Battle Map Probability

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I am Baja and this thread is meant to define a method of estimating or determining the probability of a few harder to evaluate D&D statistics such as but not limited to:

Proning enemies
CA
Enemies Adjacent to the defender
Coup de Grace

For purposes of this thread, only standard encounters will be considered.
From the DMG, it will analyze the encounter templates:
BC - Battlefield Control
CT - Commander and Troops
DL - Double Line
WP - WolfPack


The Classes and Races will be limited to the Player's Handbook.
The characters will be limited to heroic for creation, but all books can be included.
Themes will not be included.
The battlemap total size will be limited to 50x50
Half the squares you can't interact with, a quarter are cover, and laying prone grants superior cover.
Party size will be exactly 5 members.
No two characters will have the same class.

Optional Rules of Thumb (this part could use some additions like dpr per party member, average round length per template):
mimimum of 50% accuracy
non-elites have less than 100-70hp at lv 10
Elites have 250-170Hp (cave bear L6 and dire bear L11)




The Binomial Distibution is useful for determining the number of successes per trial. 
The calculation requires determining the probability of the success for a single trial.

The Poisson Distribution is useful for determining the number of occurrences over time. 


Current Goal:
First we are starting with the probabability of proning against the BC template.

Determine the probability of a single success for the party to knock an enemy prone in the first round of combat against BC.
And model how likely continued proning will be.

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Proning


If it is just a power to prone, it would be ~50% likely, but if it is an encounter power then that is just for one time.

Early estimate of proning: three attempts per encounter with 50% accuracy

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CA

Party members can move to flank on the battlefield, and classes like the Rogue can attack from hiding for CA.  

Early estimate of CA: One enemy always granting CA to flankers

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 Enemies adjacent to the defender

The defender can move to an enemy, and can mark enemies. Some powers can move the enemies to the defenders. 

Early estimate of enemies adjacent to the defender: three from round 2 until the third to last round

---------------------------------------------------------------------------------------------------------------------------------------------

Coup de Grace

The wizard has sleep and the rogue has knockout.

Early estimate of coup de grace: 25% likely to happen once, one power attempted to yield helpless and another to perform coup de grace

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

So...how did you come to get these numbers, exactly?  I mean, those sure are nice Wikipedia-level definitions of statistical distributions, but you have absolutely zero detail on how or even whether you used them.
D&D Next = D&D: Quantum Edition
So...how did you come to get these numbers, exactly?  I mean, those sure are nice Wikipedia-level definitions of statistical distributions, but you have absolutely zero detail on how or even whether you used them.


No lol, first we are starting by determining the probability of a single success for the party to knock an enemy prone in the first round of combat against BC.

All I did was the asymptotic early estimates. Their explanation is stated. If it takes two powers to perform coup de grace, then it's 25% if each power is 50% accurate. 
 
I will probably use a photo to relay the math as typing it sucks.
example: imgur.com/Qw6Mb 

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

...so?  You've just stated that hit chances apply to powers.
D&D Next = D&D: Quantum Edition
There are for more variables than you can ever hope to encorporate (and some that you can't even give a numerical value to) and if you did try to take averages, it would be so far from real play as to be useless, if not harmful.
Back to Basics - A Guide to Basic Attacks You might be playing DnD wrong if... "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." Albert Einstein
I'm with the other guys, I really have no idea what you're trying to do here.

I mean... average encounters? You're trying to apply statistics to... DM imagination?
A few people posted after I posted so it might have been looked over, but here is an example what the distribution will look like for a particular number of successes per encounter:
imgur.com/Qw6Mb

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

So? 

You have no way of translating the expected number of 'prone' events in a combat into anything that's actually meaningful.
D&D Next = D&D: Quantum Edition
why not?

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

A few people posted after I posted so it might have been looked over, but here is an example what the distribution will look like for a particular number of successes per encounter:
imgur.com/Qw6Mb



While this might be an intersting mind game for completely abstract thought it has no actual relevence to the game at all.  We don't deal in complete abstracts, we play within concrete rules that can't be boiled down to the level you are trying to boil them down.  The game is just too situational.
Currently working on making a Dex based defender. Check it out here
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Need a few pre-generated characters for a one-shot you are running? Want to get a baseline for what an effective build for a class you aren't familiar with? Check out the Pregen thread here If ever you are interested what it sounds like to be at my table check out my blog and podcast here Also, I've recently done an episode on "Refluffing". You can check that out here
The number of actions is limited, the powers have limits, the encounters have limits, movement is limited, and a slew of other factors are limited.

What if I asked you what the maximum number of CAs granted could be in an encounter with four enemies and five pcs? 

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

Someone might guess four, but then another person would say that it would be 4 per turn. I would tend to agree that the maximum is 4 per turn. So if you can quantify the maximum, and you know the minimum is 0, then you can at least get the median.

Not to mention that you can model simulations, which is what the thread is for.

Some of you are asking what is the point, and the point is that it would good to know what the average chance of getting CA is when calculating your dpr. Or for another example it would be useful if you wanted to compare headman's chop vs d8 extra damage.

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

Someone might guess four, but then another person would say that it would be 4 per turn. I would tend to agree that the maximum is 4 per turn. So if you can quantify the maximum, and you know the minimum is 0, then you can at least get the median.




Which is completely irrelevant for the purpose of optimization.  So it shouldn't be in the character optimization forums.
Currently working on making a Dex based defender. Check it out here
Show
Need a few pre-generated characters for a one-shot you are running? Want to get a baseline for what an effective build for a class you aren't familiar with? Check out the Pregen thread here If ever you are interested what it sounds like to be at my table check out my blog and podcast here Also, I've recently done an episode on "Refluffing". You can check that out here
median, maximum, minimum, and average are the core of char op......

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

The number of actions is limited,



There are at least two ways to get inifinite actions.

the powers have limits,



Infinitely recurring attack sequences are reasonably straight forward.

the encounters have limits,



No. The DM can make the encounter exactly how he likes.

movement is limited,



No. 2 Evermeet Warlocks with planestrider boots give you an infinite teleport distance.

and a slew of other factors are limited.



Failed to see any so far.

What if I asked you what the maximum number of CAs granted could be in an encounter with four enemies and five pcs? 



That is a meaningless question.

Back to Basics - A Guide to Basic Attacks You might be playing DnD wrong if... "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." Albert Einstein
The number of actions is limited,



There are at least two ways to get inifinite actions.



How do you do that in heroic? I think after your targets die, you have to stop anyhow.

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

The number of actions is limited,



There are at least two ways to get inifinite actions.



How do you do that in heroic? I think after your targets die, you have to stop anyhow.



1) Who said anything about heroic?
2) Who said anything about having a target?
3) Everyone make sure to quote Baja if you want to keep the conversation rational, as he edits his posts very frequently, which is extremely unhelpful for narrative cohesion.

Edit: The answer to #1 is now in the OP.  The fact that #3 was used in order to put #1 there is... well "interesting".
Currently working on making a Dex based defender. Check it out here
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Need a few pre-generated characters for a one-shot you are running? Want to get a baseline for what an effective build for a class you aren't familiar with? Check out the Pregen thread here If ever you are interested what it sounds like to be at my table check out my blog and podcast here Also, I've recently done an episode on "Refluffing". You can check that out here
It's in the original post. I prefer to edit, rather than double post.

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

median, maximum, minimum, and average are the core of char op......



As mentioned it is so extremely abstract, with no relevance to any particular useful game aspect, as to be completely useless.  Those things are useful when applied to specific things in order to make comparisons between other specific things.  The idea of "CA" is just too general to be useful.

Also, Frostcheese is answer #2 to the maximum CA.
Currently working on making a Dex based defender. Check it out here
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Need a few pre-generated characters for a one-shot you are running? Want to get a baseline for what an effective build for a class you aren't familiar with? Check out the Pregen thread here If ever you are interested what it sounds like to be at my table check out my blog and podcast here Also, I've recently done an episode on "Refluffing". You can check that out here
What if I asked you what the maximum number of CAs granted could be in an encounter with four enemies and five pcs? 


I'd ask you why you think it matters.
D&D Next = D&D: Quantum Edition
How exactly would you apply any of this... stuff to actual DPR calculations?

Considering the literally infinite combinations of terrain, monster abilities, monster tactics, character capabilities and strategies the majority of which is under DM control and limited only by their imagination, your "average" calculations are as average as pulling random numbers out of your head.

Frost cheese sets the maximum, but I am seeking the average.  

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

Is CA combat advantage here? Hell, All my strikers have GUARANTEED CA. ITS TRIVIAL.
10/10 Would Flame Again: An Elite Paladin|Warlock The Elemental Man (or Woman): A Genasi Handbook The Warlord, Or How to Wield a Barbarian One-Handed The Bookish Barbarian Fardiz: RAI is fairly clear, but RAZ is different That's right. Rules According to Zelink!

Frost cheese sets the maximum, but I am seeking the average.  


Why?  What purpose are you seeking the average for?  What does that average number mean?

You need to answer these things before you go do the math.
D&D Next = D&D: Quantum Edition

Frost cheese sets the maximum, but I am seeking the average.  



The average for a character with frostcheese is maximum.
Currently working on making a Dex based defender. Check it out here
Show
Need a few pre-generated characters for a one-shot you are running? Want to get a baseline for what an effective build for a class you aren't familiar with? Check out the Pregen thread here If ever you are interested what it sounds like to be at my table check out my blog and podcast here Also, I've recently done an episode on "Refluffing". You can check that out here

Frost cheese sets the maximum, but I am seeking the average.  



The average for a character with frostcheese is maximum.



I'm trying to think of the last time any of my melee characters didnt have CA...
10/10 Would Flame Again: An Elite Paladin|Warlock The Elemental Man (or Woman): A Genasi Handbook The Warlord, Or How to Wield a Barbarian One-Handed The Bookish Barbarian Fardiz: RAI is fairly clear, but RAZ is different That's right. Rules According to Zelink!
How exactly would you apply any of this... stuff to actual DPR calculations?

Considering the literally infinite combinations of terrain, monster abilities, monster tactics, character capabilities and strategies the majority of which is under DM control and limited only by their imagination, your "average" calculations are as average as pulling random numbers out of your head.



I sited an example previously, but I am happy you asked because not everyone is going to read through every page. 

Suppose you are comparing your odds of CA for an accuracy boost so you can use feats on damage vs using your feats on accuracy. Well if you see that the average for standard encounters of the templates covered in this guide yields an expectation that an average party produces CA every turn, you would see more benefit in utilizing the damage feats. 

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

How exactly would you apply any of this... stuff to actual DPR calculations?

Considering the literally infinite combinations of terrain, monster abilities, monster tactics, character capabilities and strategies the majority of which is under DM control and limited only by their imagination, your "average" calculations are as average as pulling random numbers out of your head.



I sited an example previously, but I am happy you asked because not everyone is going to read through every page. 

Suppose you are comparing your odds of CA for an accuracy boost so you can use feats on damage vs using your feats on accuracy. Well if you see that the average for standard encounters of the templates covered in this guide yields an expectation that an average party produces CA every turn, you would see more benefit in utilizing the damage feats. 




Accuracy > Damage,  The fact that you don't know this, concerns me. The damage bump has to be REALLLLLYYYY high and your riders have to be irrelevent for damage to be more important than attack.

10/10 Would Flame Again: An Elite Paladin|Warlock The Elemental Man (or Woman): A Genasi Handbook The Warlord, Or How to Wield a Barbarian One-Handed The Bookish Barbarian Fardiz: RAI is fairly clear, but RAZ is different That's right. Rules According to Zelink!
How exactly would you apply any of this... stuff to actual DPR calculations?

Considering the literally infinite combinations of terrain, monster abilities, monster tactics, character capabilities and strategies the majority of which is under DM control and limited only by their imagination, your "average" calculations are as average as pulling random numbers out of your head.



I sited an example previously, but I am happy you asked because not everyone is going to read through every page. 

Suppose you are comparing your odds of CA for an accuracy boost so you can use feats on damage vs using your feats on accuracy. Well if you see that the average for standard encounters of the templates covered in this guide yields an expectation that an average party produces CA every turn, you would see more benefit in utilizing the damage feats. 




But that's talking about spread of resources. You only have CA all the time because you have spent resources on it. If you spend those resources on damage instead you no longer have CA. Do you understand the futility of your actions?

Just come to the dark side. We have cookies! 

Back to Basics - A Guide to Basic Attacks You might be playing DnD wrong if... "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." Albert Einstein
Why?  What purpose are you seeking the average for?  What does that average number mean?

You need to answer these things before you go do the math.

I think this is the real problem here. Your numbers are meaningless with so many random variables. You're trying to figure out the average number of angels that can dance on the head of a pin. Since we know the planck constant and assume God plays by his own rules, that's somewhere between 5.1 × 1096 and 0. There, you've got numbers for an average! Now you can apply that to proper pin design to maximize individual angel dancing space.



Accuracy > Damage,  The fact that you don't know this, concerns me. The damage bump has to be REALLLLLYYYY high and your riders have to be irrelevent for damage to be more important than attack.




That was an example. For more on that topic I recommend community.wizards.com/go/thread/view/758...

Concisely: I want a system where players don't have to pick between mechanics and roleplaying. I hope 5E fails asap so a better system can be made asap.

( I can't believe what they did to the forums. The sterile lack or color is rather depressing. )

 

For more on that topic, I refer you to the fact that the fallacy is a lie.
10/10 Would Flame Again: An Elite Paladin|Warlock The Elemental Man (or Woman): A Genasi Handbook The Warlord, Or How to Wield a Barbarian One-Handed The Bookish Barbarian Fardiz: RAI is fairly clear, but RAZ is different That's right. Rules According to Zelink!
Due to complaints received about this thread, I've closed it. The thread will be reviewed by the Community leads to determine if it should be permanently closed, re-opened, and/or a new thread or threads created in its place.

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