Growth and Death by the Numbers

[OmikronWarrior]

OK, you know that the Growth Scale changes income by 2% for every tick, but what about that .2% population chance? Well, advanced spread sheet technology, I ran some equations and came up with concrete numbers.

Methodology: I basically ran two seperate serieses of equations. The first was simply to track the population chanced caused by the Growth/Death Scale. The equation was simple, (growth multiplier)^(# of Turns). Therefore, Growth 2 after 10 turns would be 1.004^10 which is approximately 1.04, or you'll have 4% more people then what you started with. And since there is a direct correlation between population and gold income, you nab an extra 4% of gold as well. The second check was a bit more complicated. For a given # of turns, I took the average population change over all turns so far, and then multiplied that averaged by the scale's money multiplier. On the spreadsheet, this looked like Average(B4:B10)*1.02. B4 through B10 represent spread sheet cells with the population adjustments for turns 1 through 6. The 1.02 multiplier represents the 2% extra money you'll recieve for Growth 1.

Caveats:

1) Unless you spread your domain then your growth/death effects won't matter. So, though my chart says Growth 3 will give you a whopping extra 46% gold after 102 turns, more likely you'll recieve less then that as most of your territories won't have converted at the game's beginning.

2) Dominions 3 has plenty of ways to kill population, and none of these are taken into account with my chart. For example, if you have a destructive domain (LE R'lyeh and Ermor), then these charts really don't apply to you.

3) Dominions 3 rounds population to the 10's. In practice this means your capital will recive/loose 60 population per every tick of Growth/Death for the first several turns. My charts don't take this staggered growht into account.

4) My numbers represent additional gold over the several turns. Not how much additional gold you recieve per turn at the end of X number of turns. Expect gold income to below my given percentage for most of the turns, and significantly higher by the later turns.

5) I recently read a developer post claiming Neutral (growth and death at zero) provinces do experience small population growth. If that's the case, I never personally observed a neutral province gain population.

With out further ado:

Turns D 3 D 2 D 1 Neutral G 1 G 2 G 3
6.. 92% 95% 97% 100% 103% 105% 108%
12. 91% 94% 97% 100% 103% 107% 110%
18. 89% 93% 96% 100% 104% 108% 112%
24. 88% 92% 96% 100% 104% 109% 114%
30. 86% 90% 95% 100% 105% 110% 116%
36. 85% 89% 95% 100% 106% 112% 118%
42. 83% 88% 94% 100% 106% 113% 121%
48. 82% 87% 93% 100% 107% 115% 123%
54. 80% 86% 93% 100% 108% 116% 125%
60. 79% 85% 92% 100% 108% 118% 128%
66. 78% 84% 92% 100% 109% 119% 130%
72. 76% 83% 91% 100% 110% 120% 133%
78. 75% 82% 91% 100% 110% 122% 135%
84. 74% 82% 90% 100% 111% 124% 138%
90. 73% 81% 90% 100% 112% 125% 140%
96. 71% 80% 89% 100% 112% 127% 143%
102 70% 79% 89% 100% 113% 128% 146%

If anyone has any comments or concerns (It's quite possible I made mistakes), feel free to let me know. I'm working on the charts in Open Office right now, but am not quite ready to release them. When I am, I'll post them as an attachment.

[DrPraetorious]

One issue is that random event differences have a significant impact.

Plagues, for example, are one of the most severe negative events - and can happen to you even if you take death-but-not-misfortune.

So the best way to get a real handle on the income is to start a bunch of games with slightly different settings run for X turns, and see how much money you have on average . Of course this is rather more work.

I had various data on this lying around, it wasn't complete, but I lost a bunch of it in the HD crash.

Also, growth has a big (but in need of quantification) effect on the severity of aging. You might throw fifty elderly mages into the mix and see how they do.

All that said, your math looks right to me.

[Hadrian_II]

there is no post from me in this thread

i should read better the next time

[Saint_Dude]

OmikronWarrior said:
4) My numbers represent additional gold over the several turns. Not how much additional gold you recieve per turn at the end of X number of turns. Expect gold income to below my given percentage for most of the turns, and significantly higher by the later turns.

[OmikronWarrior]

Saint Dude is correct, my scales tell you how much gold you get OVER THE COURSE OF THE GAME. While at the end of 102 turns you will have increased population by your 80%+ figure and will earn that much more gold per turn, you won't have that much extra gold for most of your turns (unlike Order which gives +/- 7% gold per tick no matter what turn and the aggregate won't change over number of turns.

As for the role of random events... too much variable is involved. For example, large nations are sort of "buffered" from random events due to hard limit of random events occurring. No matter how valuable the territory, if you have 50+ it won't matter how badly it gets hit with Misfortune. Then, its much harder to quantify the effects of free gems and magic items that high luck players get. Obviously, the additional effects of growth, minimizing/aggrevating old age problems, additional supply, are things players will have to consider when designing their strategy. This chart is more to quantify just how much extra money you'll get/loose using growth/death (a lot more then 2%).

[CUnknown]

Good job, OmikronWarrior! Thanks for doing that, I like looking at numbers.

It's true that Growth gives more benefits than just money, like you say. But, unfortunately, your chart there I think quantifies what most people have been saying for some time now --that Growth as a money-making strategy is just not as good as Order.

It seems that the break-even point is around turn 50 or so, according to your chart. At that point, Growth and Order will give you about equal extra money per turn. And, this is even assuming that the growth scale was in each of those provinces from the start of the game, which of course isn't true. So, in reality, we're looking at more of a turn 60-70 or so break-even point, maybe even later. On a really big map, Growth may work out to be better than Order, but for most games, the money you get from turn 1 to turn 70 will be a much bigger incentive, so Order would be better.

And this isn't even factoring in that at the "break-even point", Growth will still be far behind Order in terms of money gained to that point.

This seems like good evidence that either Growth should be changed to at least +3% (as in CB mod), or that Order should be lowered to maybe +6 or +5%. Alternatively, the Growth % per turn could be raised.

[thejeff]

Well, that's good evidence that Growth and Order should be changed if the only thing you want to balance is money.
It's harder to calculate the other effects of both scales.

[mr_Logic]

(4) My numbers represent additional gold over the several turns. Not how much additional gold you recieve per turn at the end of X number of turns. Expect gold income to below my given percentage for most of the turns, and significantly higher by the later turns.

so if you ended the chart at, say, turn 30, then the actual additional amount per turn would be higher at the turns just before turn 30, then now as youv ended the chart at turn 102?

either i am misunderstanding you, or your math is off.

[OmikronWarrior]

Keep in mind that in order to get the benefit of Order/Turmoil, you still need to spread your domain as well. What these charts show me is less that Growth is an equal alternative to Order as a money maker, but a good money maker in its own right that compliments Production.

In joke format, people without Growth or Order
take the bus to work, people with just Order drive BMWs, people with just Growth take the bus but retire early, but people Growth and Order fund the Russian space program to get to work.

mr_Logic said:

so if you ended the chart at, say, turn 30, then the actual additional amount per turn would be higher at the turns just before turn 30, then now as youv ended the chart at turn 102?

either i am misunderstanding you, or your math is off.

OK, on a given turn (lets call it T(1)), a province will make X amount of money based on Y amount of population. Unless there are modifiers in play. Lets assume Growth 3. So, you make X*1.06 money. Now on T(2), your population has changed to Y*1.006, and since base money is directly proportional to population, you'll earn X*1.006*1.06. What my figures tell you is money made on T(1) and T(2) AVERAGED. Or they would if I bothered to do Turn 2.