Some Numbers, for the Playtest Crowd

I never know how much to post in math threads, so if this is over-simplified, please forgive me.

To grasp the problem of "difficulty" in the playtest, I ran 20,000 first rounds with a total of 10 different monster conditions. To make this a "fair" test, the five player characters (none with a score above 18) used the same attacks in each one (Warhammer, Great Axe, Magic Missile, Radiant Lance, Sling) and I made the assumption for that there were an equal number of monsters and player characters (in 16,000 rounds) and there would be no possibility of a second hit on the same monster, and that a monster with multiple attacks only attacked once. I picked the monster's strongest non-magical attack where there was more than one. I tried to select monsters with the same combat style, so that I wasn't comparing something that drops poison with something that punches you. I also only ran each condition only 2000 times with each monster, which is good for getting the general 'shape' of the data. Someone w/better software can probably run it tens of thousands of times...which would get way better data. I would assume most percentages in this are +/- about 5%. Note that simulation doesn't generate the best shaped data, but is good for giving general concepts. I used excel to track the simulations. (I know, most people know my view of excel.)

To reiterate, this was a grossly simplified combat scenario. It only covered the first round, and had conditions in which the characters and the bad guys could only hit once, each. I was interested in four questions:

1. Is there ever a time where the risk of one-hit kill in the first round is equal for the players and the monsters?

2. What percentage of the time does an attack miss in different scenarios?

3. What kind of difference is the advantage making (when that is used.)

4. Does the xp-based difficulty mean a damn thing?

The 10 different monster scenarios our 1st level characters faced were:
5 fire beetles, 5 bug bears using melee weapon, 5 bug bears using ranged, 5 dark acolytes, 5 dark adepts, 5 dark priests, 5 drow (attacking once only), 5 ogres, 2 bug bears wielding ranged weapons and 2 bug bears wielding melee weapons. These last two conditions were suggested by the playtest module, in which two bug bears being sent after the party at a low level is repeatedly used as a threat.

For a graphical representation of the relative difficulty of these conditions, the chart below shows the difficulty (based on xp budget) of the 10 conditions, along with bars for the easy, average, and tough xp budgets. I also added a fourth difficulty level, supra, which is just Tough+Easy. In theory, anything above a supra difficulty should be an instant wipe out for the party, unless they run like hell. Taking the difficulty values at face value, something far above supra should be impossible to hit and should kill the party fairly easily.

Based on these numbers, you would think that the last three of these attacks would be the ones in which the party was unable to kill the bad guys and in which the party could, conceivably be killed instantly, squashed into pieces. It turns out it is almost impossible for even the ogre to kill any member of the party in one hit, coming in at only killing a party member 5.5% of the time (about the chance of rolling a natural 20 on a d20).

In fact, other than the ogre, the only chance for a single PC kill comes from the bugbears, when wielding melee weapons. These creatures, so feared in the module presented with the play test, only kill a PC 1.6% of the time per round, and can never do enough damage to kill the two players with the highest hitpoints in one attack. The party can never one-hit kill the Drow, the Dark Priests, or the ogres, but these creatures can be killed with two hits (Drow, Dark Priests) or three hits (Ogre.)

For a comparison of the party's chance of being wiped out in the first attack when facing an enemy that should smush them into oblivion instantly versus the chance of wiping out said monsters, here's another chart...showing both the chances when the party uses Advantage and when the party does not.
Here's the data for the chart.

Monsters	% monsters killed (without Advantage)	% Monsters killed (with Advantage)	% party killed
Fire Beetle (5)	57.42	81.6	0
Bug Bear (5)-Melee	0.9	1.24	1.26
Bug Bear (2)-Melee	8.388888889	8.722222222	0.166666667
Bug Bear  (2)-Ranged	8.222222222	8.555555556	0
Bug Bear (5)-Ranged	1.02	1.3	0
Dark Acolyte (5)-Mace	24.3	34.64	0
Dark Adept (5)-Mace	7.26	9.7	0
Dark Priest (5)-Mace	0	0	0
Drow-(5)-1 attk	0	0	0
Ogre (5)-greatclub	0	0	5.5

And here's your chart:

Note that you can extrapolate these numbers to figure out how many rounds it would take to kill each of these creatures, based on how often the party misses (or hits) in the 20,000 first rounds (10,000 with the party having advantage, and 10,000 with the advantage dice being thrown out altogether.) I suspect the differences between bugbear numbers are within the margin of error, by the way)

So, how frequently does the party miss?
The problem with the frequency of the party's misses is that it varies based on the character. Magic Missile, for example, always hits. This is why I chose to run the combat in a "perfect" first round where there are five monsters and 5 PCs, and they magically all attack and damage at the same time, something that could never happen in a game situation (also makes the math REALLY EASY to follow.) The problem is that this magical combat scenario should hamper the party in most scenarios. In a 'real' battle, the party is smarter than the enemy (except, maybe, the drow) and can do things like fight in a doorway (where the ogres could only hit one or two of them, and only one ogre at a time.) So bear in mind before I put the percent of missed attacks up that most parties are going to have even a better chance of hitting than given here...and that should disturb you.

So, in 10,000 first rounds, against monsters ranging in difficulty from a cakewalk to a monster that should destroy the party, how frequently did the party miss? Except for that magic missile, they should miss a lot, right? (Note these numbers are not the same as the "didn't kill instantly" numbers, because an instant kill and a hit w/out a kill is still a hit)

Monster	#times players missed w/out advantage	# Times players Missed with advantage
Fire Beetle (5)	2050	556
Bug Bear (5)-Melee	2230	539
Bug Bear (2)-Melee	2155	530
Bug Bear  (2)-Ranged	2280	575
Bug Bear (5)-Ranged	2270	506
Dark Acolyte (5)-Mace	2425	694
Dark Adept (5)-Mace	2480	655
Dark Priest (5)-Mace	2915	1033
Drow-(5)-1 attk	2460	681
Ogre (5)-greatclub	2475	703

Now, I should add a caveat.  These aren't how many times the party missed on an attack out of 10,000. Each of those conditions represent 5000 attacks. To make the data clearer, let's ignore the ones where the party is not facing an equal number of monsters to the party. Since everyone is attacking simultaneously in our impossible melee, you end up with things like the same bugbear being fatally killed twice at the same time. So, let's ignore those altogether, and convert them into percentages for ease. .

Monster	% missed w/out advantage	% missed with advantage
Fire Beetle (5)	41	11.12
Bug Bear (5)-Melee	44.6	10.78
Bug Bear (5)-Ranged	45.4	10.12
Dark Acolyte (5)-Mace	48.5	13.88
Dark Adept (5)-Mace	49.6	13.1
Dark Priest (5)-Mace	58.3	20.66
Drow-(5)-1 attk	49.2	13.62
Ogre (5)-greatclub	49.5	14.06

Or, put graphically:

People better than I have discussed the problems with the advantage dice. The answers to my 4 questions, based on this LIMITED example of first round of combat only, are as follows. Again, bear in mind that I just did this with simulations, so (for example) for a party member to die, the monster needed to both roll a hit AND roll a random damage die that was higher than the PC's :



1. Is there ever a time where the risk of one-hit kill in the first round is equal for the players and the monsters?
Not in the materials currently provided. In the worst case scenario, in which a party somehow encounters an equal number of monsters that should be at least three times the difficulty of the party, the party only has around a chance of a 1 on a 1d20 to lose a member in each round, and are three times more likely to hit the ogres than they are to die from the ogres. Such a party could win against an equal number of ogres by concentrating their attacks on one or two ogres at a time, which would lower the chance of an instant kill each round that they eliminated an ogre. This, the hardest possible scenario using the hardest possible monster, and even avoiding spells like Sleep and Command, is a fairly easy to win scenario, and based on the XP "value" of the difficulty of the encounter should be all but impossible.Your characters are basically never in danger. Running my party though the playtest module, they never got above a 2.5% chance of dying.-with an encounter that they should have higher levels for.


2. What percentage of the time does an attack miss in different scenarios?
Some attacks never miss. When those attacks can be constantly repeated, a party with fast feet can easily win any encounter. But based on nothing but simulation, a character in an "impossible" scenario can hit slightly less than half the time, and in an easy scenario can hit slightly more than half the time. Unless he has advantage dice in play, in which case he hits around 85% of the time in the worst case scenario the game allows.

3. What kind of difference is the advantage making (when that is used.)
It reduces the risk to the party down to negligible. When I got the chance of a beastie killing a member of the party at 5.5%, that was with the ogre not having any advantage or disadvantage. If he's at disadvantage, it's less than half a percentage point. Any time a chance is so low you can't get there by percentiles it bugs me as a DM.

4. Does the xp-based difficulty mean a damn thing?
In simulation? Nope, not a damn thing. The party is at very little risk, regardless of the monsters chosen. I think that's what bores me so much.

I know some people have said that the new generation of gamers isn't comfortable with characters dying, but I find the no-risk to the characters thing to be really boring. As a DM, I am a cupcake. It's almost impossible to die permanently in one of my campaigns....and I find these numbers troubling.

Different things can matter differently to different people. I tend to focus on the roleplaying, not the rolling, but if the chances of risk to the characters is so low, let's all play a diceless game instead.

It's completely possible there are data errors in my simulation. Running stuff by hand my numbers are even worse. It seems to me the simulation method actually is too parsimonious and gives too much benefit of the doubt. All I know is that the second I ran numbers I felt like it backed up what I saw play testing-too little risk makes too great a bored. :)

Skills, Classes and Background, a rational approach, part one

My working group is already adapting a skills system for DnDNext, in part because we're finding the class, specialty, background schemae of DnDNext more limiting than anything else. The problem is two-fold, in that these backgrounds don't really provide the DM much assistance on what a player can do. They provide more information that (for example) can help the DM make a ruling on something, which is great, but they are vague enough that a DM is forced to make many judgement calls that might not work from DM to DM, or worse, from the same DM in session to session.

Before I go much further, I am often considered old-school to the point of being a Luddite. I want to make it clear that a rigorous skills system proposal includes the fact that computer-assisted-gaming is here to stay. That is, the creation of a character with the assistance of a computer, data management with a computer, etc. Even those gamers who are in abject poverty usually have at least some access to a computer (or even a phone) with the ability to run aps that are this simple. It can be done hard copy with books, or easier to work with digital copy with hypertext.

The adapted skills system works with bonus skills, chosen skills and grouped skills. You can call this grouped skills set by a lot of names. Pods, kits, backgrounds, etc. Instead of giving the DM a generalized 'you know some stuff' view, these kits, backgrounds, etc., come down to specific numbers and concepts.  If writing/reading huge numbers of books with profiles and kits is something you're into, you can provide this material constantly. What it does best, however, is allow a player to use their own background and understanding of their character if having someone pick their skills for them is boring or limiting.

The first, and most basic, set of skills, are free skills given as a result of your race and background, in UAD&D we do this with the social status roll. Acknowledging the randomness of this, a player can take the default of serf (or the equivalent) or roll, understanding that choosing to go random means that you can get a benefit (more skills, more money) or you can get a penalty (less skills, less money.)

A serf, in our system, basically gets a skill that they may or may not ever use in such a thing as turnip farming, goat herding, raising chickens, etc. A clever party member may be able to use these in game play. These are essentially flavor. If a player wants to use this stuff, he can. If he plays the guy who got off the turnip truck and never looked back, he can do that, too. This skill is essentially the skill your character can fall back on if the adventuring thing doesn't work out for him. To give an idea of what it might look like in a character background, here are three racial equivalents of it. I've left off numbers to make it easier to understand. Note that in the perfect world, the background information would probably be in a different file than the character sheet, it's only important if you wanted it:

Human. Social Class: Serf. Information: You were raised on a farm growing carrots for a powerful landholder, and allowed to farm a twelfth of that land for your family. It was a hard living, but most of the people you know have the same background. You or your parents saved up for years for your starting funds, in the hopes that you could escape the carrot growing lifestyle. This background makes you an authority on growing carrots. [Bonus skills: Agriculture, general (proficient). Agriculture: Carrots(expert)]

Elf. Social Class: Serf. Information: You were raised in a lush hardwood forest which your family maintained for a powerful elf-lord. You were allowed to use a fraction of that forest for your own needs. It was a hard living, but most of the elves you know came from the same background. You got your starting funds by winning an hunting contest in the past fall. This background makes you an authority on forestry, especially the temperate forest you grew up in. [Bonus skills: Forestry (proficient), Wilderness Survival:Temperate Forest (expert)] 

Halfling. Social Class: Serf Information: You were raised in a large and fairly well off halfling village, where your family has served the well-off Underhill family since the village was founded. Your dad was a gardener, your grandad was a gardener, and by Yondalla, you are a gardener, too, and you are the best darn gardener in the town. You got your starting funds when your boss's house won the Best Posies in the Shrire contest this spring and he gave the whole reward to you because you deserve it. This background makes you an authority on landscaping, and no one knows more about posies than you. [Bonus skills: Gardening (proficient); Knowledge:Flowers (expert)]

There is a distinct chance that you don't use any of these skills for the rest of your character's life, but in a paragraph, you've been given a template that gets you started. Instead of getting "you are a serf, you have serf skills" you know what your character knows and why. If you want to create your own serf background, you can choose any two related skills that makes sense for your background. The general choice should always be Random or Choice, and computer assisted gaming makes that easier. Here are two other scenarios for your human, above:

Your Race is Human: Background: Your DM has chosen "Serf" as the default social class for this campaign. You can accept serf or roll for a random social class. You may make this choice for this character once.  [Roll? Accept Serf?]
[roll]
Background: You have rolled Yeoman.
[Information]

Yeomen have it nice. Small-time landlords, these people own the land that the serfs farm and are ruled in turn by the chivalric class. The character stands to inherit little or nothing, as most Yeoman are in debt to their lords, either due to low crop production, unruly serfs or tyranny. The character's starting funds are normal. The character gains the following skills: Accountancy, Read/Write regional language, Maths, Riding, Land based: Horse, and selects one of the following: Agriculture, Animal handling: Shepherd, Animal handling: Swineherd, Animal handling: Goatherd, Animal handling: Poultrer, or Animal handling: Fowler. 

Do you want to roll these bonus skills randomly or select?

[roll]

Human. Social Class: Yeoman Your family owned the land that was farmed by a large group of serfs, and your land was protected by a local lord. While you don't stand to inherit anything, you can always go to work for the lord of your family's land if adventuring doesn't work out. You had a couple of servants growing up, and a small amount of formal education.  Part of your duties, growing up, was making sure the serfs treated the sheep properly and riding between farms to collect taxes and goods. [Bonus skills: Accountancy (proficient), Read/Write language: Common (proficient), Maths (proficient), Riding Land based: Horse (proficient), Animal handling: Shepherd (expert.)]

OR....

[Roll? Accept Serf?]

[roll]
Background: You have rolled Poverty.
[Information]

The character grew up with nothing. If the character has a large family (s)he may want to send money to them. Half starting funds. The character does gain the bonus skills of brawling and begging, however. 

[continue]

Human. Social Class: Poverty You grew up on the back streets of a large city. I won't ask you how you came up with your starting funds, but I do wonder where my belt pouch has gone. [Bonus skills: Brawling (proficient); Begging (Expert)]

It's probably fairly unlikely you'll use many of these skills in combat. What this provides is a background that gives the DM something to roll when you say your background is as a farmer, or a beggar. The other option is that I have to choose what you know. As a DM, I don't have a problem choosing what you know, but players often can feel a disconnect with a character, not understanding why so-and-so can get this, and so-and so can't.

In the next installment of this I'll demonstrate how you use it to determine the abilities of your classes. The general understanding should be that rather than have a "pick a group of this, pick a group of that" the player has the option of going for a default option or specific option. This allows the player to have the customization that they deserve or prefer. It also generates a background for the character if the character does not want to do so themselves. I'm using skills here to get people used to the idea of picking from a group of skills, because they are easy, but when I go over to class, it will be a little harder to understand if you're not familiar with this idea.

I like the idea of doing this with a simple program that uses "DM Space" and "Player Space" so that players can roll characters, have them approved (or not) by the DM, and print them out outside of game time. There are many things that the DM really should not have to be there for in a perfect gaming world, and character creation should be part of it. I really like the idea of having a character sheet and a background/information sheet, so that a player can have as big or as small a pile of papers as s/he is comfortable with.