## 22.9.05

### Growth Formula

Several factors (f.e. housing, racepicks, boom and techs) can influence the growth rate. To demonstrate the growth formula we will analyse these factors step by step:

Basic Growth (b)

Let us first define the following 3 variables:
POPRACE: Pop of the considered race
POPAGG: Aggregated Population of the planet (natives, droids, POPRACE and annexed pop)
POPMAX: Maximum Population of the planet

The Basic Growth (b) is then determined by:

(I) b
=trunc{[2000*POPRACE*(POPMAX-POPAGG)/POPMAX]^0.5}

This value b is always rounded down (truncated) before it is multiplied with a 2nd factor (a) which contains five bonuses:

(II) a=1+g+t+r+l+h

Without any further bonus g, t, r, l and h are all zero and the factor a is obviously 1. The summands of this factor are explained in the following:

GrowthPick (g)
-50% growth: g=-0.5
no growthpick: g=0
+50% growth: g=0.5
+100% growth: g=1

TechBonus (t)
microbiotics: t=0.25
universal antidote: t=0.5

RandomBonus (r)
Boom of 100%: r=1

For example +30% medicine: l=0.3

Housing (h)
(III) h=PROD/(2.5*
POPAGG)
Of course, this just applies when you are housing.

So far, we have explained the product a*b. This value is again truncated. Additionally, we have the cloners which can generate growth:

Cloners
(c)
(IV) c=100*(POPRACE/POPAGG)

The growth formula is:

(V) GROWTH=trunc(a*b)+trunc(c)
Last but not least: Starvation - 50k pop are killed per missing food.

Or in detail:

(VI) GROWTH=trunc{(1+g+t+r+l+PROD/(2.5*POPAGG)) * trunc{[2000*POPRACE*(POPMAX-POPAGG)/POPMAX]^0.5}} + trunc{100*(POPRACE/POPAGG)}

What are the implications of these formulas?
(I) Basic Growth:
a) POPmax increases Basic Growth: The pop-multiplier tol, sub and aqua increase Basic Growth slightly.
b) With POPrace=POPagg the derivative supplies the following result:
Half full planets have the maximum basic growth.
b = [2000*POPRACE*(POPMAX-POPRACE)/POPMAX]^0.5 with POPrace=POPagg
db/dPOPrace = (2000-4000POPrace/POPmax)*0.5[2000*POPRACE*(POPMAX-POPRACE)/POPMAX]^(-0.5) and the first factor is zero when 0.5=POPrace/POPmax (half full planet)
c) droids/natives slow down: they just increase POPagg and db/dPOPagg is always negative.
d) When there is more than one race which can grow (i.e. a captured race and not natives or droids) the basic growth numbers are calculated separetely and just the sum is displayed. For an Uni race (without morale penalty) it isoptimal to mix the races.

Equations (II) and (III):
a) Surprisingly, the several bonuses were added. For example: Microbiotics improves the Growth by 50% for a -Growth Race because 0.75/0.5=1.5
b) housing is most important part.

(IV)
a) Cloners are inefficient when there are many droids on the planet.
b) You should not build cloners early on (almost empty) natives planet.