Stars!-R-Us Article

Growth Rates
by: Jason Cawley

Scott Moore wrote:
> Is it better to select "Low Starting Population" which gives you 60
> advantage points and then bump your growth rate up 1% (-69 advantage
> points) or just start with your normal population and keep the
> starting 15% growth rate?

Of course it depends...

Just in raw pop terms, yes 1% extra growth will eventually make up for the 30% lower starting level.  If space where unlimited (all 100% hab) this would take 26 years.  Since it isn't, it takes rather longer.  But by midgame you would have more pop, if say you were alone in a testbed or something.

But the lower pop curve along the way means fewer resources to spend, thus fewer factories built.  So the time it takes to catch up in total econ will be considerably longer than the time it takes to catch up simply in pop.  Also, the smaller economy from the start through the midgame makes it relatively more difficult to get planets, so you may never make up the ground - depending one how pressured you are/how much you have to fight for space.

There is another issue here, though.  Especially in Acc BBS starts and for races that don't take expensive and start at 3 construction (or JOATs, ITs which start with construction), there is early on an intense pressure to move pop off the homeworld.  This is especially true for races with high pop growth.  Before you get con 3 for medium freighters, it is virtually impossible to move meaningful quantities of pop (especially if iron is tight as well).  If you find in testing that your homeworld gets significantly bigger than 1/4 or 1/3 of capacity before you can move the people, you can deduce that LSP wouldn't really hurt you so much.  Because the 30% lower start gives you more room to grow at the best rates and more time to get things like con 3 tech and mines for iron for shipping. If you find yourself in this situation, you might find that taking LSP for 1% higher pop growth eases the moving crisis, and that the lower pop is made up (the higher start losing more pop growth to crowding before pop can move), leaving the longer-run advantage of faster pop growth.

It also depends on your overall strategy, of course.  If your race is designed to be fastest out of the gate (a quickstarter), you usually don't want LSP. If you plan on coming from behind in econ, with strongest growth 10-15 years later than the quickstarting races and some other race advantages being the key to your strategy, LSP won't hurt you so much.  Examples of the latter are - using the defensive abilities of IT or SD races, perhaps with total terraforming or an HP economic approach.  Or an SS designed to win the tech race rather than the resource race (while still being competitive in that department, of course).

> On the same note, what is the formula used to calculate the growth
> rate for a planet after it reaches 25% of capacity?

I don't have the actual formula for you, though several people here know it.

Someone actually did all this work and even plotted the second derivative of pop vs. planet capacity.  :-) It is a little complicated, but the second derivative/1st derivative issues work something like this-

  • Up to 25%, race max growth times hab
  • After 25, 2nd derivative falls to 1/3 immediately (and keeps falling after, but slowly), but 1st derivative is still rising.
  • At 33%, second derivative starts to go negative - max 1st derivative for the planet
  • At 45%, no change in curves, but 1st derivative is about where is was at 25% of capacity
  • 33-80 2nd derivative gets more and more negative, in about a straight line; 1st derivative falls slowly and smoothly.
  • After 80, 2nd derivative is rising slightly but still negative; 1st derivative falls more slowly. Pop growth is glacial by this point.

    This leads to the following maximization rules -

  • just maximiming pop over time, hold at 25% unless alternative hab is 1/3 the sending hab or worse.
  • just maximizing pop over time, hold at 33% until all available hab under 25% of cap is used - even yellows.
  • For these purposes, treat long pop runs as equivalent to 0 alternate hab (pop does not grow in freighters, but neither does it cause crowding there).
  • just maximizing current pop *growth*, hold at 33%.
  • to minimize just *time* to fill a planet, hold at 33, put pop in orbit, fill planet to the brim when you have enough pop.
  • to maximize *resources* over the period of filling a planet, while still filling it about as rapidly as possible, hold at 45%, pop in orbit, fill when have enough.  The reasoning here is that the time difference at "full" vs. the previous case makes less of a total resource difference than the lower resources on the way - e.g. 15 years to fill with 33 hold, gives 15* .33, then 1/year, while 16 years with 45 hold gives more like 33, 37, 41, 45*13, then 1/year - a higher integral.
  • to maximize *current output*, keep everyone on the ground/let everyone go up.
  • to maximize econ growth later, when planets get to 66-80% of cap or so (assuming you didn't hold lower to fill them), fill planets over 80 to 100 in one turn, using pop from higher value worlds.  The space opened up on the higher value ones will create more pop growth than is lost by going from 80 to 100 on the planets filled.
  • There are many other issues of course.  My point is just that it depends on what you are trying to maximize - long run pop growth, long run resources, speed to economic capacity, total resources generated over time, etc.  And one can easily spend too much effort on these things, often hurting something you do care about because you are trying to maximize something else and overlook the trade-off.

    Useful bottom-line rules of thumb are -

  • When you have lots of space to settle, keeping worlds in the range of 25-33% of capacity will tend to get you the people to fill those places fastest.
  • But keeping planets between 33-45% will tend to maximize your total resources generate over time, while filling those available worlds a little slower.  If you have hit the high-value greens already, this is a decent target to have.
  • Leave at least some high value worlds in the 33-45 range as "breeders" to fill lower-value worlds, settle yellows, provide invasion pop, etc.  Mineral poor worlds with high habitat value are favorites for this role.
  • If you have the time or for some important planets (e.g. homeworld, with its special mineral non-depletion), holding at 45% and putting the growth in orbit (or importing pop) until you can go to 100% in a turn can make sense.
  • If you don't do the previous for most of your worlds, still fill to 100% of capacity lower value worlds and worlds over 80% of capacity, sending the pop from other planets, preferably your higher value ones.
  • You do want to pay some attention to these things, especially avoiding things like - letting important breeders get too high too fast while other planets are unsettled or unfilled.  But don't sweat it too much if you get somewhat out of line - most of the effects from this stuff are pretty small (because of various tade-offs/costs associated with each way of tweeking things - like lost growth from travel time, lost production from pop not on the ground, etc).  You do not have to knock yourself out in MM work to get solid performance, and can even hurt yourself for your efforts if you aren't sure about what you are trying to do.

    Anyway, lots of stuff and maybe not to the point of your question, but I hope at least some of it is useful to some people.


    Jason Cawley

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