Home » Stars! 2.6/7 » The Academy » Pop Drops Calculator Bug
| Pop Drops Calculator Bug |
Mon, 03 May 2004 20:16  |
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 mlaub |
 | Lieutenant |
Messages: 744
Registered: November 2003
Location: MN, USA | |
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So I ran across an interesting little tidbit the other day on IS pop drops, and thought I'd explore it. That's when I realized I had already done so, back around '98, but just never bothered to post it. So, I did a little googling, and still couldn't come up with any posts on it.
Pop drop calculations do not seem to work correctly when large numbers of peeps are used. The typical formula that seems to be used in the spreadsheets and Starcalc:
(attackers) = (attackers)*(1 - .75*(defense_coverage))
Then the colonists fight it out, with attack/defense bonuses added into the calculation. So, let's use a normal maxed out planet (1,100,000), with 100 max tech defenses. According to common knowledge, we would need to drop ~3,800,000 to win the planet (against a non-IS). A nominal 9200 attackers are left on the planet, by all the calculators in my arsenal. With 4,000,000 against the same planet, 62,300 attackers survive.
Let's pit that 4,000,000 against 600,000 colonists on the same max tech, fully defended planet. This yields "attackers win" with 516,800 peeps left on the planet. Which is in line with the difference in defending planetary pop. That all make sense?
Reality is drastically different, though. I ran a quick simm, so I didn't bother trying to factor out planet growth. I just chose some planets that were close to the needed hold levels. I used an IS to drop on 2 SD's. One SD was a HP, the other an HG, just to check if pop eff had anything to do with the results. Here are the results:
Planetary Attacker Pop after
Population 4 million dropped
1100000 334400
1000000 674700
900000 1011500
800000 1340100
600000 2046000
1100000 337500
1000000 673000
900000 1011900
800000 1357300
600000 2027500
As I said, I used planets that had about the right hab to support the different pop. The higher attacker count on the second 1,100,000 planet was due to it being a 99% world, instead of a true 100% world. The numbers were close enough, though, to satisfy me that there was no correlation to pop eff. This is radically different than the expected "calculator" result.
So, what is the big deal here? Why do I think this is important? Well, if you think about it, you will realize that an IS with a large Orgy will be able to take planets much faster than he otherwise would have been able to do, according to the calculators.
Perhaps someone else could figure out where the calculators went wrong?
Enjoy
-Matt
P.S. Fixed the first 900K
[Updated on: Thu, 06 May 2004 09:20]
Global Warming - A climatic change eagerly awaited by most Minnesotans.
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| Re: Pop Drops Calculator Bug |
Wed, 05 May 2004 00:12  |
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The old formulas still look fine to me.
I used 2 SD races in my testbed. I imagine that for attacking WM you have to multiply the attacker value by the multiplier at begining and end. For defending IS you would have to multiply the defender value at begining and end. For IS you would also have to remember to include any pop growth from the freighters.
heres the formula I have used below:
=IF((1.1*B15-(A15/(1-0.75*C15)))>0,(1.1*B15-(A15/(1-0.75* C15)))/1.1,(1.1*B15-(A15/(1-0.75*C15)))*(1-0.75*C15)/1.1)
in english...
Basic result is: (1.1*attacker)-(defender/(1-0.75*defences))
If the attacker won you then divide by 1.1 to get the remaining pop
If the defender won you then divide by 1.1 and multiply by (1-0.75*defences) to get the remaining pop
In my testing all the pop drops were made as WP1 orders (after pop growth) and the defending pop has been adjusted to include the pop growth on the turn of invasion. None of the figures are more than 300 pop out.
Nicest thing to know is that when invading with WP1 orders you don't have to worry about excess population death due to habitability / overcrowding / defences. I might to a little test later to look at how this changes when pop dropping manually.
def pop att pop def% result predicted
1000000 4000000 0.0000 3,090,900 3,090,909
1000000 3000000 0.0000 2,090,900 2,090,909
1000000 2000000 0.0000 1,090,900 1,090,909
1000000 1000000 0.0000 90,900 90,909
1000000 3000000 0.3211 1,802,300 1,802,528
1000000 2000000 0.3211 802,300 802,528
1000000 1000000 0.3211 -144,800 -149,916
1000000 3000000 0.5392 1,473,500 1,473,655
1000000 2000000 0.5392 473,600 473,655
1000000 1000000 0.5392 -314,000 -313,491
649200 3000000 0.3211 2,222,500 2,222,601
649200 2000000 0.3211 1,222,500 1,222,601
649200 1000000 0.3211 222,500 222,601
649200 3000000 0.5392 2,009,000 2,009,097
649200 2000000 0.5392 1,009,000 1,009,097
649200 1000000 0.5392 9,000 9,097
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| Re: Pop Drops Calculator Bug |
Wed, 05 May 2004 01:24 |
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yup, exactly as suspected. If you pop drop manually then you get affected by the normal OOE post invasion
def pop att pop def% result wp1result
1000000 4000000 0 2,831,200 3,090,900
1000000 3000000 0 1,998,900 2,090,900
1000000 2000000 0 1,086,500 1,090,900
1000000 1000000 0 104,500 90,900
For the first 3, the difference between actual and predicted results was equal to the overcrowding deaths from the wp1 results. For the last the difference was equal to normal pop growth based on the surviving 90,900 colonists (as per wp1 result)
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| Re: Pop Drops Calculator Bug |
Wed, 05 May 2004 01:32 |
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In effect, the results of WP0 invasion are identical to as if you had invaded as a wp1 order the year before. These are the only events in the Stars! OOE that take place between a wp1 invasion and a wp0 invasion the following year:
Waypoint 1 load tasks
Mine Laying
Fleet Transfer
Waypoint 1 Fleet Merge
CA Instaforming
Minefield Decay
Mine sweeping
Starbase and fleet repair
Remote Terraforming (opportunity for CA to affect outcome)
Scrapping fleets (with possible tech gain)
Waypoint 0 load tasks (if done by hand) (additional opportunity to evacuate defenders)
So the argument between the methods of invasion are:
WP1 = Slightly less opportunity for enemy to retreat population. NO overcrowding deaths.
WP0 = You know exactly how many defences to expect, but may lose additional colonists to overcrowding / red hab.
[Updated on: Wed, 05 May 2004 01:33] Report message to a moderator
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| Re: Pop Drops Calculator Bug |
Wed, 05 May 2004 09:41 |
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| Kotk | 
 | Commander |
Messages: 1227
Registered: May 2003 | |
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| Dogthinkers wrote on Wed, 05 May 2004 06:12 |
in english...
Basic result is: (1.1*attacker)-(defender/(1-0.75*defences))
If the attacker won you then divide by 1.1 to get the remaining pop
If the defender won you then divide by 1.1 and multiply by (1-0.75*defences) to get the remaining pop
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Why it does not fit with Matt's experiment?
| LEit wrote on Tue, 04 May 2004 05:59 |
It should be:
(attackers) = (attackers)*1.1
(defenders) = (defenders)/(1 - .75 * (defense_coverage))
(whats left) = ((attackers)-(defenders))/1.1
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Hmmm.... it definitely sounds better than mine hypotese, but it does not fit with experiment results as good as mine!
Bit more accurate if we leave:
(whats left) = ((attackers)-(defenders))
But it is still not exact enough to assume some sort of rounding error.
Matt, did you drop waypoint 0? What was the planet value and growth for IS on case you did? Did it have OBRM? Needed in calculations because the pop grows after waypoint 0 drop.
[Updated on: Wed, 05 May 2004 09:53] Report message to a moderator
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| Re: Pop Drops Calculator Bug |
Wed, 05 May 2004 18:32 |
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| Kotk wrote on Wed, 05 May 2004 23:41 |
Hmmm.... it definitely sounds better than mine hypotese, but it does not fit with experiment results as good as mine!
Bit more accurate if we leave:
(whats left) = ((attackers)-(defenders))
But it is still not exact enough to assume some sort of rounding error.
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Nope, sorry, check your formula against the results in my first email. 'My' formula (acutally this is just the 'classic' formula) matches the results in most cases to within 100 pop, and is never more than about 250 pop out.
The reason you divide by 1.1 if the attacker wins is so they don't get left with the 1.1 attacking bonus (if you didn't then you could effectively multiply population by 10% every time you invaded an ally's 100pop world...) Similarly when the defender's win you must divide by the defender's defence multiplier to avoid having the defender's remaining pop skewed up by the multiplier (which would result in net pop growth if your ally kept invading you with 100pop....)
It's kinda funny actually, I ran the test to find out what the 'real' formula was, only to find the old formula is perfect (discounting negligable tiny pop rounding errors.) 
These are all repeated confirmed results with identical SD vs SD races. I'll run some tests with IS against SD later today to see what effects this has (I know they get a defence bonus, plus the freighter growth.)
[Updated on: Wed, 05 May 2004 18:45] Report message to a moderator
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