Jun 24, 2011

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.

Jun 23, 2011

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.

Jun 19, 2011

19 Principles of Recreation

These are Nineteen Principles of recreation from Howard Braucher, Secretary of the National Recreation Association in the mid-1930s.  I took these from Charles Smith's book, which I posted about here and here.  They are quite applicable to the children and adults of today, though there are new forms of recreation available today.  As you read, pretend that "man" means "adult".  Emphasis is mine: 

1) Every child needs to be exposed to the growth-giving activities that have brought satisfaction through the ages -- to climbing, chasing, tumbling; to tramping, swimming, dancing, skating, ball games; to singing, playing musical instruments, dramatizing; to making things with his hands, to working with sticks and stones and sand and water, to building and modeling; to caring for pets; to gardening, to nature; to trying simple scientific experiments; to learning team play, group activity and adventure, comradeship in doing things with others.

2) Every child needs to discover which activities give him personal satisfaction. In these activities he should be helped to develop the essential skills. Several of these activities should be of such a nature that he can keep them up in adult life.

3) Every man should have certain forms of recreation which require little space and which can be fitted into small fragments of time.

4) Every man needs to know well a certain limited number of indoor and outdoor games which he himself likes so that there will never be an occasion when he cannot think of anything to do.

5) Every man should be helped to form the habit of finding pleasure in reading.

6) Most men should know at least a few songs with good music so that they may sing when they feel like it.

7) Every man should be helped to learn how to make something of beauty in line, form, color, sound, or graceful use of his own body. At least he should find pleasre in what others do in painting, woodworking, sculpture, photography, if he cannot himself use these forms of expression.

8) Every man should be helped to form habits of being active, of breathing deeply in the sunlit outdoor air. Man thrives best in the sunlight. Since living, not business, is the end of life, our cities should be planned for living as well as for business and industry. Sunlight, air, open spaces, parks, playgrounds, in abundant measure are essentials to any living that is to give permanent satisfaction.

9) Every man should be encouraged to find one or more hobbies.

10) It is of the greatest importance that every person be exposed to rhythm bcause without rhythm man is incomplete.

11) About one year in every ten of a man's life is spent in eating. It is of fundamental importance that this one-tenth of a man's life shall be so lit up by play of mind upon mind that eating shall not be a hurried chore but an oppourunity for comradeship and for growth for the whole man. Eating should be a social occasion, in the home something of a ceremony.

12) Rest, repose, reflection, contemplation are in themselves a form of recreation and ought never to be crowded out by more active play.

13) Those recreation activities are most important which most completely command the individual so that he loses himself in them and gives all that he has and is to them.

14) Ultimate satisfaction in recreation comes only through one's own achievement of some kind.

15) The form of one's recreation as an adult, often, though not always, should be such as to use in part powers unused in the rest of one's life.

16) A man is successful in his recreation life in so far as the forms of activity he chooses create a play spirit, a humor, which to some extent pervades all his working hours, helping him to find enjoyment constantly in the little events of life.

17) The happy play of childhood is essential to normal growth. Normal men are most likely to grow from the children who have played well and happily. Normal men more easily continue normally as they keep up childhood habits of play.

18) Participation as a citizen in the cooperative building of a better way of life in which all may share is one of the most permanently satisfying forms of recreation.

19) That children and men and women may be more likely to live this kind of life, experience shows there is need for community action:
  • Every community needs a person, and an unpaid committee or board charged with thinking, planning, and working to provide opportunity for the best possible use of the leisure hours of men, women, and children.
  •  Community recreaion programs should continue throughout the year
  •  Support of community recreation proams should be through tax funds under some dpartment of the local government.
  •  Every community needs playgounds, parks, and recreation centers just as every city and town needs streets and sewers.
  •  Every community should provide opportunity for the children when they leave school to continue the musical and dramatic and other specialized recreation activities which they have enjoyed during school days.
  •  Community recreation progams should allow for a broad range of tastes and interests and varying degrees of mental and physical energy.
  • Every community needs persons trained to lead in recreation just as much as it needs persons trained in education.
  • Satisfying recreation, whether for the individual or for the community, involves careful planning.

The message I get from these principles in regards to role-playing games as they exist today are that RPGs are a great form of recreation for children and adults, but clearly should not be the sole form of a person's recreation.  Engage in live-action role-play.  There is joy in creation, storytelling, and community. 

Jun 16, 2011

Game Mastering: Old School Advice from Charles F. Smith part 2

This is the continuation of my presentation of Charles Smith's almost 80-year old advice on running games for groups.  Part 1 is here

Expect the Best. The text describes progressive mastery of gradually harder tasks, or learning desirable tasks that are similar to the possibly undesireable behaviors that kids will engage in on their own.  For applicability to simulation games, this reminds me of gradually introducing more complicated rules as players master basic rules (especially games like Advanced Squad Leader).  I'm drawing a blank on the second part.

Discipline Positively. Be a "cheery suggester" rather than a "dominating director." "When problems arise our first tendency is to blame the other fellow, but if we ask ourselves first, 'Is there anything wrong with my leadership?' second, 'Is the author to blame for suggesting such a game?' and finally, 'Is anything wrong with the players?' we must admit that the players are usually doing their best.  When children find pleasure in tormenting or disobeying, the leader should try to discover his own deficiencies. usually players have well founded reasons for unusual conduct or lack of cooperation.  A successful leader can secure attention by merely asking for it and refusing to talk until he gets it. He makes the group feel that the individual annoying the leader is transgressing against the group rather than against the leader."  There's a great big quote for GMing.  This philosophy is an explicit part of leadership positions in Battlemaster.

Change Plans. Situations change, and you should have a wide enough repetoire of options that you can adapt to unforeseen circumstances.  Don't railroad your players.  Players will come up with all sorts of plans and actions that don't fit your preparations, and the games will be much more fun and rewarding if you can roll with them.

Provide "Re-creation," Avoid "Wreck-Creation." "The physical well-being and happiness of the people in a leader's charge should be his first consideration." Kids need rest breaks.  Players need breaks too, but I've never known this to be a problem.

Develop Athletic Girls.  Physical games are great for girls up to age 12 or 14, just the same as boys.  Hey, role-playing games are great for girls of all ages.

Know Your People.  Offer games that the kids will actually like to play (different ages have different abilities and preferences).  This should be a no-brainer.  You will not have much of a game if you try to run games your friends do not want to play.

Consider Outside Interests. People like variety in addition to things that they are good at.  My paraphrasing of Smith's writing in this section does not really match the header, but both are good to keep in mind.  Games can integrate the varied interests of your players, as well as expose them to new topics they may enjoy.

Provide for All. Avoid games in which losers drop out. Dodge Ball is a horrible game because the kids who need most to develop skills are excluded early on and sit around.  For RPGs I think this translates into avoiding games in which characters can permanently die.  This is controversial, and your group is probably able to decide whether they want that or not, but especially new players may not accurately predict how they would be affected by permanent character death.

Consider the Place. Don't have city kids play soccer near a forest because they will just want to play hunting/seeking/exploring types of games. This may be another non-issue.  I've never known this to be a problem.  Gaming groups are generally good about coming together to play the game, and not to get distracted. 

Next up: 19 principles of recreation from Howard Braucher, Secretary of the National Recreation Association in the mid-1930s.  Then I'll get back to the math and simulation mechanics.

Jun 13, 2011

Game Mastering: Old School Advice from Charles F. Smith part 1

I had the great fortune to come across a copy of Games and Game Leadership by Charles F. Smith (the 1949 13th ed; the first was published in 1933).  Though it mostly refers to group games of physical activity for children, many of the principles apply to running table-top role-playing games (and parenting).  Professor Smith taught a university course on the topic for many years.  Here are some excerpts (in quotes), paraphrases, and notes (in italics) on how they may apply to modern RPG game mastering (dungeon mastering, storytelling, whathaveyou).  Some of these do not apply very well, but I include them for interest.

Be Enthusiastic.  Enthusiasm is contagious.  Enjoy your work.  An enthusiastic GM may have an easier time engaging the interests of players, and have a lower chance of burnout.

Develop a Sense of Humor. Be human and share in the fun of the tasks rather than being a dictator. If your players are engaging in a lot of humorous table talk instead of focusing seriously on the game, accept that that's what they're enjoying and roll with it.

Overlook Mistakes. Be sympathetic and understanding. "The person who makes he mistake invariably feels worse for having erred than any one else. If he blunders due to lack of skill, the leader should help him to develop the necessary skill. Every one who participates in athletics appreciates the coach who subtly points out errors in a general way rather than one who constantly finds fault with the individual members of the team." If someone gets a significant rule or mechanic wrong, you can remind the table of the rule while being considerate of the player's feelings.

Anticipate Blunders. Anticpate common blunders and check them without interrupting the game (like the rafting instructors blocking the bad routes on the river). "Individual reprimands are warranted only when the act in question threatens the moral growth of the entire group."  Maybe put some bookmarks in your rulebook or photocopy frequently referenced rules or tables to help people play quickly and accurately.  Scold people who seem to be bending rules on purpose.

Be Lenient. Do not nag. Let the kids have fun and not play in an exact way (but they still have to follow the rules.)  Rules may be less important to follow in an RPG.  Charles was mostly writing from the perspective of adults teaching games to kids.

Develop Confidence Through Preparadness.  "Confidence is acquired through experience, but even the experienced leader enjoys such confidence only when he is thoroughly prepared to do the particular
work at hand.... He sees ways for improving both the game and his leadership and is able to say the right thing at the right time, in order to create either the desired moral effect or happy morale. ...the way to win respect is to be prepared, even refer to notes if necessary."  Be prepared, that's the Boy Scouts' marching song.... 

Guard Against Overconfidence. You don't know everything.  Invite suggestions as to new ways of playing old games or to draw assistants to your confidence in the making or executing of your plans.  Don't pretend to be perfect, it just makes you look foolish.  I have greatly enjoyed running a huge game with a couple assistants, and I have enjoyed being a player in a game in which the players' input was solicited and used.  Not only is humility a great virtue, games are easier to run and more fun for the players when the GM accepts input and help.

Conquer Trying Situations. Maintain poise, striving always at least to appear at ease when vexatious situations arise. "Avoid petty squabbles."  Stay calm. This is good advice all the time.  Be cool.

Adopt a Positive Attitude. The descriptive text indicates that this means Be Decisive in modern English.  Make the decisions instead of deferring authority to someone else.  The GM makes the rules calls.  The GM's word is law.  I'm in favor of a One Appeal rule, but after the appeal the matter is settled.  Be assertive without being aggressive.  Be clear and firm.  Don't let a friend or overbearing player make rules calls for you.

Lead Just Enough.  "Lead just enough to set the pattern without crushing the initiative of the players." Children need experience with self-direction under supervision since they are not always supervised.  Don't railroad your players.

That's enough for part 1.  I've got a few more for part 2, then a follow-up post or two from another section of the book.  Good stuff.

Jun 10, 2011

Side Note

I finally gave GURPS 4th edition a perusal, and I was really impressed.  It looks like it fixes some of the bigger problems I had with 3rd edition.  I am happy to see that point costs for HT and ST have been decreased to reflect their in-game utility relative to DX and IQ.  Also, point costs for changing these four attributes have been made linear, which gets rid of the weird bump in 3rd ed. and looks prettier, though I will not go so far as to say a linear cost progression is necessarily the right way to go.  Since probabilities of success follow a nice normal curve, we see decreasing returns on investment either way, but less severely with the linear costs.

I am also a big fan of many powers being turned into "advantages", and the wide variety of modifiers available to customize how the powers work and how much they cost.  I haven't taken the system for a ride yet, but it looks good. 

The main downside is how bulky it is.  Well, maybe it's an upside.  My impulse is to say that players should make characters by first thinking up a detailed character concept, then going through the books from the beginning writing down what that character would cost, then selecting deleting that go over the point limit for the campaign, or enhancing what's there if the limit has not been reached.  There's way too much to memorize or keep in mind to make quick characters, but likewise it is far harder than other systems to game.  It is less obvious how to make characters that are uniformly better than others for the same points.  I'll keep poking at it over time.

Now that I've got falling deaths out of my system, I'm thinking of working on analyses and guides for strength scales or movement speeds.  I've got some good numbers hanging around, but not as much time as I'd like.

Jun 5, 2011

Death by Falling: Revisions and Simulation

One thing I realized while looking over my last post was that I only showed chance of death by impact velocity, not by distance.  Of course, you could calculate distances yourself, but I want to be more helpful than that (see second graph below).  Also, I've been bothered by my assumption of how many meters tall a "floor" is.  I had originally used the average height of the Empire State Building (12' per floor), but later used 3.5m.  This morning I checked out a resource for average floor heights by building type, and used those numbers instead, assuming that Ramos's and Delany's data was mostly from residential buildings.  Here is the revised graph of probabilities of death by impact velocity:

Here is the graph that I have put together from my estimates for chance of death for an average person by distance fallen, as well as two possible dice systems for simulation:

So, for a 3d6 system, you would try to roll higher than or equal to (meters_fallen - 9).  For a 3d10 system, just roll higher than or equal to the number of meters fallen.  For elderly characters, maybe add 2 to the number of meters fallen, or multiply by 1.5.  For children or acrobats, maybe subtract 1 from meters fallen, or multiply meters by .8.  Remember that even survivors are typically severely injured, even from falls of as little as 3m, and can require extensive medical treatment.   

Jun 4, 2011

Death by Falling: Real World Information to Guide Mechanics Development

So I don't turn away too many readers with the length of this post, here is the executive summary:

For an average person in the real world:

  • The shortest fall distance that can result in death: 0m (or I guess ~1m if we focus on center mass)
  • The average distance that will result in death: ~15m
  • The maximum distance a person can fall and survive: technically any with a lot of luck and medical attention, but practically closer to 30m (still with luck and medical attention)
[Edit: For a graph of chances of death by distance fallen, see the next post.]

My Process:

To help game designers (and for myself) with developing simulation mechanics for falling fatalities, I tried to get some real world data on fatalities and injuries from falls. My first stops, of course, were the Center for Disease Control and Prevention (CDC, because it tracks all causes of death), the National Institute of Health, and the Occupational Safety and Health Administration (OSHA, part of the Dept. of Labor). Amazingly, none of these sources made available the proportions of falls that result in fatalities or injuries by distances fallen. There was just a lot of information on the numbers of people who died from falls each year by profession, age, job, and fall context (ladder, roof, scaffold, etc...) In fact, I could only find one document via the CDC reporting a proportion of falls resulting in injuries, and it was only for Americans over the age of 65 in 2006.

I turned to regular Google searches and found a few research articles from over the last four decades with some data on fall fatalities. I also explored some information on pedestrians and unbelted drivers in front-on car collisions in case I would have to use it as a not-ideal proxy for a person hitting the ground (like the Marvel system's use of charging attack mechanics). Interestingly, the fatal car collision speeds are very close to the fatal fall speeds that I found, despite significant situational differences such as body position and impact angles. People tend to survive slightly higher speed impacts in front-on car collisions than falling.

In this graph, falling speed is estimated based on distance fallen, which was also estimated because Ramos & Delany (1986) only reported distance fallen in floors (like the Marvel system).  The rest of the data points are generated by the regression equations from the Richards (2010) document, which is why the curves are so smooth.

[I later revised this graph using different assumptions about floor heights.]

Terminal Velocity:

I learned a lot about terminal velocity, and made a calculator in Excel that works for dry air. Humidity and water vapor decrease air density, but I do not know how much. For an average spread man, terminal velocity is about 56 m/s near sea level.
Terminal Velocity = SQRT(2mg/pad)
m = mass of object in kg
g = gravity (9.81 m/s at sea level)
p = air density, which equals 1.225*0.9883^(altitude_in_meters_over_sea_level/80)
a = object surface area facing down, generally .5-.6 square meters for a spread skydiver
d = drag coefficient, which is probably .6 for a person (McIlveen, 2002)

I derived the equation for air density based on other information I found, so it may not be precise.  Terminal velocity is largely irrelevant because 99% fatality rates occur at about .6 of terminal velocity at sea level. Using v=at works well enough up to the nearly assured fatality point that I do not feel pressured to accurately model how drag affects falling acceleration. Wikipedia says that half of terminal V is reached in about 3 seconds, which matches v=at, but that .99 of terminal V takes 15 seconds instead of <6s. This equation relatively closely approximates velocity in m/s as a function of time (s) for a 70kg person falling near sea level: y = 0.0375 x^3 + -1.28 x^2 + 14.9x + -4.02.  [Edit: I do not like how the line starts at a positive value and tilts up anti-asymptotically at the end, so I would probably replace x in the equation with (x-0.35), and say that terminal velocity is fully reached at 12 seconds.]


Falls are one of the leading causes of injury and death, especially for kids and the elderly. Kids take less damage, and the elderly take a lot more. Falls are the 2nd leading cause of death for Americans age 60-72. About a quarter of elderly falls (from standing, steps, or furniture) result in injuries, and 1% of those result in death.  20-30% of elderly falls result in permanent debilitation.

Fatalities in the data here occur up to months after the falls.  I do not have real data on instant deaths.

The average survived work-related fall results in 100 days of missed work.  These falls are generally among contractors and roofers, from ladders, scaffolding, and roofs.

20-30% of fatal falls at work are not from a height!  Tripping can be fatal if the head is struck against something in a bad way.

The record speed of falling is 614 mph, achieved over 40 years ago by a guy who jumped from a balloon at 30,000 meters where the air is only 0.015 as dense as it is at sea level.

Jumps from the Golden Gate Bridge, about 70m, have a 2% survival rate, but even many who survive the fall drown quickly. 80% break bones, mostly ribs, and 75% suffer lung injuries. More than half rupture their livers, and a quarter fracture their skulls. The record high dive is from about 52m (you can find videos on YouTube). It is vital to hit the water feet first, minimizing surface area and protecting the torso and head.

The Richards document for the London DfT has a great graph on injury severities by velocity.


Center for Disease Control and Prevention. (2008). Self-Reported Falls and Fall-Related Injuries Among Persons Aged >65 Years --- United States, 2006. MMWR, 57(09), March 7, p. 225-229.

McIlveen, J. (2002). The everyday effects of wind drag on people. Weather, 57, p. 410-413.

Occupational Safety and Health Administration, Department of Labor. (2010). 29 CFR Part 1910. Federal Register 75 (99), May 24.

Ramos, S. and Delany, H. (1986). Free falls from heights: a persistent urban problem. Journal of the National Medical Association, 78 (2), p. 111-115.

Richards, D. (2010). Road Safety Web Publication No.16: Relationship between Speed and Risk of Fatal Injury: Pedestrians and Car Occupants. Department for Transport: London.

Snyder, R. and Snow, C. (1967). Fatal injuries resulting from extreme water impact. Aerospace Medicine. 38 (8).