D&D 4E Showing the Math: Proving that 4e’s Skill Challenge system is broken (math heavy)

Spatula · Jun 9, 2008

I think what you're seeing in the higher-level DCs being "easier" is the increasing gap between Trained+Prime Score and Trained+Dump Stat and Untrained as the characters level up.

A fighter who is trained in Athletics is going to start with a good bonus because he needs a good strength score. And it will improve at a rate faster than +1/2 lvl because the fighter is improving his strength as he levels up. A +9 bonus at level 1 might be a +28 bonus at level 30.

That same fighter can be trained in Intimidate, probably starting with a middling bonus because he has no particular use for charisma outside of that one skill. But his charisma barely improves with levels (+1 at 11th and 21st lvls). A +6 bonus at level 1 would be a +22 bonus at level 30, and even that is somewhat generous in assuming an above-average stat allocation.

Untrained skills will vary between +23 (better than trained+dump stat) and +15 at level 30. So the DCs have to have more slack built into them to account for non-prime skill uses.

FireLance said:
The math behind skill challenges bothered me too. Then, I looked at the higher-level DCs and noticed something interesting (numbers from pg 42 of the DMG):

For levels 1-3, a moderate check was DC 15 (DC 20 for a moderate skill check).

For levels 28-30, a moderate check was DC 29 (DC 34 for a moderate skill check)

A 30th level character would have a +15 for level, say a +6 from ability scores, a +5 for skill training, and an unknown amount from magic (I haven't digested all the powers and magic items yet), for a total of +26. A trained character would thus succeed 65% or more of the time on an individual skill check, making it more likely that he can overcome a skill challenge without assistance.

So, the skill challenge system for 4e seems to require characters to work together (using Aid Another) to have a decent chance of overcoming the skill challenges at low levels, while allowing them to function more independently at higher levels.

So, what do you think: bug or feature?

Eldorian · Jun 9, 2008

Very interesting read. Apparently no one at WotC knows what a binomial random variable is. It's obvious from first glance that a none of the standard challenges have better than 50% win rate, cause the mean for a binomial random variable is so easy to compute. If average rolls don't win, it probably isn't a good system.

FireLance · Jun 9, 2008

Eldorian said:
Very interesting read. Apparently no one at WotC knows what a binomial random variable is. It's obvious from first glance that a none of the standard challenges have better than 50% win rate, cause the mean for a binomial random variable is so easy to compute. If average rolls don't win, it probably isn't a good system.

What I find truly odd is that the high failure rate wasn't picked up in playtests. Unless, of course, the way to win at skill challenges really is to make full use of the Aid Another action at low levels.

Eldorian · Jun 9, 2008

FireLance said:
What I find truly odd is that the high failure rate wasn't picked up in playtests. Unless, of course, the way to win at skill challenges really is to make full use of the Aid Another action at low levels.

The only thing that would explain this to me is that in the playtests they weren't adding +5 to the DCs. If you lower all DCs in a skill challenge where you cannot aid another by 5, then you get average rolls give success. (+9 at first level, so 75% chance of success on a DC 15). Mean number of successes on 6 rolls is then 4, the number required to win. Not entirely accurate math here (as in the OP, only 5 rolls are necessary to consider), but better than default.

Keep on the Shadowfell spoilers:

Reading the keep on the Shadowfell skill challenge tho, yes, that thing is nearly impossible to win, obviously. The Eladrin wizard I made for a game yesterday had only a +11 to arcana, and I thought that was crazy good for first level. He'd stop attempting the skill challenge the first failure he got and the stupid thing attacks him.

rabindranath72 · Jun 9, 2008

Eldorian said:
Very interesting read. Apparently no one at WotC knows what a binomial random variable is. It's obvious from first glance that a none of the standard challenges have better than 50% win rate, cause the mean for a binomial random variable is so easy to compute. If average rolls don't win, it probably isn't a good system.

It is not a binomial random variable. It is a negative binomial (or Pascal) variable, which explicitly addresses the calculation of the probability distribution of the number of successes before a given number of failures with basic probability of success p.
I suggest the Original Poster to redo his calculations according to this model.

Plane Sailing · Jun 9, 2008

rabindranath72 said:
It is not a binomial random variable. It is a negative binomial (or Pascal) variable, which explicitly addresses the calculation of the probability distribution of the number of successes before a given number of failures with basic probability of success p.
I suggest the Original Poster to redo his calculations according to this model.

Since you apparently have familiarity with it, would you like to take a crack at doing so?

Plane Sailing · Jun 9, 2008

FireLance said:
What I find truly odd is that the high failure rate wasn't picked up in playtests. Unless, of course, the way to win at skill challenges really is to make full use of the Aid Another action at low levels.

Although playtesters remain gagged, I get the impression that a large swathe of playtesters were only given very limited subsections of the rules to work with - perhaps just single scenarios - so it may be that most playtesters weren't in a position to actually check this out in depth.

(That strikes me as a bit of a silly way to run a playtest, because your testers are unlikely to unearth real bugs... this skill challenge issue may be a case in point)

Cheers

Dyrvom · Jun 9, 2008

Stalker0 said:
Aid Another does exist in a limited form. If its supposed to be the standard in skill challenges, its not explained correctly. If for example, a group of 5 players can have 1 person make rolls, and the other four provide +8 bonuses (which is the example given), then the skill challenge is so easy you might as well not even bother.

The inclusion of a time limit in the vast majority of skill challenges seems like a fundamental of the new system to me. This means aid other would only be used extensively in a crucial climax to a skill challenge, and otherwise would be used sparingly.

Eldorian · Jun 9, 2008

rabindranath72 said:
It is not a binomial random variable. It is a negative binomial (or Pascal) variable, which explicitly addresses the calculation of the probability distribution of the number of successes before a given number of failures with basic probability of success p.
I suggest the Original Poster to redo his calculations according to this model.

Dude, I just taught a course on this stuff last semester. You can perfectly model this situation with a binomial random variable exactly as he did. Roll 5 dice at once and see if you get 4 or 5 successes is type 1. If you were to make a tree diagram and continue branches where the experiment technically stops, you'll notice that only the first 5 twigs matter.

edit: LOL. I had no idea what a Pascal variable is, so I wiki'd it. No wonder I didn't know. It's a simple subcase of a binomial.