Rebellions are built on hope

Targeting Network: Calculating Damage Probabilities For Your Attacks

In a previous article, I presented some basic odds & estimation techniques for Imperial Assault’s dice. These can be helpful when trying to figure out the capability of your and your opponent’s dice pools and the effectiveness of rerolls. But these techniques don’t properly calculate the odds of the whole attack math, which includes spending surges for modifiers.

If you’re new to Imperial Assault, you may have seen expected damage graphs from Matt Yellen’s IA Calculator posted in conversations around the IA community. The calculator allows you to specify attack & defense die pools, the range of the attack, surge abilities that can be used by the attacker (extra damage, Pierce, Accuracy) and additional static modifiers. It then does a brute-force calculation for every possible result and spends surges intelligently: If an attack doesn’t have enough Accuracy, a free surge will be spent on a surge ability for Accuracy before a surge ability for damage or Pierce. On the results graph that appears when you calculate, roll your mouse pointer over each point on the curves to reveal the percent chance of those attacks doing at least X damage, where X is the value on the X-axis.

When using the calculator, make sure you specify a basic defensive pool. Doing so will help give a more accurate representation your attack results. I typically look at a pair of results: One result that is versus 1 black die and one result versus 1 white die. I’ve found that some deployment groups that rely more on surges have noticeably worse attack outcomes versus a white die due to the white die’s 50% chance of producing at least 1 evade result. Likewise deployment groups that have one single red die will have noticeably worse attack outcomes versus a black die.

If you play around with the calculator you’ll get a feel on how it works. Take a few moments to familiarize yourself with it before continuing with this article.

TK-421, why aren’t you at your post?

In my previous post about IA dice, I claimed that that you can expect that Elite Stormtrooper figures will roll at least 5 Accuracy roughly 50% of the time. This claim is based solely on the Accuracy values listed on the dice and doesn’t factor in the surge ability to add 3 Accuracy. Using the calculator we can more accurately predict the odds.

Below is a graph that shows the damage probabilities at targets that require 5, 6 or 7 Accuracy. The dark-gray box lists the probabilities for each attack to do at least 1 damage. We can use this value as the probability that the attack will hit (not miss or do 0 damage).

Red: 5 Acc., vs. 1 black die
Green: 5 Acc., vs. 1 white die
Blue: 6 Acc., vs 1 black die
Yellow: 6 Acc., vs 1 white die
Cyan: 7 Acc., vs 1 black die
Magenta: 7 Acc., vs 1 white die

You can also combine results in the calculator in order to simulate multiple attacks from the same deployment group onto a shared target. Below the Calculate button you’ll see a button that will indicate combining the last two previous results. To see how Elite Stormtroopers would fair against a shared target, calculate a single result 3 times versus the same defensive settings, then combine those three results. The graph below shows that if all three Stormtrooper figures attack the same target, that target has roughly the same 1-in-2 chance to take at least 5<damage> whether or not the target defends with 1 black or 1 white die.

Red: Combined 3 attacks at 5 Acc., vs 1 black die
Green: Combined 3 attacks at 5 Acc., vs 1 white die

However these calculations for Elite Stormtroopers aren’t 100% accurate. The IA Calculator has no way to factor in the effects of rerolls. The ability Squad Training could further improve a Stormtrooper’s odds for doing damage. The calculator also doesn’t calculate the likelihood of applying other effects, like Stun, Blast or Cleave. It also doesn’t have a way to apply negative modifiers to the attack and defense results, like how Zillo Technique can reduce the amount Pierce applied by 2 to a minimum of 0. You’ll need to calculate or estimate the effect of these extra modifiers on your own.

Switch to Targeting Computer

After you have created an army, I recommend taking a few moments to plug each of your figure’s attack stats & calculate attacks against some basic defenses. There’s a few specific results that I recommend you should commit to your memory that will be especially helpful to know during a game.

I recommend memorizing the expected damage value that have about a 50% chance of occuring — what I call the “coinflip value”. This will give you a good indicator on about how much damage your attacker can give out without forcing you to memorize each set of odds for every potential damage output.

For melee figures, memorizing the coinflip value versus 1 black & 1 white die gives you a clearer picture of what your figure can potentially do when attacking.

For your ranged attackers, you should calculate the coinflip value for your attacker’s minimum & average Accuracy. The minimum Accuracy for a figure is the lowest possible Accuracy that figure can roll for an attack combined with any static Accuracy bonuses. The average Accuracy is the average value that can be rolled by all the dice in the dice pool, rounded to the nearest whole number, plus any static Accuracy bonuses.

Learning the damage probabilities at a figure’s minimum Accuracy reveals how much damage your attacking figure can put out when all surges are spent on adding damage or Pierce. There will be times in games where you will want to defeat an opponent’s figure before it can activate. Moving your ranged attacking figure within the minimum Accuracy ensures that your attacker will have it’s best chance at maximizing damage output.

In addition to the coinflip value, you should know the odds that your attack will do at least 1 damage from average Accuracy — what I call the “average Accuracy to-hit odds”. This knowledge will help you gauge whether or not an attack attempt at that range is worth attempting without any additional Accuracy modifiers from Command cards or other figures’ abilities. For some figures that have a dice pool of 3 or more, the average Accuracy to-hit odds may be significantly higher than 50%.

Never Tell Me The Odds

As an exercise, we’ll make like Threepio and annoy Han Solo with some statistical analysis:

Either shut him up or shut him down! 

Han Solo’s minimum Accuracy is 4; his average rounded Accuracy is 7. (You can learn more about average rounded accuracy in the IA Dice Primer post.)

Red: 4 Acc., vs 1 black die
Green: 4 Acc., vs 1 white die
Blue: 7 Acc., vs 1 black die
Yellow: 7 Acc., vs 1 white die

Looking at the chart above for Han Solo, you can reliably expect Han to do at least 5<damage> about 50% of the time against single-die defenders when attacking within his minimum Accuracy of 4 — he has a 42% chance vs 1 black die & 45% chance vs 1 white die. However at 7 Accuracy, his coinflip damage value is 4<damage> and his average Accuracy to-hit odds are 85% vs 1 black die and 65% vs 1 white die. (Remember that these odds do not reflect Han rerolling an attack die from his Rogue Smuggler skirmish attachment.)

Focused on the Kill

If your army has easy access to Beneficial conditions — yes, I’m talking about you, Rebel & Mercenary players — you can calculate more exact results of attacks your figures make while Focused or Hidden. For your primary attackers, you should be aware of how improving odds for additional rolled Accuracy & surges amplifies your attacks. For most figures a Focused attack will average an additional 2<damage> and 2 Accuracy to use.

Returning to our Han Solo exercise: When Focused, his minimum Accuracy rolled is 5 and the average rounded Accuracy is 9.

Red: 5 Acc., vs 1 black die
Green: 5 Acc., vs 1 white die
Blue: 9 Acc., vs 1 black die
Yellow: 9 Acc., vs 1 white die

Han’s coinflip value is 6<damage> for both his minimum Accuracy and his average rounded Accuracy value. (At 5 Accuracy, Han has a 40% chance vs 1 black die & a 37% chance vs 1 white die to do at least 7<damage>, which is a bit low to be considered a coinflip value in my opinion.) Compared to Han’s average Accuracy to-hit odds at 7 Accuracy we calculated earlier, Focused Han’s average Accuracy to-hit odds at 9 Acc remain at 85% vs 1 black die but drop to 60% vs 1 white die.

That a Focused Han Solo can reliably hit targets from 9 spaces away is one of the many reason why he is one of the best figures in the game. He doesn’t need to know the odds because the odds are so in his favor.

I recommend that you do calculate the Focused attack results of your support figures: Gideon Argus, Regular Alliance Smuggler, Elite Jawa Scavenger, R2-D2, Mak Eshka’rey, Hera Syndulla, etc. In some end-game situations, you may need to decide whether or not you’re likely to gain more victory points from your Focused Gideon finishing off one of your opponent’s figures instead of controlling objectives on the map.

Always In Motion is the Future

Finding the coinflip values is one of the first things I do when testing designs for changed or new IACP deployment cards. Calculating these values for the figures in your armies before games will help you do the arithmetic in-game for defeating your opponent’s figures in the most optimal way possible.

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