Chance to Hit (EU2012)

In XCOM: Enemy Unknown, the chance that any given shot will land on your target is based on the sum total of a number of variables. Some work for you, some work against you, but all are additive: if you're told that shiny new rifle gives you a +10 Aim, then indeed your final chance to hit simply goes up by 10% when you're using it. Understanding this game mechanic will help you determine whether a tile is worth moving to, whereas weighing up the chance to hit a target against the amount of damage you might deal to it is useful when considering taking a defensive action instead.

Aim (or Attack) is the base statistic each unit has which accounts for the bulk of its accuracy in battle. For XCOM soldiers, this goes up at a set rate based on rank and class, whereas for aliens it's determined by their race and the difficulty level.

Defence, on the other hand, is the statistic which lowers each unit's chance to be hit. Your units may improve their base defence stat pre-battle by donning certain forms of armour (keeping in mind that most only grant additional hitpoints, lessoning the effects of damage, rather then your chance to avoid it altogether). Some alien races have an innate defensive bonus which is further increased on higher difficulties.

In addition, units may source additional aim/defence bonuses from soldier perks, terrain factors and equipment, cover being one of the most important examples.

The chance to score a Critical Hit is calculated in much the same way, though the percentage displayed is dependant on the shot hitting in the first place. If you're shown an 80% chance to hit with a 25% chance of a critical, then your real chance to score a critical hit on the target is 20% (a 20% chance of missing, a 60% chance to score a regular hit, and a 20% (25% of 80) chance of getting a critical).

Just before OK'ing a shot on your target, you may select "More Info" within the game's HUD to see a list of which modifiers would apply to it.

Solder Stats

A typical XCOM rookie starts off with a flat 65 Aim stat. Generally, as their rank improves, they gain additional points at a static rate (that is to say, a Lieutenant Sniper will always have an Aim stat of 84). Second Wave options can instead be used to mix up the abilities of your ranks - "Not Created Equally" has them start with an aim stat of somewhere from 55 to 80, whereas "Hidden Potential" randomises their gains.

The DLC unit Shaojie Zhang has an extra +5 Aim relative to other non-Second Wave affected heavies. Heroes may also exceed the norm (Ken Levine in particular clocks in with a massive score of 200, nearly double the usual potential of his sniper class!).

In addition to their base stats, each class may choose from a variety of perks which can potentially improve accuracy, decrease it in exchange for another bonus, raise their defence, or affect the aim/defence values of other units in play:

Assaults

The Assault class sports moderate accuracy, but their shotguns grant huge bonuses at near range - and they're very good at closing the distance. At distances further then ten tiles, their pistols (or perhaps rifles, if equipped) make for more reliable damage, albeit somewhat reduced in power. They can acquire abilities that improve their defence when up in the alien's faces. Squaddie Corporal Sergeant Lieutenant Captain Major Colonel Total Gains 70 (+5) 73 (+3) 76 (+3) 79 (+3) 82 (+3) 85 (+3) 89 (+4) + 24 Related abilities: Flush: Reduced damage for a +30% aim (also forces the target to move). Rapid Fire: Two shots, but at a -15% aim penalty to each. Tactical Sense: A +5% defensive bonus for every enemy unit that the assault can see (up to 20%). Aggression: A +10% crit chance bonus for every enemy unit that the assault can see (up to 30%). Close & Personal: Up to a +30% crit chance bonus depending on the distance to the target (what distances for what bonuses?)

Heavies

Heavies have very poor aim compared to other classes, but make up for it with a number of abilities which ignore the stat, and at close range their accuracy improves somewhat. Their rockets always have at least a 90% chance to strike their targets, and having them open up on your enemies first can often result in them destroying alien cover or granting other accuracy benefits to their squad-mates (whether the heavies themselves manage to hit or not). Squaddie Corporal Sergeant Lieutenant Captain Major Colonel Total Gains 67 (+2) 68 (+1) 69 (+1) 70 (+1) 71 (+1) 73 (+2) 75 (+2) +10 Related abilities: Holo-Targeting: +10% aim to all other allied fire on the target until next turn. Suppression: -30% to the target's aim until next turn or until the heavy is damaged. If Danger Zone is taken it can affect multiple units close to the target, and with Mayhem, it also deals slight (but guaranteed) damage.

Snipers

Snipers gain no accuracy bonuses from their high-powered rifles, and in fact take a penalty if they try to use them at close range (pistols have a better chance to hit at distances less then ten tiles). However, their innate accuracy stats are through the roof, and optional abilities at higher ranks may push them even higher. Squaddie Corporal Sergeant Lieutenant Captain Major Colonel Total Gains 75 (+10) 78 (+3) 81 (+3) 84 (+3) 88 (+4) 95 (+7) 105 (+10) + 40 Related abilities: Damn Good Ground: A passive +10% aim and defence while above the target (even if flying by way of Archangel Armour). Executioner: A passive +10% aim if the target has less then 50% health. Opportunist: Removes the aim penalty (and crit restriction) from Overwatch shots. Snap Shot: Allows firing as a second action, but at a -20% aim penalty. (Due to a bug, taking this perk applies this penalty to extra shots granted by Double Tap as well.) Disabling Shot: Shot empties the target's weapon, but at a -10% aim penalty. Low Profile: The sniper receives a high cover bonus of +40% while in low cover, rather then the usual +20%. Headshot: A +30% chance to crit.

Supports

Supports are very "mid-range" in terms of accuracy, and their potential damage output isn't anything to brag about in comparison to other classes. It should be noted that regardless of range, the rifles and pistols available to them will typically each have the same chance to hit as the other (excluding any weapon-specific bonuses, such as that available to the Light Plasma Rifle or Foundry-upgraded pistols). Their smoke grenades can grant defence bonuses to units they cover. Squaddie Corporal Sergeant Lieutenant Captain Major Colonel Total Gains 70 (+5) 73 (+3) 76 (+3) 79 (+3) 82 (+3) 85 (+3) 90 (+5) + 25 Aim-related abilities: Combat Drugs: A passive bonus granting a +20% aim and +10% crit chance bonus to units firing from within the support's smoke clouds. Smoke Grenade: Creates a two-turn smoke cloud granting +20% defence to all units (friend or foe) within it. Rifle Suppression: -30% to target's aim until next turn. Dense Smoke: A passive bonus causing the support's smoke clouds to grant +40% defence instead of the regular 20%.

Alien Stats

Aliens are, for the most part, about on par with lower-ranked XCOM soldiers, though on difficulty levels above normal they receive a +10 aim/crit bonus (and an extra +10 aim for Outsiders and Muton Elites on Impossible).

Many aliens have innate defensive bonuses, which XCOM solders require certain forms of armour to acquire.

It's worth noting that the Light Plasma Rifle seen earlier on in the game (especially favoured by Thin Men) confers an additional +10 bonus to its wielder (though it's been reported that this doesn't apply to the aliens - so maybe this is only worth noting on the basis that it doesn't work?). Those aliens which use melee attacks (the Chryssalid, the Zombie, and the Muton Berserker) never miss.

Floaters in particular gain +20% defence whenever in flight. This can be circumvented if they're actually using real cover and you manage to flank them.

Name	Aim	Defence	Name	Aim	Defence
Sectoid	65	0	Outsider	70	0
Thin Man	65	0	Floater	50	0
Chryssalid	Melee	10	Muton	70	10
Zombie	Melee	0	Drone	60	10
Cyberdisc	70	10	Sectoid Commander	85	20
Muton Berserker	Melee	20	Sectopod	80	30
Heavy Floater	70	10	Muton Elite	80	20
Ethereal	n/a	40	Uber Ethereal	n/a	40

Equipment

There are three main types of equipment available to you that can affect accuracy: weapons, armour and items.

Of all the guns you may equip, only one offers improved accuracy over others of its kind - the Light Plasma Rifle, which adds +10% to any shots made with it. (Can someone please confirm with source as to whether aliens get this bonus?) However, each class of weapon - shotguns, snipers, or "other" - handles accuracy differently depending on range.

The Foundry project Improved Pistol II states that it offers a +10% to pistol aim. At the time of the current patch, this function is bugged and doesn't actually grant any bonus (although it DOES appear amongst the list of bonuses that will apply to your shots, it's NOT added on to the final total).

Hence the main item to turn to when looking for a little extra reliability is the S.C.O.P.E., which grants an additional +10% aim (and, with the right upgrade, crit chance) to all conventional weapons. Heavies in particular find this useful (due to their low base aim), but it's a solid choice for most any unit.

The Arc Thrower is notable in that it's not considered a weapon, and uses entirely different firing mechanics - its chance to hit depends only on the health of the target. Explosive weapons are another exception, in that they always hit everything within their blast radius - for those, a "miss" constitutes somehow firing them in an entirely different direction to where they were aimed.

Conversely, some forms of armour can allow you to raise your defence, reducing the chance of alien shots landing. While all types grant additional hit points, Skeleton Suits and Psi Armour grant +10% defence to the wearer at all times, whilst Ghost Armor gives +20% even without cloaking (the equivalent to being in low cover - which stacks if they really are in cover).

In fact, when you consider that Skeleton Suits also grant additional movement points and the grapple - and are actually cheaper to produce then Carapace Armour - they may be the better choice for your units regardless of class. Its one deficit is a single less hit point.

Contrary to its item description, Archangel Armour does grant bonuses to your units when taking flight (but not when they're grounded). Taking to the air above your opponents grants the usual +20% aim and defence bonuses against them (same as for units such as Floaters and Hover SHIVs), and for Snipers, also triggers the Damn Good Ground perk - granting an additional +10% to each. Airbourne snipers can practically ignore high cover guarding aliens.

Weapon Range

An aim bonus may be granted based on the distance to the target, depending on the type of weapon used. For the purposes of determining this bonus, guns always fall into one of three different categories: shotguns, sniper rifles, or "everything else".

Most - from the humble Pistol through to the legendary Heavy Plasma - are treated the same in terms of accuracy. Have two soldiers at the same distance from your target, each'll get the same range bonus as the other. Such weapons may only receive range bonuses - if you're too far away to receive one (ten tiles or more), then there's no penalty.

The rifles used by Snipers, on the other hand, are the reverse: being closer then ten tiles inflicts a penalty, and moving further away simply lessons this until it goes away completely.

The only weapon type that has access to a range bonus in addition to a penalty is the shotgun class used by Assaults. A distance of less then ten tiles sees their accuracy spike up quickly; but a distance further then ten tiles inflicts a penalty at the same rate (though oddly enough, no such penalty applies to their damage - if they happen to hit at long range, they'll be just as devastating as a point-blank blast to the face).

The following formulas describe accuracy drop-off. Again, note that if the standard weapon bonus drops below 0, it's ignored, if the sniper penalty rises above 0 it's ignored, and the shotgun formula always applies. x and y describe the distance in tiles along each axis between the target and the shooter (i.e. Pythagoras is used to get the proper distance on any angle, so ten tiles in a straight line are about equal in distance to seven along a 45° angle). Final results are rounded down.

Standard Guns	Shotgun Class	Sniper Class

In addition, a very slight fractional penalty may be applied depending on the direction the shot is coming from. For example, a soldier with a rifle sitting an exact two tiles away from an alien may have a 33% range bonus, but another soldier with the same weapon and at the same distance might only get a 32% bonus if he's on a 90° angle (it appears this is because the base bonus drops from 42 to 41.6 in such a case, though the reason for this is unknown).

A list of pre-calculated values for some ranges have been recorded here.

Note: The partial brackets used in the shotgun formula represent a floor operation, or to put it another way, "round this value down".

Note 2: These formulas may not be 100% accurate.

Other Factors

Aside from the aim/defence bonuses available to each unit through their own powers and abilities, the environment also plays a key part in determining chance to hit.

One of your primary sources of defence - especially in the early game, before you can equip some decent armour - is cover. While understanding the full mechanics of cover is important (when it applies, how to circumvent it, and the risks of relying on it), for the purposes of accuracy the rules are that a half shield gives +20% defence, a full shield gives +40% defence, and if the firing unit has a flank or the target has no cover at all, then the shooter instead gets a crit chance bonus.

If a flank isn't possible and the cover can't be removed, a good way to get around it is with the height bonus - if you're above your target, you get +20% aim and defence against it (regardless as to what the difference IS). Snipers can add another +10% to each with the Damn Good Ground perk, and the bonus is also granted for flying Floaters or [[Archangel troopers (regardless as to what the in-game item description states).

Use of the hunker down ability (available to most units so long as they're in cover) doubles your cover and armour bonus, but doesn't apply to perk bonuses such as the Assault's Tactical Sense.

The similar-sounding Head Down ability - only available to non-combatant units as their only action other then moving - grants +10% defence to that unit regardless as to whether they have cover or not.

Finally, Overwatch shots are taken at a 20% accuracy penalty, or 40% if the target is dashing. This is mitigated somewhat in that moving units don't get cover, but keep it in mind when setting up ambushes (and certainly when considering taking the Support's Covering Fire perk, which allows overwatch shots on units that ARE in cover).

Psionic Abilities

While psionic abilities have their own mechanics for determining the odds of success, two are relevant in the discussion of firing accuracy:

Mind Fray is the first ability granted to any budding psionic, and against most races, deals very reliable (if not guaranteed) damage. Assuming it doesn't pop the enemy's head outright, that unit will suffer debuffs for two turns including a -25% aim penalty (better then moving all your units from low to high cover).

Telekinetic Field is purely defensive; it acts like a dense one-turn smoke cloud, granting +40% defence to any units standing near the point it was triggered.

Critical Hits

(Stub, will need to link off to Damage for info about, well, damage)

The RNG

Random Number Generators are algorithms intended to produce sets of unpredictable numbers. They are not usually written by regular developers, but are rather provided by the programming languages they use.

Computers lack the facilities to "make numbers up". RNGs instead calculate values based on at least two bits of information: a "seed" value, and the number of values that've been returned since that seed was first used (or, if you think of an RNG as a set of dice (with as many sides as you like!), the number of "rolls" you've made with them since starting your game).

Because of this, if you choose a given seed value and ask for five rolls in a row, then reset your roll count to 0 before asking it to perform them again, you'll get the same numbers back every time - so long as you use the same seed. Hence, in order to achieve results that appear truly "random" to the user, standard technique is to choose a seed value that'd be very hard to predict (such as the exact time the program started in milliseconds) then never intentionally use that seed again.

XCOM (amongst other Firaxis games) deviates from the usual way of doing things by recording the seed and roll count when you save your game. When you fire a shot, a number from about 0 to 99 gets rolled, and if the stated chance to hit was higher it connects with the target. Because it's not feasible for the player to keep track of the number of rolls made that game - let alone understand the RNG algorithm or determine what the seed might be - the result appears random.

But what if you saved the game before firing, then reload and try it again? The same seed/roll count/algorithm gets used, and so the result generated is the same.

This may give an impression that the game's events are pre-determined, but they're truthfully only calculated when and where they're required. The goal is, of course, to prevent players from cheating - by reloading high-risk shots over and over until the dice roll in their favour and they hit.

If the system has a flaw, it's that knowing whether the next number will be high or low makes it easy to decide whether you should have your rookie chance that long-range shotgun shot, or perhaps just have everyone hunker down and let the alien suffer that particular roll of the dice on his turn.