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.
 

Point-buy Systems and Character Feature Costs - Dominion as an Example

My computer's motherboard shorted out last week, so I have no access to my files for a bit.

Liberally perceived, Dominion is a simulation of medival rulers grabbing land through human influence and resource management.  I've been playing quite a lot of the basic set, but only 2-player games.  We have decided that a few cards are worth different amounts of money than they are supposed to cost, at least in a 2-player game.

• Villages normally cost 3, but we say they cost 4 (really 4.5; they sell out quickly for 4, but are not as good as cards that cost 5)
• Spies normally cost 4, but we say they cost 5
• Cellars normally cost 2, but we say they cost 3
• Adventurers normally cost 5, but we say they cost 4
• Thieves normally cost 4, but we do not get them even when they are discounted because they are double-edged swords in a 2-player game that help as often as they hurt.

As we notice that a particular card is more advantageous than others of the same cost, we buy them all up.  A similar phenomenon occurs in RPGs with point-buy systems for any type of feature.  Almost no one gets Bioluminescence in Aberrant because it is terribly weak for the cost, and almost everyone wants 10 Willpower at character creation, the Adaptation Mega-Stamina enhancement, and Psychic Shield.  GURPS 4th edition fixed its point costs from 3rd edition to reflect how people responded to the comparative utilities of HT and ST to IQ and DX in game.  Since so many skills relied on IQ and DX, and nearly nothing on HT and ST, few people would spend the same number of points for levels of the latter as on the former.  Now HT and ST cost half as much.  Many skills in most systems are flat out more useful than others that cost the same to learn.

It is nearly impossible for game designers to figure out in advance balanced relative costs for each character feature.  This is especially due to the changes in utility across settings.  Our home rules for Dominion are for 2-player games, and may not stand in 4-player games.  Skills that are more useful in a space opera setting may be less useful in a post-apokalypse survival campaign.  We rely heavily on the GM to be aware and clever with house rules to keep players happily balanced with each other. 

A friend of mine suggested using an auction system in which players could bid on features for their characters.  Of course, this would be easier to implement in online games than in table-top games, but the line there is blurring as online resources are increasingly used for (sometimes virtual) table-top play.  If a disproportionate amount of players are choosing a particular feature for their characters, it should cost more.  If a particular feature is underrepresented, it should cost less.  This would help ensure a diverse gaming experience, and allow for better creativity with character development and play less fettered by the incentives present in an unbalanced point-buy system.

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.

White Wolf's World of Darkness Probability Tables

White Wolf's game mechanics typically look as though they were created by coked-up baboons.  I experienced a lot of frustration creating the probability tables for their 2004 version of the World of Darkness because of the mechanic of re-rolling 10s.  The whole game is like rolling damage for the arquebus in old D&D.  Technically, it is possible to roll forever, so I set some limits.  I stop calculating when the probability of an outcome drops below 0.001, or after the third roll.  It was relatively easy to find the probabilities of up to three successes with one die, then much more complicated for two dice, then after some struggles I noticed a pattern in how many separate equations must be solved and combined for each possible outcome (that meets my criteria) for a given number of dice:

So, instead of trying to solve over two thousand equations or trying to figure out how to write a computer program that would do it for me, I brute forced the problem.  I used Excel to whip up 10,000 sets of 3 rolls, then mixed them up twenty different ways, then averaged the occurrences of each number of successes.  The values in the following tables should be correct to about +/- 0.002.  (Click on the pictures to see bigger versions. I'm annoyed with blogspot's layouts.)

And, of course, by adding from the right we can find the probabilities of rolling at least any specific number of successes.  Remember that these probabilities include up to two re-rolls of 10s.

I hope that these tables will be useful to game masters (storytellers) in determining difficulty levels of challenges for characters in their campaigns.  They may also be helpful to players in deciding how much to increase a skill or attribute.

Shadowrun 4th Edition Probability Tables

This is a straightforward post of dice tables for 4th edition Shadowrun.  A player rolls a number of d6s equal to the sum of the character's relevant attribute and skill.  Dice that come up 5 or 6 count as successes.  If at least half of the dice come up 1, a Glitch occurs (something bad) even if there are also successes.  A Glitch with no successes is a Critical Glitch (something very bad).  These tables assume that players do not spend edge.  The first table shows the probability of each outcome for up to 15 dice.

What I find particularly interesting here is that the likelihood of both types of Glitch actually increases from 1 die to 2 dice, and that pattern continues for each even number of dice.  There is a kind of mechanical penalty for being better at a task half of the time, though probabilities of successes always increases.  This bizarre feature of the Glitch system does not make any sense from a simulation or game balance perspective.

This table may help game masters determine task difficulties based on characters' dice totals and the probabilities of success the GM wants in each situation.

Dream Pod 9's Silhouette System part 2

When we last left our intrepid system, I had graphed probabilities of success at various difficulty thresholds for different skill levels, holding attributes constant, and I made the claim that the system encourages min-maxing.  Let us follow up on that.

This table shows the probabilities of succeeding at tasks with a difficulty threshold of 6, which is hard, for various combinations of skill and attribute.  It also shows the character creation point cost of each skill/attribute combination, and the point cost per percentage change of success.

We see that costs mirror each other across the center diagonal, and it is a more efficient use of points to buy a high attribute than a high skill.  Even more important to note is that Attributes are applicable to many skills, and are sometimes used to determine secondary traits (Health is the average of Fitness, Psyche, and Willpower).  So, not only would it be more efficient to buy a high attribute for just one skill, there is compound efficiency for buying a high attribute in general and with multiple related skills.

This table shows the average probabilities of success across tasks with difficulty thresholds from 1 to 7.  That should be a relatively standard distribution, since a threshold of 4 is considered average.

A notable difference here is that it is actually more efficient in some cases to buy a lower attribute than skill, but only when the average probability of success is less than 51%, which is not usually desirable in a heroic simulation.  At the useful levels of success, it is still more efficient to buy a high attribute, even for a single related skill.  We also see that an attribute of 2 and a skill of 3 is a kind of sweet spot for good success at a moderate price.

There are many available skills, but the overwhelming majority of them are based on just three attributes: Agility, Knowledge, and Creativity.  As far as skills go, this means there is a strong incentive to min-max, and just pick one of the three areas to focus on while taking negative scores in the other two.  If you don't care about having a lot of skills, and want more of a brute character, scrap all three and raise the Build, Fitness, Psyche, and Willpower attributes instead.

Since those three attributes apply to so many skills, it would be more appropriate to make a new version of each of the above tables for each number of desired skills, adding in only the average attribute cost per skill.  I am not currently inclined to make a dozen more tables.  This would make it drastically more evident that a high attribute score (a 4 is possible for a starting heroic character, but a 3 is practically as high as even a min-maxer should go) allows for the most success at multiple skills for an efficient price.

Something that I did not highlight is the fact that the same point pool is not used to buy attributes and skills.  It is impossible to use a huge number of points on attributes and then buy a bunch of low level skills as it is in GURPS.  This system guarantees a set block of points for skills.  If you don't want a lot of skills, use your attribute points to build a brute, and buy high levels of the couple skills you do want.  If you want a lot of skills, pick one of the three polyskill attributes to focus on, crank it up and buy many low level related skills.  I am glad that Dream Pod 9 split the pools this way, as it does slightly limit min-maxing and forces characters to have skills, but the system still does encourage attribute min-maxing within its point pool.

Also interesting is that it is incredibly difficult to increase attributes during play.  The experience point costs are  different than the character creation point costs, and strongly incentivize buying skills during play instead of saving up to increase an attribute.

RPG Mechanics Taxonomy: Probability Scales

It's taking me longer than I wanted to finish some analyses of Dream Pod 9's Silhouette system, so part 2 will be delayed while I tell you a bit about role-playing game mechanics taxonomy.

Humans love to find patterns and name things.  Our brains do it automatically, giving us ways to predict the outcomes of novel situations by comparing features to those of situations we have been in in the past, though not always accurately, often resulting in bad stereotypes and superstitious beliefs.  When we are mindful, we can harness this wonderful ability to organize information to facilitate analyses, searches, and predictions.  We give names to groups of items that share patterns of features.

Dr. Wayne Saunders of the Museum of Man developed a taxonomy of games that identifies 20 types of game based on how they are played, and three categories of games based on victory criteria.  He classifies role-playing games as "production" games because the goal is to create something rather than to win.  Within RPGs, I further break down games into categories based on patterns in their mechanics.

 In this post, I am going to focus on scales of probabilities that characters succeed at tasks they attempt as they relate to character creation or experience point costs.  There are other mechanics that I will address in later posts.  There are two main categories of probability scale features:  the method by which the scales are determined, and the patterns of increases in probabilities of success as they depend on point costs.  I will abbreviate these to Method and RoI (Return on Investment).

There are four Methods:

• Utility: The point costs of probabilities of success at tasks are intended to reflect how useful the tasks are in the game.  Tasks that occur frequently in the game would generally cost more points for a given success probability than for less common tasks.  In a typical RPG, Karate comes up a whole lot more often than Basketball, and would cost more points to be good at even though training in those skills may take similar effort in real life.
• Realism: The point costs of probabilities of success at tasks are intended to reflect how much effort it would take in the realm world to achieve such a success probability. Being an expert historian of spoons would cost the same points as being an expert computer programmer, even though one is clearly more useful (I won't tell you which one). 
• Constancy: The point costs of probabilities of success at tasks are all the same, regardless of task utility in-game or the effort required to learn how to accomplish the tasks in real life.  
• Arbitrary: The game creators just assigned costs to success probabilities without strictly or clearly using one of the other three methods.

There are four Returns on Investment:

• Increasing: The increase in probability of success increases with additional point expenditures.
• Decreasing: The increase in probability of success decreases with additional point expenditures.
• Equal: The increase in probability of success is the same for every point expenditure. 
• Inconsistent: The increase in probability of success is sometimes higher or lower or equal for successive point expenditures.

We may be able to place RPGs on a table based on their Methods and RoIs.

How would you classify your favorite system?

Dream Pod 9's Silhouette System part 1

I had a lot of fun playing Heavy Gear by Dream Pod 9 with friends back in undergrad.  DP9 came up with a game system it calls Silhouette.  I remember a friend telling me that it was mathematically optimized for 8-sided dice, but they just changed the dice to 6-siders because people tend to have d6s lying around.  Whether or not that is true, there is a little funkiness in the system.  Here is a brief intro to the dice system, and I will have a deeper report later.

In this system, characters have attributes and skills.  To perform a task, the player rolls a number of d6s equal to his character's skill level (if the skill is 0, 2 dice are rolled and the lower result is used), and the highest result is used, with any 6s over the first adding 1 to the result.  Then the appropriate attribute is added to the die result.  So, a player whose character has an attribute of 2 and a skill of 3 will roll 3d6, take the highest die result (+1 for each 6 over the first) and add 2.  The total is then compared to a difficulty threshold, and the character succeeds if the result is higher than the difficulty.  If the total equals the difficulty, there is a draw, which usually favors a defender, and I am counting as a failure.  If all 1s are rolled, there is a "fumble" and something bad happens regardless of modifiers.

Attribute scores effectively take away from a task's difficulty (or add to it if the attribute is negative, which is common; 0 is average for an attribute).  A difficulty of 4 is supposed to be average, 8 very difficult, and 10 or more practically unattainable.  Even the game creators describe the progression of success as "peculiar."

Just a cursory glance shows us that attempting tasks with a skill of 0 significantly risks fumbles, that there are diminishing returns as skills increase (I'll go more into that in part 2), and that you shouldn't count on rolling more than one 6.  Also, you can see how important attributes are, shifting the entire graph to the left or right.

We had a sniper in our party with a dexterity of 3, which is a very high attribute.  He was ridiculously successful at dexterity tasks for which he had little or no skill, such as piloting a Gear.  This system cries out for min-maxing, and game masters should be ready to impose limits and say the magic word: "no."