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Customs Creation - May 2016 (Bonus Article)

Posted May 2nd, 2017 at 10:44 AM by HS Codex
Updated May 11th, 2017 at 07:22 PM by Xotli

Special Powers
Author: IshMEL

Back in October, I introduced YACE (Yet Another Cost Estimator), a formula to estimate the cost of your custom. This month, I’ll take a look at how to use the formula to “price” special attacks and d20 powers.

The purpose of the YACE formula is to give you an initial idea of a unit’s cost. You’ll still need to test, of course, and no formula can replace that. But, you need to start somewhere, and YACE can help get you in the right ballpark, or whatever sports metaphor you’d like to use for “close but not exact.”

To review, here’s the formula, arrived at through regression analysis:
  • Estimated Points = (20 × Lives) + (2 × Adjusted Move) + (5 × Range) + (15 × Attack) + (17 × Defense) + (4 × APT) – 115

  • “Lives” is life for heroes, or number of figures for squads
  • “Adjusted Move”: multiply the move number by 2 for Flying, by 1.5 if Stealth / Disengage, and/or by 1.25 for terrain bonus (Slither etc.)
  • “APT” is “attacks per turn.” For instance, Syvarris gets 2, and the Grut Arrows get 3.

You can play around with the formula with this spreadsheet.

As I last wrote, the formula will take into account the base stats, and everything that’s mentioned above – flying, stealth / disengage, slither, and multiple attack powers. But what about everything else that we want to put into our customs, like Crazy Awesome Special Attack and you-may-roll-the-20-sided-die powers? Well, we can use YACE to estimate what the value of those powers are, too. We just need to translate them into equivalent attack and defense numbers, making some assumptions and using a bit of math. (It’s not hard—I promise!)

Using YACE to Estimate Special Attack Costs

Now let’s say we’re designing a figure with a range of 1 and a powerful melee attack, and we want to add a ranged special attack power. Here’s how we use the YACE formula to take into account the special attack:
  1. Use YACE to get a base cost estimate with the figure’s melee stats.
  2. Replace the melee stats with the special attack’s range, attack, and APT.
  3. Whichever number is higher should be our initial estimate.

Let’s use Nilfheim as an example, and pretend that we’re designing him from scratch. (Trivia: which other Hero has the same base stats as Nilfheim?) His base stats, when fed into YACE, give us an estimated cost of 196 points. Now let’s add Ice Shard Breath Special Attack:

Range 5. Attack 4. When Nilfheim attacks with his Ice Shard Breath Special Attack, he may attack 2 additional times. He cannot attack the same figure more than once.
So we go back into YACE, change the range to 5, attack to 4, and Attacks Per Turn to 3. Which gives us a new estimate of ... 194! Losing 2 attack dice is about the same estimated “cost” as adding 4 to the range, with 2 additional attacks. So, if we were designing and testing Nilfheim, we’d start with the slightly higher estimate of 196. (Also, we can pat ourselves on the back for “balancing” the normal and special attack.)

Note: To estimate an “explosive” (area) special attack, use the number of figures affected as the Attack Per Turn. For a zig-zag special attack like Arcane Bolt, figure the range on the farthest figure the attack can theoretically reach.

Using YACE to Estimate Offensive D20 Powers

What about d20 powers? Here it gets a little trickier. Let’s assume we’re designing Braxas as an example, and we’ve come up with Poisonous Acid Breath:

Instead of attacking, you may choose up to 3 different small or medium figures within 4 clear sight spaces of Braxas. One at a time, roll the 20‑sided die for each chosen figure. If the chosen figure is a Squad figure and you roll an 8 or higher, destroy it. If the chosen figure is a Hero figure and you roll a 17 or higher, destroy the chosen Hero.
We know that PAB has a range of 4, and is like making 3 attacks in one turn, so we can use those numbers in our formula. But how can we translate this power into equivalent attack dice? In other words, how many attack dice would Braxas have to roll in order to get a statistically similar outcome as PAB?

To start, we’re going to make some assumptions about the kinds of figures that Braxas is attacking:
  1. Braxas is attacking 2 squad figures and 1 hero.
  2. The average defense of a squad figure is 2.96—so let’s say these two squad figures have a defense of 3.
  3. The average hero has 4.45 lives and 3.64 defense. So let’s give this hero a life of 4 and a defense of 4.

Let’s take the squad figures first. Since they only have 1 life, we only need to cause 1 wound. Fortunately there’s a helpful table from AliasQTip to tell us the probability of an attack causing at least 1 wound.

Braxas needs a roll of 8 or higher to destroy the squad figure, which is a 65% chance of success. Looking at our table across the 3 defense row, we see a pretty close match—an attack of 4 has a 65.5% chance to cause one wound. So PAB is equivalent to an attack of 4 on a squad figure with a defense of 3.

Now, the hero. The queen needs a 17 or higher to destroy it, which is a 20% chance. And we need to cause at least 4 wounds to destroy it. AliasQTip’s table only goes up to 3 wounds, so let’s open up this one instead.

This table gives us the probability of getting at least X wounds, given any combination of attack and defense up to 10/10. (I honestly can’t remember where I got this data from, if anyone recognizes it please let me know so I can give credit where credit is due.)

Okay, so we now we have to look for an attack that has about a 20% chance to cause at least 4 wounds against 4 defense. Seven attack has a 0.208 or 20.8% probability—just right! So if Braxas rolled 7 attack dice against a hero with a defense of 4 and 4 life remaining, she would have about a 20% chance of destroying it, which is the same as Poisonous Acid Breath.

Of course, the two aren’t equivalent in the game. If Braxas actually made such an attack, she would very likely cause at least 1 wound, but if she rolls lower than 17, that hero is unscathed. And of course, not all heroes are at 4 life and 4 defense. The ability to destroy a high-life or high-defense hero is what gives this bad breath its bad reputation.

Let’s put it all together. Rolling for PAB against 2 squaddies and 1 hero is about the same as making 2 attacks with 4 dice, and 1 attack with 7 dice. Since (4 + 4 + 7) / 3 is 5, we can estimate that (given these assumptions), PAB is about the same as a triple 4 ranged attack of 5 dice.

YACE gave us an estimated cost of 204 points for Braxas with her base stats. We’re estimating PAB is 4R/5A/3APT, so including the breath attack gives her a higher cost estimate of 227. So we could use 227 as our initial estimate when testing our custom “Braxas.”

Using YACE to Estimate Defensive D20 Powers

We can use YACE not only for offensive d20 powers, but also for defensive powers. This time, we’re designing Isamu and want to account for Vanish 9:

If Isamu is attacked and at least 1 skull is rolled, roll the 20-sided die to vanish. If you roll 1 – 8, roll defense dice normally. If you roll a 9 or higher, Isamu takes no damage and may immediately move up to 4 spaces. Isamu can vanish only if he ends his vanishing move not adjacent to any enemy figures.
Again, we’re going to do some statistics, and then find the equivalent defense dice Isamu would have to roll to get the same probable outcome. Let’s say Isamu has been attacked with 3 dice (the average attack value is 3.2, actually). Here are the possible outcomes:
  1. He rolls for Vanish successfully, and takes no wounds. He has a 60% chance of succeeding at the roll (we’ll assume that he’s not boxed in and can Vanish somewhere).
  2. He fails the Vanish roll (40% chance) and rolls his measly 1 defense die. This non-Vanish branch has two possible outcomes:
  1. He takes no wounds (which our table says is a 25% chance against 3 attack) or,
  2. He takes at least 1 wound (75% chance).

When we have a “forking path” of possible outcomes, we multiply the probability of what happens first (failing on the Vanish roll) by what happens next (succeeding or failing on the defense roll). There’s a 40% chance Isamu fails the Vanish roll, and a 25% chance that he’ll subsequently succeed on his defense anyway. 40% x 25% = 10%, so 10% of the time we’ll end up in scenario 2a. Similarly, if he fails Vanish (40%) and then fails his defense roll (75%), that’s 40% x 75% = 30% chance of hot ninja death.

(Just as a check, the total of all the branches should equal 100%, and they do: 60% Vanish + 10% fail-Vanish-and-defend-anyway + 30% shameful-destruction.)

Going back to our table, to figure out the defense equivalent of Vanish, we’re looking for something close to a 30% chance to cause at least one wound. With a defense of 5 Isamu would have a 32.1% chance of defeat, while with a defense of 6 that would drop to 25%. Five is closer, so let’s run with that.

Let’s see what this does to our dishonorable ninja’s cost when we run it through YACE. His base stats get us a whopping –6. On the other hand, when we estimate that his defense is statistically equivalent to 5 defense, his estimated cost becomes 62! That’s quite a difference (and it’s why he’s quite a bargain, and why no formula will ever accurately predict every unit’s final cost).

So there you have it. There are of course lots of other special ways that Heroscape changes the way you count dice, and I recommend Sisyphus’ Probability Tables for further study.

I hope this brief tutorial proves useful to you in estimating the cost of your customs.
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