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10 months ago ::
Jun 21, 2009 - 11:04PM
#1
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So I'm a bit of a Math Freak. And I like DND. So what do I do at work when I'm bored? I do DPR/Feat Analysis Calculations. There are some topics which are rather less discussed than others, primarily when it comes to non-DPR calculations, so I figured, I'm making a reference manual for Char Op. This thread is here for me to post current workings on my Manual, rather than cluttering with multiple threads. As well as offer a place for someone to drop in and go "Hey, can you do this calculation for me." Calculations are on a first come first serve basis and I'd rather more complex ones (Don't drop basic DPR Calculations on me!). Hopefully I will fill this with Visual Aids (Graphs) and make this a resource for people to come to when deciding which Feats/Abilities to pick. Comments, Criticism are WELCOMED if not MANDATORY. If you think my math is wrong point out where! It's a learning experience for us all. EDIT: Can someone give me advice on how to put Tables In 
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10 months ago ::
Jun 21, 2009 - 11:05PM
#2
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Okay, this works now. Quick Analysis of Saving Throws.
[code]
Value of Increasing One’s Save Chance
Formula: (Save Chance)*(1-Save Chance)^(Number of Turns-1)
Turn Saved On vs Chance to Save = Probability that it will save
75% 70% 65% 60% 55% 50% 45% 40%
1 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40
2 0.19 0.21 0.23 0.24 0.25 0.25 0.25 0.24
3 0.05 0.06 0.08 0.10 0.11 0.13 0.14 0.14
4 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.09
5 0.00 0.01 0.01 0.02 0.02 0.03 0.04 0.05
6 0.00 0.00 0.00 0.01 0.01 0.02 0.02 0.03
However here is an example of average damage taken against ongoing
Ongoing Damage vs Chance to Save = Average Damage Taken from Effect
80% 75% 70% 65% 60% 55% 50% 45% 40%
10 12.50 13.33 14.28 15.37 16.64 18.11 19.84 21.88 24.30
20 25.00 26.67 28.57 30.75 33.28 36.23 39.69 43.77 48.60
30 37.50 40.00 42.85 46.12 49.92 54.34 59.53 65.65 72.90[/code]
Recursive Formula (For Barbarians Gaining MBA on Crit)
[code]Calculate DPR ignoring extra attacked gained
∞
Σ DPR*(CC^n)
n=0
OR
∞
DPR + Σ MBA*(CC^n)
n=1
Where MBA = Melee Basic Attack DPR and CC = Crit Chance.
In layman's terms: Sum to infinity of DPR times your Crit Chance to the power n. So DPR + Crit Chance*DPR + Crit Chance * Crit Chance * DPR and so on.
Due to diminishing returns and the limit of the function tending to 0 as n approaches infinity, we can garner an approximate value for the bonus of this ability based on crit Percentage.
Attack Number Increase In DPR
1 5.00% 10.00% 15.00%
2 0.25% 1.00% 2.25%
3 0.01% 0.10% 0.34%
4 0.00% 0.01% 0.05%
5 0.00% 0.00% 0.01%
Total 5.26% 11.11% 17.65%
Thus. At 5/10/15% Crit Chance, an extra MBA on a crit ability is worth 5.26/11.11/17.65% Additional DPR[/code]
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10 months ago ::
Jun 21, 2009 - 11:19PM
#3
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To Do List!
Add Ongoing 5/10/15
Probability of Not saving in 'x' turns (Cumulative Binomial Probability)
Average Length of Effects versus Save Chance
Upcoming
Power Attack Varied Analysis Across Tiers
When to pick up Weapon Expertise
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10 months ago ::
Jun 22, 2009 - 8:17AM
#4
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I think your chart for Ongoing Damage ought to include 5 and 15, since they're fairly common. If nothing else, it'll help DPR comparisons that involve Ongoing Damage. Nice work, good to see I'm not the only one slacking off at work. 
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10 months ago ::
Jun 22, 2009 - 8:20AM
#5
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If you could find some way to create a table of expected damage per level for all defense values, that would be wildly useful.
For example, if I'm trying to decide if my Warden can go without a shield (-2 AC and Fort) in favor of a greatspear, what levels does that make sense, and how much more damage should I expect if I do so?
I don't know if you have any useful datasets out there for this, though.
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10 months ago ::
Jun 22, 2009 - 8:45AM
#6
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For example, if I'm trying to decide if my Warden can go without a shield (-2 AC and Fort) in favor of a greatspear, what levels does that make sense, and how much more damage should I expect if I do so?
You can't get any useful information out of numbers for this example.
A greatspear requires a feat - so does a bastard sword.
So essentially you have shield + bastard sword (+3, 1d10) vs a greatspeat (+3, 1d10).
The trade off is Shield vs Reach, which is not something you can perform a quantitative analysis on.
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10 months ago ::
Jun 22, 2009 - 8:49AM
#7
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Wow, I realize I was totally unclear. I mean incoming damage to the PC, not how much damage he will be doing.
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10 months ago ::
Jun 22, 2009 - 9:02AM
#8
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Yeah, it would be interesting to see how much damage taken would change from raising or lowering your defenses once monster crits are taken into account. Average monster attack is level+14 I believe for Ac and level +12 for NADs.
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10 months ago ::
Jun 22, 2009 - 9:17AM
#9
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Please post the equation you use for the probability of saving. I feel that you should post the chance that they "don't save in turns 1-(n-1)" and not "save at turn n"
In math terms, p = chance to save, q = 1-p
you calculate p*q^(n-1)
you should calculate p*sum(q^i,i,0,n-1) or don't save in turn 1 then save + don't save in turn 1, 2 then save + ... n-1 then save
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10 months ago ::
Jun 22, 2009 - 9:26AM
#10
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Please post the equation you use for the probability of saving. I feel that you should post the chance that they "don't save in turns 1-(n-1)" and not "save at turn n"
In math terms, p = chance to save, q = 1-p
you calculate p*q^(n-1)
you should calculate p*sum(q^i,i,0,n-1) or don't save in turn 1 then save + don't save in turn 1, 2 then save + ... n-1 then save
Excel sheet is at work. Most probably would clear up my terms. Updating That Post with a recursive formula and will work out some of the questions added. Maybe relabel some tables too.
Edit: Formula is p*q^(n-1) as you wrote as per binomial distribution. You're always going to take the first installment of damage so I'll offer it up as an interpretation. But yeah, I'll update the sheet when I get the file off work tomorrow (I'm in Australia). Cumulative Probability sounds like a good start.
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