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Assault soldiers can pick a perk that lets them fire their weapon twice at a -15 penalty to aim. When is it better to use this ability and when to use regular fire instead?

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I usually use it in conjunction with Run and Gun in order to use it at point blank range. If used against a berserker while your assault soldier has the close range combat perk, you will actually get three shots against the berserker that turn. – SaintWacko Oct 18 '12 at 13:15
@SaintWacko cheeky, I like it. Do you need to be more than 4 tiles away for it to work? I usually rely on extreme crit bonuses for adjacent enemies. – kotekzot Oct 18 '12 at 13:24
I suppose it would work outside 4 tiles if the berserker's post-attack dash takes them within 4 tiles of the soldier. I usually do it point blank, though, just to be safe. – SaintWacko Oct 18 '12 at 13:57
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FYI, if you select "Rapid Fire", but target dies with first shot, the "Rapid Fire" has zero cooldown. – vartec Oct 18 '12 at 14:22
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The other thing to note is that if the enemy is behind destructible cover, two shots gives you a better chance of knocking it down than just one - in fact, missing might give you an advantage in this case. – agent86♦ Oct 18 '12 at 15:51
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2 Answers

up vote 29 down vote accepted

At 30% normal accuracy (15% with rapid fire), the two will do the same amount of damage, on average. At 29% normal accuracy, a normal attack will do more. At 31% accuracy, a rapid fire attack will do more.

average damage intercept
X-Axis = Chance to hit with Normal Fire
Y-Axis = Average Damage per Ability Use (assuming 10 damage per successful hit)

Assuming you do 10 damage per hit:

  • At 29% normal accuracy, you will do 2.9 damage per normal fire on average, and rapid fire will do 2.8 (24.08% chance to hit for 10 damage plus 1.96% chance to hit for 20 damage).
  • At 30% accuracy, both will do 3 damage per ability use on average.
  • At 31% accuracy, a normal attack will do 3.1 average damage, while a rapid fire attack will do 3.2 average damage.

Here is a spreadsheet where I did the calculations.

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So much for being lazy. – StrixVaria Oct 18 '12 at 13:52
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No time for lazy when there's science to do (when I look out there it makes me GLaD I'm not you~) – Ben Brocka Oct 18 '12 at 14:10
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Note that if even if you are not trying to maximize damage, but maximize your chance of hitting at least once (e.g. if you absolutely need to hit this 5-health sectopod on this one last move by your last soldier), it is still always worth it between 35% and 95% accuracy. (more precisely, if your chance to hit is between 33.38% and 96.62%, you are more likely to hit at least once using rapidfire). See: wolframalpha.com/input/?i=x%3D1-%28%281.15-x%29%5E2%29 – RibsNGibs Oct 18 '12 at 22:01
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@Pureferret: Sorry, I shouldn't have muddled the issue. tl;dr: unless you are worried specifically about conserving ammo, always use rapid shot if your regular fire % is between 35 and 95. But to explain further - Skoodge's graph shows that your expected damage output over multiple trials is higher using rapid shot on anything over 30%, but that's not exactly the same thing as "chance to hit at least once". With the assault (who has rapid fire), often your situation will be such that one HIT will kill the alien, so you should maximize your chance of hitting, not damage. – RibsNGibs Oct 19 '12 at 15:45
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@Pureferret In my graph, the curved line is the "chance you'll hit at least once with rapidfire" and the straight line is the "chance you'll hit with regular fire". The curved line is higher than the straight one between 33.38% and 96.62%. So if you are taking a shot at a 4 health alien with your assault, and your to-hit percentage is 40%, believe it or not you are more likely to kill it taking two 25% shots instead of one 40% one. Same with taking two 75% shots instead of one 90% shot. Etc. – RibsNGibs Oct 19 '12 at 15:45
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up vote 13 down vote

If your regular chance to hit is 34% or greater (19% for Rapid Fire), it is always better to use Rapid Fire. The chance to hit at least once while rapid firing with regular accuracy at 34% is 1-(1-0.34-0.15)2=0.3439 or 34%. The chance to hit twice is only 0.0361 or 3.61% under those conditions. Using Rapid Fire at lower accuracy leads to a decreased chance to hit at least once, but the potential for hitting twice may make it worthwhile if the alternative is to let a strong enemy have a chance to attack.

According to Invader Skoodge's graph, both options will do the same damage at 30% accuracy, and above that Rapid Fire will get progressively stronger. Therefore, if your target can be killed in 1 shot, use Rapid Fire if your accuracy is 34% or more, if the target can't be killed in 1 shot, Rapid Fire is viable at accuracy as low as 30%.

One circumstance where you may want to abstain from using Rapid Fire is when your soldier may not have enough ammo to last through the engagement. Note that you will not waste ammo if the target dies on the first shot.

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I was too lazy to do this math myself, and the percentage is lower than I thought. Thanks! – StrixVaria Oct 18 '12 at 13:14
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Remember to factor in the extra ammo you use when deciding. – Nailer Oct 18 '12 at 13:31
@Nailer good point, I'll add that to the answer. – kotekzot Oct 18 '12 at 13:35
It also won't trigger the Rapid Fire cooldown if they die on the first shot. – SaintWacko Oct 18 '12 at 13:53
@SaintWacko pretty sure Rapid Fire doesn't have a cooldown. – kotekzot Oct 18 '12 at 14:08
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