Accuracy formula - Revision history

Yankes: Updated equation to match original UFO code, confirmed by Warboy1982

2025-03-01T11:26:38Z

Updated equation to match original UFO code, confirmed by Warboy1982

← Older revision		Revision as of 11:26, 1 March 2025
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	'''Accuracy Penalty''' can be calculated as:		'''Accuracy Penalty''' can be calculated as:

	::'''Accuracy Penalty = a * b * c'''		::'''Accuracy Penalty = a * (b + c)'''

	::'''If Accuracy Penalty < 10% then Accuracy Penalty = 10%'''		::'''If Accuracy Penalty < 10% then Accuracy Penalty = 10%'''
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	*'''a''' = One-handed modifier. 80% if firing a two-handed weapon without a free hand, 100% otherwise.		*'''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)		'''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))		'''c''' = Critical wounds to head and firing arm (1-handed) or both arms (2-handed). (-10% Total wounds to head and firing arm(s))

	== Example ==		== Example ==

NKF: /* Chance to Hit Formula */ Updated firing arm penalties

2015-08-18T09:18:38Z

Chance to Hit Formula: Updated firing arm penalties

← Older revision		Revision as of 09:18, 18 August 2015
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	*'''a''' = One-handed modifier. 80% if firing a two-handed weapon without a free hand, 100% otherwise.		*'''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)		'''b''' = Health modifier. Calculated as 75% + (25% current health / max health)
	'''c''' = Critical wounds to head and arms. 100% - (10% ~~Number of critical~~ wounds to head and ~~arms~~)		'''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 ==		== Example ==

NKF: Rewrote presentation of formula. It's not as simple as it was, but hopefully clarifies it a bit

2015-08-18T08:57:27Z

Rewrote presentation of formula. It's not as simple as it was, but hopefully clarifies it a bit

← Older revision		Revision as of 08:57, 18 August 2015
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	== Chance to Hit Formula ==		== Chance to Hit Formula ==

	'''% Chance to Hit = a * b * c * d * e * f'''		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:		Where:
	*a ~~= % Accuracy Stat of soldier~~		*'''a''' = One-handed modifier. 80% if firing a two-handed weapon without a free hand, 100% otherwise.
	*b = % Accuracy of weapon/shot		'''b''' = Health modifier. Calculated as 75% + (25% current health / max health)
	*c = Kneeling modifier (115% if kneeling, 100% if standing)		'''c''' = Critical wounds to head and arms. 100% - (10% Number of critical wounds to head and arms)
	*d = One-handed modifier (80% if firing a two-handed weapon without a free hand, 100% otherwise)
	e = Health modifier (75% + (25% current health / max health))
	*f = Critical wounds ~~modifier (~~100% - (10% ~~for each~~ critical ~~wound~~ to head or arms)

	~~If Chance To Hit is below 10% after all the above multipliers have been applied, it will be fixed at 10% of the soldier's base firing accuracy value.~~

	~~'''~~Example~~:'''~~		== Example ==

	A soldier has 88% Firing Accuracy, is firing a rifle snap shot (60%), is kneeling,		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:
	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 (0.75 + (0.25 * 0.5)) x 0.8 = 34%		0.88 * 0.6 * 1.15 * 0.8 * (0.75 + (0.25 * 0.5)) * 0.8 = 34%

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

	'''Accuracy * Current Health / Max Health'''		::'''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.		This means that if the unit is at 50% health, then accuracy will also be shown at 50% of its base value.
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	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:		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))'''		::'''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%.		In this case, a unit at 50% health would have 87.5% base accuracy instead of 50%.

NKF: Added bit on stat screen Accuracy. Or, inaccuracy, in this case.

2015-08-17T10:46:32Z

Added bit on stat screen Accuracy. Or, inaccuracy, in this case.

← Older revision		Revision as of 10:46, 17 August 2015
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	0.88 x 0.6 x 1.15 x 0.8 x (0.75 + (0.25 * 0.5)) x 0.8 = 34%		0.88 x 0.6 x 1.15 x 0.8 x (0.75 + (0.25 * 0.5)) x 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 ==		== Use of Accuracy ==
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	* '''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.		* '''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.		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.

NKF: Amended formula

2015-08-17T07:59:02Z

Amended formula

← Older revision		Revision as of 07:59, 17 August 2015
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	== % Chance to Hit ~~= a * b * c * d * e * f, where~~ ==		== Chance to Hit Formula ==

			'''% Chance to Hit = a * b * c * d * e * f'''

			Where:
	*a = % Accuracy Stat of soldier		*a = % Accuracy Stat of soldier
	*b = % Accuracy of weapon/shot		*b = % Accuracy of weapon/shot
	*c = Kneeling modifier (115% if kneeling, 100% if standing)		*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)		*d = One-handed modifier (80% if firing a two-handed weapon without a free hand, 100% otherwise)
	*e = Health modifier (current health / max health)		e = Health modifier (75% + (25% current health / max health))
	*f = Critical wounds modifier (100% - (10% for each critical wound to head or arms, ~~up to 90~~%))		*f = Critical wounds modifier (100% - (10% for each critical wound to head or arms)

			If Chance To Hit is below 10% after all the above multipliers have been applied, it will be fixed at 10% of the soldier's base firing accuracy value.

	'''Example:'''		'''Example:'''
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	fatal wound to his head and right arm. His % chance to hit will be:		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%		0.88 x 0.6 x 1.15 x 0.8 x (0.75 + (0.25 * 0.5)) x 0.8 = 34%

	== Use of Accuracy ==		== Use of Accuracy ==

Slider2k: Correction to the accuracy formula to be consistent with the actual game and Accuracy article.

2013-11-27T00:12:26Z

Correction to the accuracy formula to be consistent with the actual game and Accuracy article.

← Older revision		Revision as of 00:12, 27 November 2013
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	*a = % Accuracy Stat of soldier		*a = % Accuracy Stat of soldier
	*b = % Accuracy of weapon/shot		*b = % Accuracy of weapon/shot
	*c = Kneeling ~~bonus~~ (115% if kneeling, 100% if standing)		*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)		*d = One-handed modifier (80% if firing a two-handed weapon without a free hand, 100% otherwise)
	e = ~~health~~ modifier (~~75% + 25% percentage of life remaining~~)		*e = Health modifier (current health / max health)
	*f = Critical wounds modifier (100% - (10% for each critical wound to head or arms, up to 90%))		*f = Critical wounds modifier (100% - (10% for each critical wound to head or arms, up to 90%))

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	fatal wound to his head and right arm. His % chance to hit will be:		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 0.87 x 0.8 = 34%		0.88 x 0.6 x 1.15 x 0.8 x 0.5 x 0.8 = 19%

	== Use of Accuracy ==		== Use of Accuracy ==
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	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.		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 ~~divined~~, they're about well enough understood to provide a rough translation of the game figures:		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.		* '''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.

Hobbes: categorizing

2013-07-23T02:53:05Z

categorizing

← Older revision		Revision as of 02:53, 23 July 2013
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	*[[Health]]		*[[Health]]
	*''For current work in testing Firing Accuracy, see [[Firing Accuracy Testing]]''		*''For current work in testing Firing Accuracy, see [[Firing Accuracy Testing]]''

			[[Category:Enemy Unknown/UFO Defense]]

Bomb Bloke at 00:35, 6 March 2012

2012-03-06T00:35:12Z

← Older revision		Revision as of 00:35, 6 March 2012
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	*b = % Accuracy of weapon/shot		*b = % Accuracy of weapon/shot
	*c = Kneeling bonus (115% if kneeling, 100% if standing)		*c = Kneeling bonus (115% if kneeling, 100% if standing)
	*d = One-handed ~~penalty~~ (80% if firing a two-handed weapon without a free hand, 100% otherwise)		*d = One-handed modifier (80% if firing a two-handed weapon without a free hand, 100% otherwise)
	e = health ~~penalty~~ (75% + 25% percentage of life remaining)		e = health modifier (75% + 25% percentage of life remaining)
	*f = Critical wounds ~~penalty~~ (100% - (10% for each critical wound to head or arms, up to 90%))		*f = Critical wounds modifier (100% - (10% for each critical wound to head or arms, up to 90%))

	'''Example:'''		'''Example:'''
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	A soldier has 88% Firing Accuracy, is firing a rifle snap shot (60%), is kneeling,		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		is holding a grenade in his other hand, has half his health remaining, and has a
	fatal ~~would~~ to his head and right arm. His % chance to hit will be:		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 0.87 x 0.8 = 34%		0.88 x 0.6 x 1.15 x 0.8 x 0.87 x 0.8 = 34%

Bomb Bloke: /* % Chance to Hit = a * b * c * d * e * f, where */ Correction

2012-03-05T21:59:41Z

% Chance to Hit = a * b * c * d * e * f, where: Correction

← Older revision		Revision as of 21:59, 5 March 2012
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	*c = Kneeling bonus (115% if kneeling, 100% if standing)		*c = Kneeling bonus (115% if kneeling, 100% if standing)
	*d = One-handed penalty (80% if firing a two-handed weapon without a free hand, 100% otherwise)		*d = One-handed penalty (80% if firing a two-handed weapon without a free hand, 100% otherwise)
	e = health penalty (75% + 25% percentage of life ~~lost~~)		e = health penalty (75% + 25% percentage of life remaining)
	*f = Critical wounds penalty (100% - (10% for each critical wound to head or arms, up to 90%))		*f = Critical wounds penalty (100% - (10% for each critical wound to head or arms, up to 90%))

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	0.88 x 0.6 x 1.15 x 0.8 x 0.87 x 0.8 = 34%		0.88 x 0.6 x 1.15 x 0.8 x 0.87 x 0.8 = 34%


	== Use of Accuracy ==		== Use of Accuracy ==

Bomb Bloke: Sad to see the old notes go, but I'm blowing them away anyways! :(

2012-03-04T08:55:25Z

Sad to see the old notes go, but I'm blowing them away anyways! :(

← Older revision		Revision as of 08:55, 4 March 2012
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	*c = Kneeling bonus (115% if kneeling, 100% if standing)		*c = Kneeling bonus (115% if kneeling, 100% if standing)
	*d = One-handed penalty (80% if firing a two-handed weapon without a free hand, 100% otherwise)		*d = One-handed penalty (80% if firing a two-handed weapon without a free hand, 100% otherwise)
	*e = health penalty (~~current health / max health~~)		e = health penalty (75% + 25% percentage of life lost)
	*f = Critical wounds penalty (100% - (10% for each critical wound to head or arms, up to 90%))		*f = Critical wounds penalty (100% - (10% for each critical wound to head or arms, up to 90%))

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	fatal would to his head and right arm. His % chance to hit will be:		fatal would 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%		0.88 x 0.6 x 1.15 x 0.8 x 0.87 x 0.8 = 34%

	~~== Close Range ==~~
	The accuracy formula is NOT affected by distance - if you have a 100% chance to hit, you will hit, at any range - but 'missed' shots still have a chance to hit if their randomly distributed path takes them through the target tile. This is why burst shots are your best choice at close range - even if the calculated accuracy is bad, it's still hard to miss.

	~~From work by [[User:NKF\|NKF~~-~~sensei]]~~, ~~reworded by~~ -~~-[[User:JellyfishGreen\|JellyfishGreen]] 09:49~~, ~~25 Apr 2005 (BST)~~		== 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.
	'~~'[ [[User:NKF\|NKF]]~~ - ~~Addendum: I think it~~'s ~~best~~ to ~~say that~~ the ~~accuracy value is~~ the ~~level~~ of ~~accuracy that~~ the ~~bullet leaves~~ the ~~gun or~~ the ~~initial firing angle~~ of the ~~bullet. <br><br>The bullet~~, ~~after it leaves~~ the ~~gun~~, is ~~then subjected to outside forces~~ that ~~can make a pefect 100+% accurate launched bullet miss its~~ target~~. I like~~ to ~~blame it on integer rounding or in~~ other ~~words~~, ~~decimal point truncation. If~~ a ~~bullet was mean~~ to ~~have a travel velocity~~ of ~~1.25 map points on its X axis per update~~, ~~integer rounding causes~~ the ~~.25~~ to be ~~truncated~~, so the ~~bullet only increases at 1 points per update~~. ~~As I don~~'t ~~really know what~~'~~s going underneath~~, ~~this is best treated as an educated guess and no more~~. ~~Anyway~~, ~~in this case~~, ~~distance can indeed play~~ a ~~factor in~~ accuracy.~~<br><br>If the bullet is meant to go way~~ off ~~its mark~~, ~~as long as its line~~ of ~~travel happens to make it pass through the hit box~~ of ~~the alien you were aiming at (or anyone that just happens to be in the path of the bullet~~'~~s trajectory), is counted as~~ a ~~hit~~. ~~A technical hit~~, ~~but~~ a ~~hit nonetheless!<br><br>Another line~~ of ~~thought regarding drift is that the game may purposely introduce~~ a ~~very minor drift value to every attack~~. ~~A random value may explain why it isn~~'~~t always apparent~~. ~~It may be~~ a ~~simulation~~ of ~~gravity or even wind~~. ~~I find this less likely~~ a ~~<strike>excuse</strike> reason than decimal point truncation~~, ~~but it~~'~~s still a possibility worth considering~~.]''
			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 divined, 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 ==		== See Also ==