Interest

## Balance Growth

Your territory’s balance (aka. population or strength) grows in two ways:

* ***Interest growth***: Every 0.5 seconds (1 vertical tick), your current balance is increased proportionally by the **Interest** value.
* ***Income growth***: Every 5 seconds (10 vertical ticks), your current balance is increased by the **Income** value, limited to the *hard balance limit*.

## Interest

The **Interest** can be located in the statistics in the upper right corner of the game screen. It is a combination of three factors:

1. Your current *territorial interest*, based on your current balance,
2. An *initial augmentation factor*, given in the first few minutes of the round, and
3. A *balance limiting factor*, when your balance is between your territory’s soft and hard balance limits.

It can roughly be calculated as:

# Interest
territorial interest
∗
initial augmentation factor
∗
balance limiting factor

{\displaystyle \text{Interest} =
\text{territorial interest} \* \text{initial augmentation factor} \* \text{balance limiting factor}}

During an interest growth action at every tick (every 0.5 seconds), the balance of the territory is increased proportionally by the balance interest, calculated as:

# new balance
current balance
∗

(

1
Interest

)

{\displaystyle \text{new balance} =
 \text{current balance} \* \left ( 1 + \text{Interest} \right )}

## Territorial Interest

Territorial interest is a discrete percentage value based on your **Occupation** value. It can be approximately calculated as:

# territorial interest
1
%

(

0.16
∗

Occupation

)

%

{\displaystyle \text{territorial interest} = 1 \% + \left ( 0.16 \* \sqrt{\text{Occupation}} \right) \%}

, but is not continuous, especially when **Occupation** is very low. The territorial interest is 1.00% at the minimum when you control very little land, and is 2.60% at the maximum when you control all land.

## Initial Augmentation Factor

During the first 107 seconds of the round (until 1:47), an initial augmentation factor is applied to calculate the **Interest** value. The initial augmentation factor starts with a value of 7 (giving an initial balance interest of 7.00% at 0:00) and slowly degrades to 1.

## Balance Limits

There are two balance limits, based on the pixel size of a territory, that affect growth:

* a *“soft” balance limit*, at 100x the pixel size of the territory, and
* a *“hard” balance limit*, at 150x the pixel size of the territory

When the current balance exceeds the soft balance limit, the **Interest** value is continually reduced, until your balance reaches the hard limit, at which point the Interest is 0%.

A *balance limiting factor* is currently estimated to be linearly decreasing from 1 to 0 as the balance increase from the soft limit to the hard limit, calculated as follows:

# balance limiting factor

{

1
,

if balance
<
soft limit

hard limit
−
balance

hard limit
−
soft limit

,

if soft limit
≤
balance
<
hard limit

0
,

# if hard limit
balance

{\displaystyle \text{balance limiting factor} = \begin{cases}
 1, & \text{if balance} < \text{soft limit} \\
 \frac {\text{hard limit}
 - \text{balance}}
 {\text{hard limit} - \text{soft limit}}
 , & \text{if soft limit} \leq \text{balance} < \text{hard limit} \\
 0, & \text{if hard limit} = \text{balance}
 \end{cases}}

On the other hand, **Income** growth will continue unaffected until the balance reaches the hard limit, which it will not exceed. It is not affected by the soft limit.

Your territory’s balance will never exceed the hard limit. If you lose pixels due to being attacked, your hard limit will be reduced and the excess balance will be lost.