Wednesday, December 23, 2020

Toryn Farr: A Rebel Haiku

Much better than Swarm
Imperial jealousy
Dagger through their squads
Haikus are cooler than regular love letters, anyways
So let's break down what this post is about.  Based off of Eric's Skilled First Officer breakdown, I decided that I wanted to write up a lengthier post about one of MY favorite officers, Toryn Farr.  And rather than just expand on her in the Rebel officers section, I figured I'd bring her out here where I can get a bit more in depth on what makes her and her abilities so good.  Which means we get to bring everyone's favorite subject back! That's right, it's math!
Image chosen because I both love baseball and enjoyed reading Moneyball.
Toryn's ability seems pretty great, but we can do better than SEEMS.  We can QUANTIFY it so we can prove how useful she is.  This may also help me out in some future articles I'm planning on writing, so doing this NOW saves me time LATER.  We're going to build off Eric's probability article, to which we're quite grateful.

So let's start with a basic blue dice.  4 hit sides, 2 crits, 2 accuracies. It's a 50-50 shot of whether or not your blue dice is going to damage a squadron with either flak from your ships or AA fire from your own squadrons.  That's not ideal, but that's a baseline. So 50% of the time it's great and 50% of the time it's potentially useless (we'll get to accuracies a bit later).  But with Toryn around, we can reroll one of those "bad" blue dice, giving us another shot at a damage.  Even a CR90 rolling 1 blue dice then has:

[50% base chance of damage] + [(50% base chance of rolling "bad")x(50% chance of Toryn's reroll coming up as a hit)] = 75% chance of getting a hit on one blue die.  Eric proved this all before, but it's a foundation for the future of this article.

That turns a blue die worth of flak into a black die probability of damage at a much larger range!  That's crazy!  You can flak everything with a 75% probability that you'll be doing damage (provided you're at distance 1-3 of Toryn)!  And that's just 1 blue dice! What about some of those crazier ships with double blue dice flak?
Oh hai Yavaris
Well let's calculate some more numbers and probability then.  Again, taking from Eric's probability article, let's look at his bit with Swarm (because that's really where this all comes in/down to; I'm setting out to show you that Toryn is a much better version of Swarm, haha!)
Say you want to see what kind of a benefit your TIE Fighter gets from using Swarm and you're considering accuracy icons as reroll candidates. Therefore each individual die has a 50% chance of generating the crit or accuracy icon you would want to use Swarm on. Because you only need one candidate die, it works out like:
  1. The first die has a 50% chance of being a candidate.
  2. Should the first die fail (50% chance) the second die also has a 50% chance (50%*50% = +25% chance)
  3. Should the first two dice fail (25% chance), the third die has a 50% chance (25%*50%= +12.5% chance)
  4. We come to the conclusion that (50+25+12.5=)87.5% of the time, Swarm will be beneficial for a TIE Fighter rolling 3 blue dice. Because it allows a reroll of a 0.5 average damage blue die, we would multiply 0.875 (the chance of using Swarm) by 0.5 (the average damage of the rerolled die) = 0.4375, or 0.44 when rounded to the nearest hundredth.
  5. Therefore, a Swarm-using TIE Fighter improves from 1.5 to 1.94 average damage, a 29% improvement.
So, using taking Eric's example, we get a table like the below for 2 dice flak (slash Y-wings), 3 dice shots (AKA A-wings), 4 dice shots (the basic X-wing), and because why not, 5 dice (X-wings under Yavaris).
Solid improvements to all, and that's just the AVERAGE damage.  Let's look at another example, this time using that binomial distribution calculator Eric mentioned in that probability article.

An A-wing, as we know, rolls 3 blue dice.  The chances of it rolling 3 hits exactly are 1 in 8, 12.5%.  Not great, but doable.  The chance of it rolling 2 hits is 37.5%, which means that third dice is rerollable under Toryn.  So, our chance of doing 3 damage in 1 go with an A-wing is:
(37.5% chance of 2 hits)*(50% chance of Toryn reroll working for us)+(12.5% chance of straight rolling 3 hits)=31.25%  Your A-wing now has a roughly 1 in 3 shot of straight up ganking a TIE fighter.  And that's not even getting into Counter!
Don't forget the pew pew laser noises, they help.
If you want to look at even MORE fun, let's look at an X-wing.  Rolling 4 dice, it has a 31.25% chance of rolling 3 OR 4 hits, straight up killing that TIE.  It has a 37.5% chance of rolling exactly 2, which means we use a very similar equation as before, but we get:
(37.5%)*(50% Toryn)+(31.25%)=50%

How do you feel about a coin flip for your X-wing killing a TIE or an Interceptor straight up? Because that's where you're at under Toryn.

What about chasing accuracies, either on your Hammerhead locking down a brace token or your MC30 locking down that flotilla's scatter token?
We hate you and your scatterable face!
Well, we have a base 1 in 4 rolling for it, and let's make things easier on ourselves that we only need 1.  Depending on the number of blue dice you're rolling, we get a chart like the below (for a chance at an accuracy or several)

My math is hopefully so accurate!
That's a mighty nice chart, but you may be asking, "John, why would I care about 1 blue dice? What reason would that have for me caring?"

And the answer for that is that B-wings also add a black dice. The wonderful thing about blue dice is that blue dice are wonderful things that we can use that same math for hunting for criticals, should you be using something like MS-1 Ion Cannons, HIE, Ion Cannon Batteries, or (sigh) Overload Pulse.
FFG, if you're reading this, we want an alternate art of this even LESS than a Rapid Reload one.
But hold on a minute, John! That math above is for trying to get AT LEAST one accuracy.  I know when my X-wing rolls up on Howlrunner, I can't wait to roll 4 accuracies! That'll show her! This math is for the expected damage and how much it can potentially improve it.  I know there's times where I roll up with an A-wing on Maarek Stele and throw 3 crits at him, and then there's times when my Y-wing with Flight Controllers ends Major Jendon straight up.  I COULD do the math, but it's not really worth anyone's time.

Suffice it to say, Toryn helps you end the squadron game much quicker than you would think, allowing you to fish if you have to for that last damage or that accuracy you need to end an opponent's squadron component.  Relatedly, she ALSO lets you futz with a Bomber Command Center reroll.  We all know that you can't double use Bomber Command Center anymore (there was an FAQ about it! We updated our articles and everything!), but Toryn lets you reroll a blue dice and Bomber Command Center lets you reroll a bomber dice.  If you roll 2 dice and one of them happens to be blue (B-wings, Gold SquadronScurrgs), you CAN go fishing for that blue crit for Nym or one of your B-wings to trigger Norra, etc, with your first roll and then reroll again if you get an accuracy with it.  Or, if you're hunting flotillas, double roll for that accuracy! It's technically legal and within the rules! But double rolling for that Nym crit can get mighty sweet.  If I'm doing my math right, you have a 25% chance of rolling it the first time, a 44% chance with Toryn, and then a 57% chance of hitting it on the Bomber Command Center reroll.  Not bad for a chance at wrecking a defense token!
You know, I haven't used him in a while.... and with a bunch of ISDs incoming in Wave 7...
So, Toryn's giving us some great abilities to get the blue dice results we need.  All you gotta do is stay at distance 1-3 of whatever ship she's on.  And how hard is that? (Oh, very hard.  If'/when you put her on a flotilla, please try to find the points for Bright Hope to keep her alive.)  Whatever ship she's on is probably going to be a high priority target, so make sure you end the squadron phase FAST if she starts getting targeted.  But if she gets you the squadron game win early enough that your squadrons can start contributing to attacking ships? Well those are points well spent.
I was ALSO on Hoth!

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