Ruleslawyer For Free
THE APPLIED EXPERIENCE CURVE CONCEPTSergio Mascarenhas
Ruleslawyer For Free
THE APPLIED EXPERIENCE CURVE CONCEPTSergio Mascarenhas
This is the second part of RFF#04 where I present the concept of the Experience Curve. This week I'll aply the concept to several games, more exactly:
A word of caution: I'll not try to deal with all the different rules for experience present in the following games. I'll only look at the core mechanics.
Chaosium's BRPThis system can be found in games like RuneQuest, Call of Cthullu, Elric!, etc. I guess that's common knowledge that BRP deals with experience is terms of percentage-based skills. There are some minor differences among the various BRP games concerning the rate of advance in the skills. Anyway, the basic idea is that experience increases through the usage of the ability. It works like this:
So, in BRP experience is expressed in a percentage rating that goes from 0 to 100 in 5% steps (2), and resources are attempts to use the skill plus attempts to increase it. The experience curve corresponds to the marginal likelihood of advancing from a level in the skill to the next level. Based on the concepts above, we can see that the chances to advance an ability evolve the next way:
Current ability is the ability level on the skill being tested; Chance to advance is the chance to be successful in the advancement roll; Likelyhood of increase ( = current ability * chance to advance ) is how likelly it is that the character will advance his skill at each skill level; Rate of increase converts the cummulative likelihood of increase to a 0-to-100 scale; Attempts to increase gives the average number of attempts a character needs to make to increase its skill level; Cummulative attempts corresponds to the sum of the attempts to increase at each level of skill.
Now, all we have to do is to draw the Experience curve based on the rate of increase column:
As we can see, BRP's experience curve is an S-shaped curve (3). The main problem with this system is linked to the definition of which ability rolls allow for an experience roll. But this is a different question. The important thing is that, from my point of view, it handles experience in a very nice and elegant way. Notice also that character creation rules define different starting levels in different skills. No young adult has all his abilities at 0%, of course!
Do I need to explain how xD&D handles experience? Let's see the basic concepts:
For instance, let's look at the warrior class in Dragon Fist (4). The first thing to notice is that it's not easy to draw the experience curve in such a system. In fact, in Dragon Fist (DF from now on) - and the same applies to any xD&D game - experience results from a combination of factors and concepts, so we need to look at those factors and concepts in detail. Let's start with the benefits a DF warrior gets from gaining levels (5). These are: an increasing number of maneuver ranks, attacks per round, and more hit dice. The progression is summed up in the next table where the two last columns give us the the corresponding sum:
The key information is in the column level benefits. This gives us the benefits one gains by advancing to that level. (The last column gives the sum of those benefits with the ones gained in the previous levels.) As we can see, the benefits increase as the character advances to higher levels of experience.
On the other hand, in order to advance a character must invest some sort of resources. In xD&D these resources are - as I said before - experience points. So, we now turn to the investment on resources required to advance a level:
In the first column we have the levels, of course. Next we have the Experience Points (XP) one has to get in any given level to advance to the next level. The third column presents us with the average XP's a character of any given level may expect from successfuly going through an adventure. Since this varies, we've better think about resources in terms, not of XP's, but of adventures needed to advance a level (on average). This is in column four (XP divided by XP/adventure). The fifth column gives us the summ of adventures a character must outlive in order to reach level 10. Once more, the key information is in column 4: Adventures per Level. This is our resources rooster.
Since we measure resources in terms of adventures, all we need to do now is to measure how much one benefits from going successfully past one adventure in each level. To do this we just need to divide the number of adventures needed to advance from one level to the next level, by the number of benefits gained by accessing the next level:
For instance, moving from level 1 to level 2 requires 1.3 adventures, and results in the gain of the 4 benefits of level 2. This gives us a rate of 3 benfits / adventure in level 1. The % column represents this in relative terms: it provides the % of the total benefits/resources that we gain in each level (6). The final column provides the rate of cummulative gains the character gets as it advances.
Based on this data we can draw the Experience curve for the DF's warrior class:
This curve expresses how the cummulative investment in resources (adventures) allows the character to gain cummulative benefits.
As we can see, it's quite clear that DF does not use the full S-shaped curve, but only its upper half. In it, character advancement is subject to diminishing returns. This is not a design fault, though. We must remember that in xD&D starting characters are the ones that moved up from level 0. Level 0 represents the common man. So, Level 0 corresponds to what I called the comfort level. xD&D characters are the specialists, the ones that moved up above average. Of course, that means that xD&D is not the system of choice for someone that wants to be able to play the full spectrum of experience possibilities.
We can also see that this curve is far from perfect. The rate of marginal advancement is not regular. Yet, this is a minor flaw, something we can happily live with.
White Wolf's Storytelling System
As I mentionned in RFF#02 (http://www.rpg.net/news+reviews/columns/ruleslawnov99.html#Other), the Storytelling System (SS from now on) works by assigning an increasing number of dice according to experience, going from a die to five dice. The way to deal with the SS's Experience curve is by calculating the average result for any action that requires rolling dice for each dice pool, starting at 1 die. Based on this, we may draw the corresponding Experience curve:
So, we can see that the SS is based on the concept of diminishing returns. Just like xD&D, this is not a flaw, since characters in the SS are also supposed to start at the comfort level. What I said above about Dragon Fist holds true here. Unlike DF, the SS Experience curve is perfect, and not a rough aproximation, though.
(Based on Gurps Lite: http://www.sjgames.com/gurps/lite/gurpslit.pdf)
In Gurps, learnable abilities (or, to be more precise, skills) are modifiers to attributes. Each skill level gives a bonus (or a penalty, for skill levels below average) to a certain attribute. Gaining experience (acquiring skill levels) is done through the expense of character points. Skills have different costs in terms of character points depending on whether we're talking about Physical, or Mental skills. In this column I'll only present the Experience curve for physical skills, but the results are roughly the same for mental skills. Here comes the data:
Based on that we may draw the Experience curves for Gurps Physical skills:
We can see that this corresponds to a diminishing returns curve. Gurps, like xD&D or the SS, does not deal with experience the way proposed by me. Unlike xD&D or the SS, Gurps does not assume that the departing level in any given skill is the comfort level. So, we can't say that this experience curve corresponds to the upper half of my S-shaped experience curve. Needless to say, from my point of view Gurps fails to handle correctly experience, at least on what concerns skills.
Some free systems
Let's now turn the attention to some systems that can be accessed for free in the net:
In my system experience is represented by ability levels. I also apply the next conventions:
Given this, we may draw the experience curve by taking into account the average performance for each experience level:
It's obvious that my system corresponds exactly to the way I envision experience and what I consider to be the correct shape of the Experience curve: an S-shaped curve.
Since this is an imbibed characteristic of the dicing convention, this means that I don't need to provide rules to adjust the resources needed to advance in ability at different levels, like xD&D, Gurps, or FUDGE do. Just like BRP, all I need is to specify which are the conditions that entitle a character to advance the ability. This is ecconomical in rules, and results in a simpler system, with no loss in depth.
That's all for now. Next month I hope to be able to get back at this issue and look at some other topics relating to the experience curve.
(1) In fact, this is not completely correct. In the original BRP rules the rate of advancement was a flat 5%. But in RQ3 the rate was either 1d6, or 3. Notwithstanding, even in the case of 1d6 we may assume that, on average, the rate of advancement was constant. Also, I'll also ignore the rules for ability advances past 100% present in RuneQuest.
(2) For simplicity sake, we will represent everything in terms of the original rules, where advancements occured at a rate of 5% slots.
(3) So, Simmon Dennis is not correct when he states that one of it's implementations (Call of Cthulu, in fact) represents the RWm. It doesn't since it results in an S-shaped curve, not a decreasing returns curve.
(4) I decided to pick my examples from Dragon Fist, since it can be downloaded for free online at http://www.wizards.com/dnd/DF_Downloads.asp
(5) For simplicity sake, I decided to analyse only one Dragon Fist class. We could do a similar analysis to the other classes, but we may safely assume that it would lead to similar results.
(6) For simplicity sake, I'm working it as if level 10 was the highest achievable level. Of course, this is not so.