Efficiency

Efficiency refers to an army's operational performance, which is based on its size. It consists of two main components: combat effectiveness and movement speed. In this context, combat effectiveness acts as a strength modifier, while what is labeled as 'movement speed' in the efficiency menu is, in fact, a movement speed modifier.

• $Efficiency=\frac{CombatEffectiveness+MovementSpeed}{2}$

Army Stacking Penalty

Army stacks that surpass a specified size threshold incur an efficiency penalty. The penalty increases with army size.

Maximum army sizes per domain:

• Land: 10 troops
• Air: 5 troops
• Sea: 5 troops

Combat Effectiveness Penalty

Army combat effectiveness penalty reduces the strength of an army.

Formula

• $CombatEffectivenessPenalty=1-0.56\ln (\frac{StackSize}{MaxNoPenaltyStackSize})$, where $StackSize>MaxNoPenaltyStackSize$

Formula Validation history

Date	Army type	Maximum tested stack size	Formula is valid
Oct 22, 2023	Air	11	✅
Oct 23, 2023	Sea	11	✅

Movement Speed Penalty

Armies incur a movement speed penalty that increases with the size of the army stack. The specific logic behind this movement speed penalty is not yet clear and requires further research. However, it is established that larger stack sizes result in more significant penalties.

Findings

• October 23, 2023:
  • For naval fleets, there appear to be different movement speed penalty based on whether army is in shallow or ocean terrain.
    • Ocean:
      • 5-10 units: 100%
      • 11 units: 85%
      • 12+: untested
    • Shallow:
      • 5-10 units: 75%
      • 11 units: 50%
      • 12+ units: unknown