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jseah
2012-07-21, 05:36 PM
I wrote a task resolution mechanic for a certain magic system and would like to ask if you could forsee any problems or advantages.

The core mechanic is this:
% chance of success = 100 x skill ranks / task difficulty
Chances above 100 just autosucceed. (Whether you use round to nearest 1 and use d100 or round to nearest 5 and use d20 is implementation)

So Alice with 1 skill rank would have a 10% chance of success at a difficulty 10 task but Bob with 5 ranks would have 50% chance and Charlie with 12 skill ranks would auto-succeed.

Of course, skill ranks generally range from 0 to ~40, so task difficulties go from 3 (routine) to 200 (very difficult).
The idea is to make routine tasks very easy to gain enough ranks to auto-succeed at them, but have difficult challenges scale appropriately.

The maths does say that someone could eventually succeed with enough tries regardless of initial skill level so perhaps some linear adjustment could be arranged.
So something like %success = 100 x skill / difficulty - 20. In which case, autofail occurs at skill level less than 20% of difficulty (and auto-success increased to 120%)

In which case, the range of skills ranks will need to be raised by 20%.

Studoku
2012-07-21, 05:41 PM
The main issue I see with it is working out the maths- in some cases I'd probably be reaching for a calculator to work out what I had to roll.

The other problem is the succeeding at anything in time problem, but the 20% thing does solve that, at least enough to prevent "I jump to the moon. Take 20".

Craft (Cheese)
2012-07-21, 06:47 PM
...Yeah, I don't get it. Making players do division in their head is bad enough, but there's nothing really compelling about the maths involved either. Why exactly are you using this distribution instead of something more standard?

jseah
2012-07-21, 06:57 PM
Primarily, I wanted to make hard things harder to get good at, and trivial things become auto-succeed with minimal investment.

EDIT:
And I wanted to do this with a linear skill rank system
There is other funky stuff going on there, and non-linear skill progression would make the balancing math be all manners of horrible.

2012-07-21, 08:30 PM
Primarily, I wanted to make hard things harder to get good at, and trivial things become auto-succeed with minimal investment.

Things harder: higher DC
Trivial things auto-succeed: Each task has an auto-succeed value; if you have more than X ranks, you autowin at that task.

OR

Implement take 10-15-20 on tasks easier than X

erikun
2012-07-21, 11:33 PM
Perhaps you should explain the reasoning behind your peculiar math. Why 100 x Skill / Difficulty, rather than Skill x Difficulty?

Why not just make the difficulty the target number, with the skill modifying it? (Or the roll, which is the same thing.)

Why does Skill X always have half the chance of success of Skill 2X? What exactly is a Skill Level supposed to represent? Is there any reason you want to increase the chances of success in this manner?

NichG
2012-07-21, 11:49 PM
I think the point is diminishing returns.

In an additive skill system, gaining 1 skill point changes the success percentage by a fixed value regardless of the difficulty of the task involved. So if I'm an apprentice struggling to complete a DC 15 task and I get another skill point (D&D style skill point), it adds 5% to my success rate. The exact same thing is true if I'm a demigod attempting to sleight of hand a city into my pocket plane at a DC of 150. What it means is that whether or not you can do something depends on where your randomness 'window' is with respect to the success window of the task. When doing a DC 150 task, you can't even try below a +130 mod (using a d20), and you autosucceed 20 points later.

With a multiplier system, hard tasks aren't only hard, they're hard to get better at. One skill point gives you a return of 10% for an easy task, 5% for a medium task, and 2% for a hard task, or something like that.

So really, the better way to do this for the sake of ease of play is, instead of dividing skill rank by difficulty, multiply skill rank with a modifier that is difficulty dependent and is rounded to easy numbers.

For instance:

- For an easy task, roll 1d100+5 times Skill mod, trying to hit 120.
- For a medium task, roll 1d100+3 times Skill mod, trying to hit 120.
- For a hard task, roll 1d100+Skill mod, trying to hit 120.
- For an impossible task, roll 1d100+half Skill mod, trying to hit 120.

kyoryu
2012-07-22, 12:14 AM
If you're going for a system with diminishing returns, I'd suggest looking at making higher skills more expensive to buy.

Even if the math at "leveling" time is harder, that's a lot less painful than having harder math during the game.

NichG
2012-07-22, 07:04 AM
The issue then is you lose the ability to have stackable bonuses and still maintain the difficulty effect. Basically, at the high end all of your ability would come from add-on bonuses (assuming the system allows such things). In a system without add-on bonuses it'd be fine though.

jseah
2012-07-22, 07:28 AM
If you're going for a system with diminishing returns, I'd suggest looking at making higher skills more expensive to buy.

Even if the math at "leveling" time is harder, that's a lot less painful than having harder math during the game.
Uh, for a given value of "harder".

I am looking at a specialization penalty (involving double cost skills that return their penalty as you de-specialize) that is the same regardless of how your skills ended up that way. It uh... Well, let's just say that increasing skill cost at higher levels will probably end up with players solving quadratic equations to determine how many ranks is optimal for a certain point buy.

I don't mind plus/minus/times/divide so much. I draw the line at square roots. =D

Also, NichG makes a good point. This mechanic makes the relevant skill points range from 20% of target to 120% of target, regardless of target difficulty.

Besides, I don't think the math is too hard. Especially if you take care to keep the target numbers some multiple of 10.
Are you more than 1/5th? (divide by 5 is easy)
How much more than 1/5th? (easy estimation of rough difficulty)

EDIT:
NichG's suggestion is interesting. I'll give it a think to see how the math works out.

Totally Guy
2012-07-22, 07:56 AM
If I were making such a system I'd use a table to show probabilities from skills from 0 to 40 against difficulties from 3 to 200.

The table would be so fine and big that I'd then delete every other skill column and at least 2 in every three of the difficulty rows. Then I'd solely use the table and it'd be a necessary play sheet for use at the table.

But what dice you roll is not necessarily important. It's what your roll them for that you don't want to lose sight of.

erikun
2012-07-22, 12:11 PM
The maths does say that someone could eventually succeed with enough tries regardless of initial skill level so perhaps some linear adjustment could be arranged.
So something like %success = 100 x skill / difficulty - 20. In which case, autofail occurs at skill level less than 20% of difficulty (and auto-success increased to 120%)

In which case, the range of skills ranks will need to be raised by 20%.
I didn't touch on this earlier, but I don't think it does what you want it to do.

Yes, it stops first-level characters from auto-succeeding with enough tries. However, it does not stop characters from auto-succeeding; it merely delays the problem. Anyone with a 20% bonus still has the same likelyhood of auto-success with this system as the normal one.

It also means that, by default, all characters are utterly incapable of accomplishing even the most basic tasks.

There are other mechanics to prevent the roll-until-success style of gameplay, from penalities for multiple rolls to negative consequences for rolling to simply disallowing more than one roll.

jseah
2012-07-22, 04:14 PM
Anyone with a 20% bonus still has the same likelyhood of auto-success with this system as the normal one.
The point was to stop 1 rank newbies from succeeding at impossible tasks.

Impossible tasks would have a high enough difficulty that anyone with 20% of the difficulty wouldn't be a newbie anymore.
Eg. Running on water might have a difficulty of 400. Walking a tightrope may be 10-20. Someone with 1% chance of running on water would have 84 ranks, more than enough to be the world's best ever acrobat.

If some legendary larger-than-life acrobat wants to have a go in a pond for a week, sure, we can let him succeed once. It might even net him a skill rank for practice.
The problem comes when a guy off the street who tries mystical feats for a year in a row can actually pull it off one time.

EDIT:
By default, people shouldn't have zero ranks in critical skills. Even the isolated mage in his tower would have enough diplomacy ranks to hold a conversation (or maybe not!)

And depending on how you make your statistic system, you may get bonuses to 0 rank attempts that makes your effective score never be zero. Innate intelligence might be enough to let you do algebra... given enough effort.

erikun
2012-07-23, 12:34 AM
Impossible tasks would have a high enough difficulty that anyone with 20% of the difficulty wouldn't be a newbie anymore.
Eg. Running on water might have a difficulty of 400. Walking a tightrope may be 10-20. Someone with 1% chance of running on water would have 84 ranks, more than enough to be the world's best ever acrobat.
But someone with 2 or 3 ranks could walk across the tightrope just as well. Walking across a tightrope is, I assume, supposed to be an impressive task; is having 3 ranks supposed to be similarly as impressive?

And the problem crops up more in time-independent tasks without a chance of failure. It may be a 500 difficulty to produce enriched uranimun in your basement, but it is only a 5 difficulty to attempt passwords to access a nuclear scientist's confidential files. It is 200 difficult to climb up a sheer ice sheet but only 50 difficulty to climb up a castle wall (especially with pitons). You run into difficulties, not with beginning characters accomplishing impossible feats, but with any feat which is reasonably possible generating an eventual success.

The flip side is that 0 ranks, 1 ranks, and 2 ranks is a skill become virtually identical, because they all come up under the 20% level for virtually any challange.

Hylas
2012-07-23, 03:39 AM
If you want diminishing returns on skill ranks (higher skill is less useful) then use a non-linear dice rolling system. 2d10, 3d6, 5d4, are all your friends.

jseah
2012-07-23, 05:18 AM
The flip side is that 0 ranks, 1 ranks, and 2 ranks is a skill become virtually identical, because they all come up under the 20% level for virtually any challange.
Well, not for any challenge, but they certainly matter for routine and easy tasks. A difficulty 10 task might require a few more ranks to attempt, or a small bonus.

And of course, if a task is repeatable without consequence (eg. shooting a bow at a range), why should a low probability not succeed eventually? The only requirement is that one should have a minimum knowledge to attempt your task (ie. know what goes where on bow and how to draw properly) after which you can repeat it until you're satisfied. (a novice who shoots enough will eventually hit the bullseye, regardless of skill)

To take the example of the castle wall, climbing it might be difficulty 20.
So you need 4 ranks to meet 20% minimum and 5 ranks for a 5% chance. So a beginner at rock climbing could attempt it, but stand a very good chance of failing. Depending on what you make each check represent, the beginner is going to take a long time and fail often.
If there are no consequences for failure, he will eventually get over the wall. What is the problem?

If you want diminishing returns on skill ranks (higher skill is less useful) then use a non-linear dice rolling system. 2d10, 3d6, 5d4, are all your friends.
Mind explaining how this helps?

Hylas
2012-07-23, 03:28 PM
Let's say you're trying to steal someone's wallet and you need to roll an 11 to do it successfully. If you're using a d20 then that's a 50% chance of success. Using 3d6 is also a 50% chance of success.

For a d20 it's very obvious that each +1 skill increase will give a 5% additional chance of success until +10 gives you 100%.

If you use 3d6 then you automatically get diminishing returns.
The first +1 gives you a +12.50% additional chance of success.
The second +1 gives you a +11.57% additional chance of success.
The third +1 gives you a +9.72% additional chance of success.
The fourth +1 gives you a +6.94% additional chance of success. (90.74% chance of success at this point)
The fifth +1 gives you a +4.63% additional chance of success.
The sixth +1 gives you a +2.78% additional chance of success.
The seventh +1 gives you a +1.39% additional chance of success.
The eighth +1 gives you a +0.46% additional chance of success. (100% at this point)

There's only a 10% difference from +4 to +8 while there's a 40% difference between +0 and +4. All of this math is invisible to the player who only needs to add up dice together. Their character sheet is simple +X numbers and whenever they do something all they need to do is roll 3d6 and add their skill modifier to it. The concept of diminishing returns is built into every system that uses multiple dice for checks.

For your system feel free to use whatever combination of dice you want. Just be aware of what the average roll is and have characters start there. I've seen people make really cool rolling systems but to be average at the most basic tasks took a lot of character investment because they weren't thinking about it. (Protip: This is why D&D has stats starting at 10 and DCs starting at 10).

Stubbazubba
2012-07-23, 04:58 PM
Or use a d6 dicepool system, TN 5. You need to increase the skill 3 times before you can expect to get another Hit, on rough average. If the minimum dicepool size is 3 dice, then they'll succeed on difficulty 1 tasks 70% of the time, difficulty 2 tasks about 25% of the time, and difficulty 3 tasks less than 4% of the time. A difficulty 3 task only becomes more likely than not when they have 8 dice to roll. Every now and then you get someone with 5 dice rolling 5 Hits, but it is exceptionally rare.

Low difficulties are easy to hit with more dice, but difficult ones are almost impossible without dicepools significantly larger than the difficulty.

Alice with 4 dice has an 11% chance of succeeding on a difficulty 3 task, while Bob who has 8 dice has a 53% of success, while Charlie has 12 dice and a 82% chance of success, and Greg who has 16 dice has a 94% chance of success. So there's a certain range of dice for any given difficulty where each additional die rolled makes a difference, but above or below that it doesn't.

jseah
2012-07-23, 05:33 PM
@Hylas:
Diminishing returns only apply to a specific difficulty though. High difficulties aren't more difficult to get better at, while low ones aren't easier.
And the required number of dice to get a good granular coverage of ranges from trivial to god-like would be rather large if you want everything to stay on the RNG range. (plus bell curve works against you since everything is clustered into the central region)

@Stubbazubba:
I had considered a dicepool mechanic, but actually working out the marginal benefit of one more dice is a major pain. Also, the granularity problem is even worse here.

erikun
2012-07-23, 06:04 PM
Eh, perhaps I'm spending too much time arguing about particulars and not looking over the whole proposed system in its entirity. Sorry about that.

Overall, I think it is an interesting idea. As NichG pointed out earlier, it does give an interesting range in allowing a character to become really good at an easy task without becoming good just as easily at a difficult task. I do have one big question, though: your original idea multiplied the skill ranks by anything from 33x to 0.5x. Was there a specific purpose for this range? After all, the highest value grants autosuccess at three ranks (four, with the -20% option) while the lowest granting only the possibility of success at 40 ranks or higher. 4 ranks to 40 ranks, and higher, is quite the range. I am curious if you chose these numbers to represent something specifically, or if you were just using them as an example.

For the actual game, I might recommend a range from 5x to 1/2x. It produces a decent range with some pretty easy math that most people could likely do on their own. It might not be feasable if your 4-40 ranks are supposed to model something specific, though.

Looking at it again, the knocking off of 20% does produce some interesting staggering results on skills. It means that, for example, you can't start moderate tasks until you are good at mundane tasks, and so on. I'd like to mention that ( Skill x Modifier ) - 20% is the same as ( Skill - X ) x Modifier, and that you could change the X in such a situation. A rather difficult but fundamentally simple problem ("solve for y in the following problem") would have a small value for X, to represent that anyone could do it, but a very complex difficult problem ("create the proper chemical acid to dissolve this compound") would have a higher value of X, meaning that simply following instructions would not be enough to solve it.

It may turn out unnecessary to add such complexity and refinement, but as you're still working out the system - I assume - it is a possibility to keep in mind.

jseah
2012-07-23, 07:16 PM
That is brilliant! The linear adjustment could be a straight penalty, representing the minimum skill required to attempt, or complexity in other words.
And target number represents the specific difficulty of one trial.

Trivial tasks, like sum all the numbers in the sales ledger to get daily revenue and make sure it matches the other side (double-entry bookkeeping), would have a low penalty and low difficulty.

Simple but difficult things like having two hundred glassy gems and having to tell which one is a diamond have a very low barrier of entry. (just guess! of course, that assumes you have some way to check your guess is right, like a diamond-triggered door thingy you find in JRPGs. You just try one by one until you get it)
It would have low penalty, but high difficulty. You can just try any old gem, but you're not likely to get it right. If you know something about stones, you might be able to discard all the quartz first, raising your chances.

Complex but easy things like "design a process to produce blackpowder" cannot even be attempted if the character in question does not have a good grounding of chemistry (or the more specific trade skill of gunpowder recipes); but for someone who knows or was taught it, it is a matter of reciting from memory and making sure the ingredients available are up to snuff.
It would have a high penalty and a low difficulty (the system can handle penalties higher than difficulties after all).

Complex and hard things like "create a new computer chip design with 20% higher speed" would have both high penalty and high difficulty; featuring a requirement of a very large amount of background knowledge of chip design and the high likelyhood that unique challenges will occur.
So only the high skill characters can attempt it, and even they will take time.
God-like or fantastic feats probably fall under here, with ridiculously sky high difficulties.

And yeah, the difficulty ranges are just an example. The exact scale is an implementation detail.

XD Don't mind if I steal this right away!
EDIT: on second thought, I will actually have to think about how the penalty vs difficulty numbers are generated. It's not as simple as dropping it in.

erikun
2012-07-23, 07:25 PM
EDIT: on second thought, I will actually have to think about how the penalty vs difficulty numbers are generated. It's not as simple as dropping it in.
Indeed, it is not something to just drop in right away.

It is very similar to the old World of Darkness vs. new World of Darkness systems. In the old WoD, you rolled d10 dice pools and had a scaling difficulty, from 2 to 10, with rolls equal and above succeeding. In the new WoD, it is the same, but all difficulties were set at 8. (Increased penalities just took away dice from the pool.)

It seems like old WoD helps create more granularity and complexity, but it is somewhat questionable if it produced a better experience. A Game Master can easily look at the new WoD system and judge how difficult a task became after taking away dice, after all, and do so more reliably than the older system. It doesn't make the older system bad, of course, just that the added complexity may not have added enough to the system to warrant its use.

The scaling penality idea is pretty much the same thing: an added dynamic, but one that adds complexity to the system. It may need some thinking (perhaps playtesting) before determining if the extra complexity is worth adding.

Jay R
2012-07-26, 10:34 AM
There are two issues involved in any game mechanic.

1. Does it model behavior the way you intend it to?

2. Is it too complex for the people you are playing with?

(At one of the best lectures on mathematical modeling I've ever attended, the lecturer said, "The model is supposed to be less complex than reality, or it's useless as a model. If we wanted to observe reality, we'd observe reality.")

For question one, it appears to treat difficult tasks and easy tasks as you intend. The next test is to try using it with various moderate levels of tasks, and see if the probability for them makes sense.

For question two, the sense of this forum is that, for some people on this forum, it's too complex, and would get in the way of the game. Unless they are in your game, that's not a problem. But it does show that you need to consider the issue. (I'd have no problem using it at my current table, but then, we all enjoy Champions. Basic math skills aren't at issue.)

I recommend that you try it at your table. Within half an hour, you will know whether it's usable as is. You might want to set up a table so you can look up the roll for a given skill level and difficulty level.