Game design trap - Starting too close to zero.

[Pyromantic]

Yeah, I don't think it takes a mathematician to understand the math of an RPG (having a math degree I would have to say there's nothing in 4e math-wise that shouldn't be readily accessible to 8th grade algebra basically).

Understand it well enough to play? Sure.

Understand it well enough to break down the probabilities involved? No. And that's pretty important for game design.

I'm not saying everything has to be analyzed in depth from a mathematical standpoint, but some important aspects of the math have been missed in the past, sometimes resulting in errata that never should have been necessary. (See my aforementioned example on skill challenges.)

 

[Crazy Jerome]

Err, no.

D20s don't really do diminishing returns, especially if you're adjusting the DCs to suit your new minimum.

Multiplicative things (like that Speed example) do diminishing returns. Damage does diminishing returns. Skill bonuses don't get diminishing returns until they start making skill checks unfailable. And +0 to +1 doesn't make anything unfailable.
% chance to hit gets diminishing returns, the same as damage, but if you're buffing the base attack bonus and the base armour, the % chance to hit won't be changed. And honestly, if fighters end up hitting AC 100% and wizards 90% (because you wanted the diminishing returns to kick in) the system is broken.

As has also been mentioned however, things that work in a more multiplicative fashion are quite different. Here the ratios become important. For example, if a target has 20 hit points and you do 4 damage per hit, then you need to connect 5 times to reduce it to 0. Get an additional +1 to damage, and now you need 4 hits. But if you only do 1 damage per hit, the +1 to damage is huge, reducing the number of hits you need from 20 to 10.

In some areas of the mechanics then, moving away from 0 as a basis makes sense, but only to the degree to which you need room for fine adjustments.

Please note where I mentioned earlier that some options were off the table when starting at zero. That often includes introducing multiplicative effects--when we might otherwise be able to tolerate them.

That is, the diminishing returns in this case are on those possible options--not the math of the thing itself. Yeah, if all you do is linear, and nothing you could possibly want to do is anything but linear, then might as well determine your scale, and start at zero or one as makes sense.

However, if you may want to include options that are non-linear, then starting at 2 or 3 or 4 or something like that gives you more room to work than starting at zero or 1. The diminishing returns are that you often don't want to set the starting value arbitrarily high--say 100, and you'll open up most such options by getting a bit off of zero.

Damage per round times the number of rounds is a good example of this in practice, because with low damage expressions, you get sharp changes with even modest bonuses. If the lowest damage expression reasonably possible is 1d4-3, then you'll see it sharply. If the lowest damage expression is 1d4+10, it will be practically gone. (That wizard may value a +1 dagger for its to hit bonus, but if forced to use it, he won't much care about the damage change, even though if his 1st level opponents are scaled appropriately, requiring a couple of hits from the dagger, normally, it will matter occasionally.)

Somewhere short of +10 is a spot where you get most of the benefit of getting away from -3 in this respect, without then tacking on more just for the heck of it. I think it is somewhere around +3 to +5.

 

[Kingreaper]

I agree, damage is an example of diminishing returns. But attack bonus isn't. D20 rolls just aren't in that category, because of how the game functions.

So, having the damage expression be significant even for a weak wizard is possible. But, the thing is, I don't want a game built on the assumption that weak (minimum possible strength) wizards with daggers are expected to engage in melee combat.

The weak wizard shouldn't care about a +2 to melee damage with a dagger. Not because it should be a tiny % of their damage, but because it would be 0% of their damage. At which point, having them be too low damage with a dagger to matter isn't a problem.

Make the damage bonus for a first level member of a melee class big enough. Don't worry about making the wizard a capable melee fighter.

 

[Crazy Jerome]

"I like large numbers" isn't a good reason to start things above 0, IMO, because for every one who likes them you probably find someone who dislikes them. I know I do.

...

This is why 3e had 4x skill points at first level, and why PF gives you a +3 bonus on trained class skills. A +4 is big when it's the maximum you can get from ability modifiers.

Find me someone that is using the reason "I like large numbers", and they can defend that position for themselves. No one here as of yet has taken that position.

As for the skill points variants, that's great at 1st level. It does almost make the 2 point guys work--though the scope of what they can do is awfully lousy for their supposed archetypes. But it doesn't scale well. The reason it doesn't scale well is multiplication again. Let's take a reasonably bright fighter and a rogue that went with more Cha as a second focus, just to be reasonable (i.e. leave out the dumb fighter and briliant rogue for this comparison, which would make it even worse). Both have a 14 Int. I'll use 3E numbers, though the point doesn't substantially change in any of the variants. We'll make them both human, too, and assume that neither particularly wants cross-class skils.

The Fighter has 5x4=20 skill points at 1st level. The rogue has 11x4=44 skill points at 1st level. That's a ratio of 5/11. Assuming no change in Int, that skill point ratio will stay constant. Let's say that they want to maximize 5 and 11 skills, respectively. This will also stay constant. I believe this was the simple view of the math when the system was designed. A little better than 2:1 for smart rogue versus smart fighter doesn't sound that bad, especially with the rogue having a few extra things he needs to do his job.

However, when examined more closely, it has two major problems:

1. The above is pretty much the best case scenario. If you are, say, a dwarf cleric of average Int, you get your 2 skill points per level, and you'll like it. Better make that extra 6 at first level count.

2. But more important, the ratio of skill points is the math, but the ratio of "useful skills" is the thing that matters. Let's say that our rogue above wants to branch out in a couple of things. Well, if he wants to sacrifice one measly level in all of his skills, he can get two extra skills at 5 and 6 ranks (+ ability mod). Then he can maintain those skills at 11/13th effectiveness compared to his level (overall). Meanwhile, our "good case" fighter can sacrifice that same level worth of skills to get one at 5 ranks. Then he can maintain those skills at 5/6th effective compared to his level (overall). That's not bad, which shows what happens when you start at around 4 or 5 with one of these numbers.

Meanwhile, our dwarf cleric can get another skill at rank 2, under the same circumstances, and he can maintain his now three skills at 2/3--or in other words, he can just about nullify all his skill effectiveness over time by doing so. That is, he can't really afford to add a single skill.

Now of course cross-class complicated that (but got cleaned up some in later variants). And certainly feats and magic item bonuses can help (and the fighter certainly has those.) And the way an Int penalty interacts is downright criminal--and 8 Int is a skill pariah--and as bad as an Int 3 in a lot of classes, because you can't get worse than 1 skill point per level.

It has other drawbacks without other changes (and dealing with those are not always easy), but you can largely handle this particular issue by simply giving every 3E class +2 skill points per level. Now the worst case, average Int base is 4, which means that such a character can add a single skill while maintaining skills at 80% (4/5) effectiveness, which isn't enough off of the rogue's (new) 13/15 for adding 2 skills, to quibble over.

This is an example of hidden multiplication in effectiveness that is not seen by a cursory examination of the numbers. As I said before, unlike the Hero System SPD example, the effects in D&D are often subtle.

 

[Crazy Jerome]

Now this doesn't apply everywhere. There is no particular reason to start possible character level at anywhere but 1. And the only reason to boost hit chances on such a scale (using the d20 linear resolution) is if you want to do some extra things with those hit chances besides hit, that don't happen to work well near zero.

I agree, damage is an example of diminishing returns. But attack bonus isn't. D20 rolls just aren't in that category, because of how the game functions.

My quote is from the OP. You seem to have confused my reply to our combustible magic using friend as to why range size and starting point of the range are two different things, as an appeal to start hit bonuses somewhere else. The only good reason I can think of to start hit bonuses a bit higher (usually) is to simply not deal with negatives on a regular basis.

Though you'll note that D&D does often start feasible hit chances in the +4, +5 territory. I had that fact in mind in the crit thread when I suggested that if you wanted to make crits partially a function of competence, without a confirmation roll, that adding the attack bonus as damage on crits is one way to do that. Naturally, that would rather suck for, say, a Basic cleric at first level. So even here, expanding options can help. But I'll grant that is an unusual example. (Translating attack bonus to straight damage is something that D&D has traditionally been loathe to do, even when in this case it would be extremely fast in play.)

So, having the damage expression be significant even for a weak wizard is possible. But, the thing is, I don't want a game built on the assumption that weak (minimum possible strength) wizards with daggers are expected to engage in melee combat.

The weak wizard shouldn't care about a +2 to melee damage with a dagger. Not because it should be a tiny % of their damage, but because it would be 0% of their damage. At which point, having them be too low damage with a dagger to matter isn't a problem.

Make the damage bonus for a first level member of a melee class big enough. Don't worry about making the wizard a capable melee fighter.

Here, you are shifting the argument, though. However we define the usefulness or lack thereof of a wizard attacking in melee, if we want him to get a fair shake from the math and all options, chances are he'll do better with a slight shift up in the damage range scale. And if you take your position 100%, then why even let wizards attack at all in melee? They have traditionally had those lousy options for a reasons, especially at low levels where this can matter. My position is that a character bothers to carry a weapon, gets forced into melee, then the weapon should matter. It might be a relatively poor option, but it shouldn't be so terrible that it is dismissed completely out of hand, all situations.

This same kind of reason, BTW, is why Monte Cook removed the d4 as a hit point die size in Arcana Unearthed/Evolved. The "magister" (closest wizard analog) gets d6, and not everyone shifts up a die size, either.

Besides, you do not have to account for the exceptionally weak niche cases for these kind of effects. If you want to account for them in D&D, you'd need to start at around +10. Start the normal scale at around +4 or +5, and a tiny pixie with 3 Str might end up with enough penalty to net +0. So a human, 10 Str wizard gets that baseline, and might occasionally take a swing at a kobold or goblin, while the pixie fits your criteria. Hooray, playing the pixie matters now! If you set it up so that all (or nearly all, excluding 16 Str weirdo wizards) don't dare engage in melee, ever--then the pixie paid less for that small size and lousy Str, than the system first suggests.

 

[triqui]

While I can see some adventages in granularity, I'm not sure inflation makes game systems any more better than it makes economy. Everybody would be happy to earn 1 million dolars per month, but what's the point to do so if a Big Mac is worth 100.000 bucks?

 

[Crazy Jerome]

While I can see some adventages in granularity, I'm not sure inflation makes game systems any more better than it makes economy. Everybody would be happy to earn 1 million dolars per month, but what's the point to do so if a Big Mac is worth 100.000 bucks?

Ever heard the little jingle, "shave and a hair cut, two bits"? In USA currency, a bit was worth 12.5 cents, and is derived from the practice of cutting a gold dollar coin into 8 "bits". There's a scene in Ben Franklin's Autobiography where he runs away to Boston, and buys bread. He gets 3 large loaves for his "penny"--and is laughed at by his future wife when she sees him walking down the street with the two extras sticking out of his pocket. A loaf of bread was worth 1/3 of a cent in Boston.

Once inflation hits the point where nothing is worth less than a penny, future inflation is questionable. (Some economists seem to think that very slight, persistent inflation over a long time is preferable to some of the alternatives, but that's beyond the scope of game system math.) Though see the need for "micro payments" as a discussion of why digital content is hard to sell in its most useful form. Ideally, the smallest thing anyone will want to buy is worth the smallest unit.

And certainly, if you have elements of the system that require a 4 or 5 cent ante to play, then people stuck with a penny are out of those. In any case, I'm not sure that you can call moving a range from +0 to +20 to something like +5 to +25 as technically inflation. Inflation implies a multiplicative effect on the scale itself, not merely the starting point.

 

[Hassassin]

Find me someone that is using the reason "I like large numbers", and they can defend that position for themselves. No one here as of yet has taken that position.

Apologies for misrepresenting your position, but honestly that's what it IMO comes down to, since it doesn't matter at all how close to zero you start. Only the distance between modifiers (in the case of d20 checks) and the ratio of scores (in the case of hp, damage, skills) matters.

2. But more important, the ratio of skill points is the math, but the ratio of "useful skills" is the thing that matters

An Int 10 non-human Fighter can still put half ranks in four skills. That makes him reasonably competent in climbing, intimidating, jumping and riding. Sure, the rogue has a lot more skills, but that's his thing and eventually there's diminishing returns once he's covered most of them.

PF did make things easier for the fighter, since he can have +4 at four class skills by second level. Basically, any character can cover the most common tasks in his class skills just by putting one rank in each.

Maybe the ratio ought to be slightly smaller, but I'd rather just reduce the number of skills like PF and 4e did.

 

[AbdulAlhazred]

My quote is from the OP. You seem to have confused my reply to our combustible magic using friend as to why range size and starting point of the range are two different things, as an appeal to start hit bonuses somewhere else. The only good reason I can think of to start hit bonuses a bit higher (usually) is to simply not deal with negatives on a regular basis.

Though you'll note that D&D does often start feasible hit chances in the +4, +5 territory. I had that fact in mind in the crit thread when I suggested that if you wanted to make crits partially a function of competence, without a confirmation roll, that adding the attack bonus as damage on crits is one way to do that. Naturally, that would rather suck for, say, a Basic cleric at first level. So even here, expanding options can help. But I'll grant that is an unusual example. (Translating attack bonus to straight damage is something that D&D has traditionally been loathe to do, even when in this case it would be extremely fast in play.)



Here, you are shifting the argument, though. However we define the usefulness or lack thereof of a wizard attacking in melee, if we want him to get a fair shake from the math and all options, chances are he'll do better with a slight shift up in the damage range scale. And if you take your position 100%, then why even let wizards attack at all in melee? They have traditionally had those lousy options for a reasons, especially at low levels where this can matter. My position is that a character bothers to carry a weapon, gets forced into melee, then the weapon should matter. It might be a relatively poor option, but it shouldn't be so terrible that it is dismissed completely out of hand, all situations.

This same kind of reason, BTW, is why Monte Cook removed the d4 as a hit point die size in Arcana Unearthed/Evolved. The "magister" (closest wizard analog) gets d6, and not everyone shifts up a die size, either.

Besides, you do not have to account for the exceptionally weak niche cases for these kind of effects. If you want to account for them in D&D, you'd need to start at around +10. Start the normal scale at around +4 or +5, and a tiny pixie with 3 Str might end up with enough penalty to net +0. So a human, 10 Str wizard gets that baseline, and might occasionally take a swing at a kobold or goblin, while the pixie fits your criteria. Hooray, playing the pixie matters now! If you set it up so that all (or nearly all, excluding 16 Str weirdo wizards) don't dare engage in melee, ever--then the pixie paid less for that small size and lousy Str, than the system first suggests.

Yeah, I agree. I think what has to be explained is that there are 2 things at work here. RPGs (pretty much, and certainly any likely flavor of D&D) always have increments of 1, you never get to make your increments in things less than that and be meaningful. Furthermore using bigger dice, like say d100, is awkward as well, and again unlikely to ever be the case in D&D for most things. Given that you really do need to start your scale bases some ways away from zero for anything that isn't flat like to-hit. Otherwise at best your options are someone has '1' of something and even having another guy have a '2' in that thing is a 2:1 ratio, which you have already perfectly illustrated is into a problematic range right off for at least some game elements.

I'd also argue that setups like 'wizards are just inherently incompetent at melee combat compared to other PCs or other options they can take' is crushing the expressiveness of the system. If I can make a wizard who can competently swing a sword, then the system is giving me extra options that might be worthwhile to me as a player. I might well LIKE to play that wizard. As it is now 4e or other versions of D&D require making a whole other class with a different implementation to get a wizard that can swing a sword (IE I can make a swordmage, not the same thing, or I can use some complicated hybriding/MCing mechanics that don't actually produce great results). If I can have a BASELINE where the wizard CAN use a sword and have it be at least an option that will work, if not his best choice, then it is MUCH MUCH easier to add an option (or just reuse one that other classes use) to increase that option a bit. I can have my wizard that has a decent Magic Missile and a decent sword stroke, and I've done this without adding a lot of complexity to the the system, maybe not adding anything that wouldn't be there anyway.

The upshot being this is a direct result of something like say having damage bonus start at a +5 baseline. The wizard can swing a sword at 1d8+5, the fighter might be at 1d8+10. The ratio is now 9.5/14.5 or a bit better than 2:3. The wizard is in no danger of being an excellent swordsman, but if he wants to be a decent one and there's a "get a +5 damage bonus" feat, then he can shift it to 14.5/20.5 (compared to the fighter taking that option, which we assume he will). The wizard never catches up, but he can become competent and fill the 'gish' archetype.

What is the cost of this? Nothing much really. We're all adding damage bonuses already. The damage rolls are less swingy now of course, but is that a bad thing? Damage rolls add some tension because now and then there's the question of "is this hit going to kill or not?" but that question isn't any less frequently coming up or less interesting, nor any less dependent on chance, then with low or non-existent damage bonuses.

I think we all understand there's some basic aversion to having big numbers just for the sake of big numbers, but shifting the baseline for some things up a few points isn't at all the same thing as number inflation. It is just starting the numbers at a slightly higher number, the numbers need not grow any faster than they have to based on the power curve. That growth is independent of the starting point and a whole other discussion.

 

[Pyromantic]

There is however a question of how the results you want can best be achieved. I'm trying to think of how many things in D&D work in this kind of fashion. It's not likely for the game to have anything along the lines of receiving a number of actions equal to your dex bonus, for example. The most notable examples I can think of are skills (in 3.0/3.5, as skill acquisition was quite different in 4th) and hit points/damage.

From what we know it seems skills are changing quite a bit anyway, and frankly I certainly don't want them to look like they did in 3.5, mostly because of the issue of increasing specialization which lead to many of the math problems in the game.

As for damage, it's subjective how much damage a melee "competent" wizard should be doing relative to a fighter, but d8 as compared to d8+4 or so might be perfectly reasonable before any character investment. This is especially true if there are options similar to the melee training feat of 4th, but we know so little about how things like feats, proficiencies and class features are structured that it's difficult to guess.