Skill Challenges: bad odds

[themagister]

Skill Challenges in 4e can be modeled using the negative binomial distributions, as others have commented. I was curious what the odds of overall success was at the various Complexities, and I had a sneaking suspicion the d20 roll was too important.

We define a function, f, that is the probability of achieving a number of successes, S, before achieving a number of failures, F, given that each independent skill check has a probabilty of success, p(S). The overall probability of success is the sum of f where F=0, 1, 2:

sumf = negativebionomialdist( S, F=0, p(S) ) +
negativebionomialdist( S, F=1, p(S) ) +
negativebionomialdist( S, F=2, p(S) )

I won't go into the derivation, but this is equivalent to:

sumf = 1 - cumulative_bionomialdist( S-1, (F-1) + S, p(S) ) where F=3

We can then generate a chart showing the overall odds of success by the Complexity (columns) and dice roll needed to succeed (rows). By the last term, I mean after the Trained, etc, modifiers are applied, there is a certain number you have to "hit" on a d20 to succeed. Often, this will be 10 (moderate DC's) minus Trained, Attribute, cooperation, etc. bonuses.

The chart is available as an attachment (JPG). How to make nice tables in this BB system is beyond me. You can also download a tool to make these calculations yourself (XLS).

We can see that for a Complexity 1 (third column), if a "5" is needed for all of the skill checks, there's a 90% chance that the party will succeed at the Skill Challenge. In contrast, for a Complexity 5 (last column), a "5" translates to overall odds of 45%. What's happening? Well, as the Complexity rises, the total number of die rolls go up. This increases the chances that three of them will be failures.

I interpret this to mean that, for a Complexity 5 encounter, if the characters have to regularly roll higher than "3", there's fair to good odds they won't succeed. It's dramatic how fast the party's chances drop, and it has everything to do with the number of skill checks.

Comments please, but let me anticipate a few questions:

1) "But, each skill check failed or succeed changes the outcome!" No, the checks are independent. Cooperative checks, where characters help out other characters don't contribute to successes or failures. These are just bonuses to the "important" checks.

2) "But, I think your math is wrong!" That's nice--prove it. Take a look at binomial distribution functions and Bernoulli trials, and come back to me with something substantial. You might be right, but I'm going to need to see your work.

3) "But, my <insert homegrown system name> fixes all this!" Great, but that's off-topic. Let's establish what the issues are and really understand them before attempting a fix.

4) "But, the Skill Challenge system is bogus for other reasons!" Maybe, sure, but that's off topic.

5) "But, that's another reason why Fourth Edition is so bad!" Super, great. Take it to another thread.

 

[Victim]

With the errata on skill DCs, I'd think that most characters would succeed on more than a 10.

 

[Shadewyn]

Not even close.

This is where theorycraft fails in play.

As soon as you allow in "aids another", Utility powers for rerolls and +skill improvements, recommened +2 situational mods the players pretty much CRUSH all skill challenges as written.

Assumptions of players as individuals without any gaming context is the math you presented.

The reality is that players will be together as a team and that coordinated groups find the skill challenges (H1, H2, supplements from Dragon / Dungeon etc ... ) pretty much auto win cakewalks.

They are still a useful GM tool to provide flavor and an opportunity for RP development outside combat. Challenge though is not the word I would use for them. The most "dangerous" one so far as written into H2 near the end would barely hurt the parties power even on failure.

I still love to use them though as written as the party scrambles togthere to help each other out which just emphasises the team aspect of the game and that makes for a better long term game group in my mind.

 

[Nail]

Thanks, themagister. This is helpful. (bookmarked)

As I've used Skill Challenges in play, there are always several "+2s" floating around. It's nice to see how that change will affect the P(success).

 

[DM_Blake]

Not even close.

This is where theorycraft fails in play.

As soon as you allow in "aids another", Utility powers for rerolls and +skill improvements, recommened +2 situational mods the players pretty much CRUSH all skill challenges as written.

Assumptions of players as individuals without any gaming context is the math you presented.

The reality is that players will be together as a team and that coordinated groups find the skill challenges (H1, H2, supplements from Dragon / Dungeon etc ... ) pretty much auto win cakewalks.

They are still a useful GM tool to provide flavor and an opportunity for RP development outside combat. Challenge though is not the word I would use for them. The most "dangerous" one so far as written into H2 near the end would barely hurt the parties power even on failure.

I still love to use them though as written as the party scrambles togthere to help each other out which just emphasises the team aspect of the game and that makes for a better long term game group in my mind.

So what you're saying boils down to skill challenges just being flavorful free XP for the PC group?

Yikes!

Shouldn't they be at least a little challenging?

If I recall, the original early info on skill challenges, long before the books were released, said the concept was to get everyone involved. I seem to remember remarks about eliminating the concept of the party standing around, waiting for the rogue to pick a lock or ranger to find the needle in a haystack. I seem to recall comments about enhancing the contribution of the other player characters beyond simply aiding another.

With all that, I'm very disappointed that aiding another is even allowed in skill challenges.

Heck, in many situations, aiding another seems to be outright impossible. In others, the leaps of logic people use to justify their aid seem more like fast-talk and thinly veiled rationalizaitions for manipulating the rules.

Seems to me that Skill Challenges would be a whole lot more challenging if aiding another were off the table completely.

At the very least, restricted to where the person aiding must be within a few skill points (with the same skill) of the person performing the task - no chance for a skill 10 PC to aid a Skill 15 PC to finish a task - just how much help can an amateur give to an expert, anyway?

I think one of the big problems balancing the math of Skill Challenges is that when the numbers are balanced assuming 3 or 4 Aid-Another bonuses on EVERY roll, then any group not doing this is clobbered by every skill challenge they attempt. And when the math is balanced assuming no Aid-Another bonuses, or at least rare Aid-Another bonuses, then any group where the players are gung ho about aiding each other will breeze through all their skil challenges.

Having a hard-coded, set-in-stone rule stating either "Aid Another cannot be used during skill challenges" or "When each person attemps his skill roll, he must first consult every other PC and get their Aid Another results before attemping his roll - failure to do so will result in having nearly zero chance of successfully resolving the skill challenge."

One or the other.

It should not be casually mentioned in the rules that skill challenges can be enhanced by using Aid Another if you so desire. This leaves it up to the players, and the mathematical imbalance cannot be resolved across the board this way.

 

[Jhaelen]

I think you are a bit late to the game. Here is the previous discussion about the skill challenge math after the errata.

Maybe you'll want to continue the discussion there.

 

[themagister]

With the errata on skill DCs, I'd think that most characters would succeed on more than a 10.

Yes, that's correct. The problem that I point out is that the results are binary for the high Complexity Challenges. Note the last column: the players will either walk all over it or be deafeated... but the difference between the two, in terms of target number on a d20, is razor-thin.

 

[themagister]

Not even close.

This is where theorycraft fails in play.

As soon as you allow in "aids another", Utility powers for rerolls and +skill improvements, recommened +2 situational mods the players pretty much CRUSH all skill challenges as written.

Assumptions of players as individuals without any gaming context is the math you presented.

The reality is that players will be together as a team and that coordinated groups find the skill challenges (H1, H2, supplements from Dragon / Dungeon etc ... ) pretty much auto win cakewalks.

They are still a useful GM tool to provide flavor and an opportunity for RP development outside combat. Challenge though is not the word I would use for them. The most "dangerous" one so far as written into H2 near the end would barely hurt the parties power even on failure.

I still love to use them though as written as the party scrambles togthere to help each other out which just emphasises the team aspect of the game and that makes for a better long term game group in my mind.

I'm in agreement on one point "Challenge though is not the word I would use for them." As of now, it's difficult to construct a challenge that has any element of chance (translated --> risk) associated with it.

The only guidance I can offer is that you can shoot for a particular target number on a d20 to introduce an element of risk.

Complexity 5 -> "4" (65% probability of overall success)
Complexity 4 -> "5" (56% probability of overall success)
Complexity 3 -> "5" (68% probability of overall success)
Complexity 2 -> "6" (68% probability of overall success)
Complexity 1 -> "7" (74% probability of overall success)

We can assume Trained (+5), Attribute (+2-4), Situation (+2), that's a total of +9-11. So, a mixture of Moderate and Hard DC's should work out.

But, we digress: let's learn about the problem first, then look to solutions.

Again, I need to reiterate my argument. High Complexity Challenges are flawed because of the "binary" nature of their construction.

 

[themagister]

I think you are a bit late to the game. Here is the previous discussion about the skill challenge math after the errata.

Maybe you'll want to continue the discussion there.

Bomb! Thanks very much.

 

[Shadewyn]

The key issue with skill challenges is the nature of the penalty.

Fail in combat? Die ...
Fail in a negotiation? At worst maybe a combat or lack of help

That is not to say that XP should not be given for these, as they provide wonderful opportunities to RP, develop teamwork, further plots, and porvide atmosphere.

Its just not what the "INFINITE OREGANO" crowd makes them out to be where some cataclysmic result awaits you based on guesstimate of binomials.

In general you since the THREAT of the encounter is complete weak suace in most of the WotC published stuff you may want to chop the XP in half or to a quarter.

Take for example H2 in the Vecna test. Complete utter abyssmal failure of a high end challnege rating "damages" the players by removing healing surges and then opens the door. Success is opening the door.

As some players will tell you who cares ... the door is opened and if they had just come off a long rest then the loss of a couple surges is meaningless as its a solo battle where they can rest again afterwards.

If the party is extreme and reckless maaaaaybe they might get in trouble without those surges in the follow up combat. But is it the same danger as a combat challenge of tht level ... ooooohhhh not even close.


Would I remove it though? Nope ... adds to much goodness and flavor.

To make the challenges more "scary", you need to up the DC and then put in scaling sucesses based on how many wins you get before you loose.