Marvel Super Heroes - Strength and Lifting

It is time to see how Marvel Super Heroes weighs in as a simulator of human lifting abilities. Marvel includes the character creation mechanic of randomly generating the strength attribute such that half of characters are Typical, 20% are each of Poor and Good, and 5% are each of Feeble and Excellent. 

Marvel is another system, like Shadowrun, that requires a roll to determine how much a character can lift in a particular moment, and there is wide variance.  On average, a character of feeble or poor strength in Marvel can not lift anything, which is quite unrealistic.  On average rolls, characters of typical and higher strength can lift about as much as real people can.

The above graph shows the maximum amount that Marvel characters can lift given really good rolls on d100.  The maximum lift is a rare event in the game.  In the game, 5% of people have a 6% chance in any given moment to lift 2000 lbs, which is double the most that any real person has ever lifted.  The top quarter of Marvel characters is able to lift 800 lbs sometimes, which only a bare handful of men in the real world can accomplish.  It is also easily possible (45%) for a stronger than average character to fail to pick up a measly 50 lbs, which is ridiculous. 

Again, I am opposed to such wide variance within a character's moment-to-moment lifting ability.  Marvel may even be a worse simulation than Shadowrun.

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.

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.

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.   

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.

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.

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."