I have seen many posts where people claim to have figured out a formula for damage, leveling, etc. My question is how does one come up this said formula? This is not something I ever learned in school and I am curious to learn however, I am not sure what to put into google.com to learn how to create formulas. Perhaps some of the math athletes could teach me, point me in the right direction, or whatever so that I can learn to do this?
It really depends on what you mean by "formula", a lot of the math on these forums is just based on probability.
For example; If you're a level 10 character with a +16 bonus to attack rolls, and you're fighting say an Elder Air Elemental with 28 AC, you need a 12 to hit, thus you have a 9/20 chance to hit, for let's say, 3d6+18 damage, which is an average of 28.5 damage (1d6 average is 3.5).
Assuming the elemental has 152 health, you need to hit ~5.3 times, let's round up and say that's 6 times.
From there it's simple mathematics, you need 6 hits and have a 9/20 chance to hit; the average amount of rounds it will take you to kill the elemental is 12.825 or ~13 rounds. The way you get this number is to multiply your chance to hit (9/20) by your average damage hit (28.5 in this case). This is an approximate, since it doesn't take into account that non-hits do no damage, rather than the percentage of the average, but it works well for theory-crafting as it's a baseline. Of course, you also have a chance to get a critical hit, to account for that you take the chance you have to get a critical hit, let's say you're using a 20/x4 weapon in this case without improved critical. You have a 1/20 chance of getting a x4 critical which will deal, on average 114 damage, this means you get around 5.7 extra damage per round from critical hits if you can automatically confirm them, if not you get 2.565 damage per round (9/20 * 5.7)(again this is purely in theory, given you have perfectly average randomization. One of the bigger problems with this kind of analysis is that there are spikes in damage rather than a constant stream of average damages). This ups your average per-round damage to 15.39, which reduces the number of rounds to 9.87 or approximately 10.
If you want to learn how to do this sort of this, look up probability and statistics math, but it's mostly intuitive anyway. Hope that helps!
Edit: Whoops, forgot that Elder Air Elementals have DR 10/-, this complicates things, but I don't have time to fix the math right now as I've gotta go to math class (irony get!), regardless the process is still valid.
|
| 2 people marked this as a favorite. |
It really depends on what you mean by "formula", a lot of the math on these forums is just based on probability.
For example; If you're a level 10 character with a +16 bonus to attack rolls, and you're fighting say an Elder Air Elemental with 28 AC, you need a 12 to hit, thus you have a 9/20 chance to hit, for let's say, 3d6+18 damage, which is an average of 28.5 damage (1d6 average is 3.5).
Assuming the elemental has 152 health, you need to hit ~5.3 times, let's round up and say that's 6 times.
From there it's simple mathematics, you need 6 hits and have a 9/20 chance to hit; the average amount of rounds it will take you to kill the elemental is 12.825 or ~13 rounds. The way you get this number is to multiply your chance to hit (9/20) by your average damage hit (28.5 in this case). This is an approximate, since it doesn't take into account that non-hits do no damage, rather than the percentage of the average, but it works well for theory-crafting as it's a baseline. Of course, you also have a chance to get a critical hit, to account for that you take the chance you have to get a critical hit, let's say you're using a 20/x4 weapon in this case without improved critical. You have a 1/20 chance of getting a x4 critical which will deal, on average 114 damage, this means you get around 5.7 extra damage per round from critical hits if you can automatically confirm them, if not you get 2.565 damage per round (9/20 * 5.7)(again this is purely in theory, given you have perfectly average randomization. One of the bigger problems with this kind of analysis is that there are spikes in damage rather than a constant stream of average damages). This ups your average per-round damage to 15.39, which reduces the number of rounds to 9.87 or approximately 10.If you want to learn how to do this sort of this, look up probability and statistics math, but it's mostly intuitive anyway. Hope that helps!
Edit: Whoops, forgot that Elder Air Elementals have DR 10/-, this complicates things, but I don't have time to fix the...
As a future kindergarten teacher, I expect my kids to be able to do this in their heads in the next ten-fifteen years. ;)
As a future kindergarten teacher, I expect my kids to be able to do this in their heads in the next ten-fifteen years. ;)
The fact that I cannot is irrelevant!
Agreed. This is easy stuff, don't know about kindergarten students doing it in their heads though. Too likely to be distracted. Besides, doing it in your head isn't impressive on it's own, doing it faster in your head than the guy with a calculator is what's impressive. (Not saying I can though XD)
|
Most of the math that I have seen floating around on these boards deal with statistics. There is no set list of things you have to do, you just need to think about what you need to solve and use your tools (math) to figure out what you need to do to answer the problem. We will do an expected value problem for simplicity.
For example: You want to know how much damage your 9th level Rouge with a Str 18 and a +2 Morning Star will do on a successful Sneak Attack.
Now you need to figure out 2 things. The first, what is the expected value of the d8 for the Morning Star. The second, what is the expected value of the 5d6 for your Sneak Attack. Off hand I know that both of these values are 4.5 and 3.5 respectively, but there is an easy way to calculate them if you wish.
Expected Value is E(X) and any individual event is x1, x2, ..., xn
Probability of x event 1 is p1, Probability of x event 2 is p2, ect.
Now: E(X)=x1p1+x2p2+...+xnpn where you can think of n as the final number in the sequence. For the d8 we have E(8)=x1p1+x2p2+...+x8p8. What this says is the Expected value of a d8 is equal to the probability of rolling a 1 multiplied by 1 plus the probability or rolling a 2 multiplied by two plus ... plus the probability of rolling an 8 multiplied by 8. Since it is a d8 with no special stipulations the probability or rolling any given number is (1/8)
So E(8)=[(1/8)*(1)]+[(1/8)*(2)]+[(1/8)*(3)]+[(1/8)*(4)]+[(1/8)*(5)]+[(1/8)*(6)]+[(1/8)*(7)]+[(1/8)*(8)]=(1/8)+(2/8)+(3/8)+(4/8)+(5/8)+(6/8)+(7/8)+(8/8)=(36/8)= 4.5
We could do the same thing for the d6 but it is easier to use the trick that expected value of a dice roll is generally half the value of the dice +.5: so a d8 would be (8/2)+.5= 4.5
A d6 is 3.5, a d4 is 2.5, a d3 is 2, ect.
So now we have the expected value of a d8 (4.5) and a d6 (3.5). Now we just need to plug in the numbers! Your damage will look like the following: 1d8+Str+Enchantment Bonus+Sneak Attack+Anything Else. so you have 4.5+4+2+5(3.5)+Misc Mods or 28+Mis Mod. Now you know how much damage you will do on average with a successful Sneak Attack!
Now you can also use probability in conjunction with expected value to figure out how much damage you will do on average per swing of a weapon. This will factor in miss chances and critical potentials as well!
I stole the following formula from the DPR Olympics because I didn't want to have to write. Its good and simple and will work for this case.
The damage formula is h(d+s)+tchd.
h = Chance to hit, expressed as a percentage
d = Damage per hit. Average damage is assumed.
s = Precision damage per hit (or other damage that isn't multiplied on a crit). Average damage is again assumed.
t = Chance to roll a critical threat, expressed as a percentage.
c = Critical hit bonus damage. x2 = 1, x3 = 2, x4 = 3.
Now, we need a base line AC to go against lets say 20. Our rouge above will have a +12 to hit (just a random number I'm using). So with a +12 we need an 8 or better to hit, which means we will hit 13/20 or 65% or .65 of the time, which means our h=.65!
Now, lets say we use the expected damage we figured above with no other modifiers giving us a d=4.5+2+4=10.5 and s=17.5!
We only crit on a 20 so our t=(1/20)=.05 and our c=1 since our Critical Multiplier is x2.
So lets plug and Chug!
(.65)(10.5+17.5)+(.05)(1)(.65)(10.5)~18.5!
So every swing of your Morning Star will net you about 18.5 damage. That includes miss chances and critical potentials!
I'm far from a math whiz (i haven't taken a math class since my junior year in high school), but that Expected Value equation seems crazy technical.
Is that more appropriate or exact than just saying "my expected value of a die roll is the average of 1 and the highest number on the die"?
Cause they seem to amount to the same thing. I'm not being smarmy... i'm genuinely curious.
I'm far from a math whiz (i haven't taken a math class since my junior year in high school), but that Expected Value equation seems crazy technical.
Is that more appropriate or exact than just saying "my expected value of a die roll is the average of 1 and the highest number on the die"?
Cause they seem to amount to the same thing. I'm not being smarmy... i'm genuinely curious.
The expected value of a non-weighted die that increments by 1 (IE it doesn't work for a d4 with sides of 1, 3, 5, 6; if you happened to own such an oddity.) is indeed the average of the lowest and highest sides. This works fine for Pathfinder dice, but the more general form of the equation is what Please Don't Kill Me spelled out.
To answer your question, yes it is more exact, but for the purposes of this discussion, you can probably ignore it and just use the simpler equation.
Ah, good to know. I appreciate the insight.
: walks off to draw a pretty picture :
| 1 person marked this as a favorite. |
To the OP, yes there are a few accepted "equations" that do things like provide average damage for a set of variables assuming properly balanced encounters, and stuff like that.
However, I personally don't put that much faith in them since to be generically applied they have to make some pretty basic assumptions and I've found that individual builds and tactics generally make those assumptions invalid pretty quickly.
So the power gamer part of me just builds my own custom equations or, more commonly, use Excel to create spreadsheets which let me play "what if" scenarios to see what my own unique character should do with their latest gold windfall.
This may come across the wrong way, so I apologize in advance, but my experience in dealing with people with similar requests (not just gamers, I deal with lots of people in my career who say "hey, how do you do that thing you did in Excel?") is that there is a certain critical mass of mathematical knowledge, practical experience, creative intuition and skill with appropriate tools that has to exist before the effort is likely to bear any fruit.
Or the TL:DR version, most people who do these sorts of things tend to be those that don't need to ask how to do them, and most who need to ask, don't really want to learn the skills needed to understand what they are doing.
So my recommendation is crank up Excel and start figuring it out for yourself.
Well said, AD!
|
I'm far from a math whiz (i haven't taken a math class since my junior year in high school), but that Expected Value equation seems crazy technical.
Is that more appropriate or exact than just saying "my expected value of a die roll is the average of 1 and the highest number on the die"?
Cause they seem to amount to the same thing. I'm not being smarmy... i'm genuinely curious.
Mathfinder - the game within the game!
-Skeld
For damage calculations I use an Excel spreadsheet myself (well OpenOffice now actually). It takes in average crittable damage, non-crit damage, threat range, confirmation bonus, to hit bonus, target AC and crit multiplier. It does take into account hitting on 20s and missing on 1s as well.
You fill in the relevant fields and it will spit out damage per round.
Here, just for example, is one formula from one calculation in one row of one of my damage calculation spreadsheets:
=MAX(0.05,MIN(0.95,1-($A12-($B$10+$C$1+$C$4+$C$5+$C$6+1))/20))*2*($C$7+$C$8 +$C$10)
This formula is to calculate the chance to hit for one attack using separate fields for AC, multiple fields for attack bonuses (feat, enchantment, attribute, buff, etc). Multiply this by the weapon damage value and it spits out the average damage for that one attack. Since this is from a two weapon build there are several other columns for other attacks.
The "min(max" portion is the part that forces a "1" to always miss and a "20" to always hit. Take this and put it in a couple dozen fields, modified as appropriate, and you get a spreadsheet which totals them into a single result.
Then you can go in and plug in values for the AC of the target, the bonuses for the character, the weapon damage type, etc...
Just make sure to =index(data,match(A8,Smurf,Match),Damage). You need to bump you figures inorder to sort out any differences and compare. :)
| 1 person marked this as a favorite. |
Or you could just play the game.
Shogun, that's only if you're utilizing the pivot smurfing tables.
Or you could just play the game.
As Skeld points out, there are games within the game. I certainly wouldn't tell someone who enjoys drawing sketches of their characters to "just play the game." As hard as it may be to understand for some folks, some of us actually enjoy the mathfinder game.
I hate pivot smurfing tables. Around here we us it to compare data exported from different sources, but I digress. It could have a valid application if one wanted to compare multiple sources of damamge, I think anyway. My excel kung-fu is lacking.
Agent Jay, crank up the excel for beginners and fire away.
I do a lot of job interviews and Excel is one of our core skill requirements. So our job application forms all ask about Excel skills asking people to rank themselves according to skill level. It goes something like this:
1. Beginner - Basic understanding of Spreadsheets
2. Intermediate - Has used Excel for data manipulation, calculation and reporting.
3. Proficient - Understands financial, mathematical and/or statistical formula utilization and can use them to analyze and process data.
4. Expert - Can teach Excel to others, understands macros, pivot tables and workbooks.
Everyone ranks themselves as "proficient" or "expert." So we get to the interview and it goes something like this:
Me: "So, you list yourself as proficient in Excel use, specifically with financial formulas. Could you create a loan amortization spreadsheet in Excel given the initial loan amount, the interest rate and the payment schedule?"
Them: "Huh?"
Me: "Yeah, could you give me a spreadsheet that laid out the entire loan payment schedule by payment date. For extra credit, could you have it automatically apply late fees and recalculate interest based on payment date?"
Them: "Huh?"
The last one I interviewed claimed to have taught Excel at a college. They didn't even know that you could have a macro automatically download data from a database using a data connection.
So inevitably I am always asked, "Where did you learn this stuff?"
"Google."
|
|
Or you could just play the game.As Skeld points out, there are games within the game. I certainly wouldn't tell someone who enjoys drawing sketches of their characters to "just play the game." As hard as it may be to understand for some folks, some of us actually enjoy the mathfinder game.
I love mathfinder! Even though I deal with numbers all day long, I'm a Pricing Analyst, I think its one of the best parts of the game. However, I also love the playing aspect as well and I try hard not to let the number cruncher in me build characters. As for using excel, I wouldn't dream of storing the data and running the calculations any other way.
On a side note Eben, the simple way is perfectly fine unless you are using an ability that says treat all x's as y's, then the expected value formula is a god send. Take a rouge using the Deadly Sneak rouge talent. The rouge now treats 1s, 2s, and 3s as 3s. So we just assume that a 1 and 2 is now a 3. So our formula is now E(6)=(0/6)*1+(0/6)*2+(3/6)*3+(1/6)*4+(1/6)*5+(1/6)*6= (24/6) = 4.
So now I know two rouge talents net me .5 more damage per SA dice. At 11th level that will be an average of 3 damage points per SA, knowing that I'll pass for something else.
|
|
Or you could just play the game.
My job involves a bunch of math. I actively try not to think about the math hidden in my hobby.
-Skeld
Or you could just play the game.My job involves a bunch of math. I actively try not to think about the math hidden in my hobby.
-Skeld
My job doesn't require a bunch of math. But I find that a bunch of math is highly beneficial to doing things in my job that my peers can't do. But my job does require planning, coordinating, generating lots of content and leading and directing groups of people to complete difficult tasks and bring them to successful conclusions.
I'm glad I don't mind doing that as a hobby too. :)
|
If you can do math(s), you don't find it burdensome. If you can't, there's a whole lot more work involved.
I regard mathematical ability as something akin to perfect pitch. There's not a lot you can do to learn the skill - either you have it, or you don't. (If you do have it, you can train the skill to be better at it, but you can't really teach someone the basic way of thinking that comes naturally to a mathematician).
Or you could just play the game.As Skeld points out, there are games within the game. I certainly wouldn't tell someone who enjoys drawing sketches of their characters to "just play the game." As hard as it may be to understand for some folks, some of us actually enjoy the mathfinder game.I love mathfinder! Even though I deal with numbers all day long, I'm a Pricing Analyst, I think its one of the best parts of the game. However, I also love the playing aspect as well and I try hard not to let the number cruncher in me build characters. As for using excel, I wouldn't dream of storing the data and running the calculations any other way.
On a side note Eben, the simple way is perfectly fine unless you are using an ability that says treat all x's as y's, then the expected value formula is a god send. Take a rouge using the Deadly Sneak rouge talent. The rouge now treats 1s, 2s, and 3s as 3s. So we just assume that a 1 and 2 is now a 3. So our formula is now E(6)=(0/6)*1+(0/6)*2+(3/6)*3+(1/6)*4+(1/6)*5+(1/6)*6= (24/6) = 4.
So now I know two rouge talents net me .5 more damage per SA dice. At 11th level that will be an average of 3 damage points per SA, knowing that I'll pass for something else.
Now we know why he likes numbers so much, *chuckles*, just kidding, I am far from a good speller.
So to sum up....
I need to
- look up probability and statistics math
- learn to use a spreadsheet(not necessarily excel?)
- spend time using learned math with spreadsheet program to profit
| 1 person marked this as a favorite. |
So to sum up....
I need to
- look up probability and statistics math
- learn to use a spreadsheet(not necessarily excel?)
- spend time using learned math with spreadsheet program to profit
Well, more accurately it is more like:
1. It is unlikely that any specific formula will give you what you need for your circumstance.
2. To make any formula useful will probably require modifications to whatever "formula" you find.
3. To make those modifications will probably require skills that if you had already, you probably wouldn't have been asking for the formula to begin with.
The math involved is not hard. It's pretty basic probability stuff that you can find with some quick google searches. A lot of the spreadsheet work is not difficult, it's tedious and will require some checking to make sure the results are right.
Good luck with it. The skills you apply to this effort will almost certainly end up being useful in other non-gaming circumstances and could actually provide value in your career or home life. Seriously.