An issue that arises with many games is a insignificant difference at low degrees of ability. For example, if there are two small creatures in a d20 game, one with Str 1, and the other with Str 3, then the second creature has a +1 against the first; but this is strange, because the second creature is three times stronger than the first. Giving out modifiers at like this is fine at human levels, where 10-11 is the average and a two point difference isn't that big of a deal, but at the low end of the scale, it becomes very counter-intuitive.

Would it not be agreeable to make chance of success based on proportion rather than difference? So the functional distinction between two opposed characters with 2 and 6 attributes would be 1:3 rather than +4? It may or may  not be a difficult proposition to fulfill without resorting to chart look-ups. Forgive me if my terminology is off.

Are there any games that already do that (or do that well)?

DC Heroes (aka MEGS; rereleased as Blood of Heroes) does this fairly well - though as an over-the-top superhero game "very small" in DC Heroes is a human-level attribute and it scales up insanely from there (a normal human is Str 2; Batman is Str 5; Wonder Woman is Str 16; Superman is Str 25, and each point roughly doubles the character's lifting capacity--+10 points is x1000). It does use charts, though - I don't especially recommend it as a supers system.

Other than that, note that die pool games (like Storyteller or Shadowrun) inherently generate a # successes that are a proportion of the die pool (depending on the target number). However, these don't necessarily do a great job for the lower stats, just because they're so granular - 1 dot in Storyteller has to represent everything from the village idiot (hello!) to dogs, cats and possibly fish.

Quote from: The Worid;389035For example, if there are two small creatures in a d20 game, one with Str 1, and the other with Str 3, then the second creature has a +1 against the first; but this is strange, because the second creature is three times stronger than the first.

I think I kind of see what you are saying, but D&D is a bad example.  The stats aren't really linear like that, except for their own scale.  A Strength of 6 is better than a Strength of 3, but a Strength of 18 is not three times better than a Strength of 6.  The scores don't correlate directly to mechanics.

Quote from: StormBringer;389145I think I kind of see what you are saying, but D&D is a bad example.  The stats aren't really linear like that, except for their own scale.  A Strength of 6 is better than a Strength of 3, but a Strength of 18 is not three times better than a Strength of 6.  The scores don't correlate directly to mechanics.

My books haven't been sent down from Wisconsin yet, but didn't 1st or 2nd edition AD&D have weights listed by Strength score? I swear I plotted it out back in the day and found that the curve wasn't regular.

I'm actually visualising the red and green lines of the chart I think I made.

Edit: My offering towards this is the scale in Fudge. It's a bit redundant, IMHO, as 1 pt of scale equals +1 strength or its equivalent, but it works, and points the way towards a scale that would be more useful for large differences.

Similarly having 100,020 strength is VASTLY better than having 100,000 strength not just a rounding error. Stats not being proportional like this is the biggest flaw in d20, which means the game breaks down unless stats stay within a certain band (i.e. E6) or the game artificially yokes stats together so that they all advance at the same rate (i.e. 4ed).

To clarify: I'm not talking about the way you get only +1 per two points of an ability score in d20. My criticism applies to, well, any system that I can think of (and can claim to understand the math behind). So, the Fudge scale suffers from the same issue: 1 vs. 2 is a +1 difference, but 3 vs. 6 is a +3 difference, even though in terms of proportions, they should be the same.

What I'm looking for is a system in which there is a certain chance of success on 1 vs. 2, and that chance is the same for 2 vs. 4, 3 vs. 6, and so on. Or, failing that, a good workaround like some form of scale shifting, but that's not the primary goal.

Quote from: The Worid;389156To clarify: I'm not talking about the way you get only +1 per two points of an ability score in d20. My criticism applies to, well, any system that I can think of (and can claim to understand the math behind). So, the Fudge scale suffers from the same issue: 1 vs. 2 is a +1 difference, but 3 vs. 6 is a +3 difference, even though in terms of proportions, they should be the same.

What I'm looking for is a system in which there is a certain chance of success on 1 vs. 2, and that chance is the same for 2 vs. 4, 3 vs. 6, and so on. Or, failing that, a good workaround like some form of scale shifting, but that's not the primary goal.

Hmmmmm, Burning Wheel and d6 sound like they do what you like pretty exactly and ORE does it more or less as well although the probability curve isn't so smooth.

As far as FUDGE while it breaks down with big numbers +2 isn't supposed to be twice as good as +1 since 0 is the average human ability, so a zero in a score does not indicate zero ability. The scores in FUDGE indicate deviation from average ability not absolute ability.

Quote from: Daztur;389153Similarly having 100,020 strength is VASTLY better than having 100,000 strength not just a rounding error. Stats not being proportional like this is the biggest flaw in d20, which means the game breaks down unless stats stay within a certain band (i.e. E6) or the game artificially yokes stats together so that they all advance at the same rate (i.e. 4ed).

What's wrong with Str scores following an exponential progression, exactly ??
From memory, I think you'll find that +10 Strength is x4 lifting capacity in D20 - from Strength 20 up.  
So, for higher strength scores it does exactly what The World wants - someone four times as strong as you are gets +5 on Strength checks against you and so their chance of winning an opposed Str roll against you is consistent.
+5 probably isn't really enough bonus on d20 to represent that magnitude of difference IMHO, but that's probably a separate problem.

Quote from: Daztur;389157Hmmmmm, Burning Wheel and d6 sound like they do what you like pretty exactly and ORE does it more or less as well although the probability curve isn't so smooth.

Does Burning Wheel actually work like that? I've fiddled with AnyDice for a while trying to figure it out, but it didn't look like it did. Anyone good with statistics?

Quote from: Daztur;389157As far as FUDGE while it breaks down with big numbers +2 isn't supposed to be twice as good as +1 since 0 is the average human ability, so a zero in a score does not indicate zero ability. The scores in FUDGE indicate deviation from average ability not absolute ability.

Well, yes, which is exactly the same as d20 in which +0 is human average. My point is that I'd rather it not work like that, for several reasons. Among them is that I would like the ability to add together the more than one statistic (such as Str+Dex) or the efforts of more than one person into a single check, and have the result be equivalent to having rolled individually.

What you should be looking at then is a game that uses percentiles for success rates because then someone with a 50% chance of success is exactly twice as good as someone with a 25% and someone with a 10% is 10 times better then someone with 1%.

Quote from: kryyst;389434What you should be looking at then is a game that uses percentiles for success rates because then someone with a 50% chance of success is exactly twice as good as someone with a 25% and someone with a 10% is 10 times better then someone with 1%.

Excellent point.

At the risk of bringing Pundy into the thread, diceless could, of course, do that.

Quote from: Daztur;389153Similarly having 100,020 strength is VASTLY better than having 100,000 strength not just a rounding error. Stats not being proportional like this is the biggest flaw in d20, which means the game breaks down unless stats stay within a certain band (i.e. E6) or the game artificially yokes stats together so that they all advance at the same rate (i.e. 4ed).

I failed to point it out before, but this is a really good example of what I'm talking about.

Quote from: kryyst;389434What you should be looking at then is a game that uses percentiles for success rates because then someone with a 50% chance of success is exactly twice as good as someone with a 25% and someone with a 10% is 10 times better then someone with 1%.

That's tautological. Of course it works out when you set the percentages to be perfect, but the math behind a percentile system isn't anything special. It's just inverted d20 math; if you tried to roll under your stat on a d20, it's the same as using percentile dice, except that it goes in 5% increments (which percentile games tend to do anyways). Actually, BRP does do what I want: but only through the use of the resistance table, and I'd rather not do table references in the middle of a game.

Quote from: The Worid;389035An issue that arises with many games is a insignificant difference at low degrees of ability. For example, if there are two small creatures in a d20 game, one with Str 1, and the other with Str 3, then the second creature has a +1 against the first; but this is strange, because the second creature is three times stronger than the first.

Just to nitpick: you've assumed that a Strength of 3 is three times as much as a strength of 1. That's not necessarily true. Its actually only true if you assume that the scale is linear, which for D&D Strength isn't the case - its an exponential progression. i.e. each point represents a gain of more power than the point before.

In D&D's case, that's a deliberate design choice, because a linear scale - where you add the same amount of lifting ability or whatever per point - rapidly breaks down as the numbers become huge. Say if you give a normal human a Strength of 10, and define each point of Strength as being able to lift about 10 pounds.  

Strength IRL is roughly proportional to muscle cross-section, which increases as the square of height: using this and assuming a 6' tall human base you'd get a 30' tall giant having a Strength of about 250 (notwithstanding that using real world physics they should collapse under their own weight), a 60' long dragon about 1000, and Cthulhu (100' tall) around 2500. Conversely, a halfling would have a strength of between 2 and 3 (1/2 the height of a human, so 1/4 the Strength - assuming similar muscle tone and whatnot.).  

To avoid this, the designers deliberately used an exponential scale; on an exponential scale adding a given number of points multiplies the real value of the score i.e. +10 = 16x the real world lifting capacity.
Complaining that 10,020 is heaps better than 10,000 in D&D is silly because D&D doesn't have creatures with Strength scores of 10,000. And it doesn't have Strength scores of 10,000 exactly because 10,020 is heaps better than 10,000.

That's not to say that a linear scale is necessarily bad, but there's pros and cons either way.

Quote from: Bloody Stupid Johnson;389700Just to nitpick: you've assumed that a Strength of 3 is three times as much as a strength of 1. That's not necessarily true. Its actually only true if you assume that the scale is linear, which for D&D Strength isn't the case - its an exponential progression. i.e. each point represents a gain of more power than the point before.

Actually going by 3.5 listings for carrying capacity, a creature with a Strength of 3 is, in fact, 3 times stronger than a creature with a Strength of 1. However, even if it wasn't, it is strange to give out linear modifiers but exponential carrying capacity values.

Quote from: Bloody Stupid Johnson;389700To avoid this, the designers deliberately used an exponential scale; on an exponential scale adding a given number of points multiplies the real value of the score i.e. +10 = 16x the real world lifting capacity.
Complaining that 10,020 is heaps better than 10,000 in D&D is silly because D&D doesn't have creatures with Strength scores of 10,000. And it doesn't have Strength scores of 10,000 exactly because 10,020 is heaps better than 10,000.

That's not to say that a linear scale is necessarily bad, but there's pros and cons either way.

I understand the point behind using exponential stats. It's not bad logic. However, I would prefer to use a linear scale (perhaps supplemented with a "tier-shift" mechanic for scaling) for reasons of intuitivity, as well as being able to hit the proportionality goal.