Longevity and Level Limits

If the rules endow demi-humans with extremely long life-spans without level limits it seems logical that powerful, high-level demi-human NPCs would come to dominate the game world.

I am not entirely certain this is true.

I mean, I know this is not true in my campaign because I said so… but if we run the numbers I think it will be easily demonstrated to not be terribly likely.

Analysis of Longevity and Levels

Assumptions

  • Adventurers are the only characters that really advance to any meaningful degree.  Non-adventurers are not generally exposed to the breadth of experience or urgency of application needed to truly develop their skills beyond the normal limits.  In other words, most are very low level indeed, and very few reach even fifth level (Justin demonstrates Einstein could be fifth level, and he was a notably accomplished man).
  • In one unit time, some percentage of adventurers are removed from the pool being considered (‘die irrevocably’ is one way, but retiring is another — they no longer advance, even if they live, and since we are interested in advancement they are no longer important).
  • In one unit time, some percentage of all adventurers who did not die irrevocably advance to the next level.
  • Humans can live about 80 years on average, unless they are killed.  (D&D RSRD says 70+2d20)
  • Elves can live about 2000 years on average, unless they are killed.  (D&D RSRD says 350 + 4d100)
  • One ‘unit time’ is one year.

First Consideration: Same Rate of Advancement, no ‘Reinforcement’

Let’s start with a block of 100 first level adventurers of each race, and no more to follow later.  They face comparable challenges (die or advance at the same rate) regardless of race and class.  Each year, 10% die and 50% of the rest advance one level.

In the first year, 10 die and 45 advance to second level.  In the second year, 9 die, 20 advance to third level, and 21 advance to second level.  And so on.

After ten years (ten iterations), both groups have the same number of adventurers of the same levels.  No net advantage either way, beyond personal ability.  The same after twenty years, years, and the same after thirty years (at which point there are three left — my spreadsheet shows 4, but the other 1+ are ‘fractional’ adventurers).  In fact, after 32 years there are no ‘whole’ adventurers left of any level (not even ‘half’ adventurers to ’round up’), and we are just getting into the ‘old’ age bracket.

Longevity doesn’t come into it at this point.

  • If you stretch unit time to two years it hardly makes a difference (32 iterations, if you start at 16 years old, finishes at age 80).
  • If you stretch unit time to five years it makes more of a difference, since you now only have time for 13 iterations before the humans die and there are 21 elves remaining (levels five through twelve).
  • If you stretch unit time to ten years you have time for six iterations, at which point the elves still have 53 remaining of levels 1..7.  At seven iterations the humans will be gone and the elves will still have 48 remaining of levels 2..7.  In D&D campaigns, though, assuming ten years per iteration is not worth considering for adventurers.  Non-adventurers perhaps (1% die per year, 5% per year)
    • Oh wow.  That looks really promising.  At those rates almost half survive 70 iterations and have levels from 1..9.  If I increase it to 2.5% die per year and 5% advancement I’ve got 17 surviving 70 iterations and levels 2..8.  These look almost workable…
    • Help! Help!  I’m being digressed! (not Michael Palin)

In fact, the calculations I did for this section in order to get numbers (but didn’t show because they aren’t truly germane, this part is largely thought experiment) shows that working this hard uses up some 80% of all adventurers before humans reach middle age, and they are all used up before they would have reached old age.

As it happens, I have never seen a campaign that wasn’t ‘generation-based’ last long enough for age effects to come up, barring aging magics or the like.  I’ve had a couple players ask if they could start their characters older for the ability score modifiers, but it has never come up naturally in play.

Second Consideration: Different Rates

Let’s imagine the elves take it a little easier.  The adventurers, cautious of dying young, pursue less dangerous activities.  Only half as many die per unit time (5%), but the survivors also advance only half as often (25%).

Iteration Humans Elves
count levels count*level count levels count*level
0 100 1 100 100 1 100
1 90 1..2 135 95 1..2 119
5 59 1..6 207 77 1..5 174
10 35 3..9 209 60 1..7 210
15 21 5..12 175 46 1..9 220
20 12 8..14 134 36 2..10 215
25 6 11.16 97 28 3..12 201
30 3 15..17 68 21 4..13 182

(count*level may be a little off, since the spreadsheet works on the numbers behind the scenes rather than the displayed values, but they should be fairly close)

In direct competition between the two groups, the humans have something of an advantage until about ten iterations, and possibly even after that (the higher levels available become very relevant).

Third Consideration: Population

All the above assumes only a single group of 100 adventurers per race.  However, I have yet to see a setting (outside Dragaera, I suppose) where elves outnumber humans.  If humans are ten times as common as elves, they should have ten times as many adventurers.

Iteration Humans Elves (slow advancement) Elves (fast advancement)
count levels count*level count levels count*level count levels count*level
0 1000 1 1000 100 1 100 100 1 100
1 900 1..2 1350 95 1..2 119 90 1..2 135
5 590 1..6 2067 77 1..5 174 59 1..6 207
10 349 3..10 2092 60 1..7 210 35 3..9 209
15 206 5..14 1750 46 1..9 220 21 5..12 175
20 122 5..17 1337 36 2..10 215 12 8..14 134
25 72 8.19 969 28 3..12 201 6 11..16 97
30 42 10..22 678 21 4..13 182 3 15..17 21
35 25 13..24 468 17 6..14 162 0
40 15 16..26 310 13  7..15  141 0

The elves are at a distinct disadvantage now… and this is with humans having only ten times the population.

Fourth Consideration: Fecundity

I’m going to violate one of the assumptions above and pretend that the adventurer recovery rate is proportional to advancement.  That is, that humans reproduce enough that their adventurers increase at twice the rate that elven do… which is contrary to longevity/fecundity expectations, but simple, a useful number, and sufficient to my purposes here.

If recovery exactly matches death rates (10% per year) then humans more or less stabilize at 100 adventurers of levels 1..18 (aggregate 546 levels) after about 70 iterations and elves stabilize at 100 adventurers of levels 1..19 (aggregate 570 levels) after about 90.

Considering how generous this is to the elves (humans reproduce easily enough and fast enough we have to work to keep our population down), I’m going to have to consider this as putting elves at a disadvantage again.

Extreme Example

Orcs live a short, nasty, brutish life.  Let’s say they are our extreme case, fully 20% die each year (which may be low) but 100% of the survivors advance.  After 24 iterations (before they hit Old age) they are all dead… but the last one was 24th level before he died.  If their fecundity equals their death rate they stabilize after only 24 iterations (17 if you ignore the first batch) with 100 adventurers of levels 1..17 (aggregate 498 levels).

Closing Comments

As far as I can tell there is no real justification for the expectation that long-lived races will necessarily have a lot of higher-level characters than shorter-lived races, as long as the advancement rate is high enough that the shorter-lived races have time to keep up.  As long as the risks involved in advancement are proportional to the rate of advancement this should be more or less self-balancing.  Once you factor in differences in population sizes and fecundity between short-lived races and long-lived races there is no real reason to think the shorter-lived races would be at an overall disadvantage, as long as they have time to learn as much as they can.

In short, adventurers (the people who actually get to advance) tend to get killed (or quit) before potential lifespan comes into it.  Ultimately, most of them get used up before level limits are relevant.

As far as I’m concerned, from a setting standpoint small population is sufficient to balance long lifespan.  There might be other reasons to limit them (elves are usually made of awesome, after all, and can do things humans don’t get to), but long life alone isn’t one of them.

TL;DR: Level limits based on longevity are silly.

This post was prompted by the comments at the Ill-advised flamebait post: the dirty little secret of level caps at Richard’s Dystopian Pokeverse.

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1 Comment to "Longevity and Level Limits"

  1. February 15, 2012 - 3:05 pm | Permalink

    Good points, it might be something I need to consider.

    ERIC!

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