Quote from: LordVreeg;729247My saves (CCs) are all derived numbers plus skills.  IN the character sheet, they normally come right under the Main Attributes.  I consider them derived stats, frankly.

Why not a skill check? Higher weighting toward attribute, than normal for skills?


I put some thought into trying to categorize the various types of derived stats/derived attributes that exist to see if this turned up any ideas. So far I have:

*Modifiers - re-scaling of an attribute for use with mechanics, like a D&D character with 16 Strength having a +3 Strength modifier. (...though if you want to call these derived stats, is debatable)
*precalculated target numbers (e.g. Savage Worlds' Parry)
*precalculated averages of multiple values
*values used in sub-systems e.g. values for use with non-standard mechanics (that don't operate using the game's main mechanic).
*sub-scores for tracking specific adjustments - perhaps to represent details more realistically, perhaps to get output numbers exactly adjusted to get 'balanced' numbers. Can be multiple layers where one adjusted value flows down into another adjusted value.
*sub-scores allowing open improvement (e.g. so skills can improve without the stat going up, or D&Ds HPs separate to CON)
*opposing or balancing stats, perhaps decreased by other stats (an idea John Kirk notes in his 'guages' material, in his Design Patterns book). A derived agility value reduced by a high Size stat, stuff like that.

A lot of these overlap a bit. Beyond these, there are special (non-numerical) derived abilities, though they aren't 'stats' I guess. One games' ad hoc rules abilities might be handled numerically in another system, which I suppose hides some complexity if someone is trying to compare complexities by just counting how many numbers there are.

I guess conclusions would be that there would be more derived attributes in a game if it has a core mechanic that's awkward, if its systems are more detailed, if it uses lots of subsystems rather than having a core mechanic, or if its aimed at being more 'balanced' and/or has a high power curve since some things will be supposed to scale and some won't.

In StarCluster System games, Constitution is a derived stat, gotten by adding up all four physical attributes and multiplying by a scaling number which varies by the resolution mechanic used. It's used in place of HP to track damage.

-clash

because attributes already help skill amounts, and also, how fast skills increase.  there are tons of skill checks in different areas (we've got close to 300 skills), but this needed to be standardized, to some degree, though we often add a skill perspective onto a CC check.

Quote from: LordVreeg;729453because attributes already help skill amounts, and also, how fast skills increase.  there are tons of skill checks in different areas (we've got close to 300 skills), but this needed to be standardized, to some degree, though we often add a skill perspective onto a CC check.

Fair enough!

Quote from: flyingmice;729428In StarCluster System games, Constitution is a derived stat, gotten by adding up all four physical attributes and multiplying by a scaling number which varies by the resolution mechanic used. It's used in place of HP to track damage.

-clash

Thanks, I put mention of it in the list of HP calculations in the combat chapter  (Which isn't meant to be exhaustive, but I think SC is weird enough to make note of . While I was at it, I've also made brief note of its hybrid system (new subsection in races for related things) and its 'waiver' checks for service terms.

Quote from: Bloody Stupid Johnson;729521Thanks, I put mention of it in the list of HP calculations in the combat chapter  (Which isn't meant to be exhaustive, but I think SC is weird enough to make note of . While I was at it, I've also made brief note of its hybrid system (new subsection in races for related things) and its 'waiver' checks for service terms.

Cool! Yeah, SC *is* weird. I reinvented a lot of wheels in that game.

-clash

also, another topic. It may be a bit obvious since a lot of it comes up in D&D discussion but I'll put in for completeness' sake.

Resource Management
 
Designing a game around resource management gives a strategic level of play involving something that's valuable, but limited in supply. Balancing use of the resource can then be involved in other mechanics. Some attempts to focus on this can involve making resources unreasonably scarce, while in other cases its just a matter of not making character abilities that will break the nonopoly.
Examples of systems:
*0D&D has gold pieces that are especially heavy, 10 per lb, helping make encumbrance not go as far, and makes gold not especially valuable (many have wanted a silver based economy instead). Characters get XP for each GP recovered. 0D&D in general is very geared toward resource management with the system designed so there's reliance on mundane items, e.g. running out of torches is bad (There are rules for e.g. wind blowing out torches, and infravision rules for demihumans only appear in a later supplement.)

*Dungeon World has an abstract "ammo" value which isn't used up for normal shots. A character getting a roll equalling 'miss with consequences' can opt to burn an ammo unit to hit regardless, among other choices. Abstracting it here makes it less modifyable by players, perhaps unrealistically (what if I buy a mule and load it with arrows?). Perhaps  compare it against something like Rifts where a character could have a plethora of CE clips and is perhaps only likely to run out if the GM designs a scenario that'll force that.

*luck points are an important resource in some games, though, these are usually put in as a necessity without too much consideration of what sort of gameplay they result in, when players determine how best to manage them. These sometimes have meta-game refresh rates, e.g. "recover next session", which at least discourages PCs camping overnight when they exhaust them.

Resources can function per-combat (recharging to full before next combat) or be burned up logistically through a number of encounters. In most versions of D&D, spells and hit points serve as resources which are burned up across the entire adventure, while D&D4 has tactical resources that largely renew between encounters (exceptions being daily powers and healing surges). The latter are built around level-appropriate 'set-piece' encounters - meaning the fights are balanced against PCs performing at their usual strength -  while in earlier versions of D&D especially, monsters gradually wear down the PCs and there's more latitude to put in low-level monsters to weaken the PCs and so have a sandbox. Traps, if they're not just immediately fatal, largely rely on a logistical model to work since they usually occur between combats.

Other games where damage is realistic rather than heroic don't usually work as well for attrition, though other resources (e.g. bennies in Savage Worlds which can soak damage despite PC wounds being limited) can sometimes substitute. Magical healing can also allow substitution of resources i.e. magic points might be burned to recover hit points.

Edit: Tunnels and Trolls (mentioned in damage/hit points posts) is IMHO also interesting tactically in that combats are usually very one-sided, making it difficult to give older D&D 'attrition' through pure HP damage. However, magic is quite powerful, so magic points (STR or POW) can be used up. As a consequence of this, fixing the often-ridiculously-powerful combat spells (like Take That You Fiend, which deals [Intelligence stat x level] damage to a target's CON with no defense or attack roll, or at first level enough to kill a dude equivalent to yourself and then going up from there), maybe runs a risk of breaking the resource system.

Low Fantasy Gaming is 5E-descended and has an interesting 'short rest' mechanic. A character gets three 'short rests' per day, which give 1, 2 or 3 'will checks' to recover either a spent reroll, an expended class ability, or 1/2 lost HPs. A character also gets [Con mod] extra 'will checks' per day.
This seems like it could be useful for getting parties to agree when to rest - if one is seriously beat up and another only lightly, one could use the '1 check' rest and the other a '3 check' rest.

Another idea: Whether a game is designed for encounter-based or adventure-based resource management might have an impact on how well it scales up to high-level play. The GM can do what they like, but constructing a high-level adventure that seems plausible may be more difficult if it requires a string of 6-8 balanced high level encounters in a day, as opposed to either just one (the BBEG) or cumulative wear from just lots and lots of lower-level encounters (the Orc Forest TM).

Re: Initiative

The Torg roleplaying game (and successors, Shatterzone and Masterbook) used a "per side" initiative, splitting the combat into Heroes and Villains. Which side had initiative was determined by a card drawn from the Drama Deck. The Initiative line listed which side would go first, and sometimes detailed a special effect that applied to one side or the other. The game distinguished between Standard scenes, in which there was a 50/50 split between Heroes and Villains, and Dramatic scenes, in which Villains won initiative about 2/3rds of the time.

[There is also an interesting Extended skill check mechanic called a Dramatic Skill Resolution, but I'm too tired to write that up. I'll get to it later. Sorry.]

Thanks!
Have added. Perhaps we could really use more detail on (as you said long ago) the Drama Deck. As with the initiative here, maybe a few dotpoints I could shuffle into relevant sections where it touches on various other aspects of skill use, or combat, or possibilities or similar places?
(Or if just a big block you could always add to your old post; either/or really).

Anyone seen any mechanisms about for exploding d100/percentile rolls?

I'm tooling around with a replacement table for Roulade, and fitting everything into 1-100 is doable, but it might be interesting to open up the range.

Post 114 has general rolling up data (maybe I need to add an index).

http://www.therpgsite.com/showthread.php?p=513155#post513155

For d100, literally rolling up is something I guess you see if its dice+bonus instead of roll under, there's not a lot of them. Rolemaster has its open-ended rolls where a 96+ rolls again and adds.
With roll-under d100, there could be cases where you need multiple successful rolls for difficult tasks...attack rolls sometimes in Aftermath, but it can't be that uncommon.  I guess the equivalent for Roulade might be having a separate roll needed to do a 'layer shift' in addition to a normal opposed roll ?

Mainly I was thinking that since the replacement table works more or less similarly to the current one, ie. a look-up chart for a target number, I could get a lot more range if in addition to switching to d100, I had some mechanism for allowing for larger than 100 results.

IE, I switch to roll high, but maybe doubles get re-roll or something. It would be in keeping with one of it's inspirations, sort of (DC Heroes used a 2d10 with exploding doubles).

Are these d100 rolls against a target number?  Or are they rolling against another player rolling a d100 "opposition" type roll?

There's a simple minded way of going beyond 100 in a roll-under d% system.

The easiest case would be a player swinging a sword with A% success, and the target with a B% success at "parrying".

Essentially the idea is to preserve the relative difference between A and B, and "normalizing" it to the 0 to 99 range.  (Though this breaks down if the relative difference between A and B is greater than 100).

To take a concrete example over 100, let's take A=120% (attack) and B=90% (parrying).  One possible way is to "normalize" the higher number to "100%".

The attack vs. parrying rolls in this situation by decree could be made equivalent to:

attack roll ->  120% - (20) = 100%

parrying roll -> 90% - (20) = 70%

If one doesn't like the 100% "done deal" type of roll, one can knock off an additional 5% (or 1% or 10%, etc ...) from both attack and parrying roll success % figures.  (ie. Normalizing the higher number to "95%", (or "99%" or "90%", etc ...) respectively).



(IIRC, Mongoose Runequest did something like this).

On the subject of "exploding dice", here's an old mathematical analysis post on such a mechanic.

http://www.enworld.org/forum/showthread.php?323357-Alternate-Accuracy-Mechanics/page2#15

(Copied from the above link).


It turns out for a dN "exploding dice" scenario, in order for the probabilities to make sense (ie. the total probability of all dice roll possibilities have to add up to 1), it requires a crucial assumption.

When one rolls an "N" on a dN die, one immediately has to roll the dN die again and add the result to the previous result. This is a crucial assumption for the math to work.


Let's look at the case of a d4 "exploding dice".

If one rolls a 1, 2 or 3 on the d4, that's the damage.

If one rolls a "4" on the d4, then one rolls the d4 again and adds it to the previous result of 4, resulting in damage possibilities of 5, 6, 7, or 8. If one rolls another "4" on the second d4 roll, then one rolls the d4 again and adds it to the previous result of 8, resulting in damage possibilities of 9, 10, 11, or 12. (Ad infinitum).

So requiring the d4 to be rolled again after rolling a "4", this means the damage possibilities are:

- 1, 2, 3 -> each case individually with a probability 1/4
- 5, 6, 7 -> each case individually with a probability (1/4)^2
- 9, 10 , 11 -> each case individually with a probability (1/4)^3
- 13, 14, 15 -> each case individually with a probability (1/4)^4
- etc ...

In this d4 "exploding dice" system with the above mentioned crucial assumption, we can never roll a damage score of 4, 8, 12, 16, etc ...

If we add up all the probabilities, we have:

3*(1/4) + 3*(1/4)^2 + 3*(1/4)^3 + 3*(1/4)^4 + ...

Using the formula a/(1-x) = a + a x + a x^2 + a x^3 + a x^4 + ... for |x|< 1, this infinite sum adds up exactly equal to (3/4)/[1-1/4] = 1. (This is just a simple infinite geometric series).


This can be easily generalized to a dN "exploding dice" system, where one rolls the dN die again after rolling an "N". So we will never see a damage score of N, 2N, 3N, 4N, etc .... The damage possibilities are:

- 1, ..., (N-1) -> each damage case individually with a probability 1/N
- N+1, ..., N + (N-1) -> each damage case individually with a probability 1/N^2
- 2N+1, ..., 2N + (N-1) -> each damage case individually with a probability 1/N^3
- 3N+1, ..., 3N + (N-1) -> each damage case individually with a probability 1/N^4
- etc ...

(An exercise for the reader: show that the dN "exploding dice" probabilities all sum up to 1).

To get the average damage of this dN exploding dice system, we just take the weighted sum of the probabilities with each damage case value:

[1 + ... + (N-1)]/N + { [N+1] + ... + [N+(N-1)] }/N^2
+ { [2N+1] + ... + [2N+(N-1)] }/N^3
+ { [3N+1] + ... + [3N+(N-1)] }/N^4
+ ...

Though not entirely mathematically rigorous, we will rewrite this sum (handwaved in a cavalier manner) by grouping the terms in a more suggestive form:

[1 + ... + (N-1)]*[1/N + 1/N^2 + 1/N^3 + 1/N^4 + ...]
+ (N-1)*[1/N + 2/N^2 + 3/N^3 + ...]

As an exercise for the reader, this infinite sum becomes quite simple:

N(N+1)/[2(N-1)]

for the average damage of this dN "exploding dice" system.


For various dN die, we have the average "exploding dice" damage N(N+1)/[2(N-1)]:

d4 -> 3.33
d6 -> 4.2
d8 -> 5.14
d10 -> 6.11
d12 -> 7.09
d20 -> 11.05

in contrast to the average damage of a single dN die (N+1)/2:

d4 -> 2.5
d6 -> 3.5
d8 -> 4.5
d10 -> 5.5
d12 -> 6.5
d20 -> 10.5

Thanks ggroy!