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

[FireLance]

I wonder how ppl's opinions would change if the idea was not that if you failed the skill challenge, you got a penalty, but if you won the challenge, you got a bonus...?

I don't knoow about other people, but I think an 80% chance of getting a penalty is still a bad idea. Most people just don't like "losing" or being "penalized". Theoretically, a game in which you had an 80% chance of losing $1 and a 20% chance of winning $10 has the same expected payoff as a game in which you have an 80% chance of gaining (and losing) nothing, and a 20% chance of winning $6, but most people would prefer to play the second game than the first.

My general rule of thumb when setting challenges is that average characters with average tactics should succeed 50% of the time. The idea that you need optimized characters or brilliant tactics just to get a 50% chance of success rubs me the wrong way.

 

[WhatGravitas]

Hrm. I guess it's time to focus on increasing the probabilities.

Yeah, it is. Using the MathWorld website, I looked into the plots... an well, look here (just click evaluate) - on the y-axis is the probability to fail the entire challenge, whereas on the x-axis is the chance to fail a single skill check:

Complexity 1
Complexity 2
Complexity 3
Complexity 4
Complexity 5

These plots show that there is some "tipping point" and that the chance for total failure or success get more and more pronounced. Furthermore, if you look at it (just cursory glancing, not in-depth number crunching - but that's what plots are for, no?), you see that a failure chance of about 0.3 (+/- 0.05) (on a single check) gives you a good chance to win (i.e. ~0.4 failure chance) across all complexities.

Hence the target region is that your skills must succeed on a 6 - 8, then the skill challenges work well.

However, this, of course, doesn't accounts for the interplay of hard and easy checks - that can skew a lot.

Cheers, LT.

 

[Wulf Ratbane]

I wonder how ppl's opinions would change if the idea was not that if you failed the skill challenge, you got a penalty, but if you won the challenge, you got a bonus...?

That's probably a good start. It would help, but it would still be a bit broken.

If a "typical" challenge has about a 20% success rate, then a 20% chance for a bennie and an 80% chance for bupkiss seems ok.

But that still doesn't address the flip-flop problem as both skill bonuses and complexity increase. What seemed reasonable at 1st level (a small chance for a bonus) risks becoming a "freebie."

I just don't see any charitable way to spin the RAW design as "working as intended."

I do honestly want to be wrong and would welcome some WotC input.

 

[Tervin]

I wonder how ppl's opinions would change if the idea was not that if you failed the skill challenge, you got a penalty, but if you won the challenge, you got a bonus...?

Interesting point, but there is always this...

In the DMG, p121, it is explained how to reward XP for non combat enounters. Two cases are given, skill challenges and puzzles. Much as I love puzzle solving I would not call it roleplaying. Skill challenges on the other hand can be used for a whole lot of different RP scenes, which means that they become a way for me to give out XP to players for roleplaying - something that D&D has in the past been really bad at.

The problem is that the instruction to the DM is to give out XP equal to "a monster of the challenge level" * "complexity level". And only give it out on success.

So, if succeeding in a skill challenge is a "bonus", then such bonuses are meant to be the only way to get XP awards from roleplaying scenes. And that is just not something I feel that happy about.

 

[Ulthwithian]

2) Even assuming that the typical character can achieve better-than-average bonuses on typical skill checks, why does the system hand out more XP for a "challenge" that actually becomes less challenging as complexity increases?

That makes an assumption that I do not think is valid. Specifically, they assume a balance point for WotC that may not be correct. From my simulation, it seems that the 'balance point' for a level 1 skill challenge is needing a roll of 8. You have a 0.43-0.42 probability of succeeding at the challenge with complexities 1-5. If the number you need to roll is higher, you are better off with less complex tasks. If the number you need to roll is lower, the reverse is true.

If you assume that moderate difficulty is DC15 and not 20, then having an average party bonus of +7 (which is not difficult to do in the least) would even out the chances. I plan on expanding my program to take different characters into account soon.

I look at the value chart, and see something rather different. I see a system that has a balance point (though not where we expected it), and some sort of damping around that point.

I have a Dynamics test this afternoon. After that, I'll be looking at a more robust simulator.

 

[Uthred]

2) Even assuming that the typical character can achieve better-than-average bonuses on typical skill checks, why does the system hand out more XP for a "challenge" that actually becomes less challenging as complexity increases?

I remain unconvinced that this is actually a problem. As complexity increases so does the reward and the penalty for failure. Higher complexity tasks represent more dangerous tasks with higher chances of reward. If thats correct then why are people assuming that its an error not a design goal that more complex tasks are easier? The main goal of 4e appears to be "Fun" and its certainly not fun if your players cock up a complex skill test and get executed because they spat in the queens eye or some such.

If one removes the ambiguous +5 and agree's with this reasoning then the system works fine. Of course that would mean Wotc got it right, a thought which seemingly sears some posters like the heat of a thousand suns.

 

[abeattie]

Look at how much XP comes from difficulty, and how much from complexity, then you will see what I mean. A complexity 5 challenge is according to DMG p. 72-73 supposed to give 5 times the XP of a complexity 1 challenge of the same level. Increasing difficulty will instead add something like 25%.

Yes.

Like if I throw a single at-level mob at you vs. 5 at-level mobs.

The DMG makes this explicit on page 72 under Level and Complexity. Low complexity challenges take the place of a single mob, high-complexity challenges replace a whole enocounter. The difference is the significance -- presumably in both the price for failure and the reward for success.

I'm not going to go so far as to say this was explicity intended (though easily possible for a math geek to do) - but it is a happy accident that the more IMPORTANT success is, the more the deck is stacked in the PCs favor.

 

[two]

I remain unconvinced that this is actually a problem. As complexity increases so does the reward and the penalty for failure. Higher complexity tasks represent more dangerous tasks with higher chances of reward. If thats correct then why are people assuming that its an error not a design goal that more complex tasks are easier? The main goal of 4e appears to be "Fun" and its certainly not fun if your players cock up a complex skill test and get executed because they spat in the queens eye or some such.

If one removes the ambiguous +5 and agree's with this reasoning then the system works fine. Of course that would mean Wotc got it right, a thought which seemingly sears some posters like the heat of a thousand suns.

I'd like to point out that nobody is complaining about the initial "con value = hit points" change, or the flat HP values for each level thereafter, or a million other changes WOTC made to the game.

Either the people who hate WOTC are simply too tired to complain about everything, and have picked the skill challenge as their punching bag or... (could it be?)... the skill challenge actually might have some problems.

As you stated yourself. What's up with the "ambiguous +5"? And why is it ambiguous? Should we all drop it? Why should we have to figure this out for ourselves?

That's the reason for the discussion, not blind hatred. I think everyone here pretty much adores D&D.

 

[Wulf Ratbane]

I'm not going to go so far as to say this was explicity intended (though easily possible for a math geek to do) - but it is a happy accident that the more IMPORTANT success is, the more the deck is stacked in the PCs favor.

That may indeed be a good (and intended) way to look at it, but it only works if we accept all the assumptions that bring PC success into the realm of 70% or more (ie, optimization of powers, magic items, and less-than-gripping Aid Another actions).

If by "more IMPORTANT" you mean "higher complexity" then anything less than an optimal chance of skill success means that the deck is horribly stacked against the PCs.

It's that tipping-point thing.

 

[Uthred]

Complexitiy isn't difficulty, it's length.

DMG 4th edition, pg. 72, second column, fifth paragraph

"Level and complexity determine how hard the challenge is for your characters to overcome".

Considering complexity returns a greater reward than a difficulty increase (and further down that paragraph we see "Set the complexity based on how significant you want the encounter to be.") its clear that complexity is the main metric for difficulty in skill challenges.

That's the reason for the discussion, not blind hatred. I think everyone here pretty much adores D&D.

Apologies, it was meant to be a bit tongue in cheek but came across as overly snarky.