How much should a Random-5 Mage cost?

[Scott Hebert]

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.

[Teraswaerto]

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 ]

[Graeme Dice]

Originally posted by Scott Hebert:
I'm now going to go through each mage in the game, and calculate their costs. Any discrepancies (positive or negative) will be reported.

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.

[Scott Hebert]

Originally posted by Teraswaerto:
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.
Or that's what I think anyway.

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.

[Scott Hebert]

Originally posted by Graeme Dice:
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.

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.

[Scott Hebert]

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!

[PDF]

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.

[Scott Hebert]

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.

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.

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.

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.

[Scott Hebert]

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.

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

[Graeme Dice]

Originally posted by Scott Hebert:
The probability that the Master of the Five Elements is a 1/1/1/1/1/1 is 0.375. That is worth 90g.

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.