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.
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.