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Old 05-30-2022, 11:12 AM   #11
Skarg
 
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Default Re: Population Model

Quote:
Originally Posted by hcobb View Post
Each attribute point doubles the XP cost, and doubles the damage from each point of aging.
XP costs don't necessarily have a direct correlation to population numbers. Since the "average" (which doesn't necessarily mean strict mathematical average, since Steve clearly did not do that kind of math when writing or re-writing ITL) attribute total is 30, that strongly implies to me that most NPCs in the population are not regularly gaining XP nor spending it the same way that adventurer PCs do. People will have attribute levels mainly for real-world reasons rather than game system reasons (e.g. natural gifts, just being a big or small person, etc).


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Originally Posted by hcobb View Post
The existence of one 48 attribute human puts the survival of any dragons at grave risk.
Only in some game situation that exists in your own logic which you aren't even sharing. I think of the dragon stats as a baseline for spell-summoned conjured dragons with no life experience, so real dragons may also have proportionally higher attributes, and probably put their high IQ to use in staying alive.
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Old 06-01-2022, 08:28 PM   #12
David Bofinger
 
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Default Re: Population Model

Quote:
Originally Posted by hcobb View Post
Each attribute point doubles the XP cost, and doubles the damage from each point of aging.
High attribute total characters probably got there by wish.

Quote:
The existence of one 48 attribute human puts the survival of any dragons at grave risk.
Unless 48-point humans feel they have more in common with dragons than with 32-point humans.
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Old 07-13-2022, 12:06 PM   #13
Nils_Lindeberg
 
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Default Re: Population Model

Since 10.5 is supposed to be the average for an NPC, but NPCs probably don't choose their attributes they just have them.

So a somewhat lucky NPC might start out with 12/14/16 which is a 42-point character, and because of those awesome stats one would assume that it would be equally easy for them to improve, so their first attribute gains would cost 100XP. But even if they, for some unknown reason have a learning disability and can't improve over their genes without paying 1000+ XP, they still would have an easier time reaching truly awesome levels.

Likewise, there should be a lot of people running around with 8/8/8 or even lower. Otherwise, 10 wouldn't be the average.

TL;DR
NPCs and PCs have different starting attributes, and maybe different XP tables.
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Old 07-19-2022, 10:53 AM   #14
Hrothgar Rannúlfr
 
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Default Re: Population Model

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Originally Posted by hcobb View Post
Assuming that 25% (2^2) of the human population is at each of 30 or 31 attribute points (i.e. average) and each point more or less than this halves the number (due to double XPs per attribute point on the high end), then Tollenkar at 48 attribute points is from a pool that's at 2 ^ (2 +48 -31) = 2*19 or one in half a million.

Assuming that Dran has a pop of 200k (humanoids, not counting the well-fed monsters), there is a 40% chance of a Tollenkar level humanoid in Dran. (The extra memory points and mana barely nudge the total XPs required.)
This is a very interesting line of reasoning, here.

Right now, I've been going with this:

● 95% of the population has 31 attribute points or less.
● 2% have either 32 or 33 attribute points.
● 1% have either 34 or 35 points.
● 1 person in 1,000 has 36 or 37 points.
● 1 person in 5,000 has 38 or 39 points.
● 1 person in 10,000 has 40 or 41 points.
● 1 person in 50,000 has 42 or 43 points.
● 1 person in 250,000 has 44 or 45 points.
● 1 person in 1 million has 46 or 47 points.
● 1 person in 10 million has 48 or 49 points.
● 1 person in 100 million has 50 or 51 points.

As a guideline, I utilized percentages found in a rulebook for another game, Dungeon Crawl Classics RPG, and assuming that a 32 point character in TFT was 1st level and that every two points added amounted to about one DCC RPG level.

My approximation of 2 attribute points being about the same as gaining a level in and older D&D edition might not be accurate, but I like how this turned out for general info about how many people might have a certain number of attribute points within a given population.

Also, under the new TFT:ITL rules, Tollenkar would have earn at least 1,536,000 XP to get to 48 attribute points. Probably more. That is a tremendous amount of danger to have overcome. So, 1 in 10 million sounds about right, to me.
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Old 07-19-2022, 01:52 PM   #15
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We can go the other way and look at the jobs that are actually filled and what percentage of the population is qualified for those jobs.
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Old 07-20-2022, 06:34 AM   #16
Shostak
 
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Default Re: Population Model

Working in a job without meeting the qualifications is not uncommon.
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Old 07-20-2022, 08:05 AM   #17
Hrothgar Rannúlfr
 
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The question of looking at it according to job roles is interesting.
Makes me think that I should make up at least one figure that meets the minimum standard for each job role. If for no other reason than interest.

The bonus is that it'll help me prepare a lot of NPC's.
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Old 07-20-2022, 08:11 AM   #18
Hrothgar Rannúlfr
 
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Originally Posted by hcobb View Post
Assuming that 25% (2^2) of the human population is at each of 30 or 31 attribute points (i.e. average) and each point more or less than this halves the number...
Why not put X percent of the population at exactly 30 attribute points and work from there? Rather than setting the same population for both 30 and 31 points? Halving the number of persons for each attribute point in each direction.

Asking because of the statement in TFT:ITL that says that 30 attribute points is exactly average.
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Old 07-20-2022, 09:14 AM   #19
Axly Suregrip
 
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The paragraph about character points says 30 points is "the average for the villager on the street". That is a qualifying clause. It is not the average of all the population. Just the average of the commoner within the safety of a city/town.

The point being "villagers on the street" will vary from say 28 to 32. Others in skilled professions or folks typically outside the town walls will be more experienced. Anchors of society and other key skilled individuals will be well outside that average; and arguably not counted as a commoner. So may not be affecting the average.

A side note: That same first paragraph's last sentence basically states the average attribute is 10.

I think the bottom line when creating NPCs you should make key NPCs to fit your story line. Yes there should be lots of weaklings among the commoners, but not necessarily in your key rolls (unless that fits your narrative), and definitely not in professions that require more.
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Old 07-20-2022, 10:34 AM   #20
Hrothgar Rannúlfr
 
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Apologies in advance for this wall of text. As I said, this is a very interesting topic, to me...

Extrapolating from page 16 of TFT:ITL...

20 Harmless.
22 Inferior.
24 Below Average.
26 Very low average.
28 Low average.
30 Exactly average.
32 Starting character. High average.
34 Very high average.
36 Above average.
38 Superior.
40 Formidable.
42+ Extremely formidable.

"But note that many really exceptional individuals will have a stat total of 36 or less, but augment it by knowing many, many more spells or talents than they started with."

Tollenkar, as a 48 attribute point character, is extremely formidable. But, what we don't know is whether or not a 48 attribute point character is meant to be the absolute pinacle of accomplishment under the TFT:ITL rules. In my attempte to answer that, I'm going to apply some things that I do not fully understand (as I am not a statistician nor a mathematician), but I think might be helpful.

The 68–95–99.7 Rule
https://en.wikipedia.org/wiki/68%E2%...80%9399.7_rule
This rule assumes that 68% of the population will be within one standard deviation of the mean. 95% will be within two standard deviations of the mean. And, 99.7% will be within 3 standard deviations of the mean.

The Six Sigma Rule
https://en.wikipedia.org/wiki/Six_Sigma
No individuals should be outside of six standard deviations from the mean. There might be an exception, but it should be practically impossible. At most, only 3.4 individuals per million will exceed this threshold.

With Those Assumptions in Place...
All we need is the mean and the standard deviation for characters in TFT:ITL. We know from page 16 of TFT;ITL that the mean is at or very near 30 attribute points. What we don't know for certain is the standard deviation. For that, we can make some guesses.

If we assume that the standard deviation is two attribute points, that would mean that the very top end characters we should expect to exist would be of 42 attribute points or less (given the Six Sigma Rule: 6 x 2 =12 plus 30 = 42). Thus, we can reasonably expect that the standard deviation to be greater than 2.

Given that 26 attribute points is very low average and 34 attribute points is very high average, it is possible (given the 68–95–99.7 Rule) that 68 percent of the population falls between these two attribute totals. If so, then it would appear that the standard deviation is about 4 attribute points (30-26 =4 and 34-30 =4).

If the standard deviation is 4, then we can assume that
68% of the population will fall between 26 and 33 attribute points
95% of the population will fall between 22 and 37 attribute points
● and 99.7% of the population will fall between 18 and 41 attribute points.

And, the remaining 0.3% of the population will have 17 or fewer attribute points or 42 or more attribute points.

If the above is true, then (applying the Six Sigma Rule), no one or nearly no one should have 55 attribute points or more (as 54 points would be six standard deviations above average).

Conclusion
Tollenkar, as a 48 attribute point character, would be between 4 and 5 standard deviations of the average. Thus, he is truly at the reasonable top end of power. There might be a few individuals with a greater attribute point total, but they will be exceedingly rare and few and far in between.


Doubts
The number of cumulative experience points needed to achieve 48 attribute points makes me doubt that the standard deviation is actually 4. It is probably 3. If so, that means that Tollenkar is at the pinnacle of achievement and although it might be possible that there is someone out there with 49 attribute points, it's practically impossible. A standard deviation of 3 would put Tollenkar at 6 standard deviations from the mean.

If the standard deviation is 3, then we can assume that
68% of the population will fall between 27 and 32 attribute points
95% of the population will fall between 24 and 35 attribute points
● and 99.7% of the population will fall between 21 and 38 attribute points.

And, the remaining 0.3% of the population will have 20 or fewer attribute points or 39 or more attribute points.

If the above is true, then (applying the Six Sigma Rule), no one or nearly no one should have 49 attribute points or more (as 48 points would be six standard deviations above average).

Resolving My Doubts
Given the size of Cidri as well as alternate Cidri's, it's likely that the standard deviation on each Cidri varies somewhat. A truly mythical high fantasy area of Cidri probably has a standard deviation of 4 while a more gritty area of Cidri might have a standard deviation of 3 or even possibly even 2. In an area of Cidri with a standard deviation of 2, Tollenkar could exist, but he's likely to be almost the only person of that power level. And, he's most likely not a native of that area of Cidri.

Edited to Add:
Additionally, in looking at the random dungeon encounters in the TFT:ITL book on page 48, it seems that if humanoids are encountered in the labyrinth, there is at least an 11% chance that such an humanoid will be a 40 point character. To me, this confirms that the default setting for Cidri has standard deviation of 4 points from the mean, thus making 40 point characters more common.

So, here are some numbers, based upon a population of 10,000 individuals.

42—53 = 15
38—41 = 235
34—37 = 1,350
30—33 = 3,400
26—29 = 3,400
22—25 = 1,350
18—21 = 235
6—17 = 15

Last edited by Hrothgar Rannúlfr; 07-20-2022 at 04:53 PM.
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