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Customs Creation - December 2016

Posted December 17th, 2016 at 12:23 AM by HS Codex

YACE
Author: IshMEL

When designing a custom, everyone eventually comes to the same question: how much should this thing cost? Some ’Scapers seem to have an intuitive sense for costing. I am not one of them. So, like many others before me, I tried to figure out a formula. I call mine YACE, for “Yet Another Cost Estimator.”

What is YACE for? It’s good for coming up with an initial idea of what a unit might cost, which you can then test and adjust. As I’ll go into, there are a lot of things that YACE doesn’t take into account.

To come up with YACE, I did a regression analysis on the data for the (and I’m including Marvel here, but excluding them doesn’t affect the results that much).

I’m no statistician, so bear with my errors in explanation here. A “multiple linear regression” looks at several “independent variables” (in this case, unit stats like attack, range, etc.) and figures out how much of an impact they have on the “dependent variable” (in this case, the unit cost). It also tells you whether any of the variables you picked are “statistically significant”—that is, how likely is it that the relationship between that input and the output is truly causal, or the result of random chance? And finally, it can tell you whether your “model”—the collection of independent variables you are analyzing—is better at explaining the outcome than other models.

By trying various models, I’ve found one that accounts for about 72% of the cost of the official units.

What I couldn’t find to be significant:
  • Heroes vs. squads, although a common squad unit is worth more than other types.
  • Bonding. I tried all kinds of ways to account for squads that bond (with the theory that the cost of bonding is “built in” to the cost of the squad, not the hero), but none of the models found it to be significant.
  • Height. Bigger figures tend to have higher costs, but that’s really because designers are unlikely to create a 40 point huge figure.

What I built into the analysis:
  • Movement bonuses. My initial analysis found that Move wasn’t a significant factor in cost. Which in many ways makes sense—a flying figure has better mobility than a non-flying figure with the same move number. So I came up with “Adjusted Move” (AM) using the following assumptions:
    1. Flying powers multiply the move number by 2.
    2. Stealth / Disengage multiply the move by 1.5.
    3. Terrain movement (Slither, Lava Resistance) multiply the move by 1.25.
    4. Climb is not a factor, since that’s just an adjustment for height.
    For example, Cyprien has a move of 7. With Stealth Flying, his AM is 7 × 2 × 1.5 = 21.
  • Frenzy. This is a pretty easy one to model. Every time you reveal an order marker, you have a 25% chance of taking one additional turn, a 6.25% chance of taking a second additional turn (25% × 25%), a 1.5625% chance of taking three additional turns, etc. Sum those all up and you get 1.333 ... So a Frenzy unit (at 25% chance of success) is worth 33% more than a unit without it. For the analysis, I recosted the Frenzy units at ¾ of their initial cost.
  • Tough / Warforged Resolve. Adding an auto-shield isn’t the same as rolling 3 extra defense, of course, but for the purposes of the analysis I added 3 to their defense.
  • Stab in the Back / Eternal Hatred. A 5% chance of losing Sir Hawthorne means that he should be discounted 10% (since your opponent gets him). As with Marcu, I adjusted their cost up for the analysis.

What’s not considered in YACE:
  • Special Attacks. It’s possible to use YACE to “price” an SA, but I didn’t include SAs in the analysis.
  • Pretty much every other special power. Again, you can use YACE to “model” them when creating your own units, but none of the other powers are accounted for in the regression.

OK, with all that out of the way, the formula is ...

Well, there are two of them.

YACE (Common Squad edition):
  • Points = (20 × Lives) + (2 × AM) + (5 × Range) + (15 × Attack) + (17 × Defense) + (12 if CS) – 115

YACE (Attacks Per Turn edition):
  • Points = (20 × Lives) + (2 × AM) + (5 × Range) + (15 × Attack) + (17 × Defense) + (4 × APT) – 115

I’ve rounded up here for ease of use. “Lives” is either the life number, for a hero, or the number of figures in a squad. AM (Adjusted Move) was discussed above. Range, Attack, and Defense are self-explanatory. In the first formula, CS means “Common Squad”—so if it’s a common squad, add 12 points to the cost. In the second formula, APT means “Attacks Per Turn.” A figure with Double Attack would have an APT of 2, and a regular squad of 4 would have an APT of 4.

Why are there two formulae? The common squad version is statistically better at explaining unit cost. The APT version is more useful for estimating your custom units. It makes sense—a common squad of 3 will have three attacks per turn (12 points for APT), and because they’re common, you’ll have that APT for as long as you have at least 3 units. So it’s a statistically stronger explanation.

However, using the APT version lets you price units that have multiple attacks, including area attacks. Let’s take Syvarris as an example:
  • Points = (20 × 4 Lives) + (2 × 5 AM) + (5 × 9 Range) + (15 × 3 Attack) + (17 × 2 Defense) + (4 × 2 APT) – 115 = 107
Hey, that’s pretty close! (Yes, I’ve cherry picked this example!)

You can use it to estimate the cost of a Special Attack. For example, YACE would estimate that Mimring’s cost is:
  • (20 × 5L) + (2 × 12AM) + (5 × 1R) + (15 × 4A) + (15 × 4D) + (4 × 1APT) – 115 = 146
If we replace his normal attack with the stats for Fire Line (assuming he has 3 figures in a line to attack, for an APT of 3), his estimated cost becomes:
  • (20 × 5L) + (2 × 12AM) + (5 × 8R) + (15 × 4A) + (15 × 4D) + (4 × 3APT) – 115 = 189

When using YACE to design your own customs, you can analyze the price with normal attacks and with special attacks, and take the higher cost.

A word of caution!

While it’s certainly a useful tool, remember that YACE is an estimator. Remember when I said up above that the formula accounts for 72% of the variability in cost? The other 28% is pretty crucial! Statistically speaking, the analysis tells us that most of YACE’s predictions are up to 30 points off (either positive or negative). Some (especially for high-power heroes) will be off by even more.

I hope YACE is a useful part of your custom-building toolkit. In future columns I will show how I use it to price d20-based powers.
Total Comments 4

Comments

Old
Sylvano the Wasabus's Avatar
Nice, thank you!

It's a required tool for custom creators!
Posted December 20th, 2016 at 01:40 PM by Sylvano the Wasabus Sylvano the Wasabus is offline
Old
IshMEL's Avatar
Thanks Sylvano! I have uploaded a spreadsheet so you can try it out here.
Posted December 22nd, 2016 at 02:26 PM by IshMEL IshMEL is offline
Old
TheAverageFan's Avatar
Wow, that's pretty fascinating. Obviously special powers are often where a lot of units' true value is, but otherwise this seems pretty darn useful.

I'm usually okay at guesstimating costs, but if I ever get back into Customs I might run my units through this formula before figuring out a cost from there.

~TAF
Posted December 22nd, 2016 at 09:03 PM by TheAverageFan TheAverageFan is offline
Old
lefton4ya's Avatar
Just found it. Love regression analysis!
Posted October 15th, 2018 at 03:16 AM by lefton4ya lefton4ya is offline
 
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