Editing Comparison of Armorer, Offense and Archery

=== Facts ===
* At Basic, Advanced or Expert Level, [[Armorer]] reduces all damage inflicted by 5%, 10% or 15%.
* At Basic, Advanced or Expert Level, [[Offense]] increases hand-to-hand damage by 10%, 20% or 30%.
* At Basic, Advanced or Expert Level, [[Archery]] increases ranged damage by 10%, 25% or 50%.

* 13 heroes (+ 1 campaign hero [[Roland]]) start with Armorer as a secondary skill and 3 specialize in it: [[Mephala]], [[Neela]] and [[Tazar]].
* 25 heroes (+ 3 campaign heroes [[Kilgor]], [[Catherine]] and [[Boragus]]) start with Offense as a secondary skill and 2 specialize in it: [[Crag Hack]] and [[Gundula]].
* 8 heroes (+ 1 campaign hero [[Gelu]]) start with Archery as a secondary skill and 1 specialize in it: [[Orrin]].

* Rampart, Inferno, Necropolis and Fortress have 1 shooter, Tower has 3 and all other towns have 2 shooters.

* [[Beastmaster]]s from Fortress are most likely to learn Armorer (10% chance), followed by [[Alchemist]]s from Tower and [[Ranger]]s from Rampart (8% chance).
* [[Barbarian]]s from Stronghold are most likely to learn Offense (10% chance), followed by [[Planeswalker]]s from Conflux (9% chance).
* [[Ranger]]s from Rampart and [[Planeswalker]]s from Conflux are most likely to learn Archery (8% chance each).

=== Facts (adjusted for {{hota}}) ===
* 14 heroes (+ 2 campaign heroes [[Roland]] and [[Tark]]) start with Armorer as a secondary skill and 3 specialize in it: [[Mephala]], [[Neela]] and [[Tazar]].
* 30 heroes (+ 5 campaign heroes [[Kilgor]], [[Catherine]], [[Boragus]], [[Bidley]] and [[Tark]]) start with Offense as a secondary skill and 3 specialize in it: [[Crag Hack]], [[Gundula]] and [[Corkes]].
* 9 heroes (+ 1 campaign hero [[Gelu]]) start with Archery as a secondary skill and 1 specializes in it: [[Orrin]] (+1 campaign hero [[Murdoch]]). 

* Rampart, Inferno, Necropolis and Fortress have 1 shooter, Tower has 3 and all other towns have 2 shooters.

* [[Barbarian]]s from Stronghold are most likely to learn Offense (10% chance), followed by [[Captain]]s from Cove and [[Planeswalker]]s from Conflux (9% chance).
* [[Captain]]s from Cove are most likely to learn Archery (9% chance), followed by [[Ranger]]s from Rampart and [[Planeswalker]]s from Conflux (8% chance each).

=== Notes ===
* Armorer will benefit all your troops while Offense will benefit shooters less (only when they attack in melee).
* Archery has the biggest percentage bonus but will only benefit shooters.

=== Table of Specialties Percentages ===
Assuming Expert Level in the secondary skill, the percentage bonus will increase to the following values at certain levels:
(Level 74 is the maximal level in {{hota}}).

{| class="wikitable" 
|- style="text-align:center;"
! colspan="4" style="text-align:left;" | '''Bonus Percentages from Specialty'''
|- style="vertical-align:bottom;"
| 
| '''Armorer'''
| '''Offense'''
| '''Archery'''
|- style="vertical-align:bottom;"
| '''Base %'''
| 15%
| 30%
| 50%
|- style="vertical-align:bottom;"
| '''Level'''
| 
| 
| 
|- style="vertical-align:bottom;"
| 0
| 15%
| 30%
| 50%
|- style="vertical-align:bottom;"
| 1
| 16%
| 32%
| 53%
|- style="vertical-align:bottom;"
| 2
| 17%
| 33%
| 55%
|- style="vertical-align:bottom;"
| 3
| 17%
| 35%
| 58%
|- style="vertical-align:bottom;"
| 4
| 18%
| 36%
| 60%
|- style="vertical-align:bottom;"
| 5
| 19%
| 38%
| 63%
|- style="vertical-align:bottom;"
| 10
| 23%
| 45%
| 75%
|- style="vertical-align:bottom;"
| 15
| 26%
| 53%
| 88%
|- style="vertical-align:bottom;"
| 20
| 30%
| 60%
| 100%
|- style="vertical-align:bottom;"
| 25
| 34%
| 68%
| 113%
|- style="vertical-align:bottom;"
| 30
| 38%
| 75%
| 125%
|- style="vertical-align:bottom;"
| 40
| 45%
| 90%
| 150%
|- style="vertical-align:bottom;"
| 46
| 50%
| 99%
| 165%
|- style="vertical-align:bottom;"
| 47
| 50%
| 101%
| 168%
|- style="vertical-align:bottom;"
| 50
| 53%
| 105%
| 175%
|- style="vertical-align:bottom;"
| 60
| 60%
| 120%
| 200%
|- style="vertical-align:bottom;"
| 70
| 68%
| 135%
| 225%
|- style="vertical-align:bottom;"
| 73
| 70%
| 140%
| 233%
|- style="vertical-align:bottom;"
| 74
| 71%
| 141%
| 235%
|}

=== Discussion ===
Note that all three skills' percentages increase linearly when their respective specialty heroes reach higher levels.

Now, for Offense and Archery the resulting advantage also increases linearly:
Offense specialty adds a 100% (linear) bonus every 66 2/3 levels after level 46 2/3.
Archery specialty adds a 100% (linear) bonus every 40 levels after level 20.

Armorer behaves non-linear. This is because the change from 15% reduced damage to 20% reduced damage is less of a difference than 90% reduced damage to 95% reduced damage. From 15% to 20% the change is only a 5.9% improvement, but 90% to 95% '''halves''' the damage taken!

==== Tabular Overview #1 ====
Here a tabular overview of what levels would be needed to double/triple/... the damage or to receive only half/one third/... of the damage:

{| class="wikitable" style="vertical-align:bottom;"
|- style="font-weight:bold; text-align:center;"
! style="font-weight:normal; text-align:left;" | 
! colspan="3" | Armorer
! colspan="3" | Offense
! colspan="3" | Archery
|- style="text-align:center;"
| style="text-align:right;" | Base %
| colspan="3" | 15
| colspan="3" | 30
| colspan="3" | 50
|-
| 
| 
| 
| 
| 
| 
| 
| 
| 
| 
|-
| 
| Level
| Total %
| Effective Reduction Factor
| Level
| Total %
| Effective Increase Factor
| Level
| Total %
| Effective Increase Factor
|-
| style="text-align:right;" | Two times / One half of damage
| 46.67
| 50%
| 2
| 46.67
| 100%
| 2
| 20
| 100%
| 2
|-
| style="text-align:right;" | Three times / One third of   damage
| 68.89
| 67%
| 3
| 113.33
| 200%
| 3
| 60
| 200%
| 3
|-
| style="text-align:right;" | Four times / One fourth of   damage
| 80
| 75%
| 4
| 180
| 300%
| 4
| 100
| 300%
| 4
|-
| style="text-align:right;" | Five times / one fifth of   damage
| 86.67
| 80%
| 5
| 246.67
| 400%
| 5
| 140
| 400%
| 5
|-
| style="text-align:right;" | Ten times / one tenth of   damage
| 100
| 90%
| 10
| 580
| 900%
| 10
| 340
| 900%
| 10
|-
| style="text-align:right;" | At max level
| 74
| 71%
| 3.39
| 74
| 141%
| 2.41
| 74
| 235%
| 3.35
|}

==== Tabular Overview #2 ====
Here the table for achievable levels:
{| class="wikitable" style="vertical-align:bottom;"
|- style="font-weight:bold; text-align:center;"
! colspan="4" | Effective Increase / Reduction Factor
|-
| 
| '''Armorer'''
| '''Offense'''
| '''Archery'''
|-
| '''Base %'''
| 15%
| 30%
| 50%
|-
| '''Level'''
| 
| 
| 
|-
| 0
| 1.18
| 1.30
| 1.50
|-
| 1
| 1.19
| 1.32
| 1.53
|-
| 2
| 1.20
| 1.33
| 1.55
|-
| 3
| 1.21
| 1.35
| 1.58
|-
| 4
| 1.22
| 1.36
| 1.60
|-
| 5
| 1.23
| 1.38
| 1.63
|-
| 10
| 1.29
| 1.45
| 1.75
|-
| 15
| 1.36
| 1.53
| 1.88
|-
| 20
| 1.43
| 1.60
| 2
|-
| 25
| 1.51
| 1.68
| 2.13
|-
| 30
| 1.60
| 1.75
| 2.25
|-
| 40
| 1.82
| 1.90
| 2.50
|-
| 46
| 1.98
| 1.99
| 2.65
|-
| 47
| 2.01
| 2.01
| 2.68
|-
| 50
| 2.11
| 2.05
| 2.75
|-
| 60
| 2.50
| 2.20
| 3
|-
| 70
| 3.08
| 2.35
| 3.25
|-
| 73
| 3.31
| 2.40
| 3.33
|-
| 74
| 3.39
| 2.41
| 3.35
|}

=== Conclusions ===

* Without a specialty in Armorer, Offense or Archery, Armorer is statistically worse in a fight where you take similar amounts of damage as you inflict. 15% damage reduction cannot compete with 30% or even 50% damage increase. However, most of the time (hopefully) you would fight with almost no or zero losses.
* Because Armorer gets super-linearly better at higher levels for Armorer specialty heroes, it can break even with Offense at level 46 2/3 and with Archery at level 73 1/3. This means at these levels, the skills give equivalent benefits: If the base damage is 100 (with Offense specialty and Expert Offense) at level 46 2/3 the creature does 100% more damage. The defending creature (with Armorer specialty and Expert Armorer) will reduce the taken damage by 50%, so will only receive the 100 damage. This cancels each other out exactly. Before the mentioned levels, Offense and Archery will effectively increase the original damage while at later levels, the taken damage will be less than the original damage.
* Level 46 is rarely reached in any game.
* This does not mean that Armorer is worse than Offense or Archery until the mentioned levels. To preserve army hit points is a very important goal and Armorer does exactly this. 15% damage reduction can also be seen as 17.6% HP increase. Who would not want to have Ancient Behemoths with practically 353 HP?
* Offense and Archery are only preserving hit points in a proactive way: You need to kill enemy stacks before they can hit you.
* Against shooters which can't be reached in the first round, Armorer will probably be more useful.
* Against fast creatures which get the first strike, Armorer might be more useful. More of your creatures survive the initial attack. They might even do more damage than if you had Offense or Archery since there are more left.
* These are all great skills. While Archery is more situational (probably especially useful for Towers [[Titan]]s), Armorer is universally useful and Offense will significantly benefit basically any army as well. For might heroes these skills are very important while magic heroes might not have enough secondary skill slots to learn them. Also, their chance to learn these skills is generally lower.
[[Category:Comparisons]]
@@ Line 15: / Line 15: @@
 === Facts (adjusted for {{hota}}) ===
-* 17 heroes (+ 2 campaign heroes [[Roland]] and [[Tark]]) start with Armorer as a secondary skill and 4 specialize in it: [[Mephala]], [[Neela]], [[Tazar]] and [[Dury]].
+* 14 heroes (+ 2 campaign heroes [[Roland]] and [[Tark]]) start with Armorer as a secondary skill and 3 specialize in it: [[Mephala]], [[Neela]] and [[Tazar]].
-* 32 heroes (+ 6 campaign heroes [[Kilgor]], [[Catherine]], [[Boragus]], [[Bidley]], [[Tark]] and [[Tavin]]) start with Offense as a secondary skill and 3 specialize in it: [[Crag Hack]], [[Gundula]] and [[Corkes]] (+1 campaign hero [[Tavin]]). .
+* 30 heroes (+ 5 campaign heroes [[Kilgor]], [[Catherine]], [[Boragus]], [[Bidley]] and [[Tark]]) start with Offense as a secondary skill and 3 specialize in it: [[Crag Hack]], [[Gundula]] and [[Corkes]].
-* 1 heroes (+ 2 campaign heroes [[Gelu]] and [[Murdoch]]) start with Archery as a secondary skill and 1 specializes in it: [[Orrin]] (+1 campaign hero [[Murdoch]]).
+* 9 heroes (+ 1 campaign hero [[Gelu]]) start with Archery as a secondary skill and 1 specializes in it: [[Orrin]] (+1 campaign hero [[Murdoch]]).
 * Rampart, Inferno, Necropolis and Fortress have 1 shooter, Tower has 3 and all other towns have 2 shooters.
-* All [[Barbarian]]s start with [[Offense]].
-* All [[Beastmaster]]s start with [[Armorer]].
 * [[Barbarian]]s from Stronghold are most likely to learn Offense (10% chance), followed by [[Captain]]s from Cove and [[Planeswalker]]s from Conflux (9% chance).
 * [[Captain]]s from Cove are most likely to learn Archery (9% chance), followed by [[Ranger]]s from Rampart and [[Planeswalker]]s from Conflux (8% chance each).
@@ Line 32: / Line 30: @@
 === Table of Specialties Percentages ===
 Assuming Expert Level in the secondary skill, the percentage bonus will increase to the following values at certain levels:
-(Level 6424 is the maximal level in the {{sod}}) (Level 74 is the maximal level in {{hota}}).
+(Level 74 is the maximal level in {{hota}}).
 {| class="wikitable"
@@ Line 147: / Line 145: @@
 | 141%
 | 235%
-|- style="vertical-align:bottom;"
-| 6424
-| 4833%
-| 9666%
-| 16110%
 |}
@@ Line 255: / Line 248: @@
 | 10
 |-
-| style="text-align:right;" | At max level in {{hota}}
+| style="text-align:right;" | At max level
 | 74
 | 71%
@@ Line 265: / Line 258: @@
 | 235%
 | 3.35
-|-
-| style="text-align:right;" | At max level in the {{sod}}
-| 6424
-| 4833%
-| Fixed 1 damage
-| 6424
-| 9666%
-| 97.66
-| 6424
-| 16110%
-| 162.1
 |}
@@ Line 393: / Line 375: @@
 | 2.41
 | 3.35
-|-
-| 6424
-| Fixed 1 damage
-| 97.66
-| 162.1
 |}