The New Math Behind Skill Challenges

Recently, Wizards put out some new errata for D&D 4th Edition. I wholeheartedly support correcting games where they’re wrong. While the internet community’s focus seems to be on Blade Cascade and whether it was nerfed enough, the biggest change presented is skill challenges.

Here’s the official changes:
All DCs went down by 5.
The +5 modifier for skill rolls was removed.
(It was poorly implied that this didn’t apply to skill challenges. Or maybe it was supposed to. In any case, I had been using the baseline DCs.)
Help in skill challenges is limited.
Skill Challenges end after three failures.

Let’s examine this objectively, shall we?

There are basically four statuses one can be compared to any given skill- Unskilled, Fairly Skilled, Skilled, and Min-Maxed.
(Note that the numbers used are for 1st level. As your character gains levels their pluses increase, but so do their DCs. With ability score boosts, utility powers, and certain magic items, skill totals will likely climb faster, which will push people Unskilled People into Fairly Skilled people up to Skilled.)

An Unskilled person has put no effort into being good at the skill. They might have an Ability bonus, they might not. The range here is from -1 to +2, but we’ll be using +0 for the math.

A Fairly Skilled person might not have put any effort into being good at the skill, or they might be a bit of a generalist. They probably have a good appropriate Ability Score, or a decent score and a racial boost, or the Jack of All Trades feat, or training with the skill but no bonus. The range here is +3 to +5, but we’ll be using +4 for the math.

A Skilled person has training with the skill, an good modifier for it. This is probably the character’s primary skill. The range here is +6 to +10, but we’ll be using +8 for the math.

A Min-Maxed character has put a large deal of their character into being the best they can at a given skill. They start with a 20 in a score from racial modifiers, with skill training and Skill Focus in a skill their race gives a +2 bonus to. This gives them a +15 to skill checks with their favored skill. (Obscene? Not really. Remember, they’re sinking an 18 into one attribute and spending their starting feat at first level. This is what the character is all about. Every race but Humans can do this. Some can get a +17, but how to do that is left as an exercise to the reader.)

There are three types of skill DCs- Easy, Medium, and Hard. Under the old rules, the baseline DCs were 10, 15, 20, +5 if it was a skill check, resulting in 15, 20, or 25.

The DMG doesn’t define what Easy, Medium, or Hard actually mean. The PHB mentions that these are all extraordinary situation rolls- if it’s mundane or trivial, it’s not a roll.

Easy Rolls
To me, an Easy Roll is something even the Unskilled guy should have a shot at. The Fairly Skilled guy should succeed the majority of the time. Skilled characters should worry about failure rarely, if ever. Min-Maxed characters should never fail at an Easy roll.

Medium Rolls
To me, the Unskilled guy should still have a shot at Medium rolls, but they’ll fail more often than they succeed- maybe much more often. The Fairly Skilled guy should still suceed the majority of the time, but it might be dicier. The Skilled character should usually succeed, but might have to worry about failure. For a Min-Maxer, failure at this level is a grave loss of face.

Hard Rolls
The Unskilled guy should have a shot, but it’s a long one. The Fairly Skilled guy should have a shot, but he’ll fail more often than he succeeds. The Skilled Character should have about even odds. For a Min-Maxer, failure is now an option- but success should be more likely than failure. This is the character’s raison-d’etre, after all.

At DC 5- success rates are 80% (Unskilled)… 100% (Fairly)… 100% (Skilled)… 100% (Min-Maxed)
At DC 10- success rates are 55% (U) 75% (F) 95% (S) 100% (MM)
At DC 15- success rates are 30% (U) 50% (F) 70% (S) 100% (MM)
At DC 20- success rates are 5% (U) 25% (F) 45% (S) 80% (MM)
At DC 25- success rates are 0% (U) 0% (F) 20% (S) 55% (MM)

Looking at this, it’s clear the old skill DCs of 15/20/25 were far, far too high. However, I think the new DCs of 5/10/15 are far too low.

10/15/20 seems about right for non-skill challenge skill rolls. Maybe the Hard DC could be nudged down a point or two, but for the most part the probabilities are right where I want them.

Now let’s take a look at skill challenges.

A change to skill challenges was to set the number of failures needed at 3, rather than based on complexity. A complexity 1 challenge now ends after 4 successes or 3 failures. A complexity 5 challenge ends after 12 successes or 3 failures. (Before it was 2 and 6.) This is an interesting change- it’s a three-strikes-and-your-out, but it changes the ratio of success needed from 2:1 to a varying ratio based on complexity.

At complexity 1, the ratio is 4:3 (roughly 57%)
At complexity 2, the ratio is 6:3 (roughly 67%)
At complexity 3, the ratio is 8:3 (roughly 73%)
At complexity 4, the ratio is 10:3 (roughly 76%)
At complexity 5, the ratio is 12:3 (80%)

The percentage number is the skill success level needed to expect to come out on top. Vagaries of probability being what they are, failure is still possible, but success is likely. Get above that number, and success swings in your favor.

This ignores things like bonuses or automatic successes for creativity, or funky challenges with special rules. Success shouldn’t be dependent on that. I have no problem with the odds flying way in the favor for a creative group of players. Special rules are hard to examine generally.

There are basically three party skill levels- Fairly Skilled, Skilled, and Min-Maxed. It should be rare that you can’t find a skill that you’re at least Fairly Skilled with for a given challenge. Parties that are on their game should be Skilled. Min-Maxed parties should eat Skill Challenges for breakfast- but you shouldn’t have to specialize to that level to defeat a complexity 5 challenge.

I’m assuming most rolls will be made against moderate DCs.

If that is DC 10, then a Fairly Skilled party (75%) will blow through level 1 and 2 challenges, probably beat level 3 challenges, have some trouble with level 4 and 5 challenges. A Skilled party (95%) should easily get victory in all of them. DC 10 is an insult to the Min-Maxed party. I mean really now, is that all you got?

If that is DC 15, then a Fairly Skilled party (50%) is in trouble, no matter what the challenge level. They might be able to beat the level 1 challenge. Most parties should be Skilled (70%) though, and will beat level 1 and 2, have a shot at level 3, but probably lose at level 4 and 5- unless they have less skilled members use helping, in qhich case their default bonus is +10, the chance of success on a roll jumps up to 80%, and all the challenges are feasible. The Min-Maxed party skill scoffs at your challenge.

If for some reason the standard skill challenge DC is 20, everyone but the Min-Maxed party should go home. They still only succeed 80% of the time, so with some bad rolls, victory isn’t even guaranteed for them.

Clearly, 20 is too high. 10 is too low. 15 seems about right.

Based on this math, I’m setting DCs for skill rolls at 10 for easy, 15 for Moderate, and 20 for hard. This is about half-way between the rules as written, and the errata. I might end up nudging down the Moderate and Hard DCs by a point after using challenges in play, but for now, I like the looks of things.

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3 thoughts on “The New Math Behind Skill Challenges

  1. Willow says:

    While in a perfect world they would have keep the game in playtest until they had perfected skill challenges, it happens.

    This is still immensly preferable to having a flawed game and not doing anything about it.

  2. Well, yeah, obviously. It just seems like a pretty major thing to have not noticed.

    I mean, I get that in a huge, ubercrunchy game like this, the chance of errata is exponentially increased.

    I just hate the idea of having a Tome that is incomplete or incorrect… it offends my aesthetic sensibilities as well as increasing search & handling time, which is a huge pet peeve of mine.

    That said, I won’t be purchasing these books anyway (although I will probably be playing with someone else’s), so I was mostly expressing a general comment moreso than a specific one… or something.

    I’m done now.

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