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.

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.

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."

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.