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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

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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

May 1, 2012 -- 11:19AM, Mand12 wrote:

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 

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.

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

why not?