The combination of both can slow you down alot in the early game and should be understood. Your research and unity might suffer or you might not be able to effort as much leaders and edicts as would be helpful in your empires early development.
Administrative capacity, deficit and penalty are easy to understand. Everything you own that could potentially generate income must be administered. This Empire Sprawl are your systems (+2), colonies (+2) and their districts (+1). As soon as you pass your given capacity your are in a deficit and suffer for each additional sprawl point 0.3% in techology, 0.5% in unity and 1% in edict and leader costs. With many people expanding rapitly and easily having a deficit of 50 sprawl points in the early game, this results in penalties of 15% in techology, 25% in unity and 50% in edict and leader costs. But that is still not the end of it. These figures might be given an additional 50% penalty each depending on your play style and suddenly you have 22.5% in techology, 37.5% in unity and 75% in edict and leader costs. Why? Because your Empire Sprawl (ES) is muliplied by a penalty from Empire Cohesion (ECP) to a larger Total Empire Sprawl (TES).
TES = ES * ECP
Empire Cohesion (EC) is a relation between your Empire Cohesion Gains (ECG) and Empire Cohesion Losses (ECL). You start with a base gain of 5 and each system you own gives +1 and each starbase you upgrade +3. Your losses depend on your play style. If you stretch your empire early on, to make sure you secure important choke points, you end up with more adjacent hyperlanes (+1) and possibly for later conquer isolated systems (+1). This gives your:
EC = ECG / ECL
From this Empire Cohesion you can directly calulate your given penalty:
ECP = 2 * int( 100 - EC ) + 100 ..... [ ≈ 299 - 2 * EC ; not very exact but best fit ]
So your multiplier is something between 1 for cohesion gains higher than your losses, and 3 for having no conhesion gains at all. Although you never have zero gains because of a base gain of 5. For certain play styles your multiplier would be something between 1.2 and 1.8 maybe.
What can you do about it? Well, if you keep your Empire Sprawl below your Administrtive Capacity your Empire Cohesion doesn't matter anymore because zero deficit multiplied by whatever penalty is still zero. But if you don't want to stay below your capacity, try to upgrade as many starbases as possible (+3) because each will gain on Empire Cohesion and try to get rid of isolated systems (+2) because these systems have an adjacent hyperlane (+1) and are isolated (+1).
Administrative capacity, deficit and penalty are easy to understand. Everything you own that could potentially generate income must be administered. This Empire Sprawl are your systems (+2), colonies (+2) and their districts (+1). As soon as you pass your given capacity your are in a deficit and suffer for each additional sprawl point 0.3% in techology, 0.5% in unity and 1% in edict and leader costs. With many people expanding rapitly and easily having a deficit of 50 sprawl points in the early game, this results in penalties of 15% in techology, 25% in unity and 50% in edict and leader costs. But that is still not the end of it. These figures might be given an additional 50% penalty each depending on your play style and suddenly you have 22.5% in techology, 37.5% in unity and 75% in edict and leader costs. Why? Because your Empire Sprawl (ES) is muliplied by a penalty from Empire Cohesion (ECP) to a larger Total Empire Sprawl (TES).
TES = ES * ECP
Empire Cohesion (EC) is a relation between your Empire Cohesion Gains (ECG) and Empire Cohesion Losses (ECL). You start with a base gain of 5 and each system you own gives +1 and each starbase you upgrade +3. Your losses depend on your play style. If you stretch your empire early on, to make sure you secure important choke points, you end up with more adjacent hyperlanes (+1) and possibly for later conquer isolated systems (+1). This gives your:
EC = ECG / ECL
From this Empire Cohesion you can directly calulate your given penalty:
ECP = 2 * int( 100 - EC ) + 100 ..... [ ≈ 299 - 2 * EC ; not very exact but best fit ]
So your multiplier is something between 1 for cohesion gains higher than your losses, and 3 for having no conhesion gains at all. Although you never have zero gains because of a base gain of 5. For certain play styles your multiplier would be something between 1.2 and 1.8 maybe.
What can you do about it? Well, if you keep your Empire Sprawl below your Administrtive Capacity your Empire Cohesion doesn't matter anymore because zero deficit multiplied by whatever penalty is still zero. But if you don't want to stay below your capacity, try to upgrade as many starbases as possible (+3) because each will gain on Empire Cohesion and try to get rid of isolated systems (+2) because these systems have an adjacent hyperlane (+1) and are isolated (+1).
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