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The Math of Skill Challenges
2 years ago  ::  Jun 13, 2008 - 6:05PM #1
psuliin
Posts: 49
Date Joined: 08/27/07
I've been looking through the skill challenge rules, and I'm a bit concerned. For example, consider a challenge at complexity level 3, moderate difficulty, for 5th level characters. According to the tables on DMG pages 42 and 72, this means the PCs need to make 8 successes before they roll 4 failures against a DC of 17.

Now, 5th level characters can expect to have skill bonuses of +14 at best. That's for a character using a trained skill for which he gets a racial bonus (+2) with a relevant ability of 21 (18 rolled, +2 for race, +1 for the bonus at level 4). That gives them an 90% chance of success at a DC of 17. However that's for a highly min-maxed character. Most will be looking at skill bonuses in the range of +9 to +10 for trained skills and +4 to +5 for untrained skills. Those give chances of success of 60-65% at best against DC 17.

The problem is that you have to roll 8 successes before you roll 4 failures on a complexity 3 challenge. That means that you only need to roll 11 dice at most (and possibly only 4, if they're all failures) - if at least 8 of 11 rolls aren't successes then you fail the challenge. That isn't going to happen very often for characters with a 65% chance of success on any given skill check. In fact, most parties will fail on most skill challenges most of the time.

The only strategy that has a reasonable chance of success is to pick the most highly min-maxed character in a relevant skill and have that character make all the checks, while the other characters add bonuses with support rolls (using the rules on DMG 75). However any mechanic that offers one and only one reliable solution all the time is going to get old fast. And since skill challenges are almost the only credible non-combat mechanic in 4E, that looks like a fairly significant problem to me.
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2 years ago  ::  Jun 13, 2008 - 6:11PM #2
4venger
Posts: 200
Date Joined: 05/29/08
Is there a question tucked away in there somewhere?
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2 years ago  ::  Jun 13, 2008 - 6:18PM #3
psuliin
Posts: 49
Date Joined: 08/27/07
Sorry, I thought the questions were implicit if not explicit. As when most people point out possibly broken rules, I was asking the following questions:

1) Am I reading the math right?

2) Is there some way to fix this?

If the answers are 1) Yes and 2) No (or 2) Not without a lot of trouble), then I'm merely giving my fellow gamers a heads up about a broken rule, a whole week after they were first published.

How's that?
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2 years ago  ::  Jun 13, 2008 - 8:04PM #4
meshon
Posts: 254
Date Joined: 10/16/04
I was going to use KotS Area 8: Sir Keegan's Tomb as an example where several different skills can be used to gain successes and get all the characters involved, which seems like a good way to run these to me.

Then I noticed that particular skill challenge doesn't follow the rules. Four successes before four failures...
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2 years ago  ::  Jun 13, 2008 - 9:59PM #5
Kensan_Oni
Posts: 2,588
Date Joined: 10/11/05
Actually, you'll find that like me, the initial math is wrong, because it fails to add the +5 for skill checks, which makes your moderate check number a 22.

Part of me wonders when a 15 or better success chance before stats became a moderate challenge, and would have thought it would have been considered difficult, with expert or trained only being 20...

... The numbers just seem a tad bit off, and I'm thinking about dropping the difficulties by 2 just to tilt things towards characters not optimized.
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2 years ago  ::  Jun 13, 2008 - 10:05PM #6
Transformer
Posts: 266
Date Joined: 08/17/07
This has been discussed ad nauseum over at EN World, and a little bit on the Rules Q&A forum here. Short answers: yes the math is totally broken, no we don't have any clue how it got through WotC playtesting, and yes it can be fixed, but only with great difficulty. By far the best tested and most mathematically sound fix yet proposed can be found here.
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2 years ago  ::  Jun 13, 2008 - 11:33PM #7
psuliin
Posts: 49
Date Joined: 08/27/07

Transformer wrote:

This has been discussed ad nauseum over at EN World, and a little bit on the Rules Q&A forum here. Short answers: yes the math is totally broken, no we don't have any clue how it got through WotC playtesting, and yes it can be fixed, but only with great difficulty.


Indeed I did wonder how it could have gotten past playtesting, since I didn't even have to playtest it. Just looking at the numbers set off my flags. As a friend of mine wrote recently, "A complete overhaul of the mathematical base and 9 months of crowing about how they fixed it all up and apparently they didn't even *add and subtract.*"

By far the best tested and most mathematically sound fix yet proposed can be found here.


Thanks! It looks good, and I'll probably go with that version - if I decide to play 4E at all. I've already got misgivings about a lot of what I've read in the core books, and it seems that we've already had to patch a fairly major problem in the mechanic while the ink was just barely dry on the new edition. Quite honestly that doesn't give me much confidence in the design work that went into this new system, and it reinforces the impression of shoddy craft that I've gotten at several points in the rules so far.

Not criticising you at all, mind you - thanks for the helpful pointers. It just doesn't bode well, yanno?

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2 years ago  ::  Jun 14, 2008 - 10:50AM #8
Lukermon
Posts: 42
Date Joined: 08/21/09
I agree that at lower levels, it is much more difficult to beat a Skill Challenge that at higher levels. Complexity has little impact, except for at lower levels.

The practical suggestion for DMs is to manage the skill DCs based on how well your players are min/maxed. If you want them to get on with the show, go with easy DCs and circumstance bonuses. If you want the encounter to be a nail biter, go with moderate DCs with easy DCs if for the win. Hard DCs are for obscure uses of skills or the really far-fetched.

Not wanting to create the specific case math function for the higher complexity cases, I created an Excel sheet to simulate the success vs. failures in a Skill Challenge.

Hopefully, the math below helps DMs to weight their options and work with the system.

The simulation results below do not account for skill boosting magic items, but it does assume that the character is increasing the ability bonus by +1 per 8 levels.

Level, 1, 6, 11, 16, 21, 26, 30
Difficulty, easy, easy, easy, easy, easy, easy, easy
Skill Bonus, 7, 10, 13, 17, 19, 23, 25
DC, 15, 18, 22, 25, 27, 29, 30
4 before 2, 40%, 39%, 29%, 38%, 38%, 62%, 71%
6 before 4, 37%, 39%, 26%, 37%, 37%, 69%, 81%
12 before 6, 29%, 32%, 19%, 29%, 28%, 61%, 76%

Level, 1, 6, 11, 16, 21, 26, 30
Difficulty, mod, mod, mod, mod, mod, mod, mod
Skill Bonus, 7, 10, 13, 17, 19, 23, 25
DC, 20, 22, 26, 29, 31, 33, 34
4 before 2, 6%, 11%, 7%, 11%, 11%, 23%, 28%
6 before 4, 2%, 4%, 2%, 4%, 4%, 16%, 24%
12 before 6, 1%, 2%, 1%, 2%, 2%, 11%, 17%

Level, 1, 6, 11, 16, 21, 26, 30
Difficulty, hard, hard, hard, hard, hard, hard, hard
Skill Bonus, 7, 10, 13, 17, 19, 23, 25
DC, 25, 26, 30, 33, 35, 37, 38
4 before 2, 0%, 1%, 0%, 1%, 1%, 4%, 7%
6 before 4, 0%, 0%, 0%, 0%, 0%, 0%, 2%
12 before 6, 0%, 0%, 0%, 0%, 0%, 0%, 1%


The text above in in "comma delimited format". To make sense of it, copy it into a word processor and convert text to table using the comma as you delimiter.
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2 years ago  ::  Jun 14, 2008 - 11:10AM #9
NthDegree256
Posts: 784
Date Joined: 08/26/05
Couple of notes about this.

Item one is that skill challenges, unlike combat encounters, are less likely to result in immediate PC death. This means that, if you want, you can afford to have particularly difficult skill challenges, because the story is explicitly supposed to continue if they succeed or fail, just along a different course. Check the sample skill challenges in the DMG; each one of them describes exactly what happens if the PCs fail it, because failure is a distinct possibility.

Item two is that, yes, many of the listed skill challenges are pretty difficult to best without some lucky dice rolls. If you want to ease things up, I'd strongly recommend introducing more Easy skill options that don't count as success or failures but instead provide +2 to characters' checks, encouraging the players to focus on these if they're racking up failures, and to consider bumping up the threshold for failure to more than half the needed successes. Other options I've seen include awarding 2 successes if the player attempts a moderate DC but beats a hard DC on their roll, or converting a failure into a success by expending some resources (in my case, I let my PCs convert a failure in a negotiation with a dragon into a success by handing it some of the shiny jewelry they had just found.) And, of course, don't forget circumstance bonuses for particularly apt uses of skills; a Diplomacy roll is one thing, but a Diplomacy roll combined with a little flattery might be even better if the NPC in question is open to that sort of thing.
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2 years ago  ::  Jun 14, 2008 - 11:16AM #10
Neutronium_Dragon
Posts: 2,650
Date Joined: 08/11/06
I'm actually starting to wonder whether the table on P61 and the reference in the example on P42 are errors left over from a previous revision. The table on P61 is just floating there without any associated rules text around it and the reference in the P42 example seems to be the only place it talks about adding +5 for a skill check - unless there's some actual rules text about doing so that I'm missing.

If you just use the basic DCs shown on P42 and ignore the out-of-the-blue +5 in the example, the DCs for skill challenges actually work out reasonably well - but you need to bear in mind some caveats.

Suppose a 1st level character has a +8 modifier to a skill they're good at. +5 for Trained, and +3 for a good stat (making allowances for a racial +2 in there somewhere as well). A DC 15 (moderate) check requires a 7 or higher, which gives a 70% chance of success.

Now, you need an 80% success rate (4 successes, 1 failure), so they seem to be behind, but the walkthrough of skill challenges shows several ways that the odds may be tilted towards the players: Most of them allow for at least one easy check to be made, most of them allow you to make a "non-risky" check of some sort to add +2 to another character's check, and the dialogue with the Duke example shows that throwing in a +2 for good roleplaying of the check is also an accepted practice. The one easy check is almost certain to work if someone is trained in it, and all of those +2s which you can apply also help to push the odds to something more favorable to the PCs - so in the end, the 80% success rate is reasonably achievable. Not guaranteed by any means, but you've at least even chances.

Higher complexity actually helps your odds in this case - six successes/three failures means your success rate only needs to be 75%, while eight successes/four failures pushes it down to about 73%.
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