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Topic Subject: Census - Death Rates
posted 01-30-10 00:35 ET (US)   
For those who like numbers, I have some preliminary figures on the cheerful subject of deaths. I hope to expand on these soon - I haven't any figures for less than average health at the moment [edit July 5 2013: I do now ], nor for the oldest demographic groups (since they tend to die before I have chance to count them). Assumption: that only city health and demographics affect deaths (not city size, climate, sentiment, food, hydrogenated fat in the diet, etc)

Every year, in early January, the Grim Reaper stakes claim to a proportion of your population (probably a good day to stay in bed). The exact numbers depend primarily on city health, which is itself determined primarily by clinic coverage.

City health is rated in-game as a precise number between 0 and 100, but its exact level is not revealed to you. Rather, the Chief Advisor reports the approximate level (average, good, very good, etc). When it comes to deaths, that is good enough because rates are not affected by rises/falls in health within a range. That is to say, deaths with health at 50 are the same as deaths with health at 59, since both translate to 'average'.

The following table summarizes the death rates for different demographic groups at different city health levels. Ages are on the assumption that census day is everybody's birthday so if you're looking to predict the coming thinning of the ranks remember that those aged 59 will be 60 on census day and so will fall within the 60-69 group (thus shortening their chances of making it through the night).

Age groupPerfectAlmost
perfect
ExcellentVery GoodGoodAverage
1 to 900001%2%
10 to 39000000
40 to 4900002%4%
50 to 59002%4%6%8%
60 to 6904%6%8%12%15%
70 to 792%5%10%15%20%25%
80 to 895%10%15%20%30%40%
90 to 9910%20%30%40%50%60%


Added July 5 2013:

Age groupBelow AveragePoorBadTerribleAppalling
1 to 93%5%10%15%20%
10 to 192%4%6%8%10%
20 to 29002%4%5%
30 to 392%4%6%8%10%
40 to 496%8%12%16%20%
50 to 5912%15%20%25%30%
60 to 6920%25%30%45%50%
70 to 7930%40%55%70%85%
80 to 8950%65%80%90%100%
90 to 9970%80%90%100%100%


Edit - the death rate for 100-year-olds at all health levels is 100% but an apparent bug causes these to be applied unexpectedly, often killing 90-99s instead and giving rise to 'ghosts'. See reply #16.

Just because 10% of 70-somethings are due to meet their maker doesn't mean that 10% of 71-year-olds will. In apportioning deaths, the game first applies the appropriate percentage to the entire demographic group to determine how many to exterminate (ignoring fractions). It then distributes that number of deaths evenly among the constituents of the group using a what I call the sweet-sharing technique. When sharing a bag of sweets, children who lack the faculty to work out how many sweets each should have simply 'deal them out' until all are gone. One for you, one for him, one for me. So starting with the youngest, one person is taken from each age within the group and the process is repeated until the game has exhausted its need to kill more people.

It is clear that the younger ages in the group will bear the brunt of any remainder - if 55 deaths are needed from a group of 10 different ages the first 5 will suffer 6 while the remainder have 5. This is partly what gives rise to 'ghosts' - if there are 6 deaths due to befall the octogenarians the 89-year-olds will get off scot free if there are still at least six younger ages in that group at which people still live. And once you make it to 90 you've a real good chance of the ratio never making a whole number.

It also means that while 12% of a group might face the chop that will not necessarily fall evenly across the group. If you have 40 75-year-olds and 10 at 76, and 20% are due to pop their clogs, only an eigth of 75's will go while half the 76-year-olds are wiped out.

I'll try and get those blanks filled in soon, but I have a 4% chance of not living long enough to finish it.

[This message has been edited by Trium (edited 07-05-2013 @ 05:20 PM).]

Replies:
posted 01-31-10 10:29 ET (US)     1 / 27  
Now we need a chart that shows the number of different ways you are able to phrase death.
posted 01-31-10 11:09 ET (US)     2 / 27  
I think the 'Dead Parrot Sketch' covers most possibilities
posted 02-24-10 10:47 ET (US)     3 / 27  
When working on my Timeless Tarraco, I vaguely recall seeing 1 or 2 total people in an age group, who got older (without deaths) for a few years but eventually died (no ghosts) while in the same age group and (I think) without a change in city health. My memory may be wrong. I'll pay closer attention when my Pharaoh city Immortal Iunet gets to that point.
posted 02-24-10 12:34 ET (US)     4 / 27  
Brugle - that is not unlikely, and is possibly explained if other ageing citizens mature into the same group.

With only (say) two people in a group with a death rate of 30% neither will die (because the algorithm ignores fractions). If (say) 5 people enter the same group there would be a total of 7, resulting in two deaths. Because those deaths are spread evenly, only one of them will befall the new group of 5, the other will afflict one of your original two.
posted 02-24-10 13:02 ET (US)     5 / 27  
Trium,
Sorry, I forgot to mention that my recollection (which could easily be wrong) was that no new people matured into that age group. I could dig out my old saves and check it, but I'd rather concentrate on rebuilding Iunet and see what happens there.
posted 03-30-10 12:20 ET (US)     6 / 27  
Following up my previous reply after building Immortal Iunet:
The Pharaoh census chart (with a vertical scale of 400 people) appears to show no bar for an age which has 1 person. (I don't know how many people can be at an age without displaying a bar or whether this occurs with fewer people on the vertical scale.) Assuming that the C3 and Pharaoh census charts behave the same, my observations about Timeless Tarraco are worthless.
posted 03-30-10 21:32 ET (US)     7 / 27  
Brugle - as I'm sure you know, programmers like integer arithmetic wherever possible and it wouldn't be surprising if the resolution of the chart resulted in numbers too small to make up the appropriate fraction of a 'bar' being lost, though I'm pretty sure that whenever I've looked on a C3 chart a single person is just about visible. But I haven't always been looking

Exact numbers of people at each age can be dug out of the save. I know the offsets for a C3 save - I'm not sure for a Pharoah save but I can probably find it. For the purpose of supporting or debunking what I've posted in this thread, if and when you make more Iunet saves available I'll take a look - or perhaps you can send me some that you are doubtful about?
posted 03-31-10 00:16 ET (US)     8 / 27  
Trium,

To resolve the matter, I looked at blow-up of a Pharaoh census chart (and I'd guess that a C3 census chart works the same). The chart appears to use 200 pixels vertically. If the vertical scale is 100 people then there would be 2 pixels per person, and the bars I examined at that scale did have an even number of pixels. Therefore, with the vertical scale in my Immortal Iunet (or probably in my Timeless Tarraco) of 400 people, there would have been 2 people per pixel. Surmising that the programming was the simplest, at that scale no bar would represent 0 or 1 people, 1 pixel would represent 2 or 3 people, etc.

I sent you a Pharaoh save from my Immortal Iunet, right before the first ghost forms, but there is nobody in their 90s. Also, there is a single pixel at age 89 that is about to disappear (instead of turn age 90), but I'd guess that it still has 1 person in it.

I looked at the people who are about to be in their 70s in that save. With the surmise above, and assuming that your death model applies to Pharaoh, we can deduce that there are 7 people age 70 turning into 6 age 71, and that there are 2 people each age 72 and 73 and 74 turning into 1 person each age 73 and 74 and 75. I don't think any other age counts can be determined exactly looking only at the census chart of the save game when loaded and again a few moments later.

Look at the save only if you feel like it, since I'm satisfied with the surmise and your death model.
posted 04-06-10 12:46 ET (US)     9 / 27  
Brugle,

Just looking at the data in the save (I don't have Pharaoh installed right now) it seems to be out a couple of years compared to your description.

Assuming that the scale of ages starts at 0 and ends at 99 (and that I'm not misaligning the data) it shows the following:

65 - 18
66 - 15
67 - 8
68 - 7
69 - 5
70 - 2
71 - 2
72 - 2
73 - 1
76 - 2
77 - 1
87 - 2
97 - 1

[This message has been edited by Trium (edited 04-06-2010 @ 12:48 PM).]

posted 04-06-10 13:23 ET (US)     10 / 27  
Hi Trium,
I think that you "misaligned the data" by 2 years. When the save (from very early 2344 BC) is loaded into Pharaoh and let run for about 1/32 month, the yearly age-death-birth event creates a ghost, so there should be someone in the save age 99.
posted 04-06-10 19:14 ET (US)     11 / 27  
Yes, I was ten minutes on my way to work when I realized why I was wrong and I haven't had chance to post a correction. I should have looked at the births/deaths (263) and made sure that it agreed with the number of 'zero-year-olds'

The census array in a Pharaoh save starts 4 bytes earlier than I thought it did, so all the ages I gave in reply #9 need 2 years adding to them. My apologies.

I was curious, though, that there appears to be (if I'm right this time) no 12-year-olds. Though this is drifting off-topic now - we're not even in the right forum

[This message has been edited by Trium (edited 04-06-2010 @ 07:16 PM).]

posted 04-06-10 20:14 ET (US)     12 / 27  
there appears to be (if I'm right this time) no 12-year-olds
The census chart uses the same number of pixels to display the number (a little over 200) of 11-, 12-, 13-, and 14-year-olds.
posted 06-19-10 18:23 ET (US)     13 / 27  
Hi,

I'm new on this forum, from Italy.
Congratulations to everybody, I really learned a lot here.

I'm also trying to find some statistics about death rates for my personal interest.
So, Trium, please, how did you get your table ?
Personnaly, I am proceeding creating customized maps and growing eternal cities with different city healths, then counting deaths. After many years of playing there can be enough deaths to establish a death rate. Am I doing right ?

Thanks you are great

Anco
posted 06-25-10 20:01 ET (US)     14 / 27  
Hello Anco, welcome to C3 Heaven.
posted 06-28-10 17:06 ET (US)     15 / 27  
Hi, Anco

The table was derived by observing the actual census data stored in the game files on successive saves one game year to the next and drawing conclusions. This is not data that is readily available in-game (except perhaps by Brugle's pixel-counting technique) and you need to wade into the binary with a hex editor to get data sufficiently accurate to derive theories from.

You've reminded me that I didn't get around to finishing this particular research - something of which I am guilty all too often. I'll see if I can pick it up again.

[This message has been edited by Trium (edited 06-28-2010 @ 05:08 PM).]

posted 04-26-13 06:02 ET (US)     16 / 27  
Bump to draw attention to the fact that I have at long last filled in the blanks in the table in the OP. I have also adjusted a couple of originally doubtful figures following suggestions by equi in the thread Are there any truly eternal ciies in Caesar 3?

In that same thread, equi also makes a discovery that appears to explain why ghosts sometimes form and sometimes don't. I found some anomalies, and I have revised his model as follows:

The game appears to calculate deaths for the 90-99 age group in accordance with my table. It then adds 100% of those who will be (or would have been!) 100. It applies the total so derived to the 90-99 age group. If it kills everybody in that group but has still not killed enough people, the balance is applied to the 100-year-olds. Any that survive when the game has killed enough people become ghosts - they are removed from the population and not replaced by new births, they do not work but continue to occupy housing, consume food and pay taxes.

To put it more simply - ghosts will form whenever people make it to 100 and there are people surviving in the 90-99 age group.

[This message has been edited by Trium (edited 04-28-2013 @ 11:00 AM).]

posted 07-05-13 17:41 ET (US)     17 / 27  
Once again I have added some additional data to my opening post. This time, following a gentle nudge from Brugle, I have fulfilled a 42-month-old promise to explore the poorer health rates.

It's actually quite difficult at low health levels to retain sufficient people in the older age groups to be able to measure rates and I gave up trying. Instead I ran a large 64k city at Almost Perfect health for a few decades then simply edited the game file to plunge health to dire levels just before a census. The result was that I had 2640 eighty-odds and 298 in their nineties, so I can be sure those 100%s mean 100% and not 99%.

I suppose in theory ghosts might be avoided by maintaining health at Terrible or Appalling. unfortunately, you can only get down to Bad by failing to provide clinics - contaminated water or a Venus curse is required to get lower. Besides, with this population, I'd have needed nearly 200 hospitals to avoid disease!

[This message has been edited by Trium (edited 07-06-2013 @ 08:46 AM).]

posted 08-12-14 18:53 ET (US)     18 / 27  
Hi,

One thing missing in this topic is a table showing birth rates. In 2003 in reply #25 of this topic I wrote this formula (after lots of tests and lots of experimenting with trying to find a formula that would fit the data) to calculate births cap at perfect city health:

Births capacity = 0.16* #of 19-28 aged citizens + 0.08* 29-38's +0.02* 39-48's.

Maybe I should have used the term cap or ceiling instead capacity. The formula is somewhat similar to Trium's table's above but is the reverse. In the formula as the age group gets bigger the percentage drops. In Trium's table it is the opposite. Therefore a somewhat reverse version of Trium's table is needed for births cap. The formula shows only the rates at perfect city health. The other health levels are missing.

Births cap is almost always higher than the actual occurrence unless the player is intentionally trying to get the maximum births or accidentally has enough houses with empty space at the year end.

The game calculates a theoretical maximum for births at the end of each year. But how much of that actually occurs depends on number of houses that have 2 or sometimes 3 empty spaces. Empty spaces in houses can be a result of deaths or houses that have evolved but not filled yet.

How is this useful?
There is limited use but with high population cities especially if walker numbers are a concern it could be very useful. You could even drop city mood to "people are annoyed with you" which stops immigration, then evolve houses and fill them up with births only.

In Caesar3 immigration is limited to 192 people per month at very pleased or higher level. That is 2304 people per year. If you have 8862 people in each age group then births will be higher than immigration. But of course you would need 1152 houses with empty space to get 2304 births. I'm guessing population would be around 60K if census was flattened.

[This message has been edited by philon (edited 08-12-2014 @ 07:07 PM).]

posted 08-12-14 21:43 ET (US)     19 / 27  
One thing missing in this topic is a table showing birth rates.
No. The topic of this thread is deaths, not births. Anyone interested in births would search the forum for "birth" and find the thread where you posted your formula in 2003.

[This message has been edited by Brugle (edited 08-12-2014 @ 09:47 PM).]

posted 08-13-14 04:50 ET (US)     20 / 27  
The topic of this thread is deaths, not births.
Yes it is possible to separate the two issues. If we create a births table it could be in another topic. But if we put these two tables together it would show which one is bigger at that health level.

Sometimes birth cap is lower than deaths. When that happens new immigrants will arrive at the beginning of each year to fill up spaces available from deaths because births can't fill them up. I wrote about that in message #28 in the births topic.

But I don't know when immigration will happen and when it won't happen. However it is calculable because with stable census you would know the percentage of population at each census column. I don't have that data.

But if Trium decides to do more research, I'm just saying that a births table which is somewhat of a reverse of the deaths table could be a good idea because together they will answer the immigration question.
posted 08-18-14 12:52 ET (US)     21 / 27  
I was checking some topics at citybuildingcontests.net and I found the following message by Trium.
Also didn't check below average, etc since my Fishopolis falls apart if deaths exceed births.
http://citybuildingcontests.net/vbulletin/showpost.php?p=30904&postcount=207

Like I guessed deaths can exceed births and apparently this happens when city health is "Below Average", "Poor" or "Bad" but it is unclear which of these is needed.

I guess Trium didn't test birth rates because there didn't seem to be any advantage of dropping city health to those levels.

I'm guessing one reason why somebody would want to drop city health intentionally to one of those three levels could be to keep workforce percentage high.
posted 08-18-14 18:24 ET (US)     22 / 27  
if we put these two tables together it would show which one is bigger at that health level
No, it wouldn't. Births and deaths depend on demographics in different ways. Also, it has been reported that births may depend on the size of houses, while deaths do not.
I don't know when immigration will happen ... it is calculable because with stable census you would know the percentage of population at each census column
It has been reported that births may depend on the size of houses.
Like I guessed deaths can exceed births
Of course deaths can exceed births. Lots of players know that. You knew that in 2003.
apparently this happens when city health is "Below Average", "Poor" or "Bad"
It can also happen at Average health (and maybe at better healths), depending on demographics. It may not happen at Below Average health (and maybe at poorer healths), depending on demographics.

[This message has been edited by Brugle (edited 08-18-2014 @ 06:31 PM).]

posted 08-18-14 20:23 ET (US)     23 / 27  
Also, it has been reported that births may depend on the size of houses, while deaths do not.
I disagree with that based on all the tests I have done so far. The housing level affects how much of the births ceiling is materialized. It does not affect the ceiling.

Here is an analogy to explain what I mean:

Imagine there is a 4x5 meter garden. That is 20 square meters. Imagine it will rain at the intensity of 1 liter per square meter per hour and it will only rain for 1 hour. If you could collect all the rain that is going to fall into the garden, that would be 20 liters of rain water. How much of that 20 liters you will actually collect depends on your buckets.

The situation with births is the same. There is births ceiling (the maximum births you can have) and it is calculated with a similar table like those above. However, how much of the birth capacity is going to actually happen depends on number of houses with 2, 3 or 4 empty spaces.

I have just done some quick tests and luxury palaces can have up to 4 births per year while small casa has 2. However this doesn't change the births ceiling.

I have some test files to check and I have graphical overlay to read census data. I will see if I can create the table.

[This message has been edited by Philon (edited 08-18-2014 @ 08:26 PM).]

posted 08-18-14 23:36 ET (US)     24 / 27  
The housing level affects how much of the births ceiling is materialized. It does not affect the ceiling.
For a given city, what matters is the births, not the birth ceiling.
how much of the birth capacity is going to actually happen depends on number of houses with 2, 3 or 4 empty spaces
According to Trium, in reply #87 of the thread you linked to in reply #21, births will be equal to the birth ceiling only if there are sufficient houses with vacancies so that only 1 birth is placed in each house. Are your results different?
posted 08-19-14 00:23 ET (US)     25 / 27  
I think Trium might have had different results because in that message he says he used 1x1 small tents. With 2x2 small casa I never had 1 baby per house. It was always at least 2. This doesn't mean the baby pool changes. You just need different number of houses (depending on housing level) to get the maximum births.

Here is a test method.

1. Pick a small casa city
2. Drop wages and rise taxes until people are annoyed, but don't riot. This is to stop immigration. 36Dn wages, 9% taxes seems to work.
3. Delete library. Small casas will devolve to large hovel.
4. Wait until emigrants leave the map.
5. Rebuild the library. Houses will evolve to small casa with 8 empty spaces per house.

I hope to have some data later, maybe tomorrow.

[This message has been edited by Philon (edited 08-19-2014 @ 00:30 AM).]

posted 08-19-14 18:18 ET (US)     26 / 27  
I did some tests but they were not successful because of difficulty reading data from census graph when the city is large. I have to park this subject for now. My idea was to compare death rates to birth rates in eternal cities where the census graph would be flat for some age groups. The age groups that make babies seem to be 19-28, 29-38, 39-48. I thought, depending on the birth rates, selecting one health level or another might provide a different strategic outcome in terms of how you want to refresh your workforce but I'm not sure if that is the case.

[This message has been edited by Philon (edited 08-19-2014 @ 06:19 PM).]

posted 08-26-14 12:51 ET (US)     27 / 27  
Births capacity = 0.16* #of 19-28 aged citizens + 0.08* 29-38's +0.02* 39-48's.
Not too far off. My new Births thread has the correct formula (and other information).
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