D&D 5E Stupid math stuff that vaguely pertains to 5e.

[Truename]

Interesting range of responses so far, a lot of it simulationist. I'm going to look at it from a gamist perspective instead. In brief: succeed 65-70% of the time; have something interesting to do 100% of the time.

1- Trying something and failing is no fun, but always succeeding isn't fun either. So: Everyone should succeed 65-70% of the time when they're doing something their character is good at. Fighters' swords hit 65-70% of the time. Wizards' spells hit 65-70% of the time. Rogues save the party from deadly traps 65-70% of the time. Etc.

2- Waiting patiently for your turn, then whiffing, is no fun either. So: Everyone should have something interesting to do on their turn 100% of the time. Fighters can move tactically 100% of the time, although they may choose not to. Rogues can notice tantalizing details about their surroundings 100% of the time, although they may not think it's important at the moment. Wizards can apply their spells in creative ways 100% of the time, although they may not be feeling creative at the moment.

An interesting corollary is that classes aren't set apart by how often they succeed. Instead, the "feel" when playing a character depends on what they can do that's interesting and the "feel" when watching someone play a character depends on what they're particularly good at.

So you see the fighter, wizard, and rogue, and you think: "wow, that fighter's really good at hitting enemies. The wizard's really good at breaking out the bag of tricks. And the rogue's really good at exploring." But they all have the same chance to succeed... just at different things.

And you when you choose to play the fighter, wizard, or rogue, you think, "I really love the fighter's tactical approach," or "I love planning my spells for a day and coming up with creative strategies," or "I love finding clues and solving puzzles." But they all have something interesting to do all the time.

The other corollary is that challenges should scale, but chances to succeed should not. So a level 1 critter might have an AC 10, 4 hit points, and do 1 point of damage (a minor threat to a level 1 character), and a level 10 critter might have an AC of 10, 60 hit points, and do 15 hit points of damage (it hits your level 1 character, you instantly die).

And this should be true for all three pillars, for every class. Always something interesting to do in combat, exploration, and interaction; and always something to succeed at 65-70% of the time in combat, exploration, and interaction.

 

[Crazy Jerome]

Another reservation to setting base chance too low (besides that whiffing feeling in the players) is that it doesn't leave you as much room as you might think to handle high risk, high reward options. Take something that has a -4 chance to connect, and thus needs to be worth it. Sure, the math will work out setting the base anywhere close to the middle of the range, but the feel will not.

There's some lower point of low success/high output where it starts to feel like fishing--and then a point beyond that which is more desperation. You don't typically want people thinking: "Gee, if this guy gets to go again, we are hosed. So I can go with my 50% attack chance and not take him out, or my 5% chance of megadeath effect." You'd probably much prefer, "50% chance unlikely to do enough to take him out versus 30% chance of doing probably enough to take him out."

I don't mind a little of the desperation gambits, but I'd really rather it come from the wacky situation than baked in game math. I mean, a nearby group in my high school days got into the habit of mixing every unidentified potion in sight when a TPK was imminent, because a couple of times trying that got a "potion miscibility" result that bailed out half the party. Most of the time it just got someone poisoned or a free feather fall right before the TPK, but hey, no downside at that point of the battle. But even this group didn't go around stockpiling potions and refusing to identify them in case they decided to go with that gambit.

 

[Dragonblade]

Interesting range of responses so far, a lot of it simulationist. I'm going to look at it from a gamist perspective instead. In brief: succeed 65-70% of the time; have something interesting to do 100% of the time.

This exactly. Against an equal level opponent, all classes should always be able to hit with their primary attack method (which may differ from class to class) about 60-70% of the time.

Then you use damage and HP to average out combat duration and fine tune balance. Keeping damage static and relying on hit percentage as a method of balance will result in very swingy combats, where you walk over your opponent in one encounter, or are unhittable in another. Unless you roll very very poorly, the odds of missing an enemy of equal level two rounds in a row should be less than 10% to make a game that I would find fun to play and not frustrating.

Against weaker or stronger opponents, the percentage to hit should change about by about 2% per level difference to expand the sweet spot to where I want it to be. If a level 1 orc footsoldier can hit a level 1 fighter 60% of the time, they should be able to hit a level 10 fighter only about 40% of the time.

I don't like how in 3e and 4e, 5 to 10 levels of difference makes you a veritable demigod against lower level foes.

To denote a feeling of power progression across levels I would again use HP and damage output to handle that. A level 10 fighter should be able to kill a level 1 orc in a single hit with their damage output. Whereas that level 1 orc needed say 4-5 hits to kill a level 1 fighter, but should need about 14-15 to kill a level 10 fighter (about 1 hit per level difference). In other words the level 10 fighter should be able to take on and defeat approx. 5-10 level 1 orcs.

 

[KesselZero]

I definitely prefer higher hit percentages, both because missing isn't fun (for the player or the DM) and because combats that drag on and on because neither side can hit the other are the least fun kind of combats.

 

[3catcircus]

There is a really easy way to figure out the answer you want by doing some basic probability math (and you don't have to be rigorous in the mathematical sense to do this).

This is easy to do in a spreadsheet, but you could "by hand" it if you are a masochist.

Do a randbetween(1,20) a bunch of times (100 is ok, 1000 would be better, and a professional would do a metric butt-ton of iterations).

Next, number a column between and 1 and 20. Add up the total number of instances that each number appears in your total of randbetweens. The resulting distribution will give you the likelihood of rolling a specific number.

So, what you do is work outward in both directions from you highest likelihood numbers until you get a total of whatever % chance you want to hit, and the center of that spread is the basic unmodified AC of your target.

Example:

I rolled 1-20 100 times, resulting in 73% of the numbers being 2-17 (less 10, which strangely had no rolls). As a result, the median is 9 and the average is slightly less than 9.5, so, as expected, the AC for a target you want to hit 75% of the time ought to be set at 10. If you wanted to hit 80% of the time, you'd likely set the AC to 8 or 9.

 

[triqui]

I think 75% is the optimal target number. But it's easier to achieve a 50-50 balance.

Fortunatelly, 50% with reroll is 75%

 

[Living Legend]

The home system I ran for a couple years was % based and hovered around 50 - 60% chance of success on most attacks, but the better you hit by the more damage you did, so if you rolled a 1 (rolling lower was better) you could do 4 or 5 times average damage. After playing this way for a couple years I can positively confirm that the only way that success rate worked was because the system was so swingy. Players missed a lot, and were frustrated a lot, but it didn't get to them (much) because they knew that 1 lucky hit they could wipe out a perfectly healthy enemy in 1 strike. Apply that success rate to a game like D&D, where (I'm assuming based on experience) damage won't be dynamic and it will take several hits at least to kill an enemy, and you have a recipe for people playing angry birds instead of the game you're running.

Also, skill tests were brutal with a 55% success rate, sneaking sucked. Roll really well on sneak and... you're just wicked sneaky, good for you. These are my observations.

 

[Crazy Jerome]

a professional would do a metric butt-ton of iterations).

Heh, a professional should either do the math or get someone to do it for him. For this particular problem, if I read you correctly, you don't even need to remember how to do it. Just look up a binomial distribution calculator. Here's an example: Binomial Distribution: Probability Calculator

 

[hanez]

I don't like the idea of "balanced" skill checks. I hate when 20th-level characters keep facing rivers that no peasant could swim and walls that no 1st-level thief would be able to climb, for the sake of keeping increasing skill modifiers relevant.

Uhhhh.......... yeah.......... that sounds completely well asinine.. In what system do skill DCs scale!? I have always just made my own DCs (e.g DC 10 an easy task, DC 15 a task with some difficulty, DC 20 a task where someone has to have some skill, or be luck etc.) I have never ever considered scaling it by level! Let me guess, 4e did this? Something to do with balance?

 

[Quickleaf]

Trailblazer has come to the conclusion that the PC's should succeed around 70% of the time for the game experience to seem neither too easy nor too hard.

Actually, ~ 70% may be the magic number according to Mihaly Csikszentmihalyi (author of "Flow") and other psychologists. Something about that success to failure ratio increases pleasure of success and appreciation/patience with the lessons of failure.