Encumbrance Effects in the Real World

 I recently bought a weighted vest to enhance my strength-building from walking and basic calisthenics, and wondered what data is out there on the effects of different loads. My vest has spots for 10 six-pound weights, so is adjustable up to 60 lbs in six-pound increments. Too much? Not enough? A quick search led me to this very well-written article containing more information than I had hoped for.

https://www.cnas.org/publications/reports/the-soldiers-heavy-load-1

RPG systems often ignore encumbrance because tracking it and calculating movement speeds detracts from fun gameplay for a lot of folks. Some systems (D&D) break encumbrance down into levels along the lines of "unencumbered", "light", "moderate", and "heavy", and describe how each level affects movement. Sometimes there is a label for the amount a character can lift off the ground that prevents any movement.

Heaven forbid a TTRPG track fatigue! I have on-and-off worked on developing my own system that simulates the real world better than other systems, and I have incorporated fatigue and recovery based on effort and fitness. I have to say that I managed to make a fatigue-tracking simulator that no one would enjoy playing. As many complaints as I have about D&D's class and level mechanics, I like the creative compromise between tracking fatigue or ignoring it (fire-and-forget spells/abilities). It is practical and playable to say that some activities (sprinting, max lifting) can be done "once per scene" or "once until a short rest". 

The data I used for movements speeds all assumed being unencumbered, especially at higher speeds and distances. Elite runners wear shoes and clothing carefully designed to cut grams off of weight in order to provide a competitive edge. Competitive runners get lean. This soldier data is a treasure, showing realistic expectations for encumbered movement.

Valuable take-aways from this article: 

• Characters should consider having an "approach" load and a "combat" load.
• Encumbrance causes initiative, reaction, awareness, concentration, and other penalties.
• Caloric intake, fatigue, and recovery time all scale with encumbrance.
• Encumbered people are easier to hit.
• There is a large increase in the time it takes to start moving from a standstill to 5m. 
• 1/3 bodyweight is often used as a benchmark for the high end of a reasonable burden for a soldier.
  

 

Here are useful images from the article:

Thanks to Lauren Fish and Paul Scharre for their work.
 

Death by Falling

 [Edit: If you're looking for real information on deaths by falls, see my next two posts here and here.]

This is the first of several posts I have planned about simulating the results of falls from elevations.  Here I simply determined the minimum distance necessary to fall for an average human to die, the distance at which an average person would die on average, and the maximum distance that an average person could fall without dying for ten different systems.

As you can see, there are wide differences among systems.  The grades I give are subjectively based on how each mechanic models reality and contributes to game balance.

• Aberrant: For any fall under 30 meters, even the most feeble person has a 99.6% chance of only sustaining minor injuries that will heal in a day (bashing damage).  At 30 meters, damage becomes lethal and maxes out at 10 dice (an average of 4 levels of damage), with only a 1.3% chance of dying even when falling miles.  F
• Chaosium: Average health is actually 12hp, not 11, but the distances are correct.  1d6 damage for each 3 meters gives us a nice distribution of injuries and chances of death up to the assured death point at 36 meters. B
• D&D 3.5 (OGL): The average human in this system has 1d4 hp, which I round up to 3, but does not die until reaching -10 hp.  Most falls that are not immediately fatal will still result in wounds that may result in a person's eventual death if not stabilized, but I did not calculate that.  B
• D&D 4th ed.: The most appropriate stats I found for a non-heroic person in this game were for "Human Rabble", who have 1 hp.  At 1d10 damage for each 10' fallen, everybody dies from any fall of at least 10'. D
• GURPS 3rd ed.: Damage involves rolling 1d6 and subtracting a constant for each yard fallen.  Since it is possible to roll the constant or less on each 1d6, it is possible to take no damage at all when falling from any height.  Instant death requires 6xHealth damage in the GURPS systems. D
• GURPS 4th ed.: Now there is an equation for determining how many d6 to roll based on velocity.  GURPS in one of the few systems that takes acceleration into account instead of just distance.  A-
• Heavy Gear: Roll 1d6 for each meter up to 10 meters, and multiply the result by meters fallen up to 30.  Remember that the Silhouette system is funky, so "result" means the highest number rolled among the dice, and additional 6s each add 1 to the first 6.  It is possible (ridiculously unlikely) to roll all 1s and survive any fall.  It is also possible (ridiculously unlikely) to roll all 6s and die falling 5 meters.  An average person has a 40% chance of death falling 8 meters, and an 81% chance of death falling 9 meters. B-
• Marvel Super Heroes 2nd ed.: The rules as written were clearly not proofread or edited.  They make absolutely no sense in the English language.  On page 21 the rules say to take 1 point of damage for each floor fallen (a person would have to fall 24 floors), but also say to treat falling as a charge attack.  Charge attack rules on page 27 gave me the numbers I use for this post.  Using the Empire State Building for reference, I decided that a "floor" is 12 feet. F
• Rifts: People take 1 point of damage for each 10' fallen.  Instant death is at -(PE+1) hp.  A healthy average person will survive any fall under 390'.  F
• Shadowrun 4th ed.: I did not find stats for an average human.  Humans have 1-6 body points, bought up from 1 at character creation.  Looking at sample characters, I figured that an average human has a body of 2. Damage from falls over 6m is about (distance+4)/2, and characters roll (Body)d6 to resist some damage.  For someone with a Body of 3, the distances are 22m, 24m, 28m.  C
• 7th Sea: This is a game focused on dramatic swashbuckling stories, and seems to not have rules for falls.  

And here is a graph:

Graphs of Success Probability by Skill Total and Difficulty

I've given you tables of success probabilities by skill total and difficulty for two systems (World of Darkness, Shadowrun 4th ed.), plus a graph for Heavy Gear.  Here I present that information again in graphs, plus two more systems, to show some of the different patterns that exist for success probabilities with increases in skill among different systems.

Linear

Here is your standard d20 system, most popular in Dungeons and Dragons.  Each character has a skill modified by an attribute and various other junk, added to a d20 result and compared to a difficulty level.  Each increase in the skill total raises the probability of success by 5% linearly.  There is always at least a 5% chance of failure (rolling a 1).  In the D&D games, skills are not bought with general character development points, but characters are alloted a few points each level to be used only for skills.  Difficulty levels typically scale with character levels, so it behooves players to specialize in a few skills that are always increased with the character level in order to maintain good probabilities of success as characters level up.  I am not getting in to "taking 10" or "taking 20".

Inconsistent

Here is the graph for Dream Pod 9's Silhouette system, used in their Heavy Gear game.  We can see that the progression is not consistent.  The lowest skill is concave, rapidly dropping the probability of success at low difficulties relative to the drop at higher difficulties where the probability of success is already very low.  A skill of 1 has a linear descent.  Higher skills progressively maintain high success rates among lower difficulties before rapidly plunging at higher difficulties, and then there is the bent tail as it becomes more possible to roll multiple 6s.  Attribute bonuses are added to skill roll results, shifting the graph to the right without changing its shape.

Normal

Isn't that pretty?  I am not sure if I am completely representing the GURPS system accurately here, but I think players just have to roll lower than the characters' skills on 3d6 to succeed at tasks (17s and 18s fail).  So, there is no real "difficulty level" for tasks other than what is forced by skill levels.  There may be modifiers that increase or decrease a skill for the purpose of a challenge, shifting the whole curve to the left or right.  If we graphed the probabilities of each individual outcome for 3d6, the line would be shaped like a bell.  I call this "normal" because as a "normal distribution" it has higher probabilities of outcomes in the middle, progressively less likely outcomes away from the middle, and is relatively symmetrical.

Inconsistent Normal

We can see here that both Shadowrun by Catalyst Game Labs and World of Darkness by White Wolf approach the normal curve as their dice pools (skill total, or skill + attribute) increase.  With few dice in these systems, it is impossible to approximate the distribution of the normal pattern, and the results more follow the Inconsistent pattern.  These systems both involve rolling multiple dice (d6 and d10, respectively), and counting die results over a threshold as "successes".  Players need a number of successes equal to a task's difficult in order to succeed.  So, the terminology can get annoying as people get a bunch of successes but still fail at a task.

I really like how the Normal distribution of probabilities of success works in simulations, but not necessarily the way that GURPS implements it in the absence of difficulty levels.  In real life, when we encounter tasks far below our skill level, we are quite likely to succeed at them and have a low variance with our high success rate.  When we encounter tasks far above our skill level, we are quite likely to fail at them and have a low variance with our high failure rate.  Tasks closer to our skill level have increasingly variant success rates.  Because of this, I am in favor of the use of normal distributions of probability of success in simulation systems.  This typically requires rolling more than one die and summing the results.

D&D and IQ

I first started playing RPGs about two decades ago with Advanced Dungeons and Dragons.  Back before 4th edition finally defaulted to a point-buy system for attributes, character attributes were determined by rolling six-sided dice (d6).  The basic and most scary method was to roll 3d6 and add the results, providing a total from 3 to 18.  The "heroic" method was to roll 4d6 and sum the highest three results, which still provided a total from 3 to 18, but with a higher mean.

It had generally been said in my gaming circles that Intelligence (INT) in D&D was the equivalent of an intelligence quotient (IQ) divided by 10.  Or INT * 10 = IQ.  The average IQ is 100, and the D&D manuals stated that the average INT was 10 (really 10.5 by rolling 3d6).  Heroes, rolling 4d6 and dropping the lowest, have a mode of 13 and a mean of 12.2446.  The whole INT distribution, however, does not fit as well as its mean onto the real IQ distribution.

The old Stanford Binet calculated IQ as 100 times the ratio between a child's age and the age of children with the same performance on average on particular tasks.  So, a 6-year old who performed as well as the average 9-year old would have an IQ of 150.  This method of determining IQ scores becomes less useful as children grow up, and makes no sense to apply to adults.  The newer Wechsler tests calculate IQ by taking the scores of everyone in an age group and putting them on a normal distribution with a mean of 100 and a standard deviation (SD) of 15.  This is a much more clear way to evaluate how a person functions intellectually compared to same-age peers.

If we take the distribution of 3d6 rolls and associate the probability of each sum with the prevalence of corresponding IQs in the real world, we can get a better impression of what a D&D INT score means in terms of IQ.  If we say that 3d6 simulates a normal distribution of intelligence, then here are the translations (rounded) of each INT score into an IQ score:

INT     IQ 
 3      57
 4      66
 5      72
 6      78
 7      83
 8      88
 9      93
10      98
11     102
12     107
13     112
14     117
15     122
16     128
17     134
18     143

The IQ scores in this table are calculated from the z-scores for the middles of each range of probability that maps onto each INT score.   For example, an INT of 3 and of 18 each have a 0.463 chance of occurring (1 in 216, which is 6^3), but I cannot use the z-score for .00463 to calculate IQ for an INT of 3 and work my way up because I would be left trying to use the z-score for 1 with the INT of 18, which is infinity standard deviations.  Also, I would end up using the z-score for .5 for an INT of 10 when it truly applies to an INT of 10.5.  What works is to use the z-scores for the midpoints between probabilities.  So, an IQ of 57 (2.84 standard deviations below the mean) corresponds to the z-score for .0023 (the midpoint between 1/216 and 0, since it is impossible to roll less than 3) with some rounding.  The probability of rolling at least a 9 is .375, and the probability of rolling at least a 10 is .5, the midpoint is .4375 for an INT of 10, which has a z-score of
about -.157.  100 (the mean) minus (.157 * 15 (the standard deviation)) equals about 97.645, so the IQ for an INT of 10 is 98 after rounding.  Each IQ score was calculated this way.

As you can see, multiplying INT by 10 does not give you your character's IQ.  Now, this does not address differences in intellectual ability by age group.  A stereotypical D&D party consists of characters emerging from adolescence into adulthood, roughly in the same stage of development, so it should be okay to use this scale.  A 12-year old with a 120 IQ still lacks much of the functioning of a 20-year old with a 100 IQ, and a 30-year old with a 100 IQ functions a little differently than a 50-year old with a 100 IQ.  Age tends to result in a larger vocabulary and body of knowledge with a slower information processing speed, but I may go deeper into how RPGs simulate the effects of aging on intelligence in later posts.

For that matter, using an overall IQ score obfuscates the differences in each person's separate areas of intellectual functioning.  "Intelligence" refers to many different abilities that we have, and a dozen people with the same IQ can each function differently from each other on a variety of tasks.  Few simulation systems break down intelligence into components, and that is also a topic I will return to in future posts.