If you are hitting 10% of the time, a +2 to your attack will double your frequency, which will roughly double your damage. If you are hitting 85% of your time a +2 will increase your frequency of hitting by about 11% and increase your damage by roughly the same percentage.NOTE: This is why, if you have the choice to buff one of two melee combatants, it is frequently better to buff the one who is hitting LESS, not the one who is hitting MORE.
If what you want is maximizing the group DPR (ie the sum of the individual DPRs), you don't buff the one that is hitting less or the one that is hitting more, but the one that is hitting harder.
Let's say you have a fighter (hits 80% of the time for 10 hp, DPR 8) and a cleric (hits 50% of the time for 8 hp, DPR 4). If we follow the "buff the one hitting less" principle, we'll buff the cleric. Let's say it is a +2 bonus, the cleric dpr increases to: 60% * 8 = 4.8, which is a 20% increase. That buff, applied to the fighter, would have been an increase of 12.5% (DPR goes from 8 to 9). Hey look like the cleric option is better.
But for the group, the total DPR has gone from 12 (fighter 8 + cleric 4) to 12.8 (Fighter 8 + Cleric 4.8)
If we'd buffed the fighter, total DPR had gone from 12 to 13 (Figher 9 Cleric 4).
This is because the greater increase (in %) is countered by the lower base which we are increasing.
Remember that a +1 to hit means adding 5% of your average damage per hit (ie how hard you hit) to your DPR.
If the cleric hits 50% of the time for 12 hp (DPR 6), a +2 bunus is still a 20% increase (to 7.2), BUT this time the plain DPR increase is 1.2 (while the fighter is 1).
There are some reasons though (like tactical ones), to buff the cleric.
Who would've thought that wondrous lands of imagination, without the boundaries of the real world, would have such rigid statistical values...
The 5% more damage comes from the DPR formula.
Part of that formula is your chance to hit in the form of a percentage (never less than 5% and never higher than 95%) used as a multiplier.
so all else being equal, in terms of the DPR formula, a +1 to hit will add 5% of your maximum damage potential to your DPR unless you already had a 95% chance to hit.
that people misinterpret this fact is another issue.
/thread
Would it be fair to say that having a +1 makes it 5% more likely to have an end result of 20+ (call it an effective 20) with the roll of a single d20? Seems like it makes sense to me, even though it is largely useless for determining Damage or to hit chance without looking at AC and damage dice, or taking into account the auto fail rule :P At least it explains where the fallacy is coming from :)
modifier %effective 20
0 1/20
1 2/20
2 3/20
... ...
20 20/20
Who would've thought that wondrous lands of imagination, without the boundaries of the real world, would have such rigid statistical values...
Anyone who's glanced through the Core Rulebook once or twice.
I, for one, welcome the revolution.
Bob the Barbarian uses a greatsword (2d6). The avg. damage on a hit is 7. Coincidentally, his damage bonus is +13, for an avg damage, when he hits, of 20. If Bob needs a 1 to hit (we'll ignore auto misses and crits for simplicity), then Bob will do, on avg., 20 pts. of damage each rd. Sometimes he'll do more, sometimes less, but, over time, he will do an average of 20 pts of damage. We'll call this his theoretical avg. damage (Theoretical because achieving 100% of average damage is impossible due to auto miss on a 1).
Bob, however, doesn't hit on a 1, he hits on an 11. In any given round Bob has an equal chance to hit or miss. Over the course of a long battle, Bob will hit as many times as he misses. Since he has a 50/50 chance of doing either 20 or 0, his avg. damage over the course of a few battles will be 10 (.5 times theoretical avg. damage of 20).
If Bob gets a +1 to hit, he will now hit 55% of the time. His avg. damage will now increase to 11 (.55 times 20), or an additional 5% of his theoretical average damage.
If Bob gets another +1 to hit, he will now hit 60% of the time and deal an average 12 pts. of damage.
As long as Bob needs more than a 2 to hit, and less than a natural 20, each +1 to hit does, in fact, increase the damage by 5% of his theoretical average damage. Whether that doubles his chance to hit (as in going from 20 to 19-20) or doubles his average damage (again, going from 20 to 19-20), or any other target numbers, is totally irrelevant.
When deciding whom to buff the answer is simple: Buff the person who does the most damage, regardless of his/her/its To Hit number, as long as that person/creature/object hits on more than 3 and less than a natural 20.
Mynameisjake:
Using your example of Bob the Barbarian:
The damage increase from 10 DPH to 11 DPH is an increase of ((11/10)-1)100 = 10.00% rather than 5%.
The increase in from 11 DPH to 12 DPH is: ((12/11)-1)100 = 9.09%
+1 to attack does indeed result in a 5% bonus to the odds of your attack hitting. (Assuming you are not capping out at only 1's miss.) It does not necessarily translate to a 5% bonus to damage per hit. Nor does it necessarily translate to a 10% bonus to damage per hit.
Example where it does not translate to a 10% bonus to damage per hit:
Lets assume that a person is on the last attack of his sequence. He is doing an avg 20 damage but his last attack only hits on a 19+. That is an avg of 2 DPH. If we increase the accuracy by 5% his DPH becomes 3. This is a 50% damage increase. Well above the 10% the OP suggests.
- Gauss
None of which is particularly relevant. It is the average damage over time that matters, not the effect on a single data point.
Mynameisjake, the discussion is about the effect of a +1bonus to hit and whether that translates to a 5%, 10%, or something else damage boost. So it is relevant to the OPs discussion.
Your own post was about the single data point despite your using terminology such as damage per round. The reason for my statement is that you were using the calculations for a single attack. Multiple attacks would have different bonuses. However, lets go with that for a moment:
Assuming a level 20 Barbarian with an average damage of 51 per hit. Again, discounting crits as you did (although they really should be counted) we come up with:
An attack bonus in the vicinity of BAB+20, Enhancement Weapon bonus+7, Starting Strength bonus+4, Enhanced Strength bonus+3, Level strength bonus+2, Weapon Focus+1, Rage+4, Power Attack-6 = +35
And average damage of: 2d6+7weapon+13strength+6rage+18power attack = 51avg DPH
Enemy AC of 36 (avg AC listed in the Bestiary Table 1-1 for a CR20 creature)
First attack: 95% chance to hit = 48.45
Second attack: 75% chance = 38.25
Third attack: 50% = 25.5
Fourth attack: 25% = 12.75
Total: 124.95
Now lets add in a +1 bonus from say, bless.
First attack: 95% chance to hit = 48.45
Second attack: 80% chance = 40.80
Third attack: 55% = 28.05
Fourth attack: 30% = 15.30
Total: 132.60
Now what are the differences per attack and total?
First: 0.00%
Second: 6.67%
Third: 10.00%
Fourth: 20.00%
Total: 6.12%
Now, you have your average over time. It is still neither 5% nor 10%. A 5% accuracy increase does not necessarily translate to a 5% damage increase. Nor does it necessarily translate to 10%. It depends on the attack bonus initially used.
- Gauss
Dafuq is a "time pneumonia"?
Am I going to start sneezing years off the end of my life? Because that would suck.
OK - here's a simpler question.
You have two weapons, both of which do the same base damage.
One of them threatens a critical on a 19-20, for 2x damage.
The other only threatens on a 20, but does 3x damage then.Which increases your average DPR more (and by how much)?
The spoilered part is easy. If you only hit on a 20 the weapon with the x3 is clearly better because you threaten with every hit. And as the damage if you confirm this crit is higher.
In other words:
(Assuming you only hit on a 20 and you rolled one)
x2: you have a 95% chance to deal normal damage and a 5% chance to deal double damage. This equals an average hit of 105% damage.
x3: You have a 95% chance to deal normal damage and a 5% chance to deal tripple damage. This equals an average hit of 110% damage.
NOTE: This is why, if you have the choice to buff one of two melee combatants, it is frequently better to buff the one who is hitting LESS, not the one who is hitting MORE.
That largely depends on how/what you buff. If you buff his to hit chance you are right.
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Thank god none of this matters when I cast fireball.
+1 to hit means you have a 5% more of a chance to hit.
It's math and that's a fact.
11 or higher to hit is a 50% chance to hit
12 or higher to hit is a 45% chance to hit
13 or higher to hit is a 40% chance to hit
14 or higher to hit is a 35% chance to hit
15 or higher to hit is a 30% chance to hit
16 or higher to hit is a 25% chance to hit
17 or higher to hit is a 20% chance to hit
18 or higher to hit is a 15% chance to hit
19 or higher to hit is a 10% chance to hit
20 to hit is a 5% chance to hit
All the extra numbers are applied before the number that needs to be rolled. That final number then is the only thing that matters when determining percentage chance to hit. You will always roll a d20 and it will always only have 20 sides.
Oh and .05*20 = 1 or whole or 100% for this discussion, so you know this is right even before my breakdown from above.
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Thank god none of this matters when I cast fireball.
LOL thanks:) I needed that laugh.
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+1 to hit means you have a 5% more of a chance to hit.
Ambiguous language. 5% has to be 5% of something.
Ignoring crits & edge cases like super-high or super-low ACs:
Fact: "+1 to hit means you have a 5%-of-certainty more of a chance to hit."
Not a fact: "+1 to hit means you have a 5%-of-your-current-hit-chance more of a chance to hit'.
Fact: "+1 to hit means your average damage per attack increases by 0.05 times your damage per hit."
Fact: "+1 to hit means your average damage per attack increases by ((your current hit chance + 0.05) / (your current hit chance)) times your current average damage per attack."
Or something like that.
Suppose you have a lottery ticket, and I offer to sell you something that will increase your chance of winning the lottery by roughly 100%.
That could mean another unchecked lottery ticket, which increases your chance of winning by 100% of your current slim chances.
Or it could mean a winning lottery ticket, increasing your chance to an absolute 100%.
It depends on what it is 100% of.
+1 to hit means you have a 5% more of a chance to hit.
Ambiguous language. 5% has to be 5% of something.
Ignoring crits & edge cases like super-high or super-low ACs:
Fact: "+1 to hit means you have a 5%-of-certainty more of a chance to hit."
Not a fact: "+1 to hit means you have a 5%-of-your-current-hit-chance more of a chance to hit'.Fact: "+1 to hit means your average damage per attack increases by 0.05 times your damage per hit."
Fact: "+1 to hit means your average damage per attack increases by ((your current hit chance + 0.05) / (your current hit chance)) times your current average damage per attack."Or something like that.
Suppose you have a lottery ticket, and I offer to sell you something that will increase your chance of winning the lottery by roughly 100%.
That could mean another unchecked lottery ticket, which increases your chance of winning by 100% of your current slim chances.
Or it could mean a winning lottery ticket, increasing your chance to an absolute 100%.
It depends on what it is 100% of.
If you have a +1 to hit added to your die roll after all calculations are done, it's a 5% increase. It doesn't matter how you look at it or try to add other known or unknown variables (like your lottery example.)
Everyone has to roll a d20 to hit. A d20 has 20 sides. That means every time you roll a d20 you have an equal chance of getting one of those sides, regardless of the amount of times you roll it. Adding a +1 to that roll increases the number of sides that is counting as a successful hit by 1. That's an increase of 5%. 100% (total value of whole)/20 sides = 5% per side.
LOL, math is hard. Reading seems to be difficult too.
You can lead a horse to water....
@Gauss: We will just have to agree to disagree. If I may offer a piece of advice, however, stay away from poker tables. Unless it's mine, of course, then just be sure to bring lots of extra money. ;)
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I don't know whether to laugh or cry.
Mynameisjake: What are we disagreeing on exactly? The math is sound. As Matthew Downie stated it is all about the language.
Regarding poker: what does poker have to do with it?
To everyone: I think we are all getting hung up on the language.
- Gauss
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JDNYC: a +1 bonus is a 5% increase. However, it is also a fractional portion of your previous chances to hit. It depends on the language.
Correct statement: I have a +1 bonus to hit which gives me a 5% increase to hit.
Also a correct statement: I have a +1 bonus to hit which gives me a 5% increase. Because my normal accuracy is 10% that +5% is a 50% increase in my chances to hit the target.
Notice how it is both 5% and 50% in this example. It depends on the language.
- Gauss
Skeld: Nobody plays this way, they just argue this way on the boards. This is what people do for entertainment when they are not playing and actually having real fun. :)
- Gauss
I find it mind-boggling that some people play this way (and I'm a rocket scientist). O.o
More power to you guys.
-Skeld
Skeld, assuming you are making a reference to the statistical and probability postings on this thread and assuming that since some of us understand probability we must be some sort of math nerds who bring our TI-98 programmable calculator to the gaming table...
That's not how "we" play. At least it's not how I play. This is similar to the Stormwind Fallacy, you can understand math and probability and make informed decisions about game mechanics without being a nerd-savant who does differential equations at the gaming table.
If anything at the game table I am regarded as the role playing dude, not the number cruncher.
^It's a TI-83+ I bring to the table actually.
I use it to keep track of EXP.
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Ryn, that's why I abandoned the ancient mathematical abomination known as Ex Pee a long time ago.
I have never looked back. XP was a bad idea that has been propagated through sheer inertia and tradition.
Level your PCs up by plot. There's no bookkeeping and you always know what your encounter level will be.
I like EXP for a few simple reasons:
1.) It keeps leveling somewhat randomized. I enjoy that, and so does everyone else at the table, so it works out.
2.) IMO, it gives incentive to explore areas of the dungeon. You go in a room, fight some monsters, and take a look around. With event based leveling, if you find s&+!ty loot or a non-interesting room, well tough luck. With EXP based leveling you can at least say "Well this room was garbage, but at least I'm 500 EXP closer to leveling!"
3.) Playing a game without EXP feels very odd to me. It's like Xbox 360 achievements where you get 150 gamerscore for beating the game and 20 for each of the levels or something. No. Why should you get rewarded for getting somewhere you're supposed to get anyway? It seems less earned to me.
To me, the less bookkeeping is a small upside to the event based leveling system.
Not saying it's bad, just doesn't seem up my alley.
...assuming that since some of us understand probability we must be some sort of math nerds...Heh, don't take my bemusement as an indication I'm unfamiliar with or skeerd of probability and statistics. ;) Quite the opposite, actually.
-Skeld
Well, I should hope so, being a rocket scientist and all.
Although there is this...
"Rocket science isn't rocket science" - Wehrner Von Braun
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If you have a +1 to hit added to your die roll after all calculations are done, it's a 5% increase. It doesn't matter how you look at it or try to add other known or unknown variables (like your lottery example.)
Everyone has to roll a d20 to hit. A d20 has 20 sides. That means every time you roll a d20 you have an equal chance of getting one of those sides, regardless of the amount of times you roll it. Adding a +1 to that roll increases the number of sides that is counting as a successful hit by 1. That's an increase of 5%. 100% (total value of whole)/20 sides = 5% per side.
Let's see if this example is better:
You have a chicken and eat it.I give you another chicken. You eat it too.
You say "I only ate one chicken more".
I say "You have eaten today double the food you had".
Are you right? Yes. Am I right? Yes.
Now let's say I don't know how many chickens you have eaten. If I give you one chicken, you can still say "I only ate one chicken more". But what determines the utility of a new chicken is how many chickens you ate before. If you didn't ate anything before, that chicken is really meaningful to calm your hunger; if you ate 20 chickens (well let's say 19 to avoid corner cases of critical chickens), the new one is not very useful to you.
So... if you have a 20-sided die, and you only hit with a natural 20, and then I buff you for a +1 to hit, you have 5% more chances of hitting than before, but you ALSO have doubled the die sides that mean a success hit.
Skeld, "Rocket science" gained the reputation of being a highly precise and technical discipline because of many very public and dramatic failures. To the public it appeared that the science of rocket science must be very difficult.
As a physicist I understand that the science of rocket science really isn't all that difficult. It's mostly all about chemical reactions, materials, metallurgy, systems architecture, etc.
What is very very hard about rocket science is the engineering. While the basic concept of combining fuel in an engine and directing the thrust is pretty simple, the actual application of the principle requires dealing with extremes of temperature (both cold and hot), force, reaction, balance and a whole lot of other things.
Designing a rocket engine is one thing. Building one that works is a whole 'nother ball of wax.
One little rubber O ring is all that stands between brilliant success and catastrophic disaster...
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This thread has convinced me that all my monsters need an AC of three million. That way, my players will only hit on a natural 20 no matter how often they get a +1 to hit. And they'll never confirm a crit, because my monsters have all cast a reversed bless weapon on them before combat. Yeah, my monsters can reverse spells. Can't yours?
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Skeld, "Rocket science" gained the reputation of being a highly precise and technical discipline because of many very public and dramatic failures. To the public it appeared that the science of rocket science must be very difficult.
As a physicist I understand that the science of rocket science really isn't all that difficult. It's mostly all about chemical reactions, materials, metallurgy, systems architecture, etc.
What is very very hard about rocket science is the engineering. While the basic concept of combining fuel in an engine and directing the thrust is pretty simple, the actual application of the principle requires dealing with extremes of temperature (both cold and hot), force, reaction, balance and a whole lot of other things.
Designing a rocket engine is one thing. Building one that works is a whole 'nother ball of wax.
One little rubber O ring is all that stands between brilliant success and catastrophic disaster...
This made my chuckle.