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

[Stalker0]

I thought the use of secondary skills and aid-another was explained well in the DMG, and expected. I don't see how you can hand-waive them if you are going to crunch the numbers.

They explain aid another in one section, but don't go into with their skill challenges sections. Even in their example they don't use aid another, so I'm not sure when you are supposed to add it in.

Further, aid another becomes extremely easy in short order. For example, by level 4 most characters can autopass aid another rolls in their good skills, heck some character can do it at level 1. In such a case, the lead guys gets a +8 bonus, which then makes the skill challenge extremely easy, and boring as the rest of players just aid. If that's how WOTC intending skill challenges to be done then my numbers would need to be fixed, and I would say that skill challenges are too easy

As for secondary skills, many challenges don't have them, or have a combination of hard and easy skills. But I think your right that it would be good to see how those easy DCs affect things, I will run some more numbers and get back to you with them. Probably won't be today though

 

[Storminator]

You have to remember that I am looking at a non-conditional model. In your example, 4 successes and 0 failures mean that the players roll 4 die and then stop immediately, just as if they roll 2 failures out of the box they would stop. In my model, you are always rolling 5 rolls, and seeing how many of them are successes.

Both conditional and non-conditional models work for this...but the math is VERY different. You cannot place ANY conditional modifiers into a non-conditional equation. That is why I have 5 successes and 0 failures.

I forgot you also had SSSSF, which, when coupled with SSSSS, covers all possibilities of the 5th roll.

I didn't take into account easy checks because the default skill challenges don't use them, they are all medium.

That's not exactly what it says. It says to use moderate as a starting point, but point taken.

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.

In addition to the group check, the multiple players section talks about cooperating to help other players make checks. Sounds like aid other to me.

The samples also include easy checks that don't do anything but add a modifier to other checks. There's also advice about giving out +2 for good ideas.

:shrug:

PS

 

[Tervin]

Your post made me look closer at skill challenges, and regrettably you are right. As written they are a great idea that falls apart because of bad math. One simple house rule would be to allow taking 10 even though that is normally not allowed inside an encounter. That would take away some of the fun of the whole thing though.

I like that you added bells and whistels to your system, but I don't think I will want those added features from the start. They can be something to add for players who like skill challenges and want to have more things to do in them.

The rules as written have two big weaknesses:
1. Skill challenges are unnecessarily hard, punishing suboptimal party builds even more than battles do.
2. The system for complexity is useless, as more complex challenges are easier than less complex ones if difficulties are set as easy, while more complex ones are harder than the less complex ones if the difficulties are set really high. Giving more XP for more complex challenges makes sense as they involve more roleplaying, on the other hand it has nothing to do with difficulty.

I will have a closer look at your alternative system, but before going there I want to try a simple method: Being generous with RP bonus to skill rolls during challenges. If the players are reasonably imaginative in how they RP their skill uses I will give them +2-4 to rolls, which should make it possible to actually succeed (as long as they use "aid another" cleverly). This way they also have to work harder in a complex skill challenge, and thus deserve their XP.

 

[Kaodi]

When I run the numbers, I get ~0.297 for Complexity 1 with 55% Success, and ~0.195 for Complexity 5.

 

[Cadfan]

Does this math match up with anyone's play experiences? I have trouble believing that playtesters worked at this game for as long as they did without ever noticing that their party fails 80% of all skill challenges. Perhaps some factor is being omitted?

 

[nittanytbone]

It seems to me that for skill challenge design, the DM needs to be sure to include some Easy tasks, or tasks that provide bonuses to others.

For example, a successful Perception check (Easy) might grant a +2 non-stacking bonus to the all future Thievery checks until the end of the challenge.

Additionally, I think the designers deliberately low-balled things and made the skill challenge system HARD under normal circumstances. This allows the DM to hand out +2 bonuses for good ideas like candy and accounts for the players picking up magic items with significant skill bonuses without anything breaking.

+9 is perhaps a "most likely," but +5 trained +4 attribute +2 racial + 3 skill focus is not out of the question, for a total +14 mod. Throwing in a +2 circumstance modifier and a magic item jacks it up even higher. Now that players realize that skills -- not just combat mojo -- matter I think we'll see more folks investing in those feats.

 

[ondali]

In order for a character to make a skill challenge with a 50% chance, its needs to have a 65% chance for each roll.
this corresponds to the fact that you need twice as many success as failures. if you would need 3 times as many success as failures you would need to have a 75% chance of success for each roll to have a 50% chance of making the challenge

Storminator was right in that there are only 2 scenario's that enable a single character to win it, 4 times succes in 4 or rolls or 1 failure in 5 rolls.

The result changes 25.08% to 29,65%.
This doesn't change the fact that I agree with the basic conclusion that a medium skill challenge for a single character are way too difficult.

warning: heavy math

You've got the basic idea of combinations and you are right that C(17 rolls, 12 desired) = 6188
but the calculation should be the sum of
C(17 rolls, 12 desired) = 6188 *.55^12 *.45^5 = 0,087491
C(16 rolls, 12 desired) = 1820 *.55^12 *.45^4 = 0,057184
C(15 rolls, 12 desired) = 455 *.55^12 *.45^3 = 0,031769
C(14 rolls, 12 desired) = 91 *.55^12 *.45^2 = 0,014119
C(13 rolls, 12 desired) = 13 * .55^12 *.45^1 = 0,004482
C(12 rolls, 12 desired) = 1 * .55^12 = 0,000345​

which sums up to results in 19,53% chance of making that challenge
still not really feasible although 5% higher than you're calculations.

The idea of skill challenges works nicely as i've seen it for example in th closing the rift for Kots, where you add some singular easy rolls for a made difficult roll. this gives perfect roleplaying parts.
http://www.wizards.com/default.asp?x=dnd/4dnd/20080522b

 

[Tervin]

When I run the numbers, I get ~0.297 for Complexity 1 with 55% Success, and ~0.195 for Complexity 5.

Being a maths teacher I trust my numbers

Complexity 1: 0.256
Complexity 5: 0.147

(Both numbers approximate of course.)

 

[Tervin]

In order for a character to make a skill challenge with a 50% chance, its needs to have a 65% chance for each roll.
this corresponds to the fact that you need twice as many success as failures. if you would need 3 times as many success as failures you would need to have a 75% chance of success for each roll to have a 50% chance of making the challenge

Storminator was right in that there are only 2 scenario's that enable a single character to win it, 4 times succes in 4 or rolls or 1 failure in 5 rolls.

The result changes 25.08% to 29,65%.
This doesn't change the fact that I agree with the basic conclusion that a medium skill challenge for a single character are way too difficult.

warning: heavy math

You've got the basic idea of combinations and you are right that C(17 rolls, 12 desired) = 6188
but the calculation should be the sum of
C(17 rolls, 12 desired) = 6188 *.55^12 *.45^5 = 0,087491
C(16 rolls, 12 desired) = 1820 *.55^12 *.45^4 = 0,057184
C(15 rolls, 12 desired) = 455 *.55^12 *.45^3 = 0,031769
C(14 rolls, 12 desired) = 91 *.55^12 *.45^2 = 0,014119
C(13 rolls, 12 desired) = 13 * .55^12 *.45^1 = 0,004482
C(12 rolls, 12 desired) = 1 * .55^12 = 0,000345​

Sorry, bad math. This way you will count several cases several times. You have to do all 17 rolls for every case to avoid that. (Same thing for the complexity 1 case.)

Edit: Trying to explain why... Your calculations never take into account that the failed rolls in the calculated cases could take place after we had got the 12 needed successes. That is why you end up counting several cases several times.

Also, it is not enough to get twice as many successes as failures. You need more than that. Just barely more than that, but still more than that...

 

[FadedC]

Where are you getting the extra +5 to the DC from? Reading the DMG it just says to use the difficulty by level table, and that's only 15 at level 1 for a medium challenge. I'm assuming I must be missing something but I can't see anything about a +5.