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.
 

Shadowrun 4th Ed. - Strength and Lifting

In Shadowrun 4th Edition, how much a person can lift or carry is based on the character's Strength, modified by the successes from a Strength + Body roll.  Human Strength and Body attributes lie on a 1-6 scale, and the manual says that average humans have scores of 3.  With the average person's STR + BOD = 6, it is possible to roll up to 6 successes to modify his base lifting amount (though very unlikely to get all 6 successes).  Each success rolled adds 15 kg to the amount that can be lifted.  Here is a graph of the average lifting abilities (after rolling) for characters of average Body and any given Strength:

We see here that the average real-world person is as strong as a Shadowrun character with a Strength of 2, one level below average given an average Body.  The perfectly average Shadowrun character will (on an average roll) be stronger than about 70% of real people.  With the randomization in the game mechanics, it is possible for characters with strength of 2 to lift more than shown on this graph about 26% of the time.  So, it gets a little messy comparing the probability distributions of game characters to the single limits I have for real people.  Real people just do not have wide variance for how much an individual is able to lift.  A person's max lift will fluctuate a little based on factors like rest, warm-up, time of day, and how long it's been since working out, but the fluctuation will not come anywhere close to the 90 kg variance an average Shadowrun character has.

Shadowrun's mechanics have the typical trend that average characters are stronger than average real-world people, but on average the difference is not as severe as other popular systems.  What is quite deviant in the mechanics is the huge variance within a single person due to rolling so many dice to determine lifting ability during each attempt to lift something.


Here is a table of probabilities of successes based on die pool:

Here is the table of base lifting amounts and modifiers:

Rolled successes add 15 kg to lifting, and 10 kg to carrying.  I would prefer the system to have less randomization.  It is also unfortunately messy to use the real strengths that I have in comparison to Shadowrun characters all of Body 3.  I have no clear way to break real world people into six Shadowrun-equivalent groups by body size to create separate graphs by Body and Strength.  This is one of the least clear comparisons I'm making for strength, but I hold to the opinion that less randomization is better in a simulation mechanic.

Mutants and Masterminds - Strength and Lifting

Mutants and Masterminds is one of my favorite systems.  The mechanics made excellent improvements on the d20 system.  Since it uses a point-buy system, there is no real distribution of strength.  Since it is based on the d20 system, though, which originally determined strength with a 3d6, I am using the 3d6 curve as a proxy of the distribution of strength within M&M.

It is accurate enough at the far bottom and top of the distribution of lifting ability, but, as with nearly every other system, it overestimates the abilities of most people in the average range.  The average person in the M&M system is stronger than 75% of people in the real world.  The average person in the real world is only stronger than 10% of people in the M&M system. 


Here is the lifting/dragging table for M&M 2nd ed.  Weights are in pounds.

Rifts - Strength and Lifting

Palladium's Rifts system has a reputation for being ridiculous, but its rules for maximum lifting ability have some merit. 

 Since the Physical Strength (PS) attribute is randomly generated by rolling 3d6 and adding 1d6 if the sum is 16-18, the distribution is the same as D&D 3.5 up until a PS of 15, then stretches out to 24 with less than 1% of the population having each PS score from 16-24.  In fact, it is impossible to have a PS of 16. 

Lifting ability follows a linear progression, with a jump at PS 17 where the multiplier doubles.  The game pretty accurate simulates real people at PSs 3, 14, and 15 (and 16 as projected if it were possible to roll), but way overestimates ability for average and below average people.  If the multiplier did not change, and there was just one constant linear progression, the game would do a good job of simulating very strong people as well. 

What is interesting to note is that the maximum amount that an unmodified human can lift in the game (960 lbs) is pretty close the maximum that any real human has lifted.  It is just that the game mechanic overestimates the proportion of people who can lift that much.  Perhaps far more people hit the gym really hard in the grim future of Rifts.  It is important to fill up that suit of armor covered in skulls and spikes.

Here is the table of carrying and lifting ability by Physical Strength score, and the proportions of characters who would have each score by rolling.

Dungeons and Dragons 3.5: Strength and Lifting

D&D 3.5, the d20 OGL line that spawned a flood of content, actually seems to have the most accurate simulation of human lifting ability.  I have almost finished making graphs for the systems I have, and 3.5 looks best so far.  I dislike Dungeons and Dragons in general, and this came as a surprise to me, but there you have it.  It still pretty consistently overestimates people's lifting abilities, even men's by about 5-70 lbs at each score, but it has an appropriate curve.

To better simulate a real person, figure out your character's strength using the table below, then add 2 to it.  For example, if you are simulating someone who can deadlift 300 pounds in real life, the table would assign the character a Strength score of 13, but a score of 15 is more appropriate based on the proportion of the population with that lifting ability.  Here is the table of encumbrance thresholds for 3.5.  Is this the same for Pathfinder?  I do not have the Pathfinder system, but I am under the impression that it uses the same rules as 3.5.

Dungeons and Dragons 4th edition: Strength and Lifting

Now that I've finished creating a reasonable distribution of real human lifting ability, I can compare it to the distributions generated by the mechanics of role-playing games.  Let us start with the 4th edition of Dungeons and Dragons.  Here is a table showing how lifting ability is calculated in-game based on the Strength attribute:

A character holding up to a "Normal" weight does not suffer encumbrance penalties. The rules say that characters can not lift more than the "Heavy" amount, though they can still move around while holding such weight. 

If we go back to the roots of D&D, when Strength was determined by rolling 3d6, we could  create proxy values of the proportions of the population with each Strength value (mean = 10.5).  Then we can graph the amount of weight that real persons could lift along with what D&D characters can lift:

The D&D rules provide a linear progression of lifting ability.  D&D 4th edition closely simulates real people's abilities at Strengths of 3 and 14-16, but gives a greater lifting ability than realistic for characters with Strengths of 4-13, and lesser for the highest human Strengths.  I threw the values for real men into the graph to see if D&D was a better simulator of just men, and it does (the sum of the differences between D&D values and real values is smaller).

Of course, D&D 4th edition uses a point-buy system for attributes, so there are no clear proportions of characters with each lifting ability.  Let us see what the percentiles would be of D&D characters at each Strength score if the game were an accurate simulation of real people (the 3d6 line is included just for reference):

 We can see that the average D&D character should have a Strength of 6 or 7 (not 10 or 11) for the game to simulate real people.  Only a quarter of characters would have Strength scores of 11 or higher.

Next up: another game's strength system gets compared to real life.

Adult Deadlifting Distribution

Here is the aggregation of men's and women's lifting abilities.  Again, the graph is inaccurate for the bottom percent or so, and the estimate equation only really applies to the 5th-95th percentiles.  I assumed a 52% proportion of women, not that it significantly affects the graph.

We can see a few distinct segments of data.  The bottom third is pretty exclusively made up of women who do not lift weights.  The middle third consists of untrained men, and women who weight train.  We see a sharp upward slope around the 73rd percentile, which is due to elite women weightlifters. The 78th to 98th percentiles, roughly, are made up of men who weight train, and the spike at the end is elite weightlifting men.

Even small children and the very weakest adults can still lift at least 20 lbs.  60 lbs is a good estimate for the 5th percentile.  The average adult (in the US) can lift up to 125 lbs.  People in the 81st percentile can lift double the average amount.  People in the 95th percentile can lift about 310 lbs.  Over 400 lbs is the territory of elite men and a handful of women.  Over 700 lbs is the territory of just a handful of men.

Again, there are unrealistic steps in the graph due to how the data was originally collected, and the smoother curve is probably more representative of the population. There should be a steep slope up from a low weight in the lowest few percentiles, but data is not available. 

Here is the same graph in kilograms:

Men's Maximum Deadlifting Distribution in Pounds with Equation

I figured it would be helpful to readers to revisit the distribution for men's deadlifts using pounds instead of kilograms.  Also, as I have been working on graphs for future posts, I have been tweaking equations that generate good estimates of what a person can lift at any percentile.

 It is important to note that the line was not calculated to be a best-fit to the data, and that was intentional.  I do not like how the deadlifting data I have creates a large jump past the 50th percentile, and it is entirely an artifact of the way the data was collected, not representative of the population, which would follow a smoother curve.  The equation I settled on is 65 + 35 * 1.0225 ^ (100 * percentile) in pounds.  Some day I will learn how to make equations pretty.  What is it, LaTeX?

Also, the equation for the line should only be used to estimate deadlifting ability for the 5th-95th percentiles.  Over the 95th, we see a sharp turn upward as the elites truly separate themselves from the pack.  Below the 5th percentile, we would also see a sharp turn downward if any data had been available for unhealthy or particularly weak men.  The lowest value available is the average maximum weight lifted by men with body weights in the bottom 0.005 proportion.

Women's Maximum Deadlifting Distribution

As I have done for men, I came up with a reasonable distribution of the lifting capabilities of US women.  Global data just is not available. The proportion of women who lift weights has nearly tripled over the last two decades to 21%, but this does not tell us what proportion weight-train with the goal of really getting strong.  I estimated some proportions to combine with the deadlifting table for women. 

It is interesting to note that any person can almost double what they can lift with six months of diligent training.  Also, the proportions of people rigorously training are fluid over time as weight-lifting fluctuates in popularity.  As women's sports have become more popular, and the health benefits of weight training become more obvious with increased scientific research, the curve in these graphs has become less acute, and may continue to straighten out a little in the future.  These graphs are snapshots in time, and do only apply to healthy women who have had the advantages of a first-world nation.  I've got these for you in pounds and kilograms, for your convenience. 

The strongest woman in the world has deadlifted 686 pounds (311 kg), so that is the current 0.000000001 level for women, and requires a life dedicated to building strength. 

For some clean RPG mechanic guidelines, the average woman can lift about 80 lbs (or let's say 35 kg).  A woman who is small and particularly weak should still be able to lift at least half as much.  Women at the 95th percentile can lift twice as much as an average woman.  The hard-training elite can lift four times the average.  These ratios are very similar to those for the men, except that the strongest woman in the world lifts almost nine times the average.

Next post: all adults together, which should really be the standard for developing RPG strength scales.

Women's and All Adult Weight Distributions

Continuing to use the EPA data, I plotted out a weight distribution for women.  Unlike the men's distribution, though, women's does not have a normally distributed natural log, so I filled in missing values without an equation.  The women's distribution has a more pronounced curve than men's.  I then figured overall adult weights by weighting and consolodating the men's and women's distributions with the assumption that our adult population is 52% women.

This information will be useful for players of games that take weight into consideration, such as Heavy Gear and Shadowrun.  Readers may want to keep in mind that people's weights peak in late middle age, and are lowest in early adulthood, with an average difference of about 15 lbs.  Also, there are racial differences.  Some supplementary information on racial differences (the EPA only lists Blacks and Whites) can be found here.

 

 The next step will be to find the proportion of women who weight-train, combine their weights with the deadlifting table, and plot women's deadlifting ability distribution, as well as for all adults, as I have already done for men.

Men's Maximum Deadlifting Distribution

Okay, still using the best source of strength data I could find, the distribution of men's body weights, and a scant article on a CDC study on the proportion of people who work out, I made a reasonable graph of the distribution of adult male maximum lifting ability.

Now, we know for a fact that there are dudes on this Earth who can lift over 400kg, but this graph only tracks up to the top 0.0001 of men.  About 0.00000001 of men can lift 450kg.  Also, I have no lifting data for the bottom 0.0034 of men, which should not be a big deal for RPG mechanics development.

Clearly, the average man can deadlift a max of ~80kg, or about 176 lbs.  The weakest men can still lift about half that, and men at the 95th percentile can lift about double that.  Elite lifters can handle three times as much as an average man, and the strongest men in the world can lift five times as much.  Those are some clean, easy guidelines for simulations. 

This graph is the predecessor of the top graph, and shows the same data with a different x scale:

I will eventually do this for women. Men tend to lift .42 to .64 more than women of the same body weight and same training.  Since men also tend to be heavier and lift weights more often, the women's distribution is probably about half of men's.

I will also compare the strength progressions of popular RPG systems to this real distribution, and rate them by how accurately they simulate real life, as well as by playability, of course.  I am using only deadlifts because nearly every system has rules for the maximum amount that a character can lift and not be able to move with, and most systems have no mechanics for other exercises.

Men's Body Weight Distribution

On my quest for determining how much people can lift, I developed this graph of men's body weights in pounds.  The natural log of men's weights in kilograms follows a normal distribution with a standard deviation of 0.165.  The equation I used, based on the EPA's data on the weights of American men ages 18-74, is e^(Standard_Deviations * 0.165 + 4.34) in kilograms.  The proportion of men of each weight is in percent.

Some RPG systems have rules regarding character weight.  For example, Heavy Gear and Shadowrun 4th ed. have attributes for Size or Body, respectively, based on the size of a person's body.  In real life, for the purposes of determining strength, the maximum amount of weight that a man can lift is close to 3.5 times his weight.  D&D is ridiculous for allowing halflings to have a STR of 18 at creation.

Strength and Untrained Lifting in Aberrant

I am crunching data on human strength for a series of posts on how TTRPGs model it.  This post can be written early as a teaser because White Wolf's Aberrant rules separate out lifting capacity by untrained natural ability and the product of training.  Untrained strength in Aberrant has a scale from 1 to 5, with 2 being average.  There is no real standard deviation for the Aberrant stats, but it seemed reasonable enough to use each ability level as a proxy.

As I will go into in more detail in a later post, the best resource I found for lifting ability shows average weight lifted for each body weight category. While trying to find distributions of adult male body weight so that I could determine the proportion of men who could lift each amount of weight, I found a couple differing sets of numbers from the EPA and WolframAlpha, and a set for older men from an organization in Cambridge, MA.  The problem with weight is that it does not follow a normal distribution, so I cannot use the mean and standard deviation to calculate any value.  However, the natural log (ln) of weight does, and that may help me.  The differences between the data sets seem small enough not to significantly affect my work, and are at least partially explained by the general rise in Americans' weights over the last couple decades.  For the graph above, the x-axis is technically mislabeled, but each standard deviation mark refers to the percentile for that z-score, so -1 SD is about the 16th percentile, 1 SD is the 84th, 2 SD is the 97.7th, and 3 SD is about the 99.9th.

As you can see, the Aberrant rules are pretty bad at simulating real untrained strength among men.  When I finish figuring out what the distribution of strength is for all men, women, and adults together, I will show how each RPG system performs as a simulator, and I will revisit the Aberrant system to include the weightlifting skill.

GURPS Optimizing: DX and Skills

This post is a continuation of the previous post on IQ and skills. When playing GURPS (Steve Jackson's Generic Universal Role-Playing System), what is the best DX score to buy to make the most efficient use of your character creation points?

DX has the same point costs and levels as IQ, but the related skills are priced differently.  Skills are only easy, average, or hard.  An easy skill costs 1 point to buy at the same level as the character's DX, an average skill costs 2, and a hard skill costs 4.  Lower levels can be bought for half the price as the next higher level, down to .5 points (so .5 points will buy a hard skill at the DX-3 level).  Higher levels cost twice as much as the previous level until the cost is 16 points (e.g.: average skill at the DX+3 level), then each level costs 8 more points than the previous level did.  Buying hard skills above one's DX score is very expensive indeed.

Here is a graph showing the probabilities of success with average DX skills by cost and DX score:

I also created a table that you can use to easily see what DX to buy after you decide how many average DX skills (or equivalent) you want and how often you want to be successful using them (success probabilities below 25% are not shown):

*Though an DX of 3 is technically optimal in these cells, a score up to 9 may be a better choice because the point cost difference is very small and DX will have impacts on game play beyond the cost of skills.

You can see that this table is much easier to use than the IQ table.  The multipliers to convert easy and hard skills to average skill equivalents do not change (they change for some inefficient arrangements, but not for any optimal arrangements).  For all white cells: easy skills count as .5 average skills, and hard skills count as 2 average skills.  For the grey cells, the multipliers vary, but are irrelevant.  

Similarly to the IQ table, we see that a score of 13 is great if you want your character to be pretty consistently successful at a good handful of skills.  A below average (10) DX score is only appropriate if you want your character to never be effective at more than a single DX skill.  Min-maxers may be tempted to trash a stat to get points to spend on the other, but I would be hard-pressed to think up a character (okay, besides a Professor Xavier type) that would be better off with a low DX.  In fact, it seems that most characters should have both a DX and an IQ of at least 13, and would not be significantly sacrificing uniqueness or wasting points.  

A nit-picker may point out that many skills have default values (e.g.: DX-6), so characters technically have lots of skills for free.  The default values are such that even with a DX of 15, the character may have a 50% chance of success with an average skill.  A DX of 17 only gives about a 75% chance of success.  High enough DX or IQ scores to make default skill levels reliable are so expensive that a character will have significant opportunity costs for other features that were passed up.  The term "Jack of all trades, master of none" comes to mind.  It is generally more effective and efficient to be a specialist, and spend the points on actually having the skills you think will be useful for you.