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.

 

[Transformer]

I'm definitely in the >50% chance camp. Missing and accomplishing nothing fully half of the time is just plain miserable. We've even had a suggestion in this thread of a 40% hit rate for first level fighters, and another for a 50% hit rate against unarmored targets! Geez, if I sat down to play a fantasy adventure as a burly, sword-wielding hero (or at least a hearty farmboy recently turned adventurer, if you don't like 1st level characters being heroes), and my guy whiffed 60% of the time, I'm pretty sure I'd just go home!

70% would definitely be my favored baseline hit rate (perhaps 75% for fighters). It leaves a decent amount of wiggle room in the upwards direction for particularly accurate people, lower level enemies, easy to hit targets, and the like; while also keeping combats fast and frustrating chains of misses to a minimum.

I guess I just don't see the allure of a 50% hit rate. I suppose it leaves more room if your goal is increasing accuracy as a character levels. But mostly it just makes combats longer than they have to be and leads to frustration, Perhaps I'm missing something. Why a 50% hit rate?

 

[Andor]

In an active defense system I'd expect extremely high to-hit odds without an interposing defense.

D&D however assumes an active defender and folds in into passive defense target numbers.

If an attack was a single sword thrust, then that 50% would actually sound a bit high. But it's not, a single attack roll represents seconds worth of active fighting, dodging and exchanging blows. (Except possibly in the first attack of an ambush, hence the flat-footed bonus.)

Given the abstract nature of D&D combat, worrying too much about the details of dodging, parrying or soaking with armour is pointless.

So on the whole I'd say the 70-75% figure for a combatant type attacking a foe in level appropriate armour sounds about right to me.

I'm really very curious to see how they'll approach both the level 1 build-out and the leveling curve in 5e.

 

[Andor]

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.

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.

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?

And this, my friends, is the trouble with trying to make a single system please both gamists and simulationists.

The gamist says "16th level thief? Your climb DC is 42." The simulationist says "Why does a dragon who lives in a natural rock cavern apparently have walls of ice covered glass as indicated by that DC?"

I'm a simulationist. If the high level thief maxed out climb let him have his occasional cake-walk, he earned it. And if the party doesn't have a guy who could shame spiderman while exploring the ice palace of the frist giant king, then they will pay the price for their lack of vision.

 

[am181d]

I'm a bit of a heretic, but I believe in a PC-centric game. That means that PCs hit most of the time and also parry/dodge most of the time, but when they do get hit, the hits are serious and put the PCs at serious risk.

Of course, I'd also prefer that PCs roll to hit and roll to parry/dodge, and the DM only rolls opposed rolls for Big Bad types.

 

[Mokona]

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.

If player's attacks should succeed 70% of the time then the corollary would be that their defenses succeed 70% of the time.

Thus Dungeon Masters only "hit" 30% of the time.

Monsters use different math than PCs. Each player rolls one attack per round and has a 70% chance of a hit. DMs roll 5 attacks per round (at 30% chance each) and thus have a 83% chance to hit AT LEAST once. (FYI, 76% chance for the DM to hit at least once if they only have four monsters. This works better with minions as well because missing takes "less time" for the DM to resolve.)

 

[Quickleaf]

If player's attacks should succeed 70% of the time then the corollary would be that their defenses succeed 70% of the time.

Thus Dungeon Masters only "hit" 30% of the time.

Monsters use different math than PCs. Each player rolls one attack per round and has a 70% chance of a hit. DMs roll 5 attacks per round (at 30% chance each) and thus have a 83% chance to hit AT LEAST once. (FYI, 76% chance for the DM to hit at least once if they only have four monsters. This works better with minions as well because missing takes "less time" for the DM to resolve.)

I think you misunderstood the 70% theory. A character getting hit isn't invoking a sense of failure on the part of the player because (unless we're entertaining some new rules ideas) theres no action involved in defense.

The percentage change for a monster to hit a PC is another matter. I think with monsters you can mess around with Chance to hit vs. Magnitude of hit more than you can with PCs. So 30% could work for mooks with strong damage/effect, but that % could be tweaked depending on how hard they hit.

 

[Savage Wombat]

I think you misunderstood the 70% theory. A character getting hit isn't invoking a sense of failure on the part of the player because (unless we're entertaining some new rules ideas) theres no action involved in defense.

The percentage change for a monster to hit a PC is another matter. I think with monsters you can mess around with Chance to hit vs. Magnitude of hit more than you can with PCs. So 30% could work for mooks with strong damage/effect, but that % could be tweaked depending on how hard they hit.

That does depend on your players, though. I have one player who, no matter how many HP he has, thinks his character is somehow "losing" if he takes damage at all.

Clearly a player like that would want to be able to get his AC sufficiently high that he is missed "most of the time" - i.e. 70% or so.

 

[Crazy Jerome]

And this, my friends, is the trouble with trying to make a single system please both gamists and simulationists.

I think you misunderstood the 70% theory. A character getting hit isn't invoking a sense of failure on the part of the player because (unless we're entertaining some new rules ideas) theres no action involved in defense.

Then there is the narrative focus where, when the dice roll, something generally happens.

As luck would have it, if you know anything about those active defenses in reality, this happens to map really well with other preferences in the presence of active defense options--such as "Total Defense". Normally, anyone can hit most of the time if they are willing to risk a reasonable chance of a return strike. If you start getting much more defensive, the numbers go down for both sides. The D&D default, historically, has been to get on with it.

Edit: Note that to satisfy a wider ranger of play, Total Defense options should still allow a single (simple) attack, with a hefty penalty--perhaps around -8. There is no defense so total that it doesn't leave open the possibility of a riposte on someone that has over extended themselves.