MathWing: Accuracy Corrector

By MajorJuggler, in X-Wing

accuracy-corrector.png

I just did some relatively quick MathWing analysis of Accuracy Corrector. I'll come back and update this later if I do additional analysis.

For now, what I did was take the existing scripts that I have to calculate average damage, based on the entire meta game of a variety of shots and action economies, and plugged in Accuracy Corrector.

This is just a quick calculation (well, quick for me since I already have the scripts set up), but it should give a rough idea of how well this card should perform.

Assumptions:

  • Attacker has 75% chance of having a focus token
  • Defender has a 50% chance of having a focus token
  • Range 1: 30%
  • Range 2: 45%
  • Range 3 / Range 2 + obstruction: 20%
  • Range 3 + obstruction: 5%
  • Defender with 1 agility: 30%
  • Defender with 2 agility: 25%
  • Defender with 3 agility: 45%

I need to update all of the above, since it is all wave 3 meta, but for now it will be close enough to get a good estimate.

Results:
2 attack dice: 0.6679 = 1.000 normalized
2 attack dice + AC: 0.9858 = 1.476 normalized
3 attack dice: 1.1728 = 1.756 normalized
3 attack dice + AC: 1.3304 = 1.992 normalized
4 attack dice: 1.7506 = 2.621 normalized
4 attack dice + AC: 1.8309 = 2.741 normalized

Also for reference:
3 attack dice + AC w/o using focus: 1.0785

So the relative increase for 2, 3, and 4 attack dice is:
2 dice: 1.4760
3 dice: 1.1344
4 dice: 1.0459

So this would benefit 2 dice attack ships that could take this upgrade, but there currently aren't any. This should be intuitively obvious, since it would guarantee the maximum possible attack roll at ranges 2-3, and also helps significantly at range 1.

So now the question is, how much value does it really add to get this extra damage? Using Lanchester's Square Law with a slightly modified exponent , the proportional "value" of each instance is:

2 dice: 1.4760^0.52 = 1.224
3 dice: 1.1344^0.52 = 1.068
4 dice: 1.0459^0.52 = 1.024

For example, for this upgrade to be cost effective on a 3 attack ship, it needs to increase the overall cost of the ship by no more than 6.8%.


It makes no sense whatsoever using this upgrade on the TIE Phantom, as the break even point is:
x*1.024 = x + 3 --> x = 125

Solving for the break-even point on a 3-attack ship where it only costs 3 points to equip Accuracy Corrector in a System Upgrade slot:
x*1.068 = x + 3 --> x = 44.12

The Star Viper is interesting because you can spend 1 to add the System Upgrade slot with the Virago title.

virago.png


So the break even point for the Star Viper with the Virago title is:
x*1.068 = x + 4 --> x = 58.82

So, it doesn't look like this will be particularly useful on most of the 3-attack ships, with one possible exception.

  • The Lambda and B-wing only cost 21 and 22 points respectively, both at PS2.
  • The E-wing is slightly more appealing since it costs 27. The E-wing generic pilots appear to be overcosted by a couple points, both from MathWing and Regionals results. Maybe you can find a way to make this upgrade work on one of the named pilots.
  • The Star Viper costs 31 for the highest named pilot, which is barely over half of it's 58 point break even point.
  • It looks like the Aggressor (IG-2000) has a System Upgrade slot. At a cost of 36 points, it is the most likely candidate for this upgrade, with a break even point of 44.

The main benefit that I see would be on the IG-2000 (assuming it has the slot for it), but you are still paying a fairly high premium for mitigating bad dice rolls, and it obviously consumes the slot as well.

For reference, the break even point on a 2 attack ship would theoretically be:
x*1.224 = x + 3 --> x = 13.4

So, if we ever see a 2-attack ship that has a System Upgrade slot, this will almost certainly become an auto-include. So FFG has essentially backed themselves into a corner with this particular upgrade card, in regards to future ships. They can't make a 2 attack ship with a System Upgrade slot that's worth more than 13 points, otherwise mass Accuracy Corrector would risk becoming an extremely high efficiency auto-win build.

It is important to note that these break even points are only for the statistical average damages. If you value lowering the standard deviation of your rolls, and having consistent damage, then the threshold is lower. We have already seen this with C-3P0: even though he only gives 5/8 of an evade per round, the guarantee of 1 evade is very valuable in a tournament setting.

This also does not consider the benefit of keeping your focus if you were only going to have 2 hits anyway. This lets you save the focus token for defense, which increases your durability. This might make this upgrade worthwhile on the Aggressor.

Edited by MajorJuggler
So, if we ever see a 2-attack ship that has a System Upgrade slot, this will almost certainly become an auto-include.

I think this is the most important issue with this card.

With this upgrade the opportunity to not use focus and actually acquire targets with boost / barrel roll are introduced, so wouldn't it make sense to assume 0% chance of having focus because you are using a different tactic specifically because you have 2 guaranteed hits?

I just ran the damage numbers. 3 dice + AC and not spending focus on defense nets 1.0785 damage, which is a little lower than 3 dice with focus available 75% of the time. So you would be paying 3 points to do slightly less (although more consistent) damage, and to have the focus for defense instead.

Edited by MajorJuggler

Now my mathhammer skills are decent but holy moley batman, you beat me hands down. However just from looking at the card I'd say you are right. It needs a fighter with attack 2 to be worth it and, as you've already stated, no such ship exist.

You never know, the TIE/Advanced might get a reduced price sensor slot. ;)

As insurance it is still really good. A guaranteed two hits is nice. The more important piece is this. I play a Push the Limit E-wing. I focus and evade every turn. I am guarantted 2-3 hits on every attack without having to take an action or previously attack. It's more than .5 percent boost in unmodified damage on any ship that has other reasons to use focus tokens or has better actions to use.

This includes Bwings firing ordnance or Barrel Rolling, E-Wings, The Virago, Phantoms to a lesser extent, and boosting Lambdas.

You never know, the TIE/Advanced might get a reduced price sensor slot. ;)

I just ran the numbers. It would increase the TIE Advanced's jousting efficiency from about 81% to 86%. It still wouldn't be useful!

As insurance it is still really good. A guaranteed two hits is nice. The more important piece is this. I play a Push the Limit E-wing. I focus and evade every turn. I am guarantted 2-3 hits on every attack without having to take an action or previously attack. It's more than .5 percent boost in unmodified damage on any ship that has other reasons to use focus tokens or has better actions to use.

This includes Bwings firing ordnance or Barrel Rolling, E-Wings, The Virago, Phantoms to a lesser extent, and boosting Lambdas.

Interesting, that's 33 points, so you could run 3. you should playtest it and see how it goes. 6 damage per turn is extremely low, but at least you are crazy defensive.

Since I just put two and two together on the Aggressor product spread image, what would the impact of the Corrector be on a ship with an Autoblaster? With a minimum of two hits going past dice every time it attacks, would it ever really make up for the fact that you're still losing an attack die at Range 1?

Does this make a turret-less Jan or Kyle viable?

It seems to allow a guaranteed two hits from a 1 dice primary.

Does this make a turret-less Jan or Kyle viable?

It seems to allow a guaranteed two hits from a 1 dice primary.

If they had access to the System Upgrade slot, then a 1-attack ship would be taking this card every single time!

Does this make a turret-less Jan or Kyle viable?

It seems to allow a guaranteed two hits from a 1 dice primary.

It will be great on HWKs...

...just as soon as you figure out how to give them systems upgrade slots.

Does this make a turret-less Jan or Kyle viable?

It seems to allow a guaranteed two hits from a 1 dice primary.

It will be great on HWKs...

...just as soon as you figure out how to give them systems upgrade slots.

I have no idea why I was thinking it was an ept... /facepalm

Does this make a turret-less Jan or Kyle viable?

It seems to allow a guaranteed two hits from a 1 dice primary.

It will be great on HWKs...

...just as soon as you figure out how to give them systems upgrade slots.

I have no idea why I was thinking it was an ept... /facepalm

'S ok. For a while I kept thinking it was a modification, and in that slot it's pretty broken.

This would be very nice for a tie advanced!

As insurance it is still really good. A guaranteed two hits is nice. The more important piece is this. I play a Push the Limit E-wing. I focus and evade every turn. I am guarantted 2-3 hits on every attack without having to take an action or previously attack. It's more than .5 percent boost in unmodified damage on any ship that has other reasons to use focus tokens or has better actions to use.

This includes Bwings firing ordnance or Barrel Rolling, E-Wings, The Virago, Phantoms to a lesser extent, and boosting Lambdas.

Interesting, that's 33 points, so you could run 3. you should playtest it and see how it goes. 6 damage per turn is extremely low, but at least you are crazy defensive.

That said, I do have to wonder if FCS isn't still just way better against just about everything. Also, Etahn loses his ability with this, correct? It's also an interesting card on Defensive Corran...

The maths is pretty damning, but when I first saw this card I wasn't thinking about damage output so much as freeing up actions.

I'd see this upgrade perfect for a ship that wants to do something other than modify dice each turn. So, boost, barrel roll, evade etc - while retaining a consistent damage output.

This would be very nice for a tie advanced!

Yes, but sadly it still wouldn't be enough. You would basically be able to take 4x PS2 TIE Advanced. That gets you 8 damage per turn (lower than a 7 TIE Swarm), and about the same durability as a 7 TIE Swarm.

You never know, the TIE/Advanced might get a reduced price sensor slot. ;)

I just ran the numbers. It would increase the TIE Advanced's jousting efficiency from about 81% to 86%. It still wouldn't be useful!

The maths is pretty damning, but when I first saw this card I wasn't thinking about damage output so much as freeing up actions.

I'd see this upgrade perfect for a ship that wants to do something other than modify dice each turn. So, boost, barrel roll, evade etc - while retaining a consistent damage output.

You nailed why I'm so intrigued. It definitely seems more viable on something more maneuverable than a Shuttle, although I'm trying to think of what EPT might compliment it the most.

As insurance it is still really good. A guaranteed two hits is nice. The more important piece is this. I play a Push the Limit E-wing. I focus and evade every turn. I am guarantted 2-3 hits on every attack without having to take an action or previously attack. It's more than .5 percent boost in unmodified damage on any ship that has other reasons to use focus tokens or has better actions to use.

This includes Bwings firing ordnance or Barrel Rolling, E-Wings, The Virago, Phantoms to a lesser extent, and boosting Lambdas.

Interesting, that's 33 points, so you could run 3. you should playtest it and see how it goes. 6 damage per turn is extremely low, but at least you are crazy defensive.

I would only run one. Most likely Etahn. Have him tank and or survive while I kill their big hitters. But I will certainly give it a try.

That said, I do have to wonder if FCS isn't still just way better against just about everything. Also, Etahn loses his ability with this, correct? It's also an interesting card on Defensive Corran...

Yeah IF you use Etahn's ability. Since Corrector does cancel all current dice results and then doesn't allow modifications after either.

But you have the option if you role 1 hit, 1 crit to not use it, or just one crit...

EDIT: I mean if you use Corrector card lol.

Edited by dandirk

You never know, the TIE/Advanced might get a reduced price sensor slot. ;)

I just ran the numbers. It would increase the TIE Advanced's jousting efficiency from about 81% to 86%. It still wouldn't be useful!

Can you show your work? I'm making an error somewhere (possibly computational) and can't find it.

The maths is pretty damning, but when I first saw this card I wasn't thinking about damage output so much as freeing up actions.

I'd see this upgrade perfect for a ship that wants to do something other than modify dice each turn. So, boost, barrel roll, evade etc - while retaining a consistent damage output.

You nailed why I'm so intrigued. It definitely seems more viable on something more maneuverable than a Shuttle, although I'm trying to think of what EPT might compliment it the most.

I know there is another card in Wave 5 that will give a free upgrade card [Action], but this sort of does the same thing. Any upgrade cards like Daredevil, Saboteur that uses an [Action] could be also used with less penalty to your attack... but is the additional cost of 3 worth it?

I would try it with an autoblaster on a B-Wing for fun. Not sure it's a great idea but it would be neat.

You never know, the TIE/Advanced might get a reduced price sensor slot. ;)

I just ran the numbers. It would increase the TIE Advanced's jousting efficiency from about 81% to 86%. It still wouldn't be useful!

Can you show your work? I'm making an error somewhere (possibly computational) and can't find it.

Sure. Calculating by hand:

Baseline TIE Advanced:

Attack: 1.000

Durability: 1.777

PS 1 jousting value: 12*(1.000*1.777)^0.52 = 16.18

PS1 cost: 20

Jousting efficiency = 16.18 / 20 = 80.9%

TIE Advanced + Accuracy Corrector:

Attack: 1.476

Durability: 1.777

PS 1 jousting value: 12*(1.476*1.777)^0.52 = 19.81

PS1 cost: 23

Jousting efficiency = 19.81 / 23 = 86.1%

Edit: So basically the 3 point upgrade will add just under 4 points of value to the TIE Advanced.

In a hypothetical world where the TIE Advanced costed 4 points less so it had ~100% jousting efficiency, adding Accuracy Corrector would do this:

TIE Advanced + Accuracy Corrector -4 point cost reduction:

Attack: 1.476

Durability: 1.777

PS 1 jousting value: 12*(1.476*1.777)^0.52 = 19.81

PS1 cost: 19

Jousting efficiency = 19.81 / 19 = 104%

Vs a "baseline" -4 point costed TIE Advanced:

TIE Advanced -4 point cost reduction:

Attack: 1.000

Durability: 1.777

PS 1 jousting value: 12*(1.000*1.777)^0.52 = 16.18

PS1 cost: 16

Jousting efficiency = 16.18 / 16 = 101.1%

So even on a 16 point ship, the improvement would be relatively small. If you ever saw a super-durable 2 point attack ship with a System Upgrade slot though, then that would be another story entirely.

Edited by MajorJuggler
I imagine we'll see at least one pilot ability or upgrade that brings relevance to Accuracy Corrector.

Question:

How do the numbers crunch for Cluster Missiles with this upgrade? Seems like an obvious pairing - except for the fact that there are currently no ships which feature both a System Upgrade and Missile slot.

Edited by Introverdant