Piercing and Resistance

Updated 9/23/2016 with a good data point to drive accuracy..

Piercing and Resistance is a battle system in Castle Age that is used in both Player vs. Player Battles (including Guild Battles) and Monster Hunting. Piercing relates to enhanced abilities to cause damage to your opponent, while resistance relates to enhanced abilities to defend against damage from your opponent (and vice versa for them). Types are: Certain heroes, items, and gems and items will grant your character piercing or resistance values.
 * Physical Piercing / Physical Resistance
 * Fire Offense / Fire Defense
 * Water Offense / Water Defense
 * Earth Offense / Earth Defense
 * Wind Offense / Wind Defense

Note that effective July 2016 this system has undergone significant changes which are documented here.

PIERCE and RESISTANCE TYPES and effect in BATTLE:
There are five types of pierce and resistance in two broad categories. All five categories calculate independently for the battle and are added into a total battle amount. As an attacker, if your "Total" Piercing exceeds your opponent's "Total" Resistance, you obtain an additional percentage increase in your total effective attack based on the resultant "Total Net" Pierce which gives you a better chance of winning an attack.
 * 1) Physical  -  Physical pierce and resistance
 * 2) Fire, earth, water and wind are all considered ELEMENTAL and can be treated in a similar fashion.

As a defender, if your "Total" Resistance exceeds the attacker's "Total" Piercing, you obtain an additional percentage increase in your total effective defense based on the resultant "total net" resistance which gives you a better chance of defending against the attack.

Please note that "total" piercing and resistance is not a straight forward calculation at this time, but those terms are being used to be the fully calculated values using the algorithms that are currently known and a best guess at the parts that are not completely clear.

What we know about pierce and resistance includes: During a battle, the current belief on mechanics: Notes:
 * Piercing is always in play by the attacking player. Piercing is not used by the defending player.
 * Resistance is always in play by the defending player. Resistance is not used by the attacking player.
 * There is a threshold bonus applied to Physical pierce and Physical resistance that increases the amount of such bonus at every increasing amount. 4 x the physical pierce at 25 is less than the physical pierce at 100.  This curve tops out at a fixed value currently believed to be twice the physical amount.
 * There is a threshold bonus applied to Elemental pierce and Elemental resistance similar to to the bonus applied to physical pierce and resistance, however, elemental resistance threshold bonus is not as far along the curve by an amount to result in approximately 15-20% less than physical bonus, depending on position in the curve, in the range of pierce used in the game, which is roughly 0-2000.
 * Before threshold bonuses, Pierce and resistance are amounts of additional attack or defense at a rate of 10 = 1%. Threshold Bonuses will add additional attack percentages by increasing pierce or resistance values.  While the rate of 10 = 1% will always apply, the actual pierce or resistance used will not match the documented value but will be more based on the threshold bonuses it receives.
 * The devs have repeated that you can not calculate the results unless you know the data for both players. This comment, repeated several times, indicates that the threshold bonus is calculated on the net values of any element, rather than calculating the threshold bonuses on the player values and subtracting.  The difference between these two is small when the players are evenly matched, but becomes more pronounced as the values widen.
 * Note that Pierce and resistance are modifiers to attack and defense, and the threshold bonus implies that toons that work the newer monsters and gems will get significantly more advantage than older and larger toons that are not working the new content, giving those toons a tremendous advantage to win battles that they would otherwise not be able to approach.
 * Each of the 5 types of pierce and resistance are totaled, by type, for a player (10 results)
 * The NET for each pair of like types (physical pierce and physical resist, fire pierce and fire resist, etc..) are then calculated by subtracting the defenders calculated resistance value from the attackers calculated pierce value. Battle messages are produced for these values in web3 battle notes based on which number is larger.
 * The net value is then calculated using the formula provided below to get an effective net value.
 * All 5 net values are then added together to provide a "total net" amount, whether pierce for the attacker if it is positive, or resistance to the defender if its negative.
 * If the total net amount is pierce for the attacker, the attacker then receives that percent on their total effective attack in calculating battle results. For example, if the attackers total effective attack is 1000 and they receive 100 total net pierce, they get an additional 100 attack (1000 * 100/1000).
 * If the total net amount is resistance for the defender, the defender then receives that percent on their total effective attack in calculating battle results. For example,if the defenders total effective defense is 1000 and they receive 100 total net resistance they get an additional 100 defense (1000 * 100/1000).
 * In the past, there were no threshold bonuses, so documented values were the actual values. There is now a threshold bonus applied.
 * In the past, resistance did not come into play unless there was an equivalent non-zero pierce value, with the exception of physical resistance which would come into play if any pierce was included. All pierce and resistances are now considered in the calculation.
 * In the past, negative pierce was treated as zero. Now it effectively becomes resistance to the defender.
 * In the past, negative resistance may have been treated either as a pierce benefit for the attacker or as a reduction in resistance benefit for the defender. It is now simply in the formula.
 * As only the final percent is applied to the attackers or defenders total Battle strength (not the index which is divided by the level, but the true total strength), it does not matter what the actual attackers total effective attack, or defenders total effective defense are for the calculation, though those values are combined with the final net pierce or resistance to determine a winner or a loser.
 * The relative value of the physical bonus is based on this statement: "physical is 15-20% better than elemental in battle on average and for the equipment.
 * The threshold bonus being applied both to physical and elemental is supported by this statement:  "Does physical pierce and res work the same way as elemental pierce and res? Yes, they also get the threshold bonus"
 * The relative value of the threshold bonus between physical and elemental is supported by this statement: "if I have more physical pierce then you have physical resist, I get a very nice threshold bonus, The same with the elements as they are compared to each other the bonus is a bit lower than physical though so it will remain stronger as intended."
 * In order for the curve to meet the F(x) * N < F(N*X) at every point, all that is needed is a curve that always increases at ever point of x. In order to meet the graph concept that there is an asymptote, the asymptote must simply be a value at infinity.
 * This is the curve provided by the devs describing base pierce growth:

Strategy for success:

 * Physical Pierce and resistance are more valuable that equivalent amounts of elemental pierce and resistance. If you have to choose one or the other, physical will provide more value.
 * Higher Pierce and Resistance in any single type of the 5 types of pierce and resistance are more valuable than an equal amount shared across multiple elements. If you have to choose using two fire gems or a fire and water gem, two fire gems would be more valuable.
 * T his can all be simplified greatly so that if you just add 16% to the net physical amount, add it to elemental, and multiply the result by 1.6.  While this really only works in a defined range, its close enough typically in any battle. For exacting numbers, do the math.

Analysis of Pierce and Resistance formula (BEST GUESS ONLY)
Data point 1 - these two opponents "tied" in battle with 6 wins and 6 losses each in 12 battles:
 * Attacker: 12103 attack, 5326 defense, 520 physical, 10 fire, 15 water, 40 wind and 25 earth
 * Defender:17759 attack, 9512 defense, 145 physical, 86 fire, -15 water, 78 wind
 * Net pierce is 375, 30 Water, 25 earth. Net resistance is 76 fire and 38 wind "totaling" 316
 * 15,831.2 attack balances 24,417.4 defense which means that the total effective pierce is 542

Based on this result and the curve the devs provided, the formulas that are currently the best guess are: This shows up as the following graph, which is similar to the Dev issued graph: The resultant values at different levels of Pierce or Resistance would then be: Some notes: Note that in these formulas, x can be x, x to a power, or x times a factor which adjust the slope of the curve but not the actual curves involved. All of these formulas were rejected for the reasons indicated.
 * Calculate NET physical pierce (NPP) based on abs(Physical Pierce - Physical resistance)
 * Net Effective Physical Pierce = arctangent(NPP/1000*4)/(PI/2) where PI = 3.14159
 * Net Elemental Pierce (by element = NEP) based on abs(elemental pierce - elemental resistance)
 * Net Effective elemental Pierce = arctangent(NEP/1000*1.5)/(PI/2)
 * Devs indicated that effectively physical pierce and elemental pierce use the same curve, but elemental pierce is not quite as far down the table yielding about a 15-20% difference between them. This is really two different curves when plotted on the same pierce values as hailed in the graphic above.
 * Please note that the physical curve factor of 4, and the elemental curve factor of 1.5, and the assumption that the asymptote hits
 * Note that the higher the values, the "less better" physical is vs elemental, though it is always better.
 * As more testing results come in, if this curve still fits it can be fine tuned a bit to match numbers at various levels..
 * Several other formats for the graph have been tried including:

Examples of specific situations:
Note that this example assumes that both attacker and defender are exactly equally matched on total effective attacking total effective defence, and would encounter an exact tie if there were no pierce or resistance. You can see with this example that total pierce or resistance matter, and while a 50 physical vs 55 elemental loses, simply ratcheting it up to 500 and 550 actually reverses who would win the battle

PIERCE & RESISTANCE and Monsters

 * Certain monsters require physical pierce, sometimes of a particular element in order to gain maximum damage.
 * Certain monsters are require an elemental resistance in a certain element and you must have that elemental pierce in order to protect against getting a minion. This protection is not guaranteed at 100% but merely reduces the chance of getting a minion.
 * More information below in the notes for "EFFECTS IN MONSTER HUNTING"

Generals
Some generals have abilities that specialize in piercing (also called offense) and resistance. All information below are based on level 4 stats.

Notes:
 * If the generals' levels are equal, Aesir and Vanir will cancel each other out. This will result in their abilities not having any impact in the final calculation when determining the winner in PvP.
 * If the generals' levels are equal, Feredir and Erynion's Wind element cancel each other out.
 * If Ender is defending, the player will be at a greater disadvantage against Fire and Water Offenses due to the general's negative resistances to the two elements.
 * Kraxus gains a small, increasing amount of Physical Resistance after level 4.

Equipment
With the introduction of the Conquest Path Shop, some equipment now provides innate piercing and resistance power without needing any additional items forged onto them.

Remember that the following equipment must be equipped for the pierce/resistance property to be useful.

Items
Items use both Alchemy and Forge. Players can combine ingredients in alchemy to create special gems with piercing and resistance properties which in turn can be used in the forge to augment certain items with these properties. See Forge for a more in depth guide.

Remember that the following items must be forged into a weapon or armor and said weapon or armor must be equipped for the pierce/resistance property to be useful. Even if the item is the player's best item for that equipment slot, they must manually equip it on the Equipment page (or through loadouts) for the piercing or resistance properties to be used.

Effects in Monster Hunting
The new monsters in Castle Age all have some kinds of resistances which might decrease the player's damage output. There are two different types of resistances the player must keep in mind in those instances: piercing resistances and elemental resistances.

Note that players will need to manually equip their piercing general and/or items for them to counter the monsters' resistance. Newer resistance monsters spawn minions which can be avoided by having enough elemental resistance from a resistance general and/or according items.

Physical Piercing and Resistance
When fighting against a monster with physical resistance, the player needs to attack it with generals and/or items with physical piercing, otherwise some of their damage will be negated. In this context, physical resistance is very similar to the Divine Armor system.

Elemental Offense and Defense
When fighting against a monster with some kind of elemental resistance, the player needs to avoid attacking monsters with a general and/or items whose elemental offense is of the same kind as that of the monster, otherwise some of their damage will be negated.
 * Example: Attacking Fenix's fire shield (which has fire resistance) while having fire offense equipped will lessen the player's damage output.

However, monsters with elemental resistance also have a weakness to another specific element. The player needs to attack it with generals and/or items with the kind of elemental offense against which it is weak in order to inflict more damage. Currently, it is known that monsters with fire resistance are weak against water offense, and that monsters with earth resistance are weak against wind offense.
 * Example: Attacking Fenix's fire shield (which has fire resistance) while having water offense equipped will add to the player's damage output.

Monsters
Fenix, Risen From Ashes

Resistances: Physical, Fire

Kessaran, the Undying

Resistances: Physical


 * Kessaran has 315 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine armor.

Urmek, Protector of Gaia

Resistances: Physical, Earth

* Wind weakness is activated and earth resistance is deactivated when stone armor is dispatched

Poseidon, Atlantean King

Resistances: Physical, Water

* Fire weakness is activated when Trident is dispatched

** Water Elementals appear randomly to attackers before the Trident is dispatched if the attacker doesn't have Water Resistance

Vorak, Devourer of Skies

Resistances: Physical, Wind

* Earth weakness is activated when Wings are dispatched
 * Vorak, Devourer of Skies also has 330 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine armor.

** Wind Elementals appear randomly to attackers before the Wings are dispatched if the attacker doesn't have Wind Resistance

Abomination, Ancient Slime

Resistances: Physical, Water, Earth

* Fire weakness is activated when Stomach is dispatched
 * Abomination, Ancient Slime also has 340 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine armor.

** Wind weakness is activated when Tentacle is dispatched

*** Water Slimes appear randomly to players attacking Main 1 or the Stomach without Water Resistance equipped

**** Earth Slimes appear randomly to players when attacking Main 2 or the Tentacle without Earth Resistance equipped

Baal, Stealer of Souls

Resistances: Physical, Water

* Fire weakness is activated and water resistance is deactivated when Arm is dispatched
 * Baal, Stealer of Souls has 360 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine armor.

** Fire weakness is activated and water resistance is deactivated when Soul Shield is dispatched

***Dark Souls are randomly summoned to players that are attacking all areas targets (Head, Soulcage, Arm or Soul Shield), and do not have Water Resistance.

Lord of Darkness

Resistances: Physical, Fire, Wind, Water, Earth

* Water weakness is activated and fire resistance is deactivated when Left Arm is dispatched
 * Lord of Darkness has 550 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine armor.

** Earth weakness is activated and wind resistance is deactivated when Right Arm is dispatched

*** Nether Shades are randomly summoned to players that are attacking Lord of Darkness' Head and do not have Fire Resistance, or his Left Arm and do not have Water Resistance.

**** Nether Shades are randomly summoned to players that are attacking Lord of Darkness' Nether Void and do not have Wind Resistance, or his Right Arm and do not have Earth Resistance.

Svarog, the Magmapede

Resistances: Physical, Fire, Earth

* Water weakness is activated and fire resistance is deactivated when Carapace 1 is dispatched
 * Svarog, the Magmapede has 600 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine armor.

** Wind weakness is activated and earth resistance is deactivated when Carapace 2 is dispatched

***Fire Centipedes are randomly summoned to players that are attacking Svarog's Head or Carapace 1 and do not have Fire Resistance.

****Earth Centipedes are randomly summoned to players that are attacking Svarog's Underbelly or Carapace 2 and do not have Earth Resistance.

Lothorewyn, the Corrupted

Resistances: Physical, Water, Earth

* Fire weakness is activated and water resistance is deactivated when Thorny Bark is dispatched
 * Lothorewyn, the Corrupted has 630 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine armor.

** Wind weakness is activated and earth resistance is deactivated when Branch is dispatched

*** Zealous Treant are randomly summoned to players that are attacking Lothorewyn's Trunk or Thorny Bark and do not have Water Resistance.

**** Demonic Treants are randomly summoned to players that are attacking Lothorewyn's Roots or Branch and do not have Earth Resistance.

Alperon, the Corrupted

Resistances: Physical, Water

* Fire weakness is activated and water resistance is deactivated when Arm is dispatched
 * Alperon, the Corrupted has 670 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine armor.

** Fire weakness is activated and water resistance is deactivated when Soulshield is dispatched

*** Demonic Cultists are randomly summoned to players that are attacking Alperon and do not have Water Resistance.

Aspect of Death

Resistances: Physical, Fire, Water, Earth, Wind

* Water weakness is activated and fire resistance is deactivated when Scythe is dispatched
 * Aspect of Death has 700 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine power.

** Fire weakness is activated and water resistance is deactivated when Wings are dispatched

Bonegnasher, Death Rat Horde

Resistances: Physical, Fire

* Fire weakness is activated when Rat Horde is dispatched
 * Bonegnasher, Death Rat Horde has 720 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine power.

Verminarch, Death Rat Horde

Resistances: Physical, Fire

* Fire weakness is activated when Rat Horde is dispatched
 * Verminarch, Death Rat Horde has 740 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine power.

Ogrimus, Death Rat Horde

Resistances: Physical, Fire

* Fire weakness is activated when Rat Horde is dispatched
 * Ogrimus, Death Rat Horde has 760 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine power.

Rodenom, Death Rat Horde

Resistances: Physical, Fire

* Fire weakness is activated when Rat Horde is dispatched
 * Rodenom, Death Rat Horde has 780 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine power.

Cassandra

Resistances: Physical, Earth


 * Cassandra has 810 divine armor on top of her physical resistances. This entry only lists her resistance effects. See Divine Items for more information about divine power.
 * Cassandra has also some Item Requirements that you must have in your inventory to get full damage on her.

* Wind weakness is activated and earth resistance is deactivated when Snakes are dispatched

Thanatos, the Reborn

Resistances: Physical, Water, Fire, Wind, Earth

* Fire weakness is activated when Arms are dispatched
 * Thanatos, the Reborn has 700 divine armor on top of his physical resistances. This entry only lists his resistance effects. See Divine Items for more information about divine power.

** Water weakness is activated when Legs are dispatched

 Land of Mist Legendary Mine: Ouroboros 

Resistances: Physical