The Cost of Charts

Love em or hate em, you cannot escape charts in Rolemaster. This feature, more than any other, distinguishes it from other surviving game systems. I cannot have a conversation about modifying or even understanding the game system without talking about charts and their impact.

Specifically, I am going to talk about complexity and efficiency, the cost of algorithms. Nothing about this conversation is about the goodness or badness of Rolemaster, only about its expense. Charts are the elephant in the hallowed halls of Rolemaster. This post is all about weighing the elephant.

If you are familiar with algorithms, you probably already know how this post will develop and I hope you do not mind my attempts to simplify a subject that can get, um, rather complex. Much of what follows might be obvious to you even if you are not, especially if you have been living with the complexity of RM for decades, but perhaps because I am about to explain this too awesomely. Perhaps. Or, you can just wiki computational complexity and algorithmic efficiency, and know everything! More likely, I will not have explained things well enough. Otherwise…

Complexity is basically how much stuff it takes to support an operation. The usual ‘stuff’ considered is time: If I run an algorithm on an input of size N, how long will it run? But we can also consider operations: How many operations does it take? This is pretty useful to measure the agility of a game system during play: How many things do I have to do to reach a conclusion? Finally, we can consider space: How many physical resources does it consume? We will be talking a lot about this last.

Suppose I have N talents that cost the same and work the same for everyone: No special cases. How much space do I need to represent them? Well, it’s the average length of a talent write-up, which we can consider reasonably constant, multiplied by N, or k*N. We ignore the constant and call this O(N), because as N gets really huge the constant doesn’t matter very much. If I have 1000 talents in RM, the space I need is 1000 entries. If I have 4 talents, I need 4 entries. If I add a brand new talent, whether I have 1000 talents or 4, I do not have to modify any other talent and I need exactly one more entry. We call this linear.

So far so good? Well ok: The same thing happens if I decide to add a new skill to RM, right? Nope. Let’s walk through this. First, I have a chapter all about skills. I add another skill, and that’s just another entry, as for talents. But I also have different skill costs for every class. So if I have S skills and C classes, I need S*C entries, or O(S*C). Hey, that starts to look like a table, or a chart: It’s no longer linear, but quadratic. It’s representation no longer looks like a list of stuff, but a quadrangle. If I have 300 skills and 50 classes, I have 15000 entries. To add a new skill requires C=50 new entries; a new class requires S=300 new entries. Ouch.

Of course, if I add a new class, I also have to calculate and then create entries for the cost of every Lifestyle and Vocational Package too. If I have P packages, that’s O(P*C), which is also quadratic. Having to do two (or any constant number of) quadratic things is still quadratic.

If you’re wondering why so many rules tinkerers go with a single Non-Profession class, or if you are one of these tinkerers and think you are doing it for some other reason, you are really doing it to reap the benefits of greater algothmic efficiency. These quadratic algorithms become linear because you have set C=1. When balancing skill costs, you have S costs to think about rather than S*C, so you are more likely to get the balance right. When representing skills, you have S entries. That’s linear. The same reasoning holds for packages, and maybe some other charts I don’t want to think about now.

Of course, we can use skill categories to tame this problem, which has already happened :). This reduces the size of S, which is nice. Instead of S=300 we have, say, S=20. But the algorithm still consumes quadratic space, because it hasn’t changed: 20*50=1000 entries. That’s better than 15000! And if we limit ourselves to only 20 classes, we have even fewer entries: 20*20=400. But if we had a linear algorithm, O(S), we’d have 20 entries, or we could ignore skill categories and have 300 entries.

This is what a game designer I know calls “the n squared problem.” When designing a game, he never wants rules that require him to make a big table (he simplified the rectangle to a square, which is reasonable) because he then has to fill in every entry and be sure they are all correct before going to print, and then players who want to really understand what is happening have to look at N*N cases rather than N.

So, RM has “the n squared problem,” right? Nope. We should be so lucky. RM has Armor Type rather than mere Armor Class. Where lesser games are content to represent each weapon as some die roll for damage with maybe a damage type and maybe a special rule, every RM attack is unique. And where other games settle for a mathematical formula for deciding what a die roll means, RM has something like 50 entries for the range of 0 to 150+.

That’s A (number of ATs) * W (number of weapons or attacks) * D (dice roll bands on table). That’s O(A*W*D). My game designer guy would call this “the n cubed problem.” We in the biz call it cubic. It’s like a stack of tables. Let’s weigh the elephant:

If I have 20 ATs, because that sounds like a good number :), 40 different weapons and attacks and 50 dice bands, thats 20*40*50=40000 entries. (I won’t even bother with the crit charts here, but that’s also cubic.)

Add another weapon or attack type? That’s A*D new entries, or a page. Want to add a new AT, say, to support the plant people and plant armors I really want to add to my game? That’s W*D new entries, and I have to edit all the pages. You get the idea. (Here is where a purist might point out that I should represent D as a really big constant. But I’m simplifying, and I think you know why I’m not.)

I hope we are getting something for all this algorithmic inefficiency: Other rpgs usually represent weapons and armors in linear space. Remember: If I have one list of armor that doesn’t depend on weapons, and another list of weapons that don’t depend on armor, that’s two lists, both of which are linear. That’s O(N), and I have a number of entries precisely equal to A+W.

We can reduce entries too: RMU cuts the number of ATs in half, for a substantial savings. But I still cannot easily add new armors, as I can in other systems. The relative algorithmic inefficiency is forcing some hard choices! We’ll be talking about choice in another post. But could we instead change how things are done? Change the algorithm? Should we?

Maybe you don’t care about space complexity, but only about time complexity. After all, once you have a character, you can copy the few charts that character needs, and it doesn’t matter because everything is so easy for a guy who can GM this game in his sleep. We’ll talk about time complexity in a moment.

But first… it does matter. You pay for the space complexity when you buy a book and much of it is table entries like 22AK, 24AK… when it could have other kinds of content. You pay again when it takes forever to get a new book out because all of the entries have to be correct. You pay again when you find that things aren’t balanced right even after that forever: Human beings really don’t do a good job balancing 10000 table entries, and trying to reduce the problem with categories creates other problems, which have been discussed in other RM fora, though not from this perspective. You pay again when a new something or other is added, and all the charts have to be updated. You pay again when you are the one who wants to add or change something, because that’s expensive in RM. There are some other subtle prices to be paid, and RM veterans who start to look at the game through this kind of lens are more likely to find the most insidious these than I.

There’s a time penalty too, because looking things up on a matrix is often more difficult than rolling some dice and comparing to something simple. But this is not so terrible.

All rpgs have to deal with time complexity, and few do a great job of it. Time complexity here is all about the cost of each operation. Do I have to figure out how many dice to roll? If so, given the capabilities of human brainpower, what is that cost, compared to a mechanic that always has me roll the same dice? That’s the best, by the way: constant complexity, or O(1). RM can brag here. But calculating all the modifiers is a different kind of expense, and RM has that in abundance. Then there’s tracking actions, percent action, initiative… What are the real costs? Each kind of operation is just plain different. Having to open a book and reference a table has a different cost compared with finding the right dice to roll, especially if some other player borrowed one, compared to calculating a formula, even a simple addition or subtraction. And then there’s the cost of human error.

So, in the simplest sense, most rpgs seem to have linear time complexity: Add up each relevant modifier, find the necessary dice, roll them, figure out what it means. But if any of these operations requires greater than constant time, the overall time is worse than linear. I am very confident that looking anything up on a table is worse than constant for a human being. I suspect it is worse than O(logN) and would be shocked if it were better. Alas, that awaits a real study or a good Google search.

As an aside, the advantage/disadvantage mechanic of D&D5 oversimplifies, perhaps, but it has powerful, um, advantages: Although running through the possible sources of advantage and disadvantage is linear, you get to stop much earlier, because only one of each matters. Also, the math is dead simple, since there is no math, so we can be sure the operation really is constant. (I’m not sure that adding modifiers is really constant.) It is also far more reliable: If you accidentally use the same modifier twice, you still get the same result. Combined with no table lookup, this really is a safe O(N).

So, here we are. I haven’t gone through everything, some of which will come up later, like spell lists, but RM has some rather inefficient features.

I do not mean to say they are the wrong features! If the features provide you with something you don’t otherwise get and still really want, well, you paid the price for what you want. That’s the big question, isn’t it: If you’re willing to collapse classes to reap the rewards of efficiency at no loss of playability and perhaps even a gain, what else might you do?

16 Replies to “The Cost of Charts”

  1. Fascinating entry, Ken. Thinking game design through in terms of “cost” and weight should be as valuable to me now as GNS theory.

    You’re right in that the “complexity” or cost question is something to be independently resolved at individual tables. As an exercise, we can start designing a game from the ground up… To leave you out of the scenarios and possibilities I just thought of, I observe that I instantly add mechanics out of a desire for “realism” or simulationism (and because I fall into pre-worn tracks, having played many, many game systems in my day). The question is *how* many mechanics will drive players batty vs. how many removes any “game” in favor of plain old collaborative story telling or make believe.

    For my own home game right now I’m essentially running MERP with RM2 Arms Law and Spell Law tacked on. I think I much prefer the cost of charts to modifiers. My charts are all tabbed out in a binder for quick reference. Roll a die, add modifier, subtract DB, look at a chart. I find that, if I use the simplified MERP attack tables, I’m using more modifiers to simulate weapon qualities that are baked into the RM tables. I also don’t like conditions. I *hate* keeping track of combat rounds, bleeding damage, all that. I’ve been trying to think of something to simplify this — maybe roll 1d10 for bleeding damage *after* the battle is over, I don’t know. Anyway, my own preference would be to have one die roll resolved on one (and then two) charts.

    You might wonder why I choose Rolemaster, then? Honestly, nostalgia. But I also find it more porous, much like the d20 game from which it’s derived, for my own tinkering and DIY projects. Looking forward to more in this series!

    1. Hi,

      How many mechanics… batty vs flavorless:

      That’s the big question, isn’t it? From the perspective of this post, one way to assess “battiness” is to itemize the things that have to be done. Count the number of table look-ups. Count the number of times dice must be gathered. Time how long each operation takes. How long does it take to find the right page? How long does it take to agree on each modifier?

      The number of operations probably scales in a linear fashion. For each modifier, for each condition, do the thing you need to do. The number of things you have to do matters, so just measuring the complexity isn’t enough, which you allude to when you talk about modifiers being “baked in”. More on that in a bit.

      But the amount of time it takes to perform each operation is probably non-linear, and even *changes* depending on what else you have to think about.

      I deliberately avoided discussion about flavor in this post. Some future AI will probably be able to use math to understand the oh, so predictable preferences of relatively unintelligent humans! Me, being one of those folks, not so much! I definitely find that the game system colors, sometimes even defines, the play experience.

      A mechanic like L5R/7c “roll and keep” has its own tang. But is it good? Is it bad? I have deep problems with it. I think it wrenches players out of the game because you really have to have a handle on how the math works to know what to do, and that is more important than, and not always congruent with, what you think your character ought to be able to do. A lot of other people like it very much; they feel it represents the high stakes swinginess this kind of game (in their opinion) should have.

      So I cannot measure flavor.

      I do suspect that although you believe the weapon qualities are baked into the tables, they aren’t really. I plan to touch on this, at least indirectly, in The Illusion of Choice. Coming soon, I think. Regardless, even if you *think* they are baked in, the system is doing what it is supposed to, providing you an experience of having chosen a particular weapon, rather than a generic Attack Thing.

      As for your having chosen RM… why not? This is a good place for people who do that! System extensibility and customization are important features in and of themselves, that often outweigh other considerations, sometimes *all* other considerations. Not just game systems, but *any* systems.

      Anyway,

      Ken

    2. Hi

      We are also playing RM2. If you struggle with bleeding damage, how about letting your players keeping track? Just tell them the damage points per turn. Whenever it his/her turn the player takes the bleeding damage at the beginnings his/her turn.
      I think it is important to keep it this damage within the timeframe of combat (at least). For monsters you just thumbrule it.

      1. Thanks, Christian! Again I appear to be doing, mostly unconsciously, precisely what you recommend. Some of my simulationist gamers are only to happy to keep better track of bleeding and conditions than I can. And on my end, yes, just last session I determined, “This Orc lost a bunch of hits, is bleeding, and stunned; yep, he’s had enough. Next!”

  2. Collapsing classes does reap the rewards of efficiency, but at a high cost to playability (and replayability), because it erodes the distinctions between classes in some significant ways. That is why, for example, I am willing to pay the price for individual skill costs; it is also the reason why I prefer each weapon to have its own attack chart, because again, you lose some of the distinctiveness of different weapons when you just use a generic ‘axe’ chart to represent everything from a light throwing axe to a two-handed Viking axe.

    The charts can also be used to reduce the number of operations players have to perform, and in that case, I think the charts are worth it. I would for example prefer the attack charts to list results for all sizes at once rather than requiring players to be constantly doing upscaling or downscaling math.

    It is helpful thought to think of the cost of charts, even if we are willing to pay it. For me, the big question, which you do explain above, is: is the cost of the chart worth it? For me, the cost of the weapon charts is worth it if it means different weapons really do behave differently against different armor types. And the cost of the individual skill cost chart is worth it if it means that there are real differences between the classes and the classes do what I expect them to do (e.g. Rangers being good in Beast Lore rather than average or poor, Monks being good in Mental Discipline rather than average or poor, etc.). Without those distinctions, the classes and weapons become too generic for my liking. That is just my 2 cents of course.

    1. Hi,

      Like you, I like classes. I’ll save a longer discussion for the upcoming “The Splendor of Classes, Levels, Talents and Spell Lists.” But I think they add important flavor. I think that taking them out of RM takes something away. Finally, I think that RM has the *wrong classes*, in the sense that the most important RM classes are really D&D classes that belong in that system rather than this one. (Class in classic D&D is about a functional role. As RM evolved, its class strives to be about what a character is. That distinction might seems subtle, but I believe there are large implications.)

      Hmm. That upcoming post is likely to be long or broken up, because there’s a lot to say about classes in general, and classes in RM.

      As for getting the distinctions you want and accepting the cost… I suspect that you aren’t getting all of the distinctions you think you are getting, and that you are getting distinctions that you don’t realize you are getting. Does that Viking Axe chart really model a Viking Axe? If I took an AT column from that chart, and some other AT chart from a similar weapon, and then swapped them without telling anyone, who would notice? Amidst the 40000 or so entries on these tables, is there some other emergent pattern that has nothing to do with how real weapons work? Or even how we want fantasy weapons to work?

      By the way, because of the way RM now wants to distinguish size, the choice is either between scaling math (ugh!) or turning those cubic O(n**3) charts into hypercubic O(n**4) charts. There has to be a better way to represent size in a way that satisfies players, unless they plan to release a slick app rather than a book.

      I started to talk blithely about skill costs. Then I stopped and deleted, because the topic deserves pondering. RM largely creates classes by giving each class 2 unique features: 1) Base Spell Lists, which may be none. 2) Skill Costs. Different editions add a few minor distinctions (occupational/everyman skills, some bonuses…) but skill costs loom large.

      Naturally, if you want classes and if you want to develop them in the traditional RM way, getting skill costs right is of the utmost importance. Your ranger just isn’t a ranger if he cannot reasonably develop lore skills about the natural world. But I think I want to claim that there are some intrinsic problems with defining classes in this way, so that even if you solve one problem with Rangers, there remains too vast a pool of similar problems. Most players just ignore these, the same way some people are willing to ignore the (extremely reasonable, I agree) issues you have.

      *ponders* I had been planning to touch on skills and skill costs across the series, but maybe I need a post just about skills and skill costs in RM and other rpgs. What skills should we have? What is the real value of a skill? To whom?

      Anyway,

      Ken

  3. Hi!

    A very interesting Suchseite, indeed. For me as a computer scientist complexity theory is not new.
    However, what I most like about Rolemaster over other classic roleplaying systems and what still keeps me sticking to Rolemaster is that every character can learn everything. There are no hard class restrictions. This is really a thing that my friend and I value over the last 20 years.
    Regarding to the complexity discussion, I have to say that I don’t mind the quadratic complexity in skills (although I might have an easy solution for this) because you only deal with it during character creation and upgrade. In contrast I really don’t like the complexity when it comes to combat. It really slows down the gameplay and is not benefiting the players‘ experience. Therefore I even started to think about opting out that problem in my blog post https://albachronicles.wordpress.com/category/game-master/dungeon-crawler/ .

    I am not a professional game designer however I do understand rule systems. Therefore I want to discuss some approaches.

    1) I really like the advantage/disadvantage mechanism of 5e. If you do it with 2 dice you roughly get a +30% bonus/penalty.
    For us 100d users there may be another option. For advantage you just roll 2d10. Take the higher of the two rolls for your ten-digit. The disadvantage works vice versa.

    2) Complexity in character creation / skills.
    With today‘s experience I would go for a system that has one cost for any arbitrary skill. But I would allow player to select n skills where the user can assign lower costs. You get the main idea. (In a more rule restricted environment, the n skills maybe defined by the class – or even the class list z definite skills from which the player can select n for lower costs).

    3) complexity during combat
    My main claim is that combat needs to be swift. I propose to convert al situational and geographic bonuses (and penalties) to the advantage (disadvantage) mechanism.

    Secondly I thought about the weapon tables. I really like that there is only one roll to determine the damage. I am not in favour of the 5e approach. But I don’t like the time it takes to lookup a damage value. In my Rolemaster compatible dungeon crawler (https://albachronicles.wordpress.com/category/game-master/dungeon-crawler/) I designed a slide rule to over come this problem. I am happy to discuss your ideas how you would solve this.

    Finally the topic of damage types/critical types. What I really like about Rolemaster is the fact that some Armor types are better against certain weapons. I suggest that a weapon has a defined type of damage (bow with standard arrows would have “puncture”). If a weapon has multiple types (like the broadsword) you just roll a special die to determine the type of this swing.

    I would love to hear your comments.

    1. What you describe in 2) above is basically what HARP does. All skills cost 4* except each profession has a few favoured categories where all the skills cost 2*.

      I agree, I really dislike added complexity in combat that slows it down. It is ironic that the fastest actions take the greatest amount of time to resolve. If you had the time to create your own critical tables then HARP approach may also suit you, Roll your dice, add your OB, deduct the opponents DB and then look up the result on the critical table. Armour in that system adds to DB.

    2. Wow, Christian! You’re uncannily voicing my thoughts too! Ken’s comments about Cost now had me thinking about it in all aspects of Gamist, Narrativist, Simulationist theory during my MERP session last night, and I just started drafting something for my own blog, towerofthevalkyrie dot WordPress dot com. (Don’t know how otherwise to get by the spamshield.) You have a new reader. I’m seeking ways to speed up combat at the table while retaining the reasons why I choose RM in the first place. At one point I even considered using OD&D or B/X with Spell Law and RM critical charts tacked on, but that loses the weapon to AT simulationism, as you say, and keeping the criticals likewise retains bleeding, stuns, and conditions.

      1. Hi,

        Just perused your post. You’re looking at cost exactly the way I hoped for when I wrote my post, not simply agreeing and not simply using my examples, but taking the concepts and applying them to aspects of your game into which I have no visibility.

        It’s probably not coincidental that you are thinking about the cost of choice in general (the cost is higher when there are N options, at least linear to choose the best option but often much higher) and that I am planning a subsequent post about The Illusion of Choice: To the extent that choices are expensive, it makes sense to eliminate fake choices. Unfortunately, to the extent that players are willing to pay for fake choices, it makes sense to produce supplements filled with cruft.

        I’m glad that you and others find this useful.

        Anyway,

        Ken

    3. Hi,

      Glad to comment:

      No hard class restrictions: A lot of people like this. There are other ways to do it than the RM way. The one that I think has worked out best over the years, and has been adopted by most game systems in one way or another is talents/virtues/advantages: You take a few of these plus supporting stat boosts, and then even though you can take any abilities you want, some are worth it and some not. Combine this further with flaws/disadvantages and you end up with some reasonably firm soft class restrictions. But providing some hard restrictions can also be very helpful, even realistic: No, you cannot level up and expect to just pick up 12 years of formative education, and please, let me help you avoid pessimizing your character.

      Because you only deal with it during character creation and upgrade: You also deal with it when you buy books and in other subtle ways. Using a computer analogy, code bloat can have unexpected costs, even with cheap memory and storage.

      5e advantage/disadvantage: I like it too. If used consistently for all circumstantial modifiers, any math that needs to be done is already on the character sheet. Then, everything boils down to checking for a single source of advantage and a single source of disadvantage before rolling one or two d20. No addition, no subtraction, let alone more difficult ops. It might be too simple though.

      Complexity in character creation / skills: I’ll defer for now, with plenty to say later.

      Complexity during combat: As much as I like the mechanic, I’m not sure it’s great for RM. Still, I think a good RM experience can be had with some simplification. I’m not the best guy to define that part, though! Someone more into RM would do better.

      Weapon tables and one-roll: Rolling the same kind of dice once is a great win, to be sure! A good solution must not only work as a system, but also preserve sufficient RM feel to keep RM players happy. This might not be possible. As for other systems, Ironclaw has one roll for attack, but not always the same dice. (It also has a roll for defense, but active defense is an important feature of the system.)

      Attacks vs ATs: Other systems have played with this too, GURPS and others. The idea seems good, but how much is it really noticed in play, beyond “the rules have made certain armors useless, even though they were used in RL?” The main playability effect that I see is that RM armor rules historically have harmed warriors who want to wear big, bulky armor rather than dance around the battlefield in leotards. Armor in fiction deserves a PhD thesis all its own! (I mean a real thesis too.) BTW, real mail did just fine against contemporary archery. As archery evolved further, so did the armor. Everyone likes to bring up Agincourt, but that come very late in period, and is exceptional. Melee, not archery, was usually decisive. Armor in rpgs also suffers from its D&D heritage: There really was no progression from leather to studded to ring to chain to plate as people gained experience, etc.

      Anyway,

      Ken

  4. I like Christian’s idea of bringing the DnD advantage mechanic to Rolemaster by allowing characters to use either of the d10 results as the high die. That is neat and elegant (and saves a die roll). I personally don’t like the overuse of the advantage mechanic in DnD 5e though; for some situations, it doesn’t really fit, and it doesn’t stack well. But if you want a simpler game, it certainly can have its uses.

    In regards to skill costs, some of us on the RMU boards suggested making the Professional skills (the list of 10 skills that characters can take a profesional bonus in) also reduce the skill cost by a step or two. This would enable for example a Ranger to reduce his cost in Creature Lore, and help increase the distinctiveness of the classes.

    In regards to the attack charts, I understand the criticism that they aren’t really all that different from one another. But small differences can go a long way. My players do notice the differences when one uses a Warhammer to attack an opponent in Plate armor and another uses a Shortsword: one gets a critical while the other does not. That to me is priceless, because it is the thing that separates Rolemaster from DnD. The DnD weapons in 5e in particular are boring and indistinct: when you’ve seen one instance of 1d8 damage, you’ve seen them all.

    1. I think the Professional Skills modifying the skill cost is the perfect compromise between individual skill costs and category skill costs in RMU.

    2. Hi,

      Advantage: If you have advantage in your system, aren’t fumbles a thing of the past? Or maybe that’s your intent!

      Skill costs: The version I like most is to go toward the same costs for everyone (or maybe two or three basic versions for casters vs non-casters), with each class getting a bunch of Everyman/Occupational-style “Get N ranks for 1” bonuses. Talents can do this too. This works, because RM rank bonuses offer diminishing returns. This also lets you create development, occupational and cultural packages that can be represented linearly: You pay the same, but you also get to apply N for 1 and we’ll let you do that yourself.

      D&D weapons are boring: Yup!

      Anyway,

      Ken

      1. To be honest I think it is fine that there are no fumbles when a player rolls with advantage. Still keep in mind that players dont roll with advantage all the time. There are still straight roll which will have the ordinary chance to fumble and rolls with disadvantage. There the chance to fumble is even greater. For my game that would be ok.

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