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Friday, October 30, 2015

Star Wars Armada - Stats Analysis: Critical Effects

By Eric "R1H4" Riha

Welcome back to R1H4's mathematical breakdown of Star Wars: Armada.

In my previous article we talked about expected damage outputs given particular sets/colors of dice. Between articles, I've managed to create an Excel spreadsheet that can run these kinds of calculations dynamically, based on user input. I am proud to present the R1H4 Armada Attack Roller, courtesy of Google Drive.

In this article, we'll look at our chances to trigger Critical Effects. If we take a look at our dice chart again, we can see the chance to trigger a Critical Effect is (thankfully) the same across all dice.

Each die has two Crit faces, giving us a 25% chance with each die roll. Does this mean 4 dice gives us a 100% chance to crit? Nope - I'm afraid not :)

To calculate our chance to roll a Crit on X number any colored dice, we can use one of two methods:

1) Use Binomial calculations to arrive at the exact chance.

2) Use a Monte Carlo simulation to arrive at the approximate chance.

Since these calculations are built into the R1H4 Attack Roller, I'll display the output from there (using a Monte Carlo simulation). If you'd like to know exact numbers, I've found the calculator on especially useful or you can even download a Binomial Calculator on your phone! (yes, maybe I have one of those and, yes, it does make me a colossal math nerd)

Let's take a look at that Gladiator I again. Out of the side arc, we're rolling 4 black dice.

The Monte Carlo approximation swings about ~1% up or down from the true answer, but this time it's super close. A Binomial calculation puts it at 68.36% to Crit.

If we are really counting on triggering those Advanced Concussion Missiles, 4 black dice really isn't enough to hit the 80-20 Pareto rule we discussed in the previous article.

Adding a Concentrate Fire Command to roll 5 black dice gets us closer...

...but not close enough.

How about shots out the front?

Same overall chance to Crit, but only a ~44% chance to Crit on Black dice - which we need in order to trigger those ACMs.

In order to have a relatively reliable shot at triggering those Advanced Concussion Missiles, we would need to have both a Concentrate Fire Token and a Concentrate Fire Command.

Here is where we see a real value in Admiral Screed. On a dual arc shot, we can bring the chance to Crit on the Front Arc shot up to 100% (using Screed's ability) and use a Concentrate Fire command on the Side Arc shot to bring the chance to Crit up to 76% - giving us a very solid attempt at 2 Critical Effects and bringing 4 additional points of damage to the table.

Even without Screed, there is a way to boost our chance to land that Critical Effect with judicious use of our Concentrate Fire Command and Tokens. You may have noticed in the examples above that, while each die added to the roll increased our chance to critically hit, it did so at a decreasing rate.

Going from 4 dice to 5 dice increased our chance by roughly 8%.

Going from 5 dice to 6 dice increased our chance by roughly 6%.

Let's assume we have that Gladiator I in a dual arc shot scenario, with a Concentrate Fire Command ready to go. Where do we add our extra Black Die to maximize our chance to Crit (once or twice)?

If we add the Concentrate Fire die to the Front Arc Shot, it would give us one shot with 3 black dice and one shot at 4 black dice. Compared to adding the Concentrate Fire die to the Side Arc Shot, this combination results in a negligible difference in our overall chance to Crit once, but increases our chances of 2 Critical Effects by a little over 5%.

While this may not seem like much, it is a simple rule to follow that just might give you the edge you need to win - add your Concentrate Fire Commands (and Token Re-Rolls) to the attack with less dice in a dual arc shot.

That's all the math there is for today. Until next time, 01100110 01101100 01111001 00100000 01100011 01100001 01110011 01110101 01100001 01101100 00100000 01111001 01101111 01110101 00100000 01110011 01100011 01110010 01110101 01100110 01100110 01111001 00100000 01101100 01101111 01101111 01101011 01101001 01101110 01100111 00100000 01101110 01100101 01110010 01100110 00101101 01101000 01100101 01110010 01100100 01100101 01110010 01110011.

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