 0.79
Daughter of Avalon: 0.67
Mother of Avalon: 0.93
Paladin: 2.6
Chartmaker: 1.13
Missionary: 1.2
Royal Navigator: 0.99
Goetic Master: 0.95
Grand Master: 0.79
Witch Hunter: 0.94
Friar: 0.8
Initiate: 1.08
Priest King: 1.09
Black Dryad: 1.13
Panic Apostate: 1.33
Dryad(HH): 1.38
Pan (NEra): 1.46
Centaur Hierophant: 1.6
Pan (base): 1.21
Pandemoniac: 1.33
Serpent Priest: 0.79
Arch Theurg: 0.9
Battle Deacon: 1.8
Theurg: 0.75
Theurg Acolyte: 1.13
Star Child: 1.42
Starspawn(HHH): 1.11
Starspawn: 1.15
Master of the Way: 0.95
Master of the Dead: 0.94
Celestial Master(S&A): 0.94
Master of the 5 Elements: 1.06
Minister of Rituals: 1.25
Celestial Master(base): 1.05
Illuminated One: 1.33
Member of the Second Tier: 1.14
Black Acolyte: 0.8
Black Priest: 1.04
Vanherse: 2
Vanjarl: 1.47
Hangadrott: 1.19
Galderman: 0.98
Dwarven Smith: 0.88
Vanadrott: 1.69

There ya go. http://forum.shrapnelgames.com/images/icons/icon7.gif

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">All right... because it's shockingly low.</font><hr /></blockquote><font size="2" face="sans-serif, arial, verdana">Mages are sometimes greedy, sometimes not. Eg, look at the costs and descriptions of Alchemists (300 gp) or Adepts of Pyriphlegeton (180 gp) - both come with only 3 magic picks. Obviously there's more than pure mathematic formulas at work. http://forum.shrapnelgames.com/images/icons/icon12.gif

Or rarity - eg, the standard Seraph in both Caelum themes. 100 gp -> 140 gp. Otherwise same stats.

<font size="2" face="sans-serif, arial, verdana">They can't. One is elemental magic, one is sorcery.

Re: How much should a Random-5 Mage cost?
 

Hate to distract from the discussion(I applaud the effort, incidentally. You're even more pedantic than I, and you've clearly put plenty of work into this), but I just have to know:
Are these calculations for ExaltedMOD, or have you got some other MOD in mind, one with hedge mages in it?
I have a soft spot for hedge mages, I do. Masters of the miscellaneous and ineffectual.
[/Interruption]

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Erm... maybe I haven't explained myself clearly again. I am sorry.

To take the theurg acolyte:

Commander: 30
Astral 1 Magic: 30
Holy 2: 20
That comes to 80g. That is his calculated cost. His actual cost is 90g.

Serpent Acolyte:

Commander: 30
Nature 1 Magic: 30
Holy 2: 20
That comes to 80g (again). That is his calculated cost, which equals his actual cost.

The Shaman:

Commander: 30
Nature 1 Magic: 30
Astral 1 Magic: 20

That comes to 80g (again). This is his calculated cost. His actual cost is 110g.

The Mictlan Priest is the same as the Serpent Priest, as far as the pricing rubric is concerned. Therefore, his calculated price is equal to his actual price.

The Master of the Way is a little trickier, because he has a random selection. He is calculated as follows:

Commander: 30
Holy-2: 20
Magic Path:
1/8 of the time, he is a WW mage. WW costs 90. 1/8 times 90 is 11.25
7/8 of the time, he is a W(~W) mage. W(~W) costs 50. 7/8 times 50 is 43.75.
Totaling the magic path cost comes to 55.
Total: 105. 105 is his calculated cost, and 100 is his actual cost.

I'm sorry, but I don't see how my methodology is failing with the above examples. Could you explain perhaps a bit better so that I may understand?

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">While the Alchemist is obvious an outlier, I think it is rather obvious why. The Adept of Pyriphlegeton is actually priced exactly correctly, according to the modding guidelines.

And yes, that means that SS### is worth the same as FFF, in the designers' minds.

<font size="2" face="sans-serif, arial, verdana">The 140g is the 'correct' price for a 2/1 mage. I have yet to understand why Caelum's mages are so cheap.

<font size="2" face="sans-serif, arial, verdana">Ah, That means my calculation for the Galderman is slightly off. You'd think with 20 examples I'd see that pattern... http://forum.shrapnelgames.com/images/icons/icon9.gif

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Heh. I'm not exactly sure how to take that 'pedantic' comment. As for a lot of work, I hardly think so; 6 hours of work to me is not 'a lot'.

<font size="2" face="sans-serif, arial, verdana">Actually, this all came about exactly how the subject suggests: I started to wonder how much a Random-5 mage _should_ cost. When I started the Exalted mod, I didn't know that there were modding guidelines on Illwinter's site, and that gave me a way of being able to calculate it. The only problem at that point was figuring out the relative probabilities involved. That took me an hour or two this morning, and a call to my twin brother, who's had statistics courses more recently than I. Once I figured that problem out, I thought to myself: You know, 1 or 2 random picks would be a lot easier to figure out, and thus the project was born.

I find this all fascinating. An application of this will certainly be how to price the Solars. If by your mention of 'hedge mages', you meant a high number of random picks, I like them too.

I hope this might help to see more of them in the future. http://forum.shrapnelgames.com/images/icons/icon7.gif

Re: How much should a Random-5 Mage cost?
 

Only one way to take a comment about being pedantic: Slowly and methodically.
Either way, I think it's fairly obvious why Caelum's mages are underpriced: They're a magocracy. They rely on mages more so than on mammoths, raiding capabilities, sneaky cold-dominion pushing Seraphines, and pretty much any other individual merit they possess as a nation(Though not the sum of all of them).
The mix of air and water magic also makes Caelum's High Seraphs SPECTACULAR battlemages, particular for hit and run raids. Cast quickness and three rounds worth of Thunderstrike/Orb Lighting, retreat, repeat. Support with antimissile amulets, robes of shadows, and a staff of storms for best long-term results.
Now, if Ulm were to get underpriced mages, I'd be seriously concerned, but since Caelum is one of the top 3 magical superpowers in the game, it's only natural for them to be cost-efficient.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">*chuckles* Sure. http://forum.shrapnelgames.com/images/icons/icon7.gif

<font size="2" face="sans-serif, arial, verdana">While this may be so, I have my own opinions of Caelum's mages.

<font size="2" face="sans-serif, arial, verdana">Caelum is one of my favorite nations, so I'm rather familiar with how to use their strengths, I would think. I won't comment on the balance of the Caelumite mages, though; against the purpose of the thread.

Your Ulm comment is funny, however. The Master Smith's calculated cost is 140 points without the forge bonus.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Are you saying that it's only the _magic_ on the master of five elements that's worth 90? I thought you were talking about the actual cost of the unit being only 90 gold.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Er, yes. The magic path cost of a hypothetical 1/1/1/1/1/1 Master of the Five Elements would be 90g. You would have to add to this the cost of being a commander, and the cost of being a Holy-2 priest.

I am sorry if I confused you.

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">I'm not so sure it's so obvious. The closest indy mage is the Magus, same magic picks at 90 gp. To make up for the cost difference, you have to use the Alchemist to transmute 27 fire gems (or 42 earth), which looks like a hefty amount to me. Add 2 (or 3) more/turn to cover the extra upkeep. And 25 (or 40) more for the required lab. You've got to be gem-rich to take advantage of an Alchemist.

<font size="2" face="sans-serif, arial, verdana">Just look a few Posts back, someone already replied to this. It's all about nation balance. And also for thematic reasons.

Frankly, I wouldn't be surprised to learn that IW did only come up with these guidelines when they introduced modding in Dominions 2. I can't get rid of the impression that they didn't use anything but 'flair' to get these mage costs out of their minds. http://forum.shrapnelgames.com/images/icons/icon12.gif

Re: How much should a Random-5 Mage cost?
 

<font size="2" face="sans-serif, arial, verdana">Is it worth its cost? I don't know. Is it worth more than 90g? Certainly. The Alchemist's ability is unique in the game, outside of one national pretender and one unique artifact. And it's not like you'd ever have more than one.

<font size="2" face="sans-serif, arial, verdana">Well, since people seem to be making judgements, I'll level in on mine. The magocracy argument for Caelum, to me, means they should get cheap mages, or powerful mages, but not both.

When I compare to other 'magical powers' in the game, I still don't find much reason to believe Caelum's mages should be undercosted to the level that they are. Maybe I'm not comparing to the right nations...?

<font size="2" face="sans-serif, arial, verdana">Frankly, I _would_ be surprised. There's too much correlation. That'd be interesting... would anyone be interested to see the correlation coefficient of the data? http://forum.shrapnelgames.com/images/icons/icon7.gif

From this data, I would find it rather unbelievable that IW doesn't have guidelines, similar to (if not exactly) the guidelines they posted for mods, that they follow internally.

I'm going to start trying to analyze the information for threads that might be able to be condensed into other guidelines helpful to modders.

Re: How much should a Random-5 Mage cost?
 

The circle master is one of the best deals in the game.

Re: How much should a Random-5 Mage cost?
 

Yes, NTJedi. The Circle Master is. I'm glad people are able to use the numbers I came up with.