Ranged Combat

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For ranged combat the Combat score is used to determine the likelihood of a missile hitting the target (X,Y) position on the map grid. Each combat score has been hard-coded a percentage-based chance for the missile to hit its target, and if the missile is calculated to miss then it will hit one of the grid cells close to the target cell at random, causing the attack to hit any non-friendly unit on that cell instead. For ranged combat, the Combat score is capped at 25 when calculating the hit chance, meaning that having more Combat than that at the time the hit calculation is being worked out has no effect for the hit chances. However, that's not to say having more than 25 Combat to begin with is a waste, as the Combat stat can get reduced while attacking certain targets. However, no matter the Combat score, it still does not give a unit 100% chance to hit the target cell though, as no percentage can ever be higher than 99% and a target's movement can potentially evade a successful strike by changing direction during the projectile's flight.

It's useful to note that in ranged combat high Combat score is not always desirable though: In fights between large armies it's better to have your ranged units miss their intended targets and hit other enemy units to spread the damage out more evenly, than to have everyone target the same unit. Targeting the same unit can cause most of the missiles to be effectively wasted when the target unit dies in the middle of the volley of missiles. Of course exceptions to the rule exist, such as in situations where you need to focus fire on an enemy hero, a dragon or a titan. In these cases high Combat score would be more desirable.

There are quite a few stages that occur in ranged combat. Although they are arranged in how they are process by the game, here is the order at which the stages occur:
 * 1) Fighting in melee penalty (quartering combat)
 * 2) Target's evasion bonus (reducing attacker's combat)
 * 3) Hit chance worked out based on new combat value
 * 4) Height effects (increasing / decreasing hit chance based on elevation difference)
 * 5) Psyche effects penalty to hit chance
 * 6) Ensuring minimum / maximum hit chance is not exceeded (1% / 99%)

Range
Ranged combat is used when a unit with a range greater than 0 tries to attack. The range itself refers to the number of "cells" on a terrain tile that the target can be within for the attacker to be able to launch an attack. If the target is beyond the number of cells from the attacker, then the attack cannot be launched. (A standard terrain tile is 10 cells wide and 10 high) However, once the attack has been issued, then the distance between the attacker and target is ignored and the projectile will travel across what ever distance necessary to hit the intended cell. So an Imp with a range of 2 for example, has to be within 2 cells of its target to launch an attack. But its projectile can travel across the entire map if needed to reach its target. (Think using Home Portal as the Imp attacks but before it fires its projectile)

It is also the Range stat that decides whether a unit will suffer a penalty to their Combat stat when fighting in melee. Any unit with a Range value higher than 0 will suffer the penalty, even if the unit does not have the Missile unit flag. Consequently, this also means units with the Missile flag would not suffer this combat penalty if they had a Range stat of 0 (such as being under the influence of Awe). The penalty itself is a -75% reduction to the Combat stat (quartered). So a ranged unit with a Combat score of 8 would be fighting with a Combat score of just 2 when engaged in melee.

Evasion Bonuses
Although the target's combat score is not used to determine the initial hit chance, their speed stat can help them evade the attack. Faster targets, as expected, are harder to hit and the missile unit's combat score can essentially be "lowered" when trying to hit them. The formula is as follows:

Missile unit's combat - (target's speed / 6)

This makes it so a missile unit with a combat of 10 (which would normally give a hit chance of 60%) would suffer -3 to their combat when trying to hit a speed 20 unit. This gives the missile unit a new hit chance of 45%.

Hit Percentages
When a unit ties to hit with a ranged attack, the target's combat is ignored and instead has a fixed chance of hitting based initialy on the attacker's combat. Below is a table containing a missile unit's percentage of chance to hit an enemy target with their combat skill:

Height Effects
The height of the terrain can affect the hit chance and even the damage amount. Each terrain cell has a defined "elevation" that tells the game how high it is, and anything that's on top of that cell.

Hit Chance Modifiers
Terrain height also affects the accuracy of a missile unit, increasing or even decreasing the hit chance depending on the difference between the attacker and the target's height. If the attacker is actually lower than the target, then the hit chance ends up being reduced. Here is the exact formula:

Hit chance + (attacker's height - target's height x10)

So if a unit with a combat of 10 (60% chance to hit normally) was on High Grass terrain (elevation 6), they would get a bonus of +30 when attacking a target on normal Grass terrain (elevation 3). So their hit chance would become 90%. If the attacker and target switched places, the hit chance would be reduced by 30 and the new hit chance would be just 30%.

Damage Modifiers
Missile damage from both units and buildings are affected by the elevation difference between the attacker and the target, which can lead to missile attacks dealing more or even less damage when attacking targets that are on higher or lower terrain. This damage bonus (and penalty) are predefined depending on the elevation difference:

Target on lower elevation by 7 = 300% damage.

Target on lower elevation by 6 = 250% damage.

Target on lower elevation by 5 = 200% damage.

Target on lower elevation by 4 = 150% damage.

Target on lower elevation by 3 = 140% damage.

Target on lower elevation by 2 = 130% damage.

Target on lower elevation by 1 = 120% damage.

Same elevation = 100% damage.

Target on higher elevation by 1 = 80% damage.

Target on higher elevation by 2 = 70%  damage.

Target on higher elevation by 3 = 60%  damage.

Target on higher elevation by 4 = 50%  damage.

Target on higher elevation by 5 = 40%  damage.

Target on higher elevation by 6 = 30%  damage.

Target on higher elevation by 7 = 20%  damage.

This means missile units placed on High Grass terrain deal 140% damage to units on normal Grass terrain. But if those missiles units on High Grass terrain were attacking units on Desert terrain, then their damage amount would be boosted to a staggering 250%! (Desert is lower than Grass, which are both lower than High Grass)

Flying units are always treated as having +1 elevation to what ever terrain they are currently above. This makes it so they inherit the missile bonuses when attacking grounded units. However, as this is still based on the current terrain elevation, it means grounded units on higher terrain can still gain a missile bonus against flying units. I.E: An Eagle above desert terrain (elevation 0) would count as having an elevation of 1. A Squire on a nearby dirt cliff (elevation 3) would have its damage increased against the Eagle to 130% as the Eagle would still count as being lower by 2 points of elevation.

Towers also count as having +1 to their elevation for the purpose of their attacks, making them hit deceivingly harder than their stats would suggest.

Psyche Penalties
Some Psyche conditions affect a missile unit's hit chance by a fixed reduction. This reduction is applied after working out the hit chance based on combat.

Units suffering from Fear and Terror have their hit chance reduced by 20 (to a minimum of 1%).

Units suffering from Awe also have their hit chance reduced by 20, but will also lose their range stat entirely. However they can still hit flying targets despite attacking in melee combat. Since a missile unit's combat is halved when fighting in melee, it means that missile units suffering from Awe become next to useless. The loss of range of course hurts, their combat becomes halved when they make contact to attack and then the chance is reduced by 20 after all this. A missile unit with a respectable combat stat of 16 (typically giving it a hit chance of 84%) would end up with only a hit chance of 30% when under the effects of Awe!

Critical Hits
Like with melee attacks, ranged attacks can score a critical hit - dealing double damage. But like with the projectile's standard hit chance, the critical hit chance is also a fixed percentage. Under normal situations a missile will always have a 4% chance to score a critical hit. The Flaming Arrows projectile, however, can re-roll this if it failed the first time, giving it two attempts at scoring a critical hit. Once a critical hit has been assured, the critical effects for a damage type will occur once the projectile hits an enemy unit, with the only exception being slashing projectiles where the critical-cleave effect plays as soon as the projectile is launched - cleaving around the attacking unit.

Ranged projectiles can never score a Deathblow.

Lightning Projectile Exceptions
Lightning projectile attacks that miss an intended target still do not hit an enemy unit if the attack strikes a square with an enemy unit on it. In addition to that, lightning projectiles can strike through void terrain (cavern Walls).

Resistance to Missiles
Some units (and all buildings) have or can acquire a trait to make themselves highly resistant to missile, reducing the damage by 75%. For units, this special missile resistance only affects physical typed missiles (Piercing, Slashing and Crushing) but flaming arrows and flaming-poison arrows are also resisted. For buildings, this special trait is far more limited - affecting just throwing axes, Ballista / Manticore bolts, javelins and all arrow types (but not flaming-poison arrows).

Becoming Resistant to Missiles
Naturally, Dwarf Runners, Dwarf Lords, Skeletons and Husks are resistant to missiles. However, the basic Orc unit can be upgraded to become resistant to missiles via the No Pain! research. Heroes who have access to the Rune Magic spell Resist Missile can make themselves temporary resistant to missiles, too.

Ignoring Missile Resistance
Being able to bypass a special missile resistance is a trait exclusive to the Barbarians and their javelin/spear missiles, but only after researching the Hunting skill in tier 2. There is no other missile in the game that can be upgraded to ignore a special missile resistance that would otherwise be affected by it.

Affect on Spells
Ranged combat is also used for certain spells to calculate whether they hit their targets or not. Most damage spells in the game have no combat calculations at all, but the spells that use different kinds of "lightning beam"-effects such as Wildfire and Ice storm do a ranged combat check by the casting hero or unit for each target unit. Because of this it's important for heroes using these spells to have a reasonable combat score even if they won't be doing any melee fighting.