# Accuracy formula

## Chance to Hit Formula

The chance to hit for any given shot can be calculated with the following formula:

Chance to Hit% = Accuracy * Kneeling Bonus * Accuracy Penalty * Weapon Firing Mode Accuracy

Where:

• Accuracy = The unit's base Firing Accuracy level.
• Kneeling Bonus = Kneeling modifier. 115% when kneeling, 100% when standing.
• Accuracy Penalty = A percentage that modifies overall accuracy depending on injuries and weapon handling.
• Weapon Firing Mode Accuracy = The Aimed, Snap or Auto firing accuracy of the current weapon

Accuracy Penalty can be calculated as:

Accuracy Penalty = a * b * c
If Accuracy Penalty < 10% then Accuracy Penalty = 10%

Where:

• a = One-handed modifier. 80% if firing a two-handed weapon without a free hand, 100% otherwise.
• b = Health modifier. Calculated as 75% + (25% * current health / max health)
• c = Critical wounds to head and firing arm (1-handed) or both arms (2-handed). 100% - (10% * Total wounds to head and firing arm(s))

## 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 * 0.6 * 1.15 * 0.8 * (0.75 + (0.25 * 0.5)) * 0.8 = 34%

## Stat Screen Accuracy

When viewed in the stat screen, the selected unit's current remaining accuracy will be calculated as :

Accuracy * Current Health / Max Health

This means that if the unit is at 50% health, then accuracy will also be shown at 50% of its base value.

While it does serve as a visual aid to show that the unit is suffering an accuracy penalty, this information is quite inaccurate. In the actual firing calculations, the health penalty only influences 25% of the unit's base accuracy. It can be calculated as:

Accuracy * (0.75 + (0.25 * Current Health / Max Health))

In this case, a unit at 50% health would have 87.5% base accuracy instead of 50%.

## 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 odds 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.