Pricing mages

[elmokki]

EDIT: I was going to post this on unitgen thread, but made a mistake and by the looks of it this crap forum doesn't allow removing threads.

Being an economics student with courses in econometrics and having statistics as a minor and being a nerd I wanted to run a regression on mage prices to get a decent model to base UnitGen prices on. I've tried this once earlier and back then it was an utter failure.

Now I gathered new data of 63 mages. These are human or humanlike (monkey, abysian, lizard, caelian) chassises. Some mages with very notable extra abilities got left out, like anything with a forge bonus and tuatha/van mages which would be easily thugged.

I ran a linear regression with variables:
- Picks: Direct picks of magic the mage has, ie non-randoms
- Randoms: 100% chance randoms the mage has (linkeds obviously are 2 or 3 depending on link size)
- Holy: Holy levels the mage has
- Max: Maximum reachable magic level with 100% randoms

Intercept - 9.432022355 - significant at 80% confidence level
Picks - 28.98576911 - significant at 99% confidence level
Randoms - 24.0029813 - significant at 99% confidence level
Holy - 20.16660489 - significant at 99% confidence level
Max - 20.5083636 - significant at 99% confidence level

All variables except randoms and obviously intercept are significant at 99.9% confidence level too, which is fairly huge, but I'd be happy far lower anyway.

Intercept was less significant than the others by far, but seeing how it's about 10 I'm fairly happy with the result since every single chassis in the list should be worth about 10 gold as a troop with decent equipment.

R^2 was about 0.925 so it's a fairly good model as a whole too, but obviously the prices will rarely hit vanilla prices spot on. It's no wonder of course since the stock nation mage prices are valued for the nation, not with a general model in mind.

That said, if you use this model for determining a mage price you'll probably get a mage price that is -+20% or so from what the price of the mage should be. Replace the intercept with a suitable price for the chassis though (like a jotun giant should probably get 30 or something as intercept)

[shatner]

Would you mind breaking down the implications of this for the folks who aren't hip to the linear regression lingo?

[Torgon]

Originally Posted by elmokki

Now I gathered new data of 63 mages. These are human or humanlike (monkey, abysian, lizard, caelian) chassises. Some mages with very notable extra abilities got left out, like anything with a forge bonus and tuatha/van mages which would be easily thugged.

You could actually include these options as well. Just model them as dummy variables (i.e. either a 1 or 0). Might be interesting to see what value was placed on forging bonuses when everything else about the mage is taken into account.

Heck if you really wanted to get creative, see if there's any difference in value for different schools of magic. Is astral valued higher than nature? Death?

[elmokki]

Originally Posted by Torgon

You could actually include these options as well. Just model them as dummy variables (i.e. either a 1 or 0). Might be interesting to see what value was placed on forging bonuses when everything else about the mage is taken into account.

Heck if you really wanted to get creative, see if there's any difference in value for different schools of magic. Is astral valued higher than nature? Death?

I mentioned I've tried this before. Back then the data was about 30 mages (mostly primary mages and notable secondaries compared to this data having nearly all humanlike mages without very notable special abilities) and my variables at first included all separate paths. I can tell you that did not end well. Some of the paths had NEGATIVE coefficient so having them actually lowered the mage price according to the model, and some were insignificant at 95% too. This is probably just due to having a fairly small sample to go with. Some paths just appear in so few and specific cases that their value gets skewed easily even with the whole game as your sample.

I also had thuggability boolean variable for vanir etc, sacred boolean variable to signify being sacred (Rishi and Crone of Avalon for example are sacred mages but not priests) and different path amount variable. They were all pretty much insignificant.

Regardless, I added a few mages and added old age and forge bonus as boolean variables. Neither of them is significant at 95%, old isn't significant even at 80%. Coefficient for old would be just about 3, but for forgebonus it'd be 18. R^2 falls to 0.910.
-> Conclusion: Those don't affect price significantly according to the sample.

[elmokki]

Originally Posted by shatner

Would you mind breaking down the implications of this for the folks who aren't hip to the linear regression lingo?

Very roughly put you can calculate a fairly accurate mage price by calculating:

9.5 + 29 * direct magic picks + 24 * 100% random picks + 20 * holy levels + 20.5 * maximum reachable level at a magic path with 100% randoms

...and the R^2 of 0.925 means it's a fairly good model.

For more accurate coefficients get them from the first post.

Here are what the variables would be for Grand Master of MA Marignon:
direct picks: 5 (3F, 2S)
random picks: 1 (110% randoms, only the 100% part counts and it obviously counts as one)
holy levels: 2 (2H)
maximum reachable: 4 (3F + that 100% random can give fire)

-> 300.5, actual price in game is 270.

This regression does not take into account linked paths, and the amount of them in vanilla/cbm is fairly small so it's pretty much pointless to try to regress it. It should be mentioned though that I made the coefficient on randoms scale with linked path link size to get more sensible prices (linked 3? mage was pretty damn cheap compared to the potential)

For actual pricing based on useability not path types but path type combos would matter A LOT (1S-1B-1W mage vs 1A-1F-1D mage for example), but that hardly matters since a) you don't have to have the prices be exactly the same for each power level of a mage. Cheaper mages buff a nation and more expensive ones nerf it b) if those mages aren't going to be used in combat it doesn't matter even nearly as much which you can recruit since they're equivalent in research.

[Torgon]

Originally Posted by elmokki

I mentioned I've tried this before. Back then the data was about 30 mages (mostly primary mages and notable secondaries compared to this data having nearly all humanlike mages without very notable special abilities) and my variables at first included all separate paths. I can tell you that did not end well. Some of the paths had NEGATIVE coefficient so having them actually lowered the mage price according to the model, and some were insignificant at 95% too. This is probably just due to having a fairly small sample to go with. Some paths just appear in so few and specific cases that their value gets skewed easily even with the whole game as your sample.

I also had thuggability boolean variable for vanir etc, sacred boolean variable to signify being sacred (Rishi and Crone of Avalon for example are sacred mages but not priests) and different path amount variable. They were all pretty much insignificant.

Regardless, I added a few mages and added old age and forge bonus as boolean variables. Neither of them is significant at 95%, old isn't significant even at 80%. Coefficient for old would be just about 3, but for forgebonus it'd be 18. R^2 falls to 0.910.
-> Conclusion: Those don't affect price significantly according to the sample.

Although just the fact that all of these variable are insignificant is an interesting piece of information. Basically, its just a window into how the developers went about pricing the mages in the game, even if it doesn't necessarily lead to a better predictive model.

[legowarrior]

Have you taken into account the era? Looking at the Pan through the ages, it seems you get less and less for same price as you progress through the ages.

[elmokki]

Originally Posted by legowarrior

Have you taken into account the era? Looking at the Pan through the ages, it seems you get less and less for same price as you progress through the ages.

I tested by adding boolean variables MA and LA. EA was left out to avoid perfect multicollinearity, but statistically the model is still 100% correct since that is just assumed to be in the intercept (18.87 now).

Basically the base mage price goes up by about 9, but MA reduces it by about 9 too and LA by about 11. However, neither MA or LA variables are statistically significant even at 80% confidence level. The new intercept is valid at 80%, but not at 95% (and probably not at 90% either). Thus I can safely assume that era does not affect mage prices in general.