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Tactics, leadership, morale and equipment were all important in battles, however, so too was the discipline of the troops. Steady troops that could hold their formation despite the punishment of the enemy would prove much more effective in combat. Damage done is multiplied by your discipline, and damage taken is reduced or increased depending on your discipline.
Discipline is a value that measures how well troops of a nation can hold their formations despite punishment from the enemy. Regiments that are able to keep their formation prove far more effective than those that break. Discipline both amplifies the damage done to enemy troops and reduces the damage received. When calculating damage done, both raw casualties inflicted and the morale cost of these casualties is increased by discipline, in the same way that tactics reduce casualties and morale cost.
Discipline reduces damage received because it increases the military tactics value, which in turn decreases the amount of damage a unit takes.
Discipline starts off at 100% and can be changed through idea groups, advisors and events. Having at least 125% discipline is an Age Objective in the Age of Revolutions.
The longer a battle goes on and the more troops are involved in a battle, the higher discipline is needed to prevent manpower loss. In early stages of the game, one might prefer advisors that give higher morale to advisors that give discipline as early in the game, battles are mostly won by reducing the other side's morale to 0 resulting in them retreating.
As the game goes on and firearms become deadlier, battles are more dictated by the amount of casualties on either side. As discipline both increases enemy casualties and decreases your own losses, it is a very important value. Furthermore, due to a lesser drain on manpower discipline will also indirectly help a nation's ability to wage war more than just in battles.
For example:
Example 1: If an army would normally have dealt 40 casualties, and 40 morale damage to enemy troop before discipline is accounted for, and the nation has 125% discipline, they will instead deal 50 casualties, and 50 morale damage (notice that +25% discipline means +25% casualty and +25% morale damage to enemy troop).
Example 2: If an army would normally have suffered 40 casualties, and 40 morale damage for own troop before discipline is accounted for, and the nation has 125% discipline, they will instead suffer 32 casualties, and 32 morale damage (notice that +25% discipline means 1/1.25=0.8 -> -20% casualty and -20% morale damage for own troop).