Linear Die Roll Modifiers Are Broken (long and math-full)

[Mike Holmes]

Pale Fire addresses a slightly different issue, the whiff factor and deprotagonization that all fortune-based systems can suffer from.

...

If you do want fortune, but don't want whiffing, then use a concessions or fortune in the middle mechanism, which takes care of all outcomes including those where a character with world class skill gets unlucky with the dice.

Amen. I used the same logic recently when considering whether or not to use something like Story Engine's Auto-Odds or just add dice to a pool. I came down on adding dice, for exactly the reason you mention. If you use a Fortune System, let it do what it does.

James, the biggest problem with using a computer is having to give the computer the information it needs to make a determination. (Unless all the information is already in a computer, which has other profound implications for how the game is conducted.) Sure, a computer program equipped with tables of modifiers and a few probability calculation algorithm could quickly determine what the exact chances should be, and then do the necessary random "die rolling" to determine success on the basis of that chance. But you?d have to tell the program all the currently applicable situational factors for it to be able to use that information. (Or you could tell the computer all the individual modifiers, but then you?ve already done half the work.) Designing computer tools to augment game play is something I?m very interested in, but it?s also something I approach with great caution.

I've done quite a lot of work with stuff like this. You are right, Walt, by far the most pround part is simply the idea of player having computers in front of them as they play. Selecting modifiers from lists is no more onerous than looking them up in a book or chart, and grabbing extra dice (at least for someone who enjoys using computers :-) ). As people become more familiar with having laptops around for things other than labor intensive work, I think that they'll warm upto this. OTOH, there will probably always be detractors.

Mike

[Christoffer Lernö]

Pale Fire addresses a slightly different issue, the whiff factor and deprotagonization that all fortune-based systems can suffer from. I don't see a resolution system that frequently goes off the table as a solution to that problem, except in the same rather unsatisfying sense that having your TV break down solves the problem of which program to watch.

What I'm thinking about is not so much to be able to fail as the ability to be able to fail miserably. Linear systems which prescribes a minimum chance of failure usually still doesn't reach the abysmal failures you get in flat distributed systems. And even if it does you know the odds well beforehand. RM is a an example of something which has the worst of all worlds. You have a lousy chance of success but not only that, but success is graded so your rating doesn't quite give you what you need to succeed all of the time (if I have 20, then maybe I need a roll of 90+ to succeed fully, an 80 is only a partial success). And then in addition it adds special ranges (96-00, 01-04?) where you reroll and get exceptionally high or low results.

Now, if it would be clear exactly what the odds are of jumping 1 metre despite you having a skill of +70, then that's fine. It's just that it isn't very clear in non-flat systems. Which is the whole problem. If you know: oh 5% chance of falling into the cliff, then that's fine. Then you can treat that as fumble or circumstances messing with you.

But with the SKILL roll giving extreme results it seems more like your skill is totally unreliable. I don't know about you guys, but if I try to jump 1 metre of more, I think I can safely say that I can do that more than 99 times out of a 100. :)
Now of course we get into the situation of what rolls are supposed to cover and when to roll and all that, which is a completely different thing. Sorry.

The main point is: Flat is good because it gives you the odds straight and then you know what you're dealing with.

[Eric J.]

This can have worse effects than you would normally anticipate.  Think about all of the times when the oponets defense is equal to 20 and your attack is 1d20+19.  Didn't it frusterate you when you rolled a one?  Dicepool systems are an excellent option that allows for a realistic curve and a reasonably versitle chance of failure and success.  I have yet to try the symetry system, so I'll post when you do.

[Christoffer Lernö]

Pyron: No, I don't think that's a bad effect. Chances you keep rolling 1's are pretty low. Once is nothing. Twice is a habit.

Let's look at system I thoroughly dislike: Earthdawn. Let's assume the opponent's defense is around 9.

You kick ass so you roll D10+D6. That give's you an average of what? 9? I don't remember if it's beat defense or roll equal or over. Let's pretend it's a 50-50 chance. Now let's say you up that significantly. From 10 to 17. That's a big jump. I think it's like D20+D10. Averaging of course 16. So far so good, but what's the odds of missing? (I'm assuming 9 is a miss here).. I think that's 18% (you can check that). A fairly significant chance although you ought to KICK ASS AND TAKE NAMES at that skill level. Even worse, if you're playing a character with D20+D10 attack roll, you're probably beating on enemies with friggin thick hide, so you pretty much need armour defeating hits, which would mean kicking up that target number to 20 or something.

However, ED uses a mechanism where a maximum roll on a die means you get to roll that die again so you can get results that high. Which means it's RM all over again (meaning you usually don't have a chance in hell to succeed in the beginning no matter how high you tried to boost your skills so you pray you roll that 5% to give you a bonus roll D100 roll)

So what I mean. Linear distribution at least is honest with what you get. Now it might suck, like AD&D where chances to hit usually is very small and you end up with long combats of misses. But at least you know what you get.

Now there are more or less opaque systems. ED I think is among the worst ones. I don't particularly like SR, but I think that system is more honest that ED's when it comes to the outcome.

Sorry for that rant.

[Le Joueur]

And the answer to all this is Gordon's point, which is that the most important thing is understanding the behavior to make good design decisions, whether you end up wanting to "fix" anything or not.

Fang's point is superficially similar, but actually very different. He points out that concern for realism is often misguided. I agree. But I also think there's a valid concern for consistency that can apply even if reality is not being modeled. The real universe is very consistent, so one often draws on reality as a means of achieving consistency, but consistency can be desired even if reality is not. Consistency is harder to achieve when the system's outcome doesn't behave the way you think it does.

Minor point: if you always use the "broken" additive modifier scheme it has its own consistency.  I remain unconvinced that the 'sense of consistency' will fail at the relatively minor levels you describe in practice for human beings.  (The most likely reason this has never been discussed before, too few people notice.)

Showing that A or B is not strictly in line with A + B seems to miss the point of abstraction.  The Symmetry system works great, but you have defined everything else as broken; I don't see it.  My point is, yes, it is the pursuit of 'brokeness' to put caps (or such) on an additive modifier system, because actually you want what the Symmetry system provides in that action.  I'm just saying that you go a little far saying that all additive modifier schemes are therefore broken.

More important, many system designs do appear to aspire to both intra-player-character effectiveness "balance" and combinatorial flexibility. Whether they should or not, and how important balance really is, is an issue on which I believe I agree with Forge consensus. But I also believe that if a system is going to attempt to achieve both, it should find a way to really do it. The biggest problem with additive modifiers, as I said before, is that they rule out the simplest way to combine balance with combinatorial flexibility, which is being able to apply the principle "if a is balanced, and b is balanced, then the combination of a and b is balanced." That doesn't mean if you use a dice pool or Symmetry that principle will suddenly apply everywhere, but it does remove on major source of problems.

You have a very peculiar definition for 'balance.'  As far as I can tell, if all characters are subject to a rule and everyone knows its effects 'going in,' it is balanced.

How can A be 'balanced?'  That is the root problem I have with your supposition that 'all but pools are broken' thesis.  In abstraction, how can you ever know that A is 'truly balanced?'  If A is 'as balanced as seems necessary at the current granularity of abstraction,' you'd have to make the argument that the addition of A and B is always noticably 'broken' or 'unbalanced' at the same abstracted granularity.  Note: "noticably."

My argument is piddly in the fact that all I am saying is that the degree of 'brokeness' stays somewhat fixed relative to the granularity of a abstraction.  When more granular, the problem stays about as perceptible as when less.  In my experience, what you are calling "broken" falls well inside the tolerance levels of the bulk of the audience; they don't notice it.  No abstraction escapes some degree of 'brokeness;' I believe this simply 'disappears' in the 'noise' of all the other 'sacrifices' made in order to abstract consistency (parallel to that of reality) into game mechanics.

In other words, statistically what you say is true, but the granularity of abstraction makes it hard to notice.  Better it would be to say that 'caps' (and other draconian limitations) are a bad design strategy rather than that additive die roll modifiers in a Fortune-based system are 'broken.'

Fang Langford

[damion]

The Computer Stuff:Yeah, I don't think it's practical either. Perhaps in 10 years there will be a fairly common platform that one can count on people having that could be used to povide a mechanic that fit's ones exact needs.

I think it depends on what one wants from a system. Unfortunatly, I think it also depends on the situation.

In some cases, one may like a system where failure is always possible. For example most combat systems features some mechanic so a miss is always possible verses a non-subdued opponent. Conversely a D20 has the coup de grais mechanic. I think the difference is narrative. Missing the sniper shot is dramatic. Missing the the troll body as you hack it up to burn it is silly.  Of course on the other side situations can change things. Say if you had one round to kill an enemy before backup arrived and saved them, suddely missing becomes dramatic.

[Victor Gijsbers]

The problem with linear scales + additive modifiers is, in my opinion, not so much the statistical problem adressed by wfreitag, but the 'boundary effects'. Whether it is or is not a problem that +1 and +1 should not be quite as good as +2 is open to discussion... but that it is a problem that a +1 bonus is much better when you have to roll 10 or higher on a d10, then when you have to roll a 4 or higher is only too obvious.

In the first case, the meager +1 modifier effectively doubles your chance of succes, in the second case it gives you only a 17% success-bonus. The effectiveness of a modifier thus depends too much on the situation in which it is used. I think this is a more effective argument against linear-scale + additive modifiers than the one wfreitag has offered us.

[Walt Freitag]

Actually, Lord D, what you describe may be a better way of pointing out the problem, but it's the exact same problem. The "statistical effects" I described become more noticeable at the boundaries, creating the effects you describe.

Yet another symptom of the same problem is going off the scale, which really means that the system has yielded a less than 0% or greater than 100% probability of something ocurring.

Fang, I use the adjective "broken" in the same sense that I've seen other mechanics described as "broken" here. One could just as easily argue that calling attribute + skill systems broken is improper, because most designers and players don't mind that such systems create breakpoints and reward minmaxing, and the mechanism remains popular. If there's a consensus against such usage of "broken," then I'll consider another term instead, but so far I think my usage has been comparable to others' examples.

As for my usage of "balance," I explicitly stated the type of balance I was talking about in the text you quoted ("intra-player-character effectiveness balance"). To be more precise, the type of balance I'm talking about is the condition of all options for spending character creation currency being equally attractive from an effectivness standpoint throughout the character creation process. This condition is desirable because it allows players to make char gen decisions based on their character concepts without having to sacrifice effectiveness. A particular option such as, spend one build point for one point of strength, is balanced if the option is worth the cost relative to all other options, being neither a "bargain" nor a "ripoff" from the effectiveness point of view.

I don't find your definition of balance (the condition of all characters being subject to all rules and all players knowing their effects going in) at all useful. By that definition, no game could ever be unbalanced unless its rules contain provisions that specifically single out individual players or characters before the game begins. And since the characters don't exist before the char gen portion of the game begins, it would have to come down to singling out players. I've never run across a game with a rule like "Walt Freitag receives three bonus points, all other players receive five," and I doubt this is a very common problem.

Suppose there were a system in which each character had a single effectiveness score that applied to all attempted actions and determined the chance of success as a roll-under target on 1d10. Suppose that score is rolled randomly by each player on 1d10 during char gen. I'd call that pretty thoroughly unbalanced. Would the fact that everybody knew going in that that's how the game would work, and the fact that the rule works the same for every character, prove that it's actually balanced? If so, then you've pretty much defined "unbalanced" out of existence.

- Walt

[Le Joueur]

I use the adjective "broken" in the same sense that I've seen other mechanics described as "broken" here. One could just as easily argue that calling attribute + skill systems broken is improper, because most designers and players don't mind that such systems create breakpoints and reward minmaxing, and the mechanism remains popular. If there's a consensus against such usage of "broken," then I'll consider another term instead, but so far I think my usage has been comparable to others' examples.

And I've seen "broken" to mean no one should use it.  A single mechanic, alone, cannot be 'broken;' it is only a system which can be broken.  If that's not your intention, my statements have little value; ignore them.  

As for my usage of "balance," I explicitly stated the type of balance I was talking about in the text you quoted ("intra-player-character effectiveness balance"). To be more precise, the type of balance I'm talking about is the condition of all options for spending character creation currency being equally attractive from an effectivness standpoint throughout the character creation process. This condition is desirable because it allows players to make char gen decisions based on their character concepts without having to sacrifice effectiveness. A particular option such as, spend one build point for one point of strength, is balanced if the option is worth the cost relative to all other options, being neither a "bargain" nor a "ripoff" from the effectiveness point of view.

That makes sense in the 'universal' sense, but it runs right into the problem of the system therefore unconsciously encouraging characters that don't fit the tenor of the game.  Taking such a system to this level of 'perfection' means that I would be as likely to make a nuclear scientist for a game set in the Sherwood Forest.  In some ways playing these 'flaws' so that they nudge character generation into 'usable,' or at least relevant, forms is not 'broken,' but I think rather clever.

The only value I can see in your argument is if you're saying that many people practice too much unconscious design and therefore either succeed accidentally or fail because of the trap you illuminate.  'In the open,' I don't see it as a 'flaw' or 'broken,' just another option.

I don't find your definition of balance (the condition of all characters being subject to all rules and all players knowing their effects going in) at all useful. By that definition, no game could ever be unbalanced unless its rules contain provisions that specifically single out individual players or characters before the game begins. And since the characters don't exist before the char gen portion of the game begins, it would have to come down to singling out players. I've never run across a game with a rule like "Walt Freitag receives three bonus points, all other players receive five," and I doubt this is a very common problem.

Actually what it says is that the word 'balance' is not of much use unless you restrict its meaning before using it.  In the broad sense no game is 'unbalanced.'

And if a game "specifically singles out individual...characters before the game begins," and prevents them from making ineffectual or unpleasant characters that would be a bad thing?  That's what character classes are supposed to do.  Is universal freedom truly a laudible goal?

I have lost what your purpose is.  There are problems using linear die roll modifiers to model realism, granted.  Knowing how they behave and making use of those 'flaws' is a tool not 'broken.'  The 'anything goes' character generation you speak of at first sounds like a perfect game until you realize there are few 'perfect' settings for those 'any' characters.

Your point could be that sometimes linear die roll modifiers are used badly and that there are examples of games that, themselves, are 'broken' for this usage, but that neither supports the idea that the mechanic itself is broken, nor that truly unfettered character generation is better.

Really, if you'd not say that the mechanic were broken, but that certain applications were, I'd never have said anything.

Fang Langford

[Victor Gijsbers]

Actually, Lord D, what you describe may be a better way of pointing out the problem, but it's the exact same problem. The "statistical effects" I described become more noticeable at the boundaries, creating the effects you describe.

You stressed what happened when two or more modifiers are added - in the case I describe, there is no need for this to happen. Of course, you could claim that rolling 18 or higher is really the same as rolling 10 or higher with a -8 modifier; so the one problem could be reduced to the other. However, I think my explanation is a lot clearer in systems that don't see everything as a modifier on a certain base-roll.

Yet another symptom of the same problem is going off the scale, which really means that the system has yielded a less than 0% or greater than 100% probability of something ocurring.

All too true - the most severe boundary effects are there when you cross it. ;)

Suppose there were a system in which each character had a single effectiveness score that applied to all attempted actions and determined the chance of success as a roll-under target on 1d10. Suppose that score is rolled randomly by each player on 1d10 during char gen. I'd call that pretty thoroughly unbalanced. Would the fact that everybody knew going in that that's how the game would work, and the fact that the rule works the same for every character, prove that it's actually balanced? If so, then you've pretty much defined "unbalanced" out of existence.

I'd say that something is balanced if, and only if, a group of rational observers would agree on a set of rules, knowing they would be using them in the future, while each of them doesn't want any of the other players to have a 'stronger' character. (A bit like Rawls' Theory of Justice; and well, balance and justice do have something to do with each other.) The case you mention would not be considered balanced, because each observer would have a chance of getting a much weaker character than another observer.

[Christoffer Lernö]

There's also another point to take into consideration. Now Walt you mention that many linear based systems tries to keep the ranges to the middle, where the system works.

However, I'd like to point out that there's another reason to keep modifiers low in certain cases. If you're using D20 or bigger, additions are gonna be slower the bigger the modifier. 18+15 is not difficult to add maybe, but it's slower than 18+1 or 18+3. So in many linear systems the modifier ought to be small enough that the problem remains insignificant. Now in practice this is not necessarily so, but still.

[Eric J.]

The argument seems to be something like:

There's a big problem with linear dice rolls.  It's broken, and I've got an interresting solution to the problem.

I've known about this for a while. Clarify.

{Clarifies}

The problem isn't that big.  Few notice it.

But it has larger reprocussions.

Yeah, but no one care's.  Let's argue over semantics of the term broken.


Eh, I like steriotyping problems in semi-humerous ways to simplify the setting.  My opinion is that linear dice rolls ARE broken, where the term broken means it's an unusable mechanic for me.  It forces them to make even more unusable rules, such as the "coupe de grace" because it doesn't account for range, and other optional rules.  This is why I use dice pools.

[Jaif]

Pyron,

You can still use straight addition without running into the trap you describe.  Consider:

1        - Feeble
2-3     - Poor
4-6     - Typical
7-10   - Good
11-15  - Excellent
16-21  - Remarkable
....so on.

The point being that adding 1 at the bottom of the chart is a lot more important than the top of the chart.  It won't be an exact model of adding independant probabilities, but it's easy to do.

-Jeff

P.S. Chart created solely to illustrate a point.  I used Marvel's (the good Marvel's) naming scheme because it was cool. 'nuff said.