ok here ya go dave, i had to look around and find my notes (did them in lieu of listening to a history lecture the other day):
Monk, lvl6 with +4 attack bonus and +5 dex mod vs Rogue, lvl6 with +3 attack bonus and +5 dex mod and using (for the sake of a level playing field) a 1d6 weapon and has 100% sneak attack chance.
the monster they are attacking has AC 15 for this test.
*15.5 is 1 weapon attack plus 2 sneak attack dice plus dex mod, .91 is the rogue's chance to hit with advantage, 21.5 is the bonus damage that would be done on a critical hit, .0975 is the chance to roll a natural 20 (crit) with advantage
*8.5 is 1 weapon attack plus dex mod, 3.5 is 1 weapon attack with a 2x multiplier since the trial is done twice, 16.5 is bonus damage done on a critical hit, .05 is the chance for a critical per roll, and there is a 3x multiplier as all 3 rolls have a chance for this bonus damage
I might as well include the Fighter data while I'm here. Fighter will again be using (a laughable) 1d6 weapon for the sake of comparison:
*8.5 is 1 weapon hit plus strength mod with a 2x multiplier since he gets 2 attacks, 7 is the average damage of deadly strike, .9375 is the chance the fighter will get a hit with either attack and thus be able to use deadly strike, 16.5 is the bonus damage to the regular attacks gained from a critical with a 5% chance and a 2x multiplier for the second attack, 5 is the bonus damage recieved from a critical added to the deadly strikes, .0975 is the chance that either of the original 2 attacks will crit which would allow for the deadly strike damage to be maxed
By these values, fighter is definitely higher, rogue next, and monk last and this is with EVERYONE using a 1d6 weapon. that is of course absurd, but at least the numbers are on a level field.
2) A monk gets 10+wis mod+dex mod AC. If a monk gets +5 in both his AC is 20, which is better than a fighter without magical armor. It does require maxing his stats, but Dex and Wis are primary stats for the monk so it isn't too far out. The monk then, once he has high enough stats, can have the same defense as a sword and board fighter. They cannot choice to lose this AC for better damage, but if we build to close to the greatsword fighter then he has comparable damage to the best a fighter can dish out, and AC to match the fighter's best AC at the same time. I'd say this is better than being able to choose betwen defense and offense
So, the stat spread of D&DN is 15, 14, 13, 12, 10, 8. At level 4 and 8 you get a +1 to two ability scores. The only way to have a +5 stat bonus is to get a stat to 20. The only way to get a stat to 20 is to play a human, put that 15 into Wis, put your class bonus into Wis, put your race bonus into Wis, and increase Wis at levels 4 and 8. A fighter is going to do the same to its primary attack stat. You can't, because you just did that to Wis. You will probably put your 14 and the other two level based bonuses into your primary attack stat. So, to do what you just proposed, you will end up with a fighter who has an AC of at least 18 (heavy armor), possibly 19 (shield), and a +5 to hit and damage. A monk will have an AC of 20, but it will only have a +3 bonus to hit and damage. That amounts to a very large hit in its DPR (5.05 points to be exact). A monk having that bonus at level 10 is "too far out." Realistically, an optimized monk is going to have a Wis of 16, and an AC of 18, at level 10. That is the same AC a two-handed sword fighter will have at level 10. If the monk wants a higher AC they will take a hit to their DPR just like a fighter will by choosing to use a sword and board.
In fact, a fighter can achieve an AC of 20. You build a Dex fighter, spike Dex, use light armor, end up with a +5 bonus to AC from dex, and still get a +5 bonus to hit and damage. You then use a shield and a 1d6 finesse weapon. Your AC will be 20 and your DPR will be 33.10625; the monks DPR, with that AC, will be 19.95. Are you seeing the problem? And, this is ignoring the fact that the fighter can, at-will, swap out his +1 to AC for a katana and boost his DPR to 34.80625 . Or he can pick up a longbow and get a great DPR at range. All of which are options a monk does not have…
Do you see why I do the calculations the way I do? You have to balance things out at their maximized levels, because once you get to the space inside the boundaries, both classes can do the sorts of things you propose. If things are not balanced out at the highest end, at the fringes, then the things inside the space created by those fringe boundaries will not end up balanced either.
EDIT: Big FUBAR on my part. Lowering your Dex also lowers your AC. In other words, a monk simply cannot get an AC of 20 by level 10. A fighter, however, as I showed, can. And, when doing so, his DPR will be 33.10625. That is 8.10625 points above what a monk can achieve. And the fighter will have 2 points higher AC. And the fighter will have better ranged capabilities. And the fighter will be able to stow his shield and shortsword for a katana in order to boost his DPR to 34.80625, while still achieving an AC of 19, which is one point better than the monk's AC.
Because the monk has put its 15 starting stat, class bonus, and stat bonus into its Wisdom at character creation. That leaves it with a 14 to put into Dex. At level 4 that will become a 15. At level 8 that will become a 16. A 16 nets you a +3 bonus to hit and damage.
There is also a number of mistakes in your math. I am in the process of writing a post which shows what the numbers should look like.
So, first of all, I don’t understand why (Saffah) your monk and fighter have a +5 ability bonus at level 6. The best they could manage is +4. So, let us drop that to +4. That means the monk has a 70% chance of hitting AC 15. The rogue has a 65% chance of hitting that AC.
And, let’s not even the playing field. The rogue is using a 1d8 katana.
Rogue’s critical hit: 8 + 12 + 4 + 4d6 (14 average) for a total average of 38
Formula to calculate the rogue’s statistical damage per round: (15.5*0.60)+(38*0.05)=11.2
A monk’s damage with its first hit: 1d6 fist (3.5 average) + 4 (total average: 7.5)
Monk’s critical with its first hit: 6+4+4d6 (14 average) for a total average of 24
A monk’s damage with each of its flurry of blows: 1d6 (3.5 average)
Monk’s critical with each of its flurry of blows: 6+4d6 (14 average) for a total average of 20
Formula to calculate a monk’s statistical damage per round with its first hit: (7.5*0.65)+(24*0.05)=6.075
Formula to calculate a monk’s statistical damage per round with each of its flurry of blows: (3.5*0.65)+(20*0.05)= 3.275
Monk’s DPR: 6.075+3.275+3.275= 12.625
With a 1d6 fist a monk is dealing a greater DPR than a rogue with a katana…
That being said, those numbers are fairly well balanced against each other. Neither is well balanced against the fighter. The rogue, however, is far less conceptually interesting (as it is just a weaker fighter). The monk needs a minor power boost. The rogue also needs a power boost, but more importantly it needs to be made conceptually interesting.
Because the monk has put its 15 starting stat, class bonus, and stat bonus into its Wisdom at character creation. That leaves it with a 14 to put into Dex. At level 4 that will become a 15. At level 8 that will become a 16. A 16 nets you a +3 bonus to hit and damage.
There is also a number of mistakes in your math. I am in the process of writing a post which shows what the numbers should look like.
umm... If you had to sacrifice one of your two primaries to achieve a 20, why wouldn't it be Wis? Get a 20 Dex for your +5 to AC and since you wield finesse weapons you have a +5 attack bonus as well. Then that 16 is in Wis giving you an AC 18 and to-hit of +5 just like the fighter.
Also, I, for some reason, though that the +5 was at 19-20, not 20-21. I was going by odds first instead of evens. Guess I should have double checked the chart
Because the monk has put its 15 starting stat, class bonus, and stat bonus into its Wisdom at character creation. That leaves it with a 14 to put into Dex. At level 4 that will become a 15. At level 8 that will become a 16. A 16 nets you a +3 bonus to hit and damage.
umm... If you had to sacrifice one of your two primaries to achieve a 20, why wouldn't it be Wis? Get a 20 Dex for your +5 to AC and since you wield finesse weapons you have a +5 attack bonus as well. Then that 16 is in Wis giving you an AC 18 and to-hit of +5 just like the fighter.
I have no idea why you would choose to take a 20 in Wis. It should be Dex. My point was that you need a 20 in Wis in order to get a 20 AC. Where I FUBARED big is that I ignored the fact that doing so would not only decrease your bonus to hit and damage from Dex but also your bonus to AC from Dex. So, your AC would still be 18. In other words, there is no way for a monk to get a 20 AC by level 10. All he can manage is an AC of 18. A fighter, however, can manage an AC of 20. In doing so he will still have a DPR of 33.10625, which is about 8 points higher than the monks. In other words, a monk has absolutely nothing going for it at all... which, again, shows why you have to balance things from the highest end numbers. IE: a monks fists vs. a fighter's greatsword.
Have some company over so I can't get too detailed at the moment Dave, but you are definitely making some mistakes there, i'll try to get some time later to review it more.
Just some quick points for you to take into account quick:
first i think you are confusing the 2 characters you're working with for these comparisons. Like when I post about damage i think you are referring to your max AC monk for values rather than the damage monk. obviously you can't max everything at once neccessarily. Everything must be on a level playing field to do calculations though. So for example, when I do the numbers, the monk is of course going to have his best stats in the dexterity to get his hit chance up. All characters in the test are going to be assumed to be putting their maximum in the primary damage stat in a damage comparison.
2nd, i don't have the time atm to go into detail reading your math just yet but the rogue put up a big flag that both me and the guys at my house were like "OOOOOH NO /point fingers n laugh". when you do you rogue's accuracy, you are forgetting that if he's getting a sneak attack, he has advantage. there's no question of that, as advantage is a prerequisite of the sneak attack in the first place. therefore you need to adjust that accuracy rating. in the case you used where his base accuracy is 60%, you need to have it become (0.6 + ((1 - 0.6) * 0.6). That is the chance for the rogue to hit with advantage (in textbooks would be called something like the union of A and B).
additionally, the rogue's chance for a critical hit would also be increased by that same system, (0.05 + ((1 - 0.05) * 0.05).
3rd, as for the bonus damage from criticals, i saw you mention something about you weren't sure how to do that. the method i've been using is to simply say if the average damage of a 1d6 roll is ((1 + 6) / 2) = 3.5 then to increase that to maximum you would add (also on average) 2.5. so anywhere i see a max damage roll (for a 1d6 at least) that's an increase of 2.5.
4th, i think you are just assuming that everyone uses a point-buy system. Honestly I don't know any players (IRL that is, I'm sure people here are diffrent) that likes that method. With both the rolling method and the standard array system the player can have at least 1 17-18 to put into their primary stat. a 17 being all you need in order to get dexterity to 20 by level 6. (racial bonus + class bonus + level 4 stat increase, and an 18 would allow any race to have 20 dex at level 6)
first i think you are confusing the 2 characters you're working with for these comparisons. Like when I post about damage i think you are referring to your max AC monk for values rather than the damage monk. obviously you can't max everything at once neccessarily. Everything must be on a level playing field to do calculations though. So for example, when I do the numbers, the monk is of course going to have his best stats in the dexterity to get his hit chance up. All characters in the test are going to be assumed to be putting their maximum in the primary damage stat in a damage comparison.
Sorry, what? I did all the calculations assuming an 19 in your primary stat for attack and damage. I think you are getting different posts on different topics mixed up... I am not really sure what you are talking about. I am keeping the playing field level. I am giving all characters in the test their maximum value in their primary stat. At least in my post responding to you. There is another post where I talk to Chaos about what a monk would have to give up to get a 20 AC (and I did mess up in that post, but not in the way you are claiming, but we have already been over that in this thread).
2nd, i don't have the time atm to go into detail reading your math just yet but the rogue put up a big flag that both me and the guys at my house were like "OOOOOH NO /point fingers n laugh". when you do you rogue's accuracy, you are forgetting that if he's getting a sneak attack, he has advantage. there's no question of that, as advantage is a prerequisite of the sneak attack in the first place. therefore you need to adjust that accuracy rating. in the case you used where his base accuracy is 60%, you need to have it become (0.6 + ((1 - 0.6) * 0.6). That is the chance for the rogue to hit with advantage (in textbooks would be called something like the union of A and B).
additionally, the rogue's chance for a critical hit would also be increased by that same system, (0.05 + ((1 - 0.05) * 0.05).
You guys should be a little more careful, because now I am the one "pointing fingers and laughing." You don't need advantage to deal sneak attack damage. In fact, most of the time you will not have advantage. You merely need an ally to be adjacent to your target. Now, sometimes a rogue will have advantage. But then, sometimes the monk will too. The damage increase will raise in ratio. Sort of. Actually, in fact, it will be better overall for the monk, because he will now have 6d20 with which to try and roll a critical.
What is true, however, is that sometimes a rogue won't be able to deal Sneak Attack damage at all. A monk will always be able to deal flurry of blows. So, a monk will have an even higher overall DPR over the course of an encounter. My calculation for the rogue assumes Sneak Attack every round. If he doesn’t get Sneak Attack every round, it will actually be lower. The monk, however, has a flat DPR calculation.
3rd, as for the bonus damage from criticals, i saw you mention something about you weren't sure how to do that. the method i've been using is to simply say if the average damage of a 1d6 roll is ((1 + 6) / 2) = 3.5 then to increase that to maximum you would add (also on average) 2.5. so anywhere i see a max damage roll (for a 1d6 at least) that's an increase of 2.5.
What are you talking about? I said that calculating the damage for a proposed "roll expertise dice and take the highest number as a damage add" is somewhat complicated to calculate. Calculating the bonus damage from criticals is easy. And, in my math I did do so. It is the reason the monk’s flurry of blows is so much better than Sneak Attack or Deadly Strike. Although, I have no idea what you are trying to write there. That is not how you calculate the damage of a critical... unless I have misunderstood what you were trying to say. See my math. I show all my calculations. The formula for any given attack should be (X*Y) + (Z*0.05) where X is your average damage, Y is your statistical probability of hitting – 0.05, and Z is your average critical damage (maximize all dice and then add the average damage you would roll with your bonus critical dice).
4th, i think you are just assuming that everyone uses a point-buy system. Honestly I don't know any players (IRL that is, I'm sure people here are diffrent) that likes that method. With both the rolling method and the standard array system the player can have at least 1 17-18 to put into their primary stat. a 17 being all you need in order to get dexterity to 20 by level 6. (racial bonus + class bonus + level 4 stat increase, and an 18 would allow any race to have 20 dex at level 6)
anyway, i'll look more later when i have time.
Yes, I am assuming a point-buy system. Or rather, the standard array system, which is just a pre-build of the point buy system. Rolling stats is imbalanced. It will result in imbalanced builds. If you want to see how well classes are balanced you build characters using the pre-assigned/point buy stats. If you randomize stats/roll stats sometimes you will create, randomly, imbalanced characters. That is what happens when you use an imbalanced system like rolling stats. That is also why we don’t calculate balance on the basis of rolled stats. We take the assumed point buy values and calculate from there. So, at level one, any given character will start with a 15, 14, 13, 12, 10, and 8 in their stats (before they are modified by class and race). If you play a human you can get a 15+2 (from race) + 1 (from class) as your highest starting stat. That means that the highest stat you can start with is 18. At level 4 that turns into a 19. A 19 grants you a +4 bonus to hit and damage. At level 8 that turns into a 20. So, no, at level 6 you cannot have a +5 bonus to hit and damage (unless you rolled your stats. But, we have been over that).
I am 99.9% certain I did not make any mistakes in my math. When I look over what you wrote, it looks very wrong. Everyone who has done the math on Deadly Strike and Flurry of Blows is posting the same thing. Flurry of Blows deals a better average damage. Sneak Attack is just Deadly Strike with a restriction... I hate to say it, but I think you are wrong. Maybe I am missing something. Maybe I am out to lunch. But, in this instance, especially after reading your last post (which has information that is flat out untrue), I think you are just wrong...
