Partial Success Probabilities [pt. 3]

So let’s talk about the internals of Partial Successes. To keep it simple, we’ll assume that the Challenge Rating (CR) is equal to the Skill Rating (SR), and that any second Challenges are made with the same skill against the same CR. (An assumption that doesn’t usually hold true, but which simplifies the math no end.)

Against an equal CR, the math breaks down as follows:

Result % Chance (Exact Result)
Failure 45%
0 SR, Partial Success 27%
1 SR, Success 18%
2 SR, Solid Success 9%
3 SR, Spectacular Success 1%

What the table is saying is that, if you only rolled once, you have an 18% chance of getting a Success (or 1 SR). Roughly 1 time out of 5, you just succeed. And 1 out of 100 times, you Succeed so well, people are impressed.

Which makes sense. When attempting a challenging task, we often fail. Sometimes we do spectacularly well, sometimes middling, and sometimes we only succeed by doing more work than other people. This my not be an exact match for the real world, but it is true-to-life: it matches what we experience in day-to-day life.

(And yes, the mechanics should match what we experience in day-to-day life, or should allow players to vicariously experience things they have no direct experience of, like fighting a grim, to-the-death sword duel or gun battle. “True-to-life” is my design goal.)

But there’s more, and describing it is a little complicated. (The mechanics are simple, it’s just the description that’s complicated.) A Partial Success (0 SR) happens 27% of the time. Getting 0 SR means you have to attempt another Challenge (or just take a Failure).

On that second roll, you can Fail or get 1 SR or higher. (Because, if you roll another Partial Success, it counts as a Success.) So, when everything is taken into account, that 27% gets divided up and distributed among the other results. That looks like the following:

Result % Chance (w/ 2nd roll)
Failure 57%
0 SR, Partial Success 0%
1 SR, Success 30%
2 SR, Solid Success 11%
3 SR, Spectacular Success 1.2%

So your chance of just Failing, giving the above assumptions, is 57%. Success is a 30%, and so forth. (The numbers in the chart are rounded off, which is why they don’t equal 100%.)

To some people, the 57% figure may seem high. It really isn’t, in two ways. First, it’s lower than the comparable number under the 5-count system (which was 60%).

Second, making a Declaration (a short in-character description of what you’re attempting) gives a +1 to the roll, which makes that Failure rate 46%. (Yes, when SR = CR, a +1 is a huge difference.) Spending a point of Resolve with that Declaration makes an even bigger difference (36% Failure), and having an applicable Distinction is even more influential (18%).

I’ve calculated the odds from SR = CR-9 (SR 10, CR 19) to SR = CR+8 (SR 10, CR 2), including how Declarations, Resolve, and Distinctions all affect the odds. Looking at the statistics, the model seems to hold up well.

It gives results that are true-to-life, while also being quite gameable. And since the mechanics themselves are very simple, all these probabilities are transparent to the end user.

It seems solid. At least, solid enough to take to testing.

Partial Success, In-Character [pt. 2]

Skill Challenges are fairly simple, the basics being explained here. Negative results are failures, 0 SR is a Partial Success, and so forth.

A Partial Success is an odd duck. It’s neither a Success or Failure you have to try again in order to succeed (sometimes with the same skill, sometimes with a different skill).

In-character, this represents a decision point: do you want to try again, or do you accept the Failure? (Not attempting the 2nd Challenge on a Partial Success means it’s a Failure.) Let’s translate that to real world terms.

A writer is penning an opinion column (using his artist skill, with a writing Specialization). If he does poorly, that’s a Failure. If he does well, that’s some level of Success. If he does middling, that’s a Partial Success: it’s a muddled, mediocre column that can be salvaged, but only if he puts some more effort in.

Maybe it needs rewriting (another artist Challenge) or maybe some more research (using the appropriate skill). Whatever he does, he needs more effort to succeed.

This “more effort” is represented by a second Skill Challenge. Another Partial Success is counted as 1 SR: he put in twice the work, but still succeeded. (Failure on the second Challenge is still Failure; 1 SR or higher is that level of Success.)

Is this true-to-life? Of course. All of us have worked on specific tasks, where we just didn’t do as well as we’d hoped, and had to invest some more time or effort to make it work (and sometimes, it didn’t). Happens all the time.

That’s why this rule is a core part of Skill Challenges: it’s true-to-life, it makes the fictional world of the game (which runs off the game mechanics) feel more like reality.

With some noodling, you can see why I started this series off with a discussion of probability: with Partial Success, there’s a second roll involved, so we have to do some probability multiplication to figure out the overall chance of success. I’ll talk about those internals, next post.

The Long-Promised Skill Post, pt. 1: Probabilities

I’ve wanted to talk about some of the gritty details, with respect to skills, probability, and verisimilitude. Let’s start with probabilities.

Probability

When you flip a coin, you have a 50% chance of getting heads or tails*. Mathematically, “50%” is represented as “.5”.

Suppose we flip the coin twice: what’s the chances of getting two heads in a row? That’s actually pretty simple to calculate: we multiply .5 by .5, to get .25 (which is 25%). With two events, you multiply the odds of the first by the odds of the second to get a composite chance.

Let’s apply that to d10’s. The chance of rolling a 0 is 1 out of 10, which is 10%, or .1. The chance of rolling a second 0 is . 1 x .1, which is .01 or 1%. And, indeed, “00” is a 1% chance on d%.

I started with this, because probabilities are tricky little buggers, and I wanted people to know I did all the calculations right. (Technically, I set up all the formulas right, my spreadsheet program did all the calculations.) The following discussion depends on the above calculation of probabilities.

(*In a statistically ideal universe. In ours, the side that’s face-up when you flip has a greater probability of occurring.)

The Genius of Gygax?

The hottest movement in RPG’s right now is “OSR”, which stands for Old School Roleplaying. OSR adherents mix and remix pre-1986 (A)D&D (in all its many variants), sometimes in new genres, sometimes in new settings, sometimes in old settings updated and revamped.

OSR adherents often, and loudly trumpet the virtues of Gygax. (Which, given their focus, you’d expect.) My opinion on the subject can best be illustrated by this quote from the AD&D 1e DMG.

Routines

When one or more creatures involved in combat are permitted to use their attack routines twice or more often during the round, then the following initiative determinants are employed. When the attack routine may be used twice, then allow the side with this advantage to attack FIRST and LAST with those members of its group who have this advantage. If it is possessed by both parties, the initiative roll determines which group strikes FIRST and THIRD, which group strikes SECOND and LAST. If one or both groups have members allowed only one attack routine, it will always fall in the middle of the other attacks, the order determined by dicing for initiative, when necessary. If one party has the ability to employ its attack routines thrice, then the other party dices for initiative to see if it, or the multi-routine group, strikes first in the mid-point of the round. Extrapolate for routines which occur four or more times in a round by following the method above. Note that a routine is the attack or attacks usual to the creature concerned, i.e. a weapon (or weapons) for a character, a claw/claw/bite routine for a bear (with incidental; damage assessed as it occurs – the hug, for example). A 12th level fighter is allowed attack routines twice in every odd numbered melee round, for example, and this moves up to three per round if a haste spell is cast upon the fighter. Damage from successful attacks is assessed when the “to hit” score is made and damage determined, the creature so taking damage having to survive it in order to follow its attack routine.

– AD&D DMG, pgs. 62-63 – Initiative For Creatures With Multiple Attack

Here’s my problem: it isn’t that this is bad game design. (Although it is.) It’s that it’s bad writing. It’s dense, convoluted, and overwritten. It’s the antithesis of my ideal prose.

Reading this, I cringed. If playing AD&D the right way means reading and parsing junk like this, then it’s no wonder I left the game a long time ago.

I know how hard it is to phrase something clearly, even when you understand your own ideas fairly well. And I’m not saying Gygax was a bad game designer, or that he should be scorned or insulted. He was a pioneer.

But the man. Could. Not. Write. Not well and not clearly.

The best writing should aspire to be transparent, so the language is nothing more than a medium to convey the words. Convoluted or overly flowery language that draws attention  to itself is bad writing. (It’s a result of a writer who wants to boast more than he wants to inform.) And language that throws up a barrier between the reader and the ideas is just sub-par.

Whatever his other virtues, I couldn’t ever fully appreciate AD&D now, despite the fact I cut my teeth on the game. And Gygax’s prose is to blame.