Accuracy formula
% Chance to Hit = a * b * c * d * e * f, where
- a = % Accuracy Stat of soldier
- b = % Accuracy of weapon/shot
- c = Kneeling modifier (115% if kneeling, 100% if standing)
- d = One-handed modifier (80% if firing a two-handed weapon without a free hand, 100% otherwise)
- e = Health modifier (current health / max health)
- f = Critical wounds modifier (100% - (10% for each critical wound to head or arms, up to 90%))
Example: A soldier has 88% Firing Accuracy, is firing a rifle snap shot (60%), is kneeling, is holding a grenade in his other hand, has half his health remaining, and has a fatal wound to his head and right arm. His % chance to hit will be: 0.88 x 0.6 x 1.15 x 0.8 x 0.5 x 0.8 = 19%
Use of Accuracy
The stated accuracy of a shot is not the same thing as it's chance to hit - rather it defines how badly the unit can fire.
At low accuracy, shots may go wider then at high accuracy. At 0% stated accuracy, they may go anywhere up to half a radian to the left or right of the target - this is as "bad" as it gets. As accuracy goes up, you completely lose the ability to fire along such extreme deviations from the target.
Even at 100% stated accuracy you're not guaranteed a precise shot - there's nearly always about a third of a degree of error present. However, whether they hit the intended target or not, shots with a listed accuracy of 100% aren't going to go off on a massive angle and clip your Commander in the head by accident.
As you get closer to the target, this range of angles becomes less important, as you need to fire on increasingly bad angles in order to miss. Likewise, the size of the target affects your final odds - Sectoids have the smallest profile, and out of the single-tile units, your soldiers present the largest one! (Unless they kneel - this makes them shorter then Sectoids, even if they remain wider).
It is always most likely that the angle of your shot will be right on target, as opposed to any other specific angle. For example, the half-radian angle a 0% accuracy shot can take (which actually requires the unit to turn on the spot!) happens far less often then the right-on-target shot he can also take. Because of this, your actual chance to hit the target is always somewhat higher then what the game appears to be telling you, though the difference gets lower as the stated accuracy gets higher.
Although the exact processes used to determine shot angles haven't been completely divided, they're about well enough understood to provide a rough translation of the game figures:
- 0% stated accuracy: roughly a 6.2% chance of firing within a degree of your target, worst possible shot being about 28.4 degrees off.
- 10% stated accuracy: roughly a 14.7% chance of firing within a degree of your target, worst possible shot being about 26.5 degrees off.
- 20% stated accuracy: roughly a 24.3% chance of firing within a degree of your target, worst possible shot being about 24.6 degrees off.
- 30% stated accuracy: roughly a 33.9% chance of firing within a degree of your target, worst possible shot being about 22.7 degrees off.
- 40% stated accuracy: roughly a 43.3% chance of firing within a degree of your target, worst possible shot being about 20.8 degrees off.
- 50% stated accuracy: roughly a 52.9% chance of firing within a degree of your target, worst possible shot being about 18.9 degrees off.
- 60% stated accuracy: roughly a 62.2% chance of firing within a degree of your target, worst possible shot being about 17 degrees off.
- 70% stated accuracy: roughly a 71.7% chance of firing within a degree of your target, worst possible shot being about 15.1 degrees off.
- 80% stated accuracy: roughly a 81% chance of firing within a degree of your target, worst possible shot being about 13.2 degrees off.
- 90% stated accuracy: roughly a 90.2% chance of firing within a degree of your target, worst possible shot being about 11.2 degrees off.
- 100% stated accuracy: roughly a 98.8% chance of firing within a degree of your target, worst possible shot being about 1.7 degrees off.
Of course, whether these oddss are actually of any value depends on the average minimum angle required to actually hit a target! They also don't account for vertical deviations, so consider them a very rough guide when picking your shots in-game.
See Also
- Firing Accuracy
- Fatal Wounds
- Health
- For current work in testing Firing Accuracy, see Firing Accuracy Testing