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'''Damage''' is a general term for the amount of [[health]] loss a [[creature]] or a [[spell]] can cause to a single creature or to a creatures [[stack]]. If a creature suffers more damage than its current health, it is eliminated, while in a stack of creatures, the topmost dies. The remainder of the damage is dealt to the next one and so forth until all damage is dealt or the whole stack is eliminated. | '''Damage''' is a general term for the amount of [[health]] loss a [[creature]] or a [[spell]] can cause to a single creature or to a creatures [[stack]]. If a creature suffers more damage than its current health, it is eliminated, while in a stack of creatures, the topmost dies. The remainder of the damage is dealt to the next one and so forth until all damage is dealt or the whole stack is eliminated. | ||
Creature's ability to deal damage typically has a range, which means that it causes randomly chosen damage between the minimum and maximum value. Some creatures like [[Naga]]s do not have a damage | Creature's ability to deal damage typically has a range, which means that it causes randomly chosen damage between the minimum and maximum value. Some creatures like [[Naga]]s do not have a damage treshold meaning they always do the same amount of damage. Creatures in a stack cause individual damages, and the combined damage of the stack is calculated by adding them together. However, the final damage can deviate from the combined damage greatly because of different additions and reductions, which are covered in the next section. | ||
Spells can deal damage much like creatures do, except that the amount of inflicted damage does not vary within a range but is fixed. The exact amount of unmodified spell damage can always be calculated with a linear formula. For example, basic [[Lightning Bolt]] cast by a hero with 7 [[Primary skill#Power skill|spell power]] does 7 × 25 + 10 = 185 damage. For other spells different values than 25 and 10 need to be substituted. The eventual amount of spell damage is modified as follows: | Spells can deal damage much like creatures do, except that the amount of inflicted damage does not vary within a range but is fixed. The exact amount of unmodified spell damage can always be calculated with a linear formula. For example, basic [[Lightning Bolt]] cast by a hero with 7 [[Primary skill#Power skill|spell power]] does 7 × 25 + 10 = 185 damage. For other spells different values than 25 and 10 need to be substituted. The eventual amount of spell damage is modified as follows: | ||
*The [[Sorcery]] secondary skill increases spell damage. | *The [[Sorcery]] secondary skill increases spell damage. | ||
* | *Heroes increase spell damage with 3% per hero level when casting the spell they [[Hero specialty#Spell specialties|specialize]] in. | ||
*[[Elemental]]s take double damage from certain spells. [[Fire Elemental]]s, for example, are vulnerable to [[Ice Bolt]]. | *[[Elemental]]s take double damage from certain spells. [[Fire Elemental]]s, for example, are vulnerable to [[Ice Bolt]]. | ||
*The damage that [[Stone Golem]]s, [[Iron Golem]]s, [[Gold Golem]]s and [[Diamond Golem]]s take from spells is reduced by, respectively, 50%, 75%, 85% and 95%. | *The damage that [[Stone Golem]]s, [[Iron Golem]]s, [[Gold Golem]]s and [[Diamond Golem]]s take from spells is reduced by, respectively, 50%, 75%, 85% and 95%. | ||
*The spells [[Protection from Air]], [[Protection from Earth|Earth]], [[Protection from Fire|Fire]] and [[Protection from Water|Water]] reduce spell damage from the school they protect against by 30%, or even by 50% when cast at | *The spells [[Protection from Air]], [[Protection from Earth|Earth]], [[Protection from Fire|Fire]] and [[Protection from Water|Water]] reduce spell damage from the school they protect against by 30%, or even by 50% when cast at advanced or expert level. | ||
*[[Dwarf|Dwarves]] have a 20% chance and [[Battle Dwarf|Battle Dwarves]] a 40% chance to completely resist any (damage) spells. | |||
*Creatures adjacent to [[Unicorn]]s and [[War Unicorn]]s have a 20% chance to completely resist any (damage) spells. | |||
*The [[Resistance]] secondary skill and resistance artifacts such as the [[Boots of Polarity]] provide each creature stack of a hero's army with a chance to resist any (damage) spell. | |||
*Some creatures are naturally [[immunity|immune]] to certain (damage) spells. | |||
== Damage calculation of creature stacks == | == Damage calculation of creature stacks == | ||
=== The damage calculation formula === | === The damage calculation formula === | ||
{| | {| border=1 cellspacing=0 style="margin: 0 0 0 1em; float:right; border: 1px solid; background:#{{Grey 3}};" | ||
|+ <big>'''Table 1: Damage calculation variables'''</big> | |+ <big>'''Table 1: Damage calculation variables'''</big> | ||
|- | |- bgcolor={{Grey 1}} | ||
! {{-}}Description{{-}} | ! {{-}}Description{{-}} | ||
|- | |- | ||
| {{-}}I<sub>1</sub>   = 0.05 × ([[Attack]] - [[Defense]]) (if A ≥ D) | | {{-}}I<sub>1</sub>   = 0.05 × ([[Attack]] - [[Defense]]) (if A ≥ D) | ||
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| {{-}}I<sub>4</sub>   = 1.00 for [[luck]]y strikes | | {{-}}I<sub>4</sub>   = 1.00 for [[luck]]y strikes | ||
|- | |- | ||
| {{-}}I<sub>5</sub> | | {{-}}I<sub>5</sub>   = 1.00 for [[Death Blow]], [[Ballista]] double damage<br> | ||
     = 1.00 if [[Elemental]] attacks opposite [[Elemental]] type<br> |      = 1.00 if [[Elemental]] attacks opposite [[Elemental]] type<br> | ||
     = 0.50 for [[hate]]<br> |      = 0.50 for [[hate]]<br> | ||
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| {{-}}R<sub>3</sub> = 0.05 × R<sub>2</sub> × hero level for Armorer [[Hero_specialty#Secondary_skill_specialties|specialty]] | | {{-}}R<sub>3</sub> = 0.05 × R<sub>2</sub> × hero level for Armorer [[Hero_specialty#Secondary_skill_specialties|specialty]] | ||
|- | |- | ||
| {{-}}R<sub>4</sub> = 0.15, 0.30 | | {{-}}R<sub>4</sub> = 0.15 for [[Shield]], 0.30 at advanced, expert level<br> | ||
   = |    = 0.25 for [[Air Shield]], 0.50 at advanced, expert level<br> | ||
   = 0.50 for shooter with (basic) [[Forgetfulness]] | |||
|- | |- | ||
| {{-}}R<sub>5</sub> = 0.50 if attacker has [[range penalty|range]] or [[melee penalty]]{{-}} | | {{-}}R<sub>5</sub> = 0.50 if attacker has [[range penalty|range]] or [[melee penalty]]{{-}} | ||
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|- | |- | ||
| {{-}}R<sub>7</sub> = 0.50 for retaliation after being [[Blind]]ed<br> | | {{-}}R<sub>7</sub> = 0.50 for retaliation after being [[Blind]]ed<br> | ||
   = 0.75 for retaliation after advanced [[Blind |    = 0.75 for retaliation after advanced [[Blind]] | ||
|- | |- | ||
| {{-}}R<sub>8</sub> = 0.50 for Psychic Elemental vs. [[mind spell]] immunity<br> | | {{-}}R<sub>8</sub> = 0.50 for Psychic Elemental vs. [[mind spell]] immunity<br> | ||
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   = 0.50 if target is [[Petrify|petrified]]<br> |    = 0.50 if target is [[Petrify|petrified]]<br> | ||
   = 0.75 for retaliation after being [[paralyze]]d |    = 0.75 for retaliation after being [[paralyze]]d | ||
|} | |} | ||
Mathematical formula for calculating the final damage (DMG< | Mathematical formula for calculating the final damage (DMG<sub>f</sub>) is: | ||
<big><code> DMG<sub>f</sub> = DMG<sub>b</sub> × (1 + I<sub>1</sub> + I<sub>2</sub> + I<sub>3</sub> + I<sub>4</sub> + I<sub>5</sub>) × (1 - R<sub>1</sub>)×(1 - R<sub>2</sub>)×(1 - R<sub>3</sub>)×(1 - R<sub>4</sub>)×(1 - R<sub>5</sub>)×(1 - R<sub>6</sub>)×(1 - R<sub>7</sub>)×(1 - R<sub>8</sub>)</code></big> | |||
Primary determinant for the final damage is the base damage (DMG< | Primary determinant for the final damage is the base damage (DMG<small>b</small>), which is affected by the number of attacking creatures and their damage range. All other variables are basically modifiers of the base damage. Variables are denoted as I if they (i)ncrease damage and as R if they (r)educe it. I<small>1</small> and R<small>1</small> are mutually exclusive, but all other variables may simultaneously affect the final damage (DMG<small>f</small>). A brief summary of the variables have been given in the table on the right. | ||
To summarize the above formula, the content of the first parentheses increase the base damage by multiplying it with a modifier varying from 1.00 to 8.00, and the content of the second parentheses reduces the damage with a modifier varying from 0.00 to 1.00. | |||
=== Attack-Defense difference – variables I<sub>1</sub> and R<sub>1</sub> === | |||
The Attack-Defense difference, denoted by I<small>1</small> and R<small>1</small> in the formula, is typically the main modifier of base damage. It is calculated as the difference between the attacker's attack value and the defender's defense value. These are determined by adding up the attack skill of the attacking hero and of the attacking creature type, and by adding up defense skill of the defending hero and defending creature type. Spells and creature abilities that affect attack or defense values, such as [[Bloodlust]] and [[disease]], are also taken into account in this part of the formula, as are any bonuses from [[native terrain]] or [[Hero_specialty#Creature_specialties|creature specialties]]. | |||
If the attacking creature's total attack value is higher than the defending creature's total defense value (i.e., the difference is positive), then the attacking creature receives a 5% bonus to its base damage for every point the attack value is higher. If the difference is negative, then the attacking creature receives a 2.5% penalty to its total damage for every point the attack value is lower. A positive Attack-Defense difference therefore increases damage, meaning that the variable I<sub>1</sub> in the formula is positive whereas R<sub>1</sub> is 0. Conversely, a negative Attack-Defense difference decreases damage, meaning that R<sub>1</sub> is positive whereas I<sub>1</sub> is 0. An Attack-Defense difference of 0 does not modify base damage. | |||
The Attack-Defense difference can modify base damage only within a specific limit. This limit is reached by a positive Attack-Defense difference of +60 and a negative Attack-Defense difference of -28. This means that a high attack skill can grant no more than +300% bonus damage, whereas a high defense skill can grant no more than a -70% penalty. Thus, the Attack-Defense difference can modify a base damage of 100 to no more than 400, and to no less than 30. | |||
The Attack-Defense difference | |||
=== Secondary skill factors – variables I<sub>2</sub> and I<sub>3</sub> === | |||
Variable I<small>2</small> represents [[secondary skill]] modifier of either [[Archery]] or [[Offense]] depending on the attack type. Creatures able to [[Ranged attack|attack from the distance]] gain bonus from the Archery secondary skill when using their ability. If a creature engages into [[melee]] combat, it gains bonus to its damage from Offense secondary skill. | |||
Variable I<sub>2</sub> is related to secondary skills [[Archery]] and [[Offense]], and I<sub>3</sub> to heroes specializing in these skills. Archery and Offense cannot affect damage simultaneously, because they are related to [[ranged attack|ranged]] and [[melee]] attacks, respectively. For ranged attacks, Archery secondary skill may give 0, 0.10, 0.25 or 0.50 depending on whether the hero has the skill and on what level the skill is. Similarly, Offense may give 0, 0.10, 0.20 or 0.30 to melee attacks. | |||
Three heroes specialize in Archery or Offense. Orrin has Archery as a specialty while Gundula and Crag Hack has Offense. They receive additional bonus from Archery or Offense secondary skill, as calculated with the following formula: | |||
<big><code>I<sub>3</sub> = 0.05 × hero level × I<sub>2</sub></code></big> | <big><code>I<sub>3</sub> = 0.05 × hero level × I<sub>2</sub></code></big> | ||
As can be seen from the formula, the specialty bonus requires that the hero has the appropriate secondary skill, otherwise I<sub>2</sub> becomes 0, which leads I<sub>3</sub> to become 0 as well. In other words, Orrin does not receive his specialty bonus if he does not have Archery secondary skill; same applies to Gundula and Crag Hack with Offense | As can be seen from the formula, the specialty bonus requires that the hero has the appropriate secondary skill, otherwise I<sub>2</sub> becomes 0, which leads I<sub>3</sub></code> to become 0 as well. In other words, Orrin does not receive his specialty bonus if he does not have Archery secondary skill; same applies to Gundula and Crag Hack with Offense. By default these heroes start with the skill they specialize in, but in custom maps the map-maker may change the starting skills. | ||
Additionally, [[Adela]] and her [[Bless]] specialty is a special case of variable I<sub>3</sub>. Adela's Bless maximizes base damage as usual, but also deals extra damage according to the following formula: | |||
<big><code> | <big><code>SP = 0.03 × hero level '''÷''' creature level</code></big> | ||
Because of the division, Adela's Bless bonus is greater for low- | Because of the division, Adela's Bless bonus is greater for low-level than high-level creatures. Her Bless grants +3% damage per hero level to level 1 creatures, whereas it grants +0.6% per hero level for level 5 creatures. | ||
==== Luck as combat modifier – variable I<sub>4</sub> ==== | ==== Luck as combat modifier – variable I<sub>4</sub> ==== | ||
The | The luck variable may be either 0 or 1.00, depending on whether or not the attacking creatures gets "a lucky strike". This is determined by the combat variable [[luck]], which may be 0 (neutral), +1 (positive), +2 (good) or +3 (excellent). These values determine how often lucky strikes occur. These probabilities are, respectively, 0/24 (0%), 1/24 (4.17%), 1/12 (8.33%) and 1/8 (12.5%). Luck may be affected by artifacts, adventure map locations, spells and the secondary skill [[Luck (secondary skill)|Luck]]. | ||
==== Creature abilities – variable I<sub>5</sub> ==== | ==== Creature abilities – variable I<sub>5</sub> ==== | ||
The final variable capable of increasing total damage is I<sub>5</sub>, which denotes creature specialties from | The final variable capable of increasing total damage is I<sub>5</sub>, which denotes creature specialties from Cavaliers and Champions, Dread Knights, Ballistas, Elementals, and creatures that hate each other. | ||
The jousting specialty of [[Cavalier and Champion|Cavaliers and Champions]] lets them deal 5% extra damage for every hex they travel during the combat turn in which they attack their target: | |||
<big><code>I<sub>5</sub> = 0.05 × squares travelled</code></big> | <big><code>I<sub>5</sub> = 0.05 × squares travelled</code></big> | ||
[[Dread Knight]]s can make [[Death Blow]] attacks, which gives variable I<sub>5</sub> a value of 1.00, effectovely doubling base damage (though not necessarily total damage). The I<sub>5</sub> variable is also 1.00 for a [[Ballista]] whose shots deal double (base) damage. Additionally, there are a few creatures who [[hate]] each other, which gives I<sub>5</sub> a value of 0.50 when they attack each other. This is true for [[Angel]]s and [[Devil]]s, [[Titan]]s and [[Black Dragon]]s, and [[Genie]]s and [[Efreet]]i. Finally, [[Fire Elemental]]s and [[Water Elemental]]s, as well as [[Air Elemental]]s and [[Earth Elemental]]s do double base damage against each other (i.e., I<sub>5</sub> = 1). | |||
==== | === Defense variables === | ||
==== Secondary skill factors – variables R<sub>1</sub> and R<sub>2</sub>==== | |||
Just like the variables I<sub>2</sub> and I<sub>3</sub> denote how learning and specializing in Archery and Offense increases, respectively, ranged and melee damage, so do the variables R<sub>2</sub> and R<sub>3</sub> denote how learning and specializing in [[Armorer]] reduces both ranged and melee damage. R<sub>2</sub> can take the values 0.05, 0.10 and 0.15, indicating that basic, advanced and expert Armorer reduce damage by, respectively, 5%, 10% and 15%. The three heroes with an Armorer specialty - [[Mephala]], [[Neela]] and [[Tazar]] - double the effectiveness of the Armorer skill when they reach level 20, as shown by the following formula: | |||
<big><code>D<sub>2</sub> = 0.05 × hero level × D<sub>1</sub></code></big> | |||
Armorer has two unexpected side effects. First, heroes with Armorer take double damage from [[arrow tower]]s. Second, damage is reduced by 1 if creatures from a hero with Armorer take an amount of damage that is exactly an integer value. Thus, if 100 [[Peasant]]s attack a stack of Peasants commanded by a hero with basic Armorer (and the Attack-Defense difference is 0), damage is not 100 × 1 ×(1 - 0.05) = 95, but 94. If the attack had instead been performed by 99 Peasants, the damage would be 99 × 1 ×(1 - 0.05) = 94.05, which is not an integer value and therefore rounded off in the usual way, that is, to 94. | |||
==== Spells - Variable R<sub>4</sub> ==== | |||
There are many spells that modify damage, but most do so by increasing or decreasing the attack and defense skills of allied or enemy troops. [[Stone Skin]], for example, increases an allied unit's defense skill, and therefore modifies damage by affecting variable R<sub>1</sub>. The only spells that modify damage directly are [[Shield]], [[Air Shield]], and [[Forgetfulness]]. Shield reduces all [[melee]] damage done to the hero's troops by 15% (R<sub>4</sub> = 0.15), or even by 30% when cast with advanced or expert proficiency. [[Air shield]] reduces all [[ranged attack|ranged]] damage done to the hero's troops by 25% (R<sub>4</sub> = 0.25), or even by 50% when cast with advanced or expert proficiency. [[Forgetfulness]], when cast with basic or no proficiency, causes half of an enemy creature stack to forget to use its ranged attack, effectively halving its ranged damage (R<sub>4</sub> = 0.50). | |||
====Range and Melee penalty - variable R<sub>5</sub>==== | |||
[[Ranged attack|Ranged units]] do only 50% damage (R<sub>5</sub> = .50) to targets that are situated at a distance of ten or more [[hex]]es on the combat field. This range penalty is negated by [[Sharpshooter]]s and by heroes carrying the [[Golden Bow]] or [[Bow of the Sharpshooter]]. When a target occupies two hexes, it is possible for a range penalty to apply to the second hex, but not to the first hex the creature is standing on. | |||
[[ | |||
When a hex adjacent to a ranged unit is occupied by an enemy unit, the ranged unit is unable to shoot (i.e., blocked). It has to resort to [[melee]] attacks. This typically reduces its damage by 50% (R<sub>5</sub> = .50). [[Beholder]]s, [[Evil Eye]]s, [[Medusa]]s, [[Medusa Queen]]s, [[Mage|Magi]], [[Arch Mage|Arch Magi]], [[Zealot]]s, [[Enchanter]]s and [[Titan]]s are the only ranged units that do not suffer from this [[melee penalty]]. | |||
====Obstacle Penalty - variable R<sub>6</sub>==== | |||
[[Ranged attack|Ranged units]] that during a siege attack a target behind a wall receive an [[obstacle penalty]] if the wall protecing the target is not destroyed. As a result, their damage is reduced by 50% (R<sub>6</sub> = .50). This damage is halved once again if a range penalty applies. The obstacle penalty is negated by [[Arch Mage|Arch Magi]] and [[Sharpshooter]]s, and by heroes carrying the [[Golden Bow]] or [[Bow of the Sharpshooter]]. | |||
==== Blind - variable R<sub>7</sub> ==== | |||
The spell [[Blind]] is deactivated when a blinded creature stack is attacked. Any retaliation against this attack will not be at full strength. It will be at only 50% strength (R<sub>7</sub> = 0.50) when Blind is cast with basic or no proficiency, and at 25% (R<sub>7</sub> = 0.25) when cast with advanced proficiency. An attack that deactivates expert Blind cannot be retaliated against, but the targeted creature stack does retain its ability to retaliate against another attack in that same combat round. [[Unicorn]]s and [[War Unicorn]]s cast Blind with basic proficiency, unless the battle takes place on [[Magic Plains]]. | |||
==== Creature Specialties - variables R<sub>8</sub> ==== | |||
* Creatures | |||
** Attacker is Psychic Elemental, defender is immune to Mind spells | |||
** Attacker is Magic Elemental, defender is Magic Elemental or the Black Dragon | |||
** Petrified | |||
** Paralyzed | |||
== Examples == | |||
''No heroes are assumed to be present in the battle.'' | |||
*'''2''' [[Naga]]s attack a stack of [[Pikeman|Pikemen]]. | |||
*The [[Naga]]s have a single unit damage value of '''20''' and their Attack skill is '''16'''. | |||
*A [[Pikeman]] has '''10''' [[health]] and their Defense skill is '''5'''. | |||
*The base stack damage done by the stack of [[Naga]]s is '''2 * 20 = 40'''. | |||
*The [[Pikeman|Pikemen]]'s Defense skill ('''5''') is subtracted from the [[Naga]]s' Attack skill ('''16'''), which gives us '''11''', giving the [[naga]]s an att/def damage bonus. | |||
*The dealt damage will after the att/def consideration thusly have the bonus percentage modificator of '''5%''', multiplied with the damage bonus number in this case, '''11''', resulting in '''55%''' bonus percentage of the [[Naga]]s damage towards the [[Pikeman|Pikemen]]. | |||
*So the damage is increased by a '''55%''' increase and the [[naga]]s through superior attack skill have '''155% damage''' on the [[Pikeman|Pikemen]] stack. | |||
*The total damage thus is '''40 * 1.55 = 62''' damage points. | |||
*'''6''' [[Pikeman|Pikemen]] will be killed, and the top [[Pikeman|Pikemen]] of the remaining stack will have '''8''' health left. | |||
When the remaining (if any) '''[[Pikeman|Pikemen]]''' (attack points of 4) '''attack''' the '''[[naga]]s''' (sporting 13 points of defense): | |||
*-22.5% damage would be dealt by the [[Pikeman|Pikemen]] to the 5 creature level higher [[naga]] chimera stack. | |||
*The '''difference''' between the [[Pikeman|Pikemen]] attack ('''4''') and the [[naga]]s defense ('''13''') would mean '''9 malus points''' with a malus point resulting in 2.5 % each malus point (the half of the bonus points). | |||
* ((2.5)*-9)% is -22.5% damage the [[Pikeman|Pikemen]] can damage the [[naga]]s with. | |||
[[Category: Combat]] | [[Category: Combat]] | ||
[[Category: Terms]] | [[Category: Terms]] |