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Damage and Damage Reduction are calculated AFTER Attack, Defense and Health have all offset each other; thus Damage has the biggest impact on battle results. Similar to Attack, Damage is broken out into different parts:

1) Normal attack Damage/(Reduction) only impacts normal attacks that happen each turn (helpful for more offensive marches)

2) Counter Attack Damage/(Reduction) only impacts Counter Attacks (helpful for more defensive/garrison marches that will be attacked by many marches)

3) Skill Damage/(Reduction) only impacts Skills (Direct Damage Factor).

- Skill Damage should be prioritized with commanders with large Direct Damage Factor Skills (Edward, Guan Yu, YSG, Khan, Minamoto, etc)

- Skill Damage Reduction is great for all commanders since it helps you take less damage from those enemy Commanders Damage

If it just says "Damage" or "Troop's Damage" then it should impact all 3 types of Damage.