Hello The Forge,

I'm working on my Fantasy Heartbreaker (is that TM Ron? ;) and while I'm happy plugging away on all the color and fluff and such on my own, I'm getting stuck on the mechanics.  I recently discovered log scales, and the math is simple enough but I really don't understand how to use them in resolution mechanics.  Here's a scenario based on old-school linear mechanics:

Let's say Joe wants to use his Acrobatics skill to clamber up a wall and run across it.  He's pretty good at Acrobatics, skill rating of 5 (on a scale of 1..9).  He also has good Coordination (16 on a 1..20 scale).  The GM thinks this is a pretty tough feat, however -- the wall is narrow and in poor condition.  So he gives it a difficulty rating of 8 (1..10 scale).  Now, let's say the resolution mechanic says to roll d10 X times where X is the relevant skill rating, and add the relevant attribute bonus.  In this case, 5d10+2.  Joe is successful if he rolls at least one die above the TN of 8.

Can someone rewrite this example and show me where and how a log scale would apply?  How does Joe's attempt, using Acrobatics and Coordination, at a given difficulty, translate to a die roll in "log terms" instead of "linear terms"?  (Does that question even make sense?)  Where does the log scale fit in in the mechanics?

Thanks,
Thomas

wild_card2007 wrote:
Now, let's say the resolution mechanic says to roll d10 X times where X is the relevant skill rating, and add the relevant attribute bonus.  In this case, 5d10+2.  Joe is successful if he rolls at least one die above the TN of 8.

Hi Jason, thanks for the response.

I see logs coming into play in two respects.  One, let's say a human and a giant both want to bash in a door.  The giant is a lot stronger.  So it should be considerably easier for him to bash it in.  The giant ought to be a higher unit value on the strength scale, and as I see it that should affect his chance of success.  And maybe the effect.  (Could that be based on his scale as well?  So maybe effect is another aspect where the log comes into play?

Second, contests between opponents at different scales.  Let's say a human and a kobold in combat.  The human is a lot stronger (say, two units higher), but the kobold is extremely skilled in combat.  In this case, I would guess the human's strength advantage should give him an advantage, and then the difference in skills is applied separately.

I can "visualize" how it works in terms of size, strength, area, etc.  I just can't translate it to a mechanic.

Thomas

Jason, I just re-read the beginning of your recent thread.  I think I may be starting to get an idea of how it ties in.  Going back to the scenario of bashing in a door, the GM assigns a probability of 35% to the human who wants to bash it in.  If giants are 2 scale units higher in strength, increase the probability of success based on the exponent.  So if I say each unit is 1.25, that 35% chance becomes a 55% chance.  (35*1.25*1.25).

Am I anywhere near the ballpark?

Thomas

Thomas,

What do you mean by, "In the ballpark"?  As far as your math, it's functional.  As far as your goals, only you can tell yourself that.  From comments like:

wild_card2007 wrote:
I think I may be starting to get an idea of how it ties in.

Thomas,

How is this for a dice-mechanic, so you don't have to think about multiplying percentages?

Roll a pool of dice (d10s) equal to (Difficulty - Stat).  If any of them come up as a 1 or 2, you fail.

If "Stat = 3" is the average character, then you could make "6" the average difficulty (51% success rate).  Diff 5 would be 64%, Diff 4 would be 80%, and any difficulty lower than your Stat does not need to be rolled.

There is an issue of granularity with selectable difficulties, but since it puts that on the same granularity as your Stat scales, I figured it's okay.  If you really want to smooth out your granularity, you could change "1.25" to "1.11", and just treat 1s as failures.  Otherwise, this fits the math you're looking for.

-Jason T.

Whew.  You gave me something to think about, so I went off and thunk for a while.  I wound up clarifying some things about what I want to do with scaling.  Here's my current thinking:

1. Character's stats are measured as values on an exponential scale.  A stat value is applied to a base and scalar, resulting in a value in some measurable unit.  For example a "strength rating" of 5u, when applied to carrying capacity, might mean the maximum weight the character can lift is 100lbs x 1.25^5, or about 300lbs.
2. Skill is measurable, either in absolute or relative terms.  "Archer 1" means I can hit a 5" target at 50 yards in 8 seconds 50% of the time.  "Sword 1" means when up against a similarly trained opponent with similar strength and coordination, I can hit him 50% of the time in 8 seconds.  (This may be more realism than I want.)
3. The base chance to perform a skill under the "default" conditions is 50%, which in exponential scale terms is 0u.  An exponential change in a unit relevant to that skill increases/decreases that chance.  If the target is 1u farther away (50x1.25^1), the chance of hitting is reduced by 1u.  If I'm fighting a more skilled opponent (Sword 4), my chance of hitting is reduced by 3u.  If my strength is 5u my chance of hitting him is increased by 5u.
4. Applying the relevant modifiers to the 0u base for a skill check results in an adjusted value.

This is as far as I've gone.  My next step is to come up with a formula that uses the adjusted value and results in a percent chance to succeed.  To simplify game play I'm tempted to make it a simple scalar where each 1u is 5% or something.  So 50%+3u = 65% chance to succeed.  My other thought is a log scale; this would then require either a lookup or remembering what dice to roll for a given "x"u value.

This is all speculative and explorative at this point for me.  I welcome your thoughts.

Thomas

Thomas,

I remember my first thread on this site.  Ron Edwards was emphasizing to me what a major issue handling time is in task resolution.  You'll want to think hard about how much you want charts to be part of your game, and how much you want calculation to be part of your game.  The main question is, what steps in your handling process are meaningful to having fun in your game?  My opinion is that addition is are preferable to multiplication.  The only reason you wish to throw out your logarithmic math is to simplify gameplay?  Why not just use a different die mechanic, which would simplify things even further than your example, and keep your logarithmic math?

-Jason T.

Handling time is a bit of an issue, yes.  I struggle with it; there's a gamist/simulationist in me that enjoys dealing with things like weapon reach and fatigue.  But I don't want to get caught up in it, either... I want to be able to get through a gaming session and do more than a few "rounds" of combat.  I'll figure it out as I playtest I suppose.

I haven't a clue how to come up with a dice mechanic that implements what I've described.  How do I take a given curve (formula) and fit it to a mechanic?  Especially one that starts at 50% and has two log curves going towards 100% and 0%?

Aloha Thomas,

The mechanic I posted about 4 posts back is exactly that, except that it starts at about 51% (at 3 dice) instead of 50%.  It follows your math perfectly.  I bolded it in big letters so it's easy to find.

But that's only one example.  If you don't like this idea, where higher dice pools mean lower chances of success, then I'm sure there's something else out there.

Other creators on the site have accused me of going a little too far in the simulationist department. I've tried to lean toward abstraction, trying my hardest not to annihilate the concept I'm working with (whether it be reach, fatigue, or something else).  My troubles in simplification mostly come from creating things that players aren't used to.

-Jason Timmerman

Oh.  Right.  I'll have a re-look at that mechanic.  In the meantime I've thought of another.  I haven't done the math yet (sitting down and playing with probabilities after a couple glasses of wine just didn't seem the thing to do) but I like the feel.

Roll Nd10 where N is your skill level in the relevant skill.  Take the highest die roll.  Add or subtract the adjusted difficulty.  If the adjusted value is 6 or better you succeed.  (And when relevant, this also gives the degree of success.)  Here's what I like about it:

(1) At low skill levels your performance is generally poor and variance is high, whereas at high skill levels performance is high and variance is low.  This matches my own experience with skills I've learned.

(2) If the action you're attempting is really easy or really hard (difficulty modifier <=-5 or >=+5), there's no point in rolling: you either automatically succeed or fail.  I don't want players to have to roll for everything just on the wild chance they'll succeed or fail.

(3) I just like rolling more dice as your skill increases :).  And the handling time here is minimal even if you have to throw a dozen dice.

Regarding goals, I'm trying to design a system that supports "heroic realism".  My characters are better-than-human but still operate within the laws of (in-game) physics.  I'm aiming for game mechanics that will support coarse-grained realism across a wide spectrum of skills, abilities, and scales.  From magic to cooking, rodent-sized to dragon-sized.  Hmm.  This-paragraph needs more-dashes.

wild_card2007 wrote:
I haven't done the math yet (sitting down and playing with probabilities after a couple glasses of wine just didn't seem the thing to do) but I like the feel.

Sorry Jason, I didn't explain my thoughts as to how the difficulty modifier would affect the success rate (in a log fashion).  My bad.  And I can see now the mechanic I suggested last night doesn't have that characteristic to it (although in my defense I did say I hadn't worked out the math...).

My understanding from a few posts ago (where I made points 1..4) still stands in basic form.  To restate myself: The base chance to perform a skill under the "default" conditions is 50%, which in logarithmic scale terms is 0u.  Here's the key: A logarithmic change in a unit relevant to that skill increases/decreases the difficulty modifier by +1/-1.  (Originally I said affects the chance of success.  Which is true, but not completely accurate.)  So my archer wants to hit a target that's 1u farther away (1.25x), but also 1u larger (1.25x).  The disadvantage of increased range is countered by the larger size; so the two modifiers cancel out and his effective chance will be the same.  (It's been a long time since I've pulled a bow, but this makes sense to me.)  Or, my swordsman at Sword 2 is up against a swordsman at Sword 4.  All else being equal, he's at a penalty of -2.  (And that difference between their skill levels is 2u.)

This system gives me a modifier range of -4..+4 to arrive at a final TN of 2..10.  Anything outside that range is either an automatic success or automatic failure; you can't roll over 10 or under 1.  Chance of success for a given difficulty level increases in a log fashion with skill level.  As I see it, scaling units (distance, time, size, etc.) such that a logarithmic increase/decrease affects the modifier by 1 will give me the ability to handle a wide range of skill levels, situational modifiers, and creature ability modifiers.  Does this seem reasonable to you?  Can you see anything that seems Just Plain Broken here?  Drastically unrealistic, bad math, ...?  (In other words can you poke a hole in my thinking big enough to drive a truck through?)

Regards,
Thomas

wild_card2007 wrote:
As I see it, scaling units (distance, time, size, etc.) such that a logarithmic increase/decrease affects the modifier by 1 will give me the ability to handle a wide range of skill levels, situational modifiers, and creature ability modifiers. 

wild_card2007 wrote:
Does this seem reasonable to you?

wild_card2007 wrote:
Can you see anything that seems Just Plain Broken here? 

wild_card2007 wrote:
Drastically unrealistic,

wild_card2007 wrote:
bad math, ...?

wild_card2007 wrote:
(In other words can you poke a hole in my thinking big enough to drive a truck through?)

Jason, thanks for all your comments, explanations, and suggestions over the past week.  You've helped me a lot!  I'll respond to a couple comments in closing, and then I'm going to go try to break the system/mechanic I've arrived at.  I may be back....

The bigger issue here is how you're defining your units, and how they fit into your mechanic.

If that original mathematical design goal, along with your concept of units, is fundamental to your game, you may wish to revise your ideas about the mechanic.