This thread has been kicking around in my mind for a while. It is partly inspired by some of the dicussions on high level casters vs non-casters in the 4th ed thread. And by the discussion on the skill system in 3rd in the same thread (or maybe the pinch points 5th ed thread). Also informed by Anti-Fragile a book on risk.
So most systems deal well with the arithmatic scale. The standard is 'hit the orc with my sword, subtract my damage from its hp." Pretty simple. And if thats your only option it gets dull pretty quick. Any thing that is subtracting from hp is on the Arithmetic scale.
Now magic has options not on this scale. Save or die, sleep, sometimes charm. There is no subtraction it goes completely around ac and hp. Different kind of thing. Because the range of options is so much bigger rules for this are harder to make, and it makes it much harder to balance a game.
Log scale is even bigger. It can only be done through role playing and because the range of options is so impossibly large no system can be designed for it, the rules can only live in the DM. Real world example. The Comanche's favorite tatic for the Spanash, and Mexican and Texans and Americans was to steal or stampead their horses and ride off leaving the plains to kill their enemies. Which it did at a higher rate then even the Comanche's.
Another example. The orc's are invading. The PC's use magic to get their attention (but geography could work by standing on the right ledge) The half Orc challenges for the right to lead the tribes. If he wins its a different game now.
In one episode of Critical Role they end up black mailed into killing a white dragon to collect its body parts. They talk for a bit. If they had made an alliance with the dragon to team up and burn down the Slayers Take guild (the butchers who want the parts) that would have changed the game.
One more example. The standard fire ball. This spell can operate on all three scalls. If you hit one or two targets its aritmetic and really underwhelming, the fighter does more damage on average. If you hit a half dozen or more weaker creatures you can kill all or most of the mooks. Thats geometric. If you cast it against a mob or an unprepared army (and you are using moral rules) the whole army could be broken and scattered. Log scale effects.
As I said most games deal well with arithmetic or linear scale effects. They can do well with geometric scale effects but issues of balancecare going to come up. Save or die spells are on this scale, probably back stab. We could put the wgole advantage/disadvantage system maybe. Role master combat simultaneously operates on linear and geometric scales. You do concussive hits which are subtracted from hp and role for a crit which could kill in a single shot.
Rules go to shit on the log scale. Diplomacy roles, flying forms of the Druid, utility spells. This is where the DM picks up the prepared adventure and tosses it over his shoulder. Then walks out of the room or takes a deep breath and asks what you do next.
There are no charts where you are going but there is some advice. Someone on here says when they make a npc they always give them a want and a fear. Pundit in his Olympus book and probably else where says to "Play the character not the plot." In the white dragon example above the DM would need to decide what the dragon wants. Sure he's got the fight prepped but killing the Slayers Take would be really cool. Thats meta, not the rightvway to go. The Dragon deffanatly wants to kill these intruders. But he also would love to attack the butchers in their own lair that would be sweet justice. Its totally fair if you can't decide to ask for a role, the dice are there as a crutch when we can't decide. But if you as for a role it means the dragon can't decide he's tempted either way.
If you are going to have log scale actions in your game you need flexiblity and good comunication. Linear scale has few decision points. If you are on the linear scale every action is the same, 'I hit it with my axe' and you will do some variation of that as long as you have plenty of hit points and so do the enemies. If you are on the geometric scale every action is a decision cause every action could either win or lose the fight.
If you are on the log scale every action could change the whole game. If you are set up to play a tatical game of warring arimes, and your players burn the crops, or introduce ergot to the rye, well thats effective but maybe not the game I want to play. I may not know enough about crop yeilds and accounting to even play that game. If your elvan cleric decides to seduce the half orc warlord and avert the invasion that way. Well I know the effects of being seduced by a mystical elven princess but I know I don't want to play that game.
Are you aware that you've taken terms with clear, mathematical definitions and used them to mean completely different things? It's a strange choice.
Minor, major and grand would work better. Or micro, macro, grand macro.
Logarithmic a scale for measuring things that might be orders of magnitude larger or smaller. I am happy with that one. Linear of arithmetic. We are literally preforming arithmetic (subtraction) I am happy with that one. Geomethric, not so happy with that one but its the one in the middle.
I am open to other names. I like 'grand', not keen on the other two.
"Local <---> Regional <---> World Shattering" could be called a logarithmic scale.
"World Shattering" on it's own isn't logarithmic, it's a point on the scale, just like "50 decibels".
There is further confusion in your theory because it seems to posit that the arithmetic scale is at least partially defined by the actual existence of simple arithmetic, which is apparently impossible at higher levels.
Overall, it sounds a lot like taking some reasonable concepts then trying to redefine those concepts to match some arbitrarily chosen and ultimately misleading terminology.
If you're thoroughly smitten with the term "logarithmic", use it in the name of the theory, not as an internal term.
When I design adventures, I often think of the plot in terms of circles on a page, with a clear branching structure. This event can lead to this event, with paths between mapped to player choices and likely outcomes. This is also the underlying structure of a dungeon (closed environment with focused structure). These circle's aren't necessarily encounters - in a super heroic game, for example, these might be elements of the villain's plan, or a timeline of problems.
Now, player characters may have abilities to form new paths between the circles (spells and powers), jump over circles (ignore intervening plot events), or wander onto the blank page (break paths/circles). Sometimes you just nudge a circle in the way of them and no one is the wiser.
How screwed my scenario is depends entirely on how tight and precise the structure of my scenario was in the first place.
I once whipped up a zombie infestation on the streets in an occult horror game (Witchcraft 2nd ed), and like a bonehead forgot one of the PCs was a necromancer. She said "take me to your maker", and the zombie compliantly lead the group of characters to their maker. The entire scenario was ruined - but it wasn't the power that used it. The players had a ball watching me crumple up my notes and thrown them over my shoulder btw.
My super hero games are rarely screwed though. If there's a problem in the reservoir, and the players ignore it, people die. In your example, the butcher / white dragon quest should totally be designed with a contingency that the players say "no, we're not being blackmailed". This is why having more than one outcome in mind, and more than one structured environment helps.
I'm just not sure the definitions you've used help. A fighter's sword interaction is "arithmetic" but if the fighter decides "hey, that noble's crown looks quite valuable, I draw my sword..." than the implications are logarithmic. Not mocking, just looking to evolve your idea.
I have to echo Sable Wyvren's first post regarding improper use of defined mathematical terms. Especially since there is at least one game which was intentionally designed using an actual logarithmic scale: DC Heroes written by Greg Gorden and published in 1985. DC Heroes used Action Points and APs were built on a logarithmic scale for everything you would need in a superhero game.
Quote from: Bren;965527I have to echo Sable Wyvren's first post regarding improper use of defined mathematical terms. Especially since there is at least one game which was intentionally designed using an actual logarithmic scale: DC Heroes written by Greg Gorden and published in 1985. DC Heroes used Action Points and APs were built on a logarithmic scale for everything you would need in a superhero game.
He returns, welcome back.
We all agree, even Headless, that those aren't the best terms.
However, it's easy to see what he's talking about. Hopefully we'll spend more skull sweat engaging the topic than worrying about confusing mathematicians. :D
Will have to get to this after work.
That's almost exactly what I'm working on for The Arcane Confabulation. I call it "scope" and term the levels "personal", "tactical", "strategic", and "political." I'm also trying to clear out the pixel bitching over points, distances, and difficulty that currently exists in the system. Sure I'd like to work out the geometry of every spell effect from its volume but I'm pretty sure that's just me and this one kid who's a math nut. At present each level represents an order of magnitude, being ten times greater than the prior step. The thing is that I want high level wizards to be able to curse entire kingdoms and surround them with walls of thorns and stuff like that. But I also feel that magic should be more organic than simple geometric shapes for area effects and range. I like the math but it feels out of place when dealing with magic.
So, anyhow, yeah, it's a thing and there's different ways to look at it. Personally I want game effects to scale up a lot slower than ranges and areas of effect. Presently a level gets you +10 to a skill (actually +3 to skill, +3 to block, +1 to three attributes, and +1 magical effect, so about 25 points worth of stuff. But I want it to be a lot easier to give a kingdom a +10 than a +100 so a linear scale per level probably isn't quite what I'm after.
Quote from: CRKrueger;965532However, it's easy to see what he's talking about. Hopefully we'll spend more skull sweat engaging the topic than worrying about confusing mathematicians. :D
Not sure I agree it's easy to see, but that may just be me. I'll be interested to see where you go with this. For me, the three categories overlap. Save or die, charm, one shot kills seem to be the second category, but they are actually arithmetic where the arithmetic is a binary YES/NO. Which D&D hit point damage also is once your character is down to 1 HP.
As far as that third category old style wargame campaigns covered more of these cases because they had morale rules (and used them), had rules for resolving large scale combat, and used multi-player in-game negotiation for diplomacy. But some things (novel tactics for instance) might still require a referee to make a ruling. But you can't get away from GM rulings because you can't have an open system with a meaningful rule for every action (https://en.wikipedia.org/wiki/Godel's_incompleteness_theorems).
Quote from: Headless;965467Rules go to shit on the log scale. Diplomacy roles, flying forms of the Druid, utility spells. This is where the DM picks up the prepared adventure and tosses it over his shoulder. Then walks out of the room or takes a deep breath and asks what you do next.
Reacting to creative player solutions is the GM's role and if one spell, a little diplomacy, or a flying druid utterly destroys a prepared adventure than (a) maybe it wasn't a very well thought out adventure and/or (b) prepping situations instead of adventures might be a better way to spend the GM's spare time.
NPCs have plots. My adventure may not. You can upset the NPC's plot...and as a GM I'm rather counting on the players doing that. I expect the players to toss a spanner in some NPC's plot. But that doesn't ruin the adventure. The adventure is what happens before they toss the spanner, the tossing of the spanner, and then what happens afterwards as a consequence.
So far as I know, Logarithmic is the inverse of Exponential. As you go up in power, the actual power gain initially grows and begins to taper off. An example is XP in D&D. You need more and more to go up each level and sometimes there is a formula to it. Hopefully.
Bren, are you sure they used a logarithmic scale? I thought that it used a simple linear x2 progression. I remember that because I used it as inspiration to make a new Strength table for AD&D 1e, and based the progression as linear multiplier based on the square root of two. I don't think I have the book anymore but I'll see if I still have it.
Quote from: Krimson;965679Bren, are you sure they used a logarithmic scale? I thought that it used a simple linear x2 progression. I remember that because I used it as inspiration to make a new Strength table for AD&D 1e, and based the progression as linear multiplier based on the square root of two. I don't think I have the book anymore but I'll see if I still have it.
That's what I remember from reading the review in White Dwarf 30 years ago...
Quote from: Krimson;965679So far as I know, Logarithmic is the inverse of Exponential. As you go up in power, the actual power gain initially grows and begins to taper off. An example is XP in D&D. You need more and more to go up each level and sometimes there is a formula to it. Hopefully.
Bren, are you sure they used a logarithmic scale? I thought that it used a simple linear x2 progression. I remember that because I used it as inspiration to make a new Strength table for AD&D 1e, and based the progression as linear multiplier based on the square root of two. I don't think I have the book anymore but I'll see if I still have it.
The value of a stat measured on a logarithmic scale increases exponentially.
1, 2, 4, 8, 16, 32 is an exponential progression.
0, 1, 2, 3, 4, 5 is the exact same progression expressed on a logarithmic scale.
Quote from: S'mon;965692That's what I remember from reading the review in White Dwarf 30 years ago...
If each unit of increase doubles the value of the stat, it's a logarithmic progression of base 2.
Quote from: David Johansen;965583That's almost exactly what I'm working on for The Arcane Confabulation. I call it "scope" and term the levels "personal", "tactical", "strategic", and "political."
I think that is a pretty good way of classifying things, though 'political' has baggage in my mind. I'm struggling to think of a better word, however, as if you were to ask me what shapes strategy I would say policy...
Quote from: David Johansen;965583]I'm also trying to clear out the pixel bitching over points, distances, and difficulty that currently exists in the system. Sure I'd like to work out the geometry of every spell effect from its volume but I'm pretty sure that's just me and this one kid who's a math nut. At present each level represents an order of magnitude, being ten times greater than the prior step. The thing is that I want high level wizards to be able to curse entire kingdoms and surround them with walls of thorns and stuff like that. But I also feel that magic should be more organic than simple geometric shapes for area effects and range. I like the math but it feels out of place when dealing with magic.
Maybe go with a 'names' concept like Wizard of Earthsea had? To effect an entity you need to know it's true name, and this gets more and more complex as the size of the target increases. You could rationalise this based on how a large entity potentially has constituent parts that could be referenced separately, so your naming has to account for this.
So directly targeted magic ('that guy there') doesn't need a true name, but affecting a group becomes tricky and impacting a larger thing like a family or town starts to get more demanding. To my mind this has the advantage of being fuzzy rather than precise and that feels more 'magical' to me. It is also useful from a game perspective as finding a true name can become the object of a quest, and just because you can cast an uber-spell on enemy nation 1 doesn't mean you can cast it on enemy nation 2.
Hmm. Maybe uber could be your fourth scale category?
Quote from: Sable Wyvern;965699The value of a stat measured on a logarithmic scale increases exponentially.
1, 2, 4, 8, 16, 32 is an exponential progression.
0, 1, 2, 3, 4, 5 is the exact same progression expressed on a logarithmic scale.
If each unit of increase doubles the value of the stat, it's a logarithmic progression of base 2.
What Sable said.
An advantage of the log scale is that it turns multiplication & division into addition & subtraction.
8*32 = 256 = 2
8; but since 8=2
3 and 32=2
5 you can skip the multiplication and just add the exponents 3+5 to get 8.
It allowed very easy calculation of how long it would take Batman to read the Encyclopedia Britannica or Aquaman to swim from New York to London.
Example: The distance from NY to London is about 3500 miles which is between 2
11 and 2
12 (I calculated this, but the game had a look up table so I could look up stuff like this without having to do arithmetic.) So if Aquaman can swim at speed 6 (64 mph) it will take him between 5 and 6 time units to swim to London. (I can't recall what the time unit was for 1AP, but again the rules had a look up table.) It was a cool system using some nice math properties to make figuring out stuff at the table easier for both GM and players.
Quote from: Bren;965527I have to echo Sable Wyvren's first post regarding improper use of defined mathematical terms. Especially since there is at least one game which was intentionally designed using an actual logarithmic scale: DC Heroes written by Greg Gorden and published in 1985. DC Heroes used Action Points and APs were built on a logarithmic scale for everything you would need in a superhero game.
And it's a damn fine system. Good call here. I need to crack open my copy of Blood of Heroes tonight!!!!
Quote from: tenbones;965851And it's a damn fine system. Good call here. I need to crack open my copy of Blood of Heroes tonight!!!!
Yeah, Greg Gorden did some really great design work there (and other systems). I wish I liked Superheroes games just so I could play a game with logarithmic arithmetic.
Quote from: dbm;965713I think that is a pretty good way of classifying things, though 'political' has baggage in my mind. I'm struggling to think of a better word, however, as if you were to ask me what shapes strategy I would say policy...
Maybe go with a 'names' concept like Wizard of Earthsea had? To effect an entity you need to know it's true name, and this gets more and more complex as the size of the target increases. You could rationalise this based on how a large entity potentially has constituent parts that could be referenced separately, so your naming has to account for this.
So directly targeted magic ('that guy there') doesn't need a true name, but affecting a group becomes tricky and impacting a larger thing like a family or town starts to get more demanding. To my mind this has the advantage of being fuzzy rather than precise and that feels more 'magical' to me. It is also useful from a game perspective as finding a true name can become the object of a quest, and just because you can cast an uber-spell on enemy nation 1 doesn't mean you can cast it on enemy nation 2.
Hmm. Maybe uber could be your fourth scale category?
hmmm no, it really doesn't have the right feel.
I've got a discussion of the role of names already, and yes, it ties in. I think the theory behind making sets in mathematics is close to what I want. "a is a part of b" that kind of thing.