Number crunching - child attributes, education, genetics

[shandou]

I haven't been playing CK2 for too long, but already got hooked on it big time. In fact, you will see very shortly that it borders on obsession. So without further ado, I have made loads of statistics about child attribute gains, education outcomes and genetics.

Note that all these findings are without the Conclave DLC

Education
I'll start with education, since that will be the shortest: I can confirm the findings of this thread with an even larger sample size:
https://forum.paradoxplaza.com/foru...ducation-trait-outcomes-an-experiment.683397/

Attributes
Test was for attribute growth for children aged between 6 and 10. None of the children had guardians assigned. Sample size was 501 children with godlike parents and 903 children with low-stat parents, 1404 children in total.

Findings:
1) Base attribute growth is totally independent from anything.
2) Children grow a random attribute every 0.83 years, or grow 1.2 attributes each year
3) By the age of 10 an average child has each attribute between 2 and 3
4) By the age of 10 an average child has 12 attributes in total, while 68% of children have total attributes between 9 and 15
5) Interestingly the base stats of children with zero-attribute inbred imbecile parents were somewhat higher than the stats with godlike genius parents. This could be a statistical fluke though.
6) Due to random events and the actual need to wait out the 10 years to pass makes testing this quite difficult. Altogether I had 4 different runs, 3 with 300 children with zero-stat parents and 1 with 500 children with godlike parents. In the second run all of my children were imprisoned due to a revolt event or something. Imprisonment did not have any effect either. Interestingly in the godlike run, none of the children gained any traits (except child: Cancer - funny because all of them had 35.00 health) this could be because processing 500 children might have overloaded the RNG making events not fire or something (indeed my computer went to a crawl). In all the others many children gained the "bullied_in_childhood" flag which resulted in traits (only positive traits!). Anyway the trait results were kind of weird, and I haven't looked into it much.

Genetics

Males vs Females
Sample size: 18018 children
1) Conventional wisdom says 50-50% but statistics show that it is a little bit skewed in favor of males, in 16000 children born, 51.5% were males and 48.5% were females. Interestingly with a "supermom" the ratio of females went higher. Could be a statistical fluke.
2) Parents have absolutely no effect on the health and fertility of children
3) All children are born with an average fertility of 50%, with most children between 42% and 58%
4) Females are born with 0.5 more health on average than males. Most females are are born with health between 5.26 and 5.96, average being 5.56. Males are born between 4.78 and 5.08, average being 5.05. It is extremely rare for a male to be born with higher health than the weakest female.
5) The trait Sickly is acquired shortly after birth, not at birth.
6) The fact of a mother having twins is determined at conception, everything else is determined at birth.

Congenital traits
This has been tested with 6 different categories:
a) Both the mother and the father are genius strong attractive (sample: 2002 children)
b) The father is genius strong attractive, the mother has no traits (sample: 2002 children)
c) Neither the father nor the mother have any traits (sample: 8008 children)
d) Father is imbecile weak ugly, mother is genius strong attractive (sample: 2002 children)
e) Father is imbecile weak ugly, mother has no traits (sample: 2002 children)
f) Both parents are imbecile weak ugly (sample: 2002 children)

Findings:
1) The best and safest choice is obviously both parents having the positive trait, while it is also a very safe option to have one superparent and one without congenital traits.
2) All things considered it is a very bad idea to breed with any parent with bad congenital traits. Statistics favor the bad traits.
3) Statistics suggest that competing traits cancel each other out. I haven't really found proof to confirm but the probabilities suggest that a child receiving Genius from one parent and Imbecile from another at the same time will not gain any trait. It is also very likely that stronger traits of the same kind override the weaker trait. For example if a child inherits both Genius and Quick, the Genius prevails. Same with Slow and Imbecile.
4) Theoretically there is an average of 14% chance of a child getting Strong if at least one of the parents is Strong, regardless of any other factor and a 28% chance when both parents are Strong. Sample statistics seem to confirm this theory.
5) The formula of Genius is potentially more complex as it has 6 competing traits instead of 2, but generally the chance shouldn't be very different.
6) There is a possibility that Paradox developers took a shortcut and used simpler formulas than a true probability calculating monster formula. Anyway, the effect on probabilities would not be significant.

Inbreeding
I have only tested inbreeding for 3 different "levels" with a sample size of 2000 children each. Levels represent the distance in the bloodline, level 1 being the children of brother and sister (father+daughter and mother+son does not seem possible in the game thank god and paradox for making the game potentially less depraved than it already is), level 2 being the children of the sons and daugthers of siblings with unrelated spouses, level 3 being the children of the grandchildren of siblings.

1) Level 1 inbreeding carries the chance of 25% the child being born Inbred
2) Level 2 inbreeding carries the chance of 5% the child being born Inbred
3) Level 3 inbreeding carries the chance of 2% the child being born Inbred
4) In summary, marrying nieces, nephews and less related dynasty members are relatively safe, but not risk-free
5) The trait Inbred is hereditary like any other congenital trait and its inheritance probability is added to the natural inbreeding probabilities, making the child of siblings that both have the Inbred trait much more likely to receive the Inbred trait (58%) than the child of siblings without Inbred traits (25%)

Hope this helps any fellow CK2 nerd

 

[shandou]

Apologies for the duplicate attachments, the forum didn't provide much feedback that I have actually uploaded anything...

 

[Rydelfox]

For the attributes, are you looking at the child and educator's base attributes, or their total attributes? IIRC, the child's base attributes (before traits and modifiers) increase based off their educator's base attributes. Things like inbred and imbecile (mentioned in 5) wouldn't affect stat growth.

 

[shandou]

For the attributes, are you looking at the child and educator's base attributes, or their total attributes? IIRC, the child's base attributes (before traits and modifiers) increase based off their educator's base attributes. Things like inbred and imbecile (mentioned in 5) wouldn't affect stat growth.

Base attributes. It had absolutely no effect. In the first scenario the base attributes were all 0 for the educator and to be on the safe side I've also given him Imbecile and Inbred. In the other scenario the educator had 100 base in every attribute

However! I havent assigned a guardian after age 6 so it remains unknown if the guardian's attributes affect the child's attributes. My experience from gaming is that it somewhat does. I once played a ruler designed minmaxed ruler in multiplayer for the lolz, it had huge base stats in everything except Martial which was 0. My children (the ones that I educated anyway) had a noticably low Martial when they turned 16

 

[-Myth-]

Upvote for sheer effort.

 

[Rags17]

Not enough +1's for you good sir - sterling work !

 

[shandou]

Allright... new statistics!

Health and Death
A total of 4002 characters were observed (from age 16 to death) regarding their life expectancy based on health as the variable. Other variables, such as epidemics, assassinations etc. were eliminated. There were two sets of samples, one with a health value of 6.00 which is pretty much the highest base health any character can achieve without trait/event modifiers. The other set had 5.00 health, which is the average base health of males. All characters were males, but sex here is irrelevant, the only advantage females have is their average 0.5 higher starting health. They live longer because their base health is higher on average. I should have done a 4.00 health set (which is pretty much the floor) but this experiment was pretty annoying to do (requires to actually process 90 years ingame)

Findings:
1) There seems to be a flat 4.5% chance that a character will have a mortal illness irrespective of health. Ironically this percentage was higher for the high health group, but that is just statistical randomness I think.
2) This one is a bit difficult to understand. The game distinguishes between 3 types of "natural" death. In case of "Natural" death, the character just dies apparently without any reason. The tooltip on the skull icon also says this. Someone here on the forums or reddit, can't remember pointed out that the game has a "culling" system: it does a health check every once in a while, and kills off characters who cannot make the check. The check is per individual, that is why you see people with cancer outliving healthy characters. It was also found that there are age brackets. Characters who are killed by this random check and are below age 45 automatically get the "Poor health" reason instead of the "natural death". It is possible (though very unlikely) that a Ruler Designer character with a health of 20.00 dies in a year in "poor health". The third type, "Trait" are deaths related to the character having a trait that is used as an explanation for death. The culling is the same, but if the character has a health condition, it is given in the tooltip instead of "natural".
So, without epidemics, characters on average have a 0.6% chance (for 6.00 health characters) or a 0.9% chance (for 5.00 health characters) to develop a health condition on their own, without any epidemic and die from that condition.
3) Approximately 4.5% are killed of before the age 45 by the culling.
4) The average age of characters with 5.00 health is 63.8 years, 68% falling into the 62.1-65.5 year range. Median is 65 years.
5) The average age of characters with 6.00 health is 64.8 years, 68% falling into the 63.0-66.6 year range. Median is 66 years.
6) It appears, that 1.00 health translates to one additional year lived on average, BUT most likely this is NOT linear. I expect that characters with 4.00 health would live MUCH shorter on average than those of 5.00 or 6.00, not just 1 year shorter on average. This is because they are more susceptible to developing conditions on their own, not to mention they are very unlikely to survive epidemics.

NOTES
The experiment did not include child survivability. Much like in real life, taking child mortality into account, that 1.00 health would have made a much greater difference as low health characters are very likely to die before age 6 (this is hardcoded in the game, the culling system is harsher for infants and people over 70). My suspicion that a character with 4.00 health is quite unlikely to survive childhood.
The experiment also excluded epidemics. They cannot be really tested because epidemics are extremely random (when, where and which sickness occurs). My guess is that epidemics on average lower the life expectancy by around 10 years.

CONCLUSION
My unsubstantiated estimation is that life expectancy with Reaper's Due epidemics and child mortality should be around the age of 50. War and assassinations also need to be included, but again, they are very arbitrary. The conclusion is, that expecting your ruler to reach age 60 is not a good strategy. Make sure you have a competent heir ready to take over when your ruler hits age 45.
So, the value of the health attribute largely depends on where you rule. Rulers of coastal regions are much more susceptible to epidemics than those deep inland making the health attribute very valuable to them. If you are in the very middle of the HRE you can focus more on other attributes.

 

[Allastair]

Great job!

Have you had opportunity to correlate your experiment with hardcoded data:
- on attribute gain:

Spoiler

CONCLAVE_CHILDHOOD_ATTRIBUTE_INCREASE_CHANCE = 20, -- The chance of increasing an attribute during childhood
CONCLAVE_ADOLESCENCE_ATTRIBUTE_INCREASE_CHANCE = 25, -- The chance of increasing an attribute during adolescence
CONCLAVE_UNKNOWN_PARENT_DEFAULT_STAT = 5, -- If a child has no parents represented as characters in the game, this stat value is used when getting stat increases
CONCLAVE_INHERITED_ATTRIBUTE_INCREASE_CHANCE = 1.0, -- The parent's base stats influence stat increases in children by this much

- on mortality:

Spoiler

NATURAL_DEATH_CHANCE_AGE_0 = 5, -- Natural deaths per decade out of 10000 people: Age 0-9
NATURAL_DEATH_CHANCE_AGE_10 = 1, -- Natural deaths per decade out of 10000 people: Age 10-19
NATURAL_DEATH_CHANCE_AGE_20 = 15, -- Natural deaths per decade out of 10000 people: Age 20-29
NATURAL_DEATH_CHANCE_AGE_30 = 20, -- Natural deaths per decade out of 10000 people: Age 30-39
NATURAL_DEATH_CHANCE_AGE_40 = 51, -- Natural deaths per decade out of 10000 people: Age 40-49
NATURAL_DEATH_CHANCE_AGE_50 = 100, -- Natural deaths per decade out of 10000 people: Age 50-59
NATURAL_DEATH_CHANCE_AGE_60 = 400, -- Natural deaths per decade out of 10000 people: Age 60-69
NATURAL_DEATH_CHANCE_AGE_70 = 1400, -- Natural deaths per decade out of 10000 people: Age 70-79
NATURAL_DEATH_CHANCE_AGE_80 = 3500, -- Natural deaths per decade out of 10000 people: Age 80-90
NATURAL_DEATH_CHANCE_AGE_90 = 7000, -- Natural deaths per decade out of 10000 people: Age 90-99
NATURAL_DEATH_CHANCE_AGE_100 = 9000, -- Natural deaths per decade out of 10000 people: Age 100+

Also, had you consider the "trimming system" which "naturally kills" the courtiers on death of the liege? (I mean, their death is still labeled as "natural" but in fact is more like... IDK funeral sacrifice of sort)

 

[faiuwle]

I've definitely had boys born with 6 health before, I spend a lot of time looking at things with charinfo.

 

[Fediuld76]

@shandou mate thank you
These are fabulous statistical researches. Good work.

Imho might explain why some times, a good healthy ruler dies at the age of 40, while another one who was crippled, chopped numerous times by his physician and had terrible traits, lived to the age of 70.

 

[mudcrabmerchant]

Great job!

Have you had opportunity to correlate your experiment with hardcoded data:
- on attribute gain:

Spoiler

CONCLAVE_CHILDHOOD_ATTRIBUTE_INCREASE_CHANCE = 20, -- The chance of increasing an attribute during childhood
CONCLAVE_ADOLESCENCE_ATTRIBUTE_INCREASE_CHANCE = 25, -- The chance of increasing an attribute during adolescence
CONCLAVE_UNKNOWN_PARENT_DEFAULT_STAT = 5, -- If a child has no parents represented as characters in the game, this stat value is used when getting stat increases
CONCLAVE_INHERITED_ATTRIBUTE_INCREASE_CHANCE = 1.0, -- The parent's base stats influence stat increases in children by this much

- on mortality:

Spoiler

NATURAL_DEATH_CHANCE_AGE_0 = 5, -- Natural deaths per decade out of 10000 people: Age 0-9
NATURAL_DEATH_CHANCE_AGE_10 = 1, -- Natural deaths per decade out of 10000 people: Age 10-19
NATURAL_DEATH_CHANCE_AGE_20 = 15, -- Natural deaths per decade out of 10000 people: Age 20-29
NATURAL_DEATH_CHANCE_AGE_30 = 20, -- Natural deaths per decade out of 10000 people: Age 30-39
NATURAL_DEATH_CHANCE_AGE_40 = 51, -- Natural deaths per decade out of 10000 people: Age 40-49
NATURAL_DEATH_CHANCE_AGE_50 = 100, -- Natural deaths per decade out of 10000 people: Age 50-59
NATURAL_DEATH_CHANCE_AGE_60 = 400, -- Natural deaths per decade out of 10000 people: Age 60-69
NATURAL_DEATH_CHANCE_AGE_70 = 1400, -- Natural deaths per decade out of 10000 people: Age 70-79
NATURAL_DEATH_CHANCE_AGE_80 = 3500, -- Natural deaths per decade out of 10000 people: Age 80-90
NATURAL_DEATH_CHANCE_AGE_90 = 7000, -- Natural deaths per decade out of 10000 people: Age 90-99
NATURAL_DEATH_CHANCE_AGE_100 = 9000, -- Natural deaths per decade out of 10000 people: Age 100+

Also, had you consider the "trimming system" which "naturally kills" the courtiers on death of the liege? (I mean, their death is still labeled as "natural" but in fact is more like... IDK funeral sacrifice of sort)

Am I misunderstanding the math here? Assuming a starting population of 10000 people, losing the appropriate amount of people every 10 years, just over 50% of people should be able to make it to age 90 without dying of natural causes, which is way too high.

 

[Allastair]

Am I misunderstanding the math here? Assuming a starting population of 10000 people, losing the appropriate amount of people every 10 years, just over 50% of people should be able to make it to age 90 without dying of natural causes, which is way too high.

In fact, it is the chanse that is chescked 18 times a year (so 180 times per decade, approximately) If your check it for yearly "pulse" the results are as follows:

Note that at start were 1 milion people.

 

[DPS]

I have only tested inbreeding for 3 different "levels" with a sample size of 2000 children each. Levels represent the distance in the bloodline, level 1 being the children of brother and sister (father+daughter and mother+son does not seem possible in the game thank god and paradox for making the game potentially less depraved than it already is)

I thought that you could do parent-child as a Zoroastrian.

 

[BeyondExpectation]

I thought that you could do parent-child as a Zoroastrian.

You can. You can also have father-daughter inbreeding through marriage/seduction of cuckoo bastards.