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So, it's been awhile since I posted anything. This latest playtest packet, the clamor on the boards over skill dice and how it can be used as proficiency dice, and the fact that I have some extra free time due to the holiday schedule at work have all aligned to make this post possible.

I will warn you now that there is math involved with this post. I'll try to keep it as terse as possible so as not to bore you, but I guarantee nothing as far as your actual boredom level goes.

Skill Dice

I won't rehash it, it's been all over the boards. Basically skill dice makes the new DC table for skills make perfect sense, is mathematically sound, and in my opinion is probably one of the best inventions for the game to date. It has also been suggested to take those skill dice, call them proficiency (or something similar) dice and apply them to attacks instead of static bonuses based on class. If it fixes much of the math behind skills, it should do the same for attacks.

Bounded Accuracy and Proficiency Die

To this end, we basically replace the +1 with a 1d4, and step up the dice as we step up the attack bonus based on class. But how does this look for the actual chances to hit, what are the new AC bounds monsters will have to have?

Calculations, Standard Deviation, and Bounds

When I was first doing my calculations, I looked at a PC and their ability bonuses. Which can range from -1 to +5. This gives the average ability bonus of a PC of +2. The next thing I looked at was what is the average proficiency dice, which ranges from no proficiency to 1d12. This puts the average proficiency dice between 1d6 and 1d8. Finally, I looked at what I believe to be the average chance to hit. I've always liked 50%. The psychology of success for humans has been debated on the boards that the percentage should be closer to 70%, but for D&D I've always liked 50%, it gives me that feel of "anything can happen" which in combat, anything can. It feels right to me, and it gives us the most room to play with on either side of the average in case something doesn't work quite right.

At this point I pulled up anydice.com and looked at the output of 1d20 + 1d7 + 2 (the d20 + the average proficiency dice + the average ability bonus), and it turns out that 17 has a 50% hit chance. At this point, I have discovered what the average AC should be. For the real dice, it means 1d6 puts us just under 50%, and 1d8 puts us just over 50% to hit a 17.

Next, I looked at what ranges of AC's would determine a mean of 17. There could be any number of them on the high side, so I started by looking at the lowest possible AC. In my mind, once something hits 0 AC, it is an inanimate object, and can always be hit. You can't miss it, it's impossible. So, that means a 1 is the lowest possible AC for anything that you have a chance to miss. If 1 is the lowest end, and 17 is the average, then 33 becomes the high end.

Now, I called upon my business statistics classes (I found an actual use for them, yay!) and started working on the standard deviations of the population of 1..33. I then realized why do that when there are online calculators out there to do it for me, so I plugged the numbers in using this calculator, because I'm lazy. So, anyway, it turns out since we are looking at the entire population of possible AC values, the standard deviation for them is ~9.5.

Now, honestly, we really don't care too much about the lower limits. After all, they are just easier to hit the lower we go, however, in interest of showing the full ranges, I am including them.

This is where things become interesting for me. The maximum AC a PC can reach while not using any magic is a Mountain Dwarf with Plate and a shield, which gives a 20 AC. This gives the range of non magical AC's ranging between 14 and 20. If anything with a +3 bonus is considered an epic/legendary magic item, and the character is a Mountain Dwarf wearing both epic plate, and an epic shield, his highest possible AC becomes 26. This AC value is 9 from the mean, within 1 standard deviation from the mean. It is also the maximum possible magical AC a player can reach. Taking it the other direction, the lowest AC within the standard deviation is 8. This is basically a naked person with a 6 Dexterity, which to me seems about the lowest Dex something living, and amblitory would have. This could just be a mathematical coincidence, but so far I am liking how it looks and feels, and honestly surprised on how well it actually worked out.

However, I'm thinking that maybe the non-magical range is too small, while the magical range is just about right. So perhaps the non magical range should be 13 to 21. This means non magic is 4 from the mean, and magic is 9 from the mean.

But what about anything over 26? At that point, we are in no man's land for AC. Anything over 26 and we start getting into god level Armor Classes. Not just god level, but god on their home plane level. Nearly to the point that if you don't come prepared, you are going to die. I don't find this to be a bad thing. If your PC's are going to hell to kill one of the lords there, they should be smart enough to collect everything they can to make them successful. Outside of his home plane the demon lord's AC shouldn't be over 26.

On the low end, anything under 8 AC really doesn't matter for the most part. Any character starting with a +2 ability bonus and no proficiency dice starts at an 80% chance to hit, and only gets better from there as they increase their ability bonus and their proficiency die goes up.

Chances of Hitting

Now that we have our ranges, what are the actual percentages to hit something? Well, there are quite a few factors. One, proficiency die used; two, ability bonus; three, target AC. To go through all of them would make this post even stupidly longer than it is already turning out to be. So, for brevity's sake I will break it down by levels 1,5,10,15, and 20, attacking AC's of 13, 17, 21, and 26. Basically, every proficiency dice bonus, against the lowest non-magical, the mean, highest non-magical, and highest magical AC. However, the majority of AC's that PCs will have to hit will fall between 13 and 21.

For the fighter, rogue, and monk, I will start with a +3 at level 1, a +4 at level 10, and a +5 at level 20 for their ability bonus. For the Cleric and Wizard, I will start them with a +2 at level 1, a +3 at levels 5 and 10, a +4 at 15 and a +5 at 20. For the wizard I am assuming they are upgrading their Dex and using a finesse weapon.

	13	17	21	26	33
F/M/R
1	67.50%	47.50%	27.50%	3.75%	0.00%
5	72.50%	52.50%	32.50%	8.33%	0.00%
10	82.50%	62.50%	42.50%	17.50%	0.00%
15	86.00%	67.50%	47.50%	22.50%	1.50%
20	91.25%	77.08%	57.50%	32.50%	6.25%
C
1	50.00%	30.00%	10.00%	0.00%	0.00%
5	55.00%	35.00%	15.00%	0.00%	0.00%
10	67.50%	47.50%	27.50%	3.75%	0.00%
15	77.50%	57.50%	37.50%	12.50%	0.00%
20	82.50%	62.50%	42.50%	17.50%	0.00%
W
1	50.00%	30.00%	10.00%	0.00%	0.00%
5	55.00%	35.00%	15.00%	0.00%	0.00%
10	55.00%	35.00%	15.00%	0.00%	0.00%
15	60.00%	40.00%	20.00%	0.00%	0.00%
20	65.00%	45.00%	25.00%	0.00%	0.00%

What I like about this table, is that it really shows it works well. Even a character with no magical weaponry has a chance of hitting someone with 2 epic magic defensive items. It's only a 32%, but it's possible.

On the average 17 AC though you can see the main martial classes going past the 50% hit rate at level 5 and hitting it just under 80% at level 20, while the cleric hits the average at level 20, where the primary martial classes do at 10, or about half the speed.

The non-melee class of course sucks at hitting things in melee (which is why they have spells) while they are good on the low end, they can never hit the average AC 50% of the time, and while they can hit the highest non magical AC, they have no chance to hit the highest magic boosted AC.

These percentages look about right to me overall. Perhaps a bit of fiddling is in order, but I think these AC numbers and using proficiency dice goes a long way to making the bounded accuracy system work, and work quite well.

Martial Damage Dice

Now that we have our base chances to hit, we can start looking at the MDD. I wasn't sure at first about MDD to be honest, but it goes a long way to keeping damage numbers similar as characters go up in level. It does marginalize weapon choice, however it means you can pick a weapon and not worry about how gimped you will make yourself later on down the road. The difference between a dagger and a dwarf wielding a great axe stays the same throughout their leveling career of about 4.5 points average damage. Quite a bit at level 1, not so much at level 20.

Some people have stated that they think that the MDD should become [W] dice. However now the difference between a dagger and great axe becomes a whopping 27 average damage. Unless you give dagger wielders something phenomenal to make up that difference it just will not work. I find it a workable solution to keeping damage levels equal across the board.

Also, they are used to power maneuvers. Some people have said that some of the maneuvers offer no kind of save against them. Part of me wonders if the actual attack hitting isn't included in that, and the fact that you burn using the dice to add to damage in order to pull off this maneuver. So perhaps the costs need to go up some, maybe just spending one die allows for a save, but if you spend 2 you can forgo the save.

Martial Damage Bonus

I will start by saying I don't really like the MDB. It just kinda seems tacked on. Now it's purpose might be to increase damage even if you use up all your MDD on maneuvers, but it just kinda seems wonky, and I feel it should probably be done away with.

However, if it is to be kept, I wonder if we couldn't change it to a ability modifier multiplier. For example, a cleric would just use his STR or DEX to add to damage for the first 17 levels, but for levels 18 through 20 they would use twice their STR or DEX bonus to damage. A fighter and rogue would use their normal STR or DEX modifier until level 7 to 10 where they would get double, 11 through 13 it would triple, 14 thorough 16 it would quadruple, and from 17 to 20 it would quintuple the ability bonus damage. One of the reasons I like this idea is that it still make ability modifiers mean something to damage. So your high STR (20) medium DEX (15) fighter would do 1d8 + 6d6 + 25 with his longsword, and 1d8 + 6d6 + 10 with his longbow.

Summary

Breaking it all down, I think static attack bonuses from class should go the way of the dodo, and proficiency dice, that is using no dice, 1d4, 1d6, 1d8, 1d10, and 1d12 to represent increased accuracy as you level is a better way to go both mathematically, and feel.

Martial Damage Dice work as both a damage increase and as a resource to be used to power maneuvers. There needs to be some work to balance MDD costs for maneuvers and there is some debate on if those should have saves involved for some of them, but perhaps the die cost should go up some to avoid allowing a save.

Martial Damage Bonus feels kinda tacked on, and I feel it doesn't need to be part of the game. However, if MDB is to stay, I think it may be better to attach it to the ability modifiers and use it as a multiplier to that bonus.

---

I'm not done with this topic. I just looked at melee for this post. I haven't even begun to look into how this works with spells. With attack roll spells it should be fine, however, saves will be a whole different matter. I think I will be covering this in my next post (unless something else happens that I find more interesting).

That said, I'd like to wish you all a Happy New Year, and I will speak with you again in 2013.

My first question is a rhetorical one: If you make an obviously controversial blog title so more people read it, are you a bad person?

There has been a few threads on speculating about the Monk, our eastern flavored unarmed, and unarmored fighting type. I've had one complaint about every single one of them, and that is, what about a boxer, or a wrestler, or a barroom brawler. Every single monk speculative post had that fast on their feet eastern flavored monk, and with next I don't think that should happen.

I have the writeup on a google doc and the link and the full writeup will be at the bottom of this post, but before you get to that I want to explain why I did what I did, what to expect, and what not to expect. None of this is set in stone of course, and if they create a monk it will all be moot, but I thought it was a neat idea and came up with a rough draft of the idea.

Distilling the Basics

Before I started I had to distil down what made a monk a monk, and what made a generic unarmed fighter, or a wrestler, or a boxer, or whatever. This meant deleting things like quivering palm and the like. I also got rid of the high mobility, because not all unarmed fighters are the quick nimble type. After doing this for awhile and slowly pruning away the layers I finally broke it down to the following.

• Unarmed damage that goes up with time.
• Armor that goes up with time as long as you aren't wearing any.
• A fighting Style.
• Abilities that have riders.
• Flurry of Blows

Stripping all else away, this is the main 5 things that monks have with a generic unarmed fighting type. Then I decided that a generic person that uses his body as a weapon would be well served by the name Martial Artist.

Class Features

So now that I have that nice and distilled down into a generic martial artist soup, I went ahead and thought about those things and how they apply to the character. First I thought about save DC's for the riders, armor bonuses, and attacks and damage. A monk used Wisdom as well as Dexterity and had AC that went up with time. So I came up with the idea of a Defensive Ability Mod that changes depending on the Tradition. Next I looked at what makes their attack and damage modifiers, and decided there would be another ability modifier for that. Finally still another ability mod would be used for Save DCs. Having 4 separate modifiers for each tradition created more of a MAD issue that I felt was warranted, so I decided that those 4 things would be tied to 2 abilities.

I then decided that a martial artist would have an encounter resource to power their abilities. I started with the generic Focus, but realized that each tradition could change that to whatever fit the tradition best.

When it came to Flurry, I looked at the basic thought of giving up accuracy for more attacks. At first I thought that it should be powered by Focus, allowing an extra attack per point of focus spent, but after mulling it over it seemed that the focus cost was too much. I settled on taking disadvantage on attacks in order to get more of them.

When it came to attack modifiers for the class and the raising of unarmed damage I decided that they should use the rogue progression for attack rolls, and unarmed damage would start at a d6 and go up a die at level 5, 9, 13, 17 to d8, d10, d12, and 2d6. I felt that this may be the best middle ground to start from.

Finally, I started working on Traditions. I figured that traditions would be made up of techniques. Some of these major, and cost focus to use, and some that are minor, and cost no focus.

Now at first I was thinking that the Tradition taken is something that you carry with you throughout your career, but I also thought that it would be more interesting if you starting coming up with your own fighting style by mixing with other traditions. In the end I settled on the ability to take new traditions as you level, but those that focus on a single tradition get extra bonuses than those that decide to spread out their talents. Basically you give up a wider range of abilities for a bonus ability tied to the tradition.

So What Traditions?

Well of course I started with a monk, after all some really want the eastern flavored fast moving type. I wanted a fighter that uses their smarts as well as their body, and decided that the pugilist fits the bill. I then came up with two slow lumbering types, the Brawler, and a Wrestler.

Where is the File?

Right here!

I've seen a bunch of talk lately with the newest play test and the scaling attack bonuses that you can't have scaling in a bounded system.

First, let us look at the definition of bounded from dictionary.reference.com/browse/bounded?...

Having bounds or limits.
Having a range of an upper bound and lower bound.

Nothing in the definition of bounded says no scaling. It simply means there is a maximum number that can be reached. Scaling in no way, shape, or form breaks bounding.

Do remember they said that creatures would be useful for longer with this system, not that any creature will be useful forever.

Class Increases

So let's look at the scaling done from the new playtest packet. First, let's eliminate the +2 from everyone as this represents profiency with either spell casting or weapons. When we do this we can see the following:

1. The cleric gains no bonuses for melee or casting in 5 levels.
2. The fighter starts with a +1 and gains +1 at level 4.
3. The Rogue starts with a +0 and gains +1 at level 5.
4. The wizard starts at +1 for spells, and gains +1 at level 4. He also starts with 0 and gains nothing for melee in 5 levels.

So let us postulate that the increases are linear in nature, which means if a character gains a +1 at level 4, they also gain one at any level divisible by 4, giving them a total +6 by level 20. If a character gains +1 at level 5, they will gain another +1 on any level divisible by 5, giving them a +4 at level 20. Now I hardly think at this point looking at the pattern, we wouldn't be too far off if we assumed that the characters that currently show no scaling could reasonably scale +1 at every level divisible by 6, meaning they will have a +3 by level 20. This gives us a maximum of +8, +6, +5 from best to worst when including the +2 proficiency.

What I find interesting about that spread of bonuses, is that there is a 15% difference as far as dice rolls between the best and worst, which is the same as the +3 given for trained skill bonuses, the spread between best and worst (trained and untrained) for skills. This seems to be the spread they are aiming for.

So far this still fits into the definition of bounded, we have limits, and we have an upper bound of +8 and a lower bound of +5.

Ability Increases

From the play we know that 2 abilities are increased by one at level 4. Let us also postulate that it happens at level 8, 12, 16, and 20. We also know from the play test that no ability can go over 20. The last part is what makes ability scores bounded. Your upper bound for ability modifiers is +5. Using the standard array, we know the lower bound is -1. This gives our spread to -1, 0, +1, +2, +3, +4, +5. The mean of this list is 2, the median is 2, and there is no mode. So from this we can say that +2 is an average adventurer ability mod.

Now, assuming that the highest ability is put in a primary attack ability, and race and class are chosen to augment that ability, we can range anywhere from a 17 to an 18 to start off and if all ability bonuses are put in this primary ability until it is maximized then it will be a gain of +2 or +1 over 20 levels. Even if the ability score starts as a 15, it can still be maxed out by level 20, this is a gain of +3.

Again we are still bounded, we are limited by the rules on what a maximum bonus can be for ability scores, our lower bound is -1 and our upper bound is +5.

Adding it All Up

Now adding everything together we can see where our maximum and minimum bounds lie. For the minimum bonus, we assume an 8 ability score, not putting any ability bonuses in it during leveling, and the weakest scaling, and not proficient we have:

-1 (Ability mod) + 0 (prof) + 0 (class mod) = -1 at level 1
-1 (ability mod) + 0 (prof) + 3 (class mod) = +2 at level 18 and onward

At the absolute maximum bonus, we assume a starting 18 ability score, putting ability bonuses to max it out, and the best scaling, and proficient we have:

+4 (Ability mod) + 2 (prof) + 1 (class mod) = +7 at level 1
+5 (ability mod) + 2 (prof) + 6 (class mod) = +13 at level 20

Now our ranges at level 1 go from -1, 0, 1, 2, 3, 4, 5, 6, 7; average of 3, and median of 3. Our ranges at level 20 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13; an average of 7.5, and a median of 7.5. So the average scaling between all characters between levels 1 through 20 is 4.5.

Scaling per Level

So if our average scaling is 3.5, this means that each level averages +0.225 increase per level. On the low end we have a 0.15 increase per level, and the high end of +0.3 per level. This is much slower than any previous edition. 

Nonthreatening Creatures

So when is a creature no longer a threat when it comes to attacking that creature? Is it when you only roll to make sure you don't have a 1, or perhaps when you have a 75% chance or better to hit? That is all a matter of opinion. So let's look at a 16 AC. This is a hard DC for skills, and will work fine for a numbers experiment. How long is Hard, well, hard to hit?

At level 1, our weak character needs a 17 or better, or a 20% hit chance, our strong level 1 character needs a 9 or better, or a 60% hit chance. At level 20, our weak character needs a 14 or better, or a 30% hit chance, and our strong character needs a 3, or a 90% hit chance.

But this isn't really a fair comparison, after all, how many players would gimp themselves to put their worst ability in their primary attack stat, and use a weapon that they aren't proficient with? I would wager none. So we can probably realistically assume that a player would not do anything less than a +2 ability mod (14 or 15), with +2 proficiency, and boosting that ability each time available. This means with the worst scaling we have a +4 at level 1, and a +7 or +8 at level 20. Using these numbers with your 16 AC it means our slow scaling character has a 50% chance to hit at level 1, and a 65% hit rate at level 20. A 10% difference from our best level 1, and a 25% difference at level 20.

Putting it all Together

Looking over it all, while gimping yourself horribly, you really do gimp yourself over the 20 levels, but something reasonable still keeps you very close to someone that maximizes everything. A 16AC is not a guarantee to be hit from level 1-20 no matter your scaling level, but obviously much easier to hit over time.

This fits bounded accuracy in the way they have described it. It allows for creatures to stay threatening longer. One can do well if they take a moderate approach, but can do very well if they overtly specialize. Scaling exists, but it's not breaking bounded accuracy, it allows for both scaling, but keeping scaling from getting into crazy numbers.

Bottom line, it works pretty well as is.

I've been looking at some people's criticism lately on the HP, rolling, not rolling, and how much healing one actually gets in a game compared to it. The playtest doesn't even seem to be using this rolled HP right now, I'm sure for ease of play issues, or quick starts at higher level.

This made me curious enough to sit down and do the maths on it all. At a point in this there will be a ton of charts. If you aren't interested in the charts don't click the link to the spreadsheet and just move on to the analysis.

Assumptions

The following list is the assumptions I will be using for this exercise. Much of this comes from the Constitution section of the current playtest.

• Level 1 HP is Constitution Score plus Hit Die Roll.
• Mundane healing is Hit Die plus Con bonus.
• Hit Die roll or Con bonus whichever is higher for leveling gains, adjusting the average accordingly.
• For the average number I will be adding all the possible numbers from a roll and dividing by the number of sides (example, a 2 con bonus on a d4 is 2,2,3,4 or 2.75).
• Any healing done is lossless. Basically I'm assuming every point healed actually heals hp and doesn't go over over max HP.
• No changes of the Con score throughout a career.
• Hit Dice are d4, d6, d8, d10, d12.
• Constitution scores between 8 and 20 used at the bonus threshold values.

The numbers that will be used will all be averages. While possible a fighter could end up with only 40 hp over his career, the odds of that are really really small, not even taking in account survivability, just probability.

The Charts

To make my life easy I plugged everything in an excel spreadsheet. Because really, who wants to do all that by hand? I can't just paste the spreadsheet here as it takes up far too much room. However, I uploaded it as a google doc here, so you can play with it yourself. The only thing you need to change is the Constitution Value in cell 21B. Everything else adjusts accordingly.

The Analysis

This proves what was already known with Con affecting the HP totals of low hit die characters more than high hit die. The d4 hit die doubles from 8 to 20 con, while d12 hit dice gain about 30 hp on average.

But playing with it more I found that a +1 is pretty good overall for all classes. This is the level that you can actually double your hp through your mundane healing. And oddly enough, it happens at 12th level for all classes. At level 13 the level where all classes are over 100% healing is 13th, oddly enough. At Con 14 the level you reach over 100% healing is 8. Between 14 and 19 it moves very slowly over level 7 to finish with everyone over 100% at level 6 with 20 con.

I also noticed that the total amount of healing stays mostly equal among all levels of con. Which I didn't expect at all.

So if rolls are truely random and the average is achieved it's really not a bad system to roll. Things stay pretty even over time.

But what if we want to have static HP? This works fine if nobody has a con over 13. Once you get a 14 or over on Con the average amount of HP changes by various amounts, again affecting wizards more than other classes. It's hard to say that you just take their HD/2 to get static HP. If you do this you are actually going to underpower yourself if you have high Con.

So basically rolling should work, and the con floor for HP does help overall hp, again more for the lower hit die characters, but overall between hit die healing and hp gained, they stay generally level throughout the leveling process except at the low (8) and high (20) levels of Con. Most characters however, will get the most by having an average con. My guess is about 12-14 is the sweet spot for most characters, so between a +1 or +2 bonus. But this doesn't mean that extreme levels of con aren't useful.

Ladies and Gentlemen of the Wizards community. I come before you a humble Cleric of Reason to impart my wisdom. Long have we been subjected to angry tirades by individuals that seem to be having knee jerk, and perhaps even violent reactions towards the playtest, it's materials, and even other posters.

This violence must be quelled.

If you come forth with a certain dislike, it is fine to say you have this dislike. It is even productive to do so. However, to dislike something with no reasoning behind your anger only serves to make you look like a buffoon.

I, as a messenger of Reason, wish to help you in this regard.

Back up your words of disdain with an organized rebuttal to why you believe this course of action does not work. It is preferable if you also have a solution to this problem, and how your solution can fix the issue, and not cause other issues in the process.

If you disagree with someone, the same rules apply. A well reasoned argument against someone elses opinion goes a long way not only to get your opposing view across, but it makes you seem like a reasonable person, and not a madman. If you do come agross as a madman, you are most likely going to be dismissed outright, and your words will fall upon deaf ears. This goes both ways. If someone disagrees with you they should approach you in the same manner.

When two people of opposing viewpoints speak to each other in a tone of reason and respect we have what is called debate. You do not need to win this debate. Sometimes viewpoints cannot be swayed, and sometimes they can. If two people discover that neither of them, even with their well laid out and explained opinions will switch to the other's side, or they find a fundamental difference in their approach to the same problem, they then agree to disagree. This does not make either of them right or wrong. Even if you sway someone to your side, you did not "win", nor did they "lose" you only found that the common ground was closer to one side than the other.

This debate may spark an idea in another reasonable individual, and perhaps this person can come up with a solution that satisfies both parties. They bring forth this idea in the same reasonable fashion, and both parties at odds may find themselves on common ground far from where they originally started.


If enough of you in this small community adopt the tenants of Reason, you shall find that while disagreements can and will happen, overall it becomes a more tolerable, informative, and pleasant place to be.

Thank you for your time, and may Reason guide you.

(Does that give me advantage on my charisma check?) Rolls 2d20.