calculating party level

[xyamius]

Hi all just attempting to understand this one.

When i use and online party calculator they always show party level = average member level and +1 per every two pc's over 4 in the party.

So 8 level 3 pc's show as a party level of 5.
when i look for something that shows this i can't seem to find anything. I thought it was add up parties level and divide by 4 to find it so 8 level 3's would be a 6.

Is it written some where that it's average party members level +1 for every 2 members past 4 in the party?

[ayvango]

The formula is quite simple. Assume that every monster, encounter, character, party has level assigned to it. The question is how do that level corresponds to its power? The power should be additive, so if you have two party members, you convert level of each member to additive power, adds number and convert back to party level. The dependency is simple exponent: for every two levels power raises two times.

[zlefin]

it's not that average party level +1 per 2 members is exactly correct; it's that it's close enough to be a good rule of thumb that's easier to do than the precise math (which would involve exponentiation and logarithms, done through a table, but still a bit more complicated than the simple rules, and the extra precision is generally unnecessary. I can spell out the details for you if you want them though)

all the math comes out of the 2 basic rule: 2 of a creature of cr X results in an encounter of cr X+2. so doubling the numbers increases cr by 2 (there are also some rules which note that continuing that indefinitely doesn't work so well, because huge numbers of weak things sometimes can't do anything)
and a player character has a cr = its level (or more precisely it's ECL, since that occasionally may be different from its level if other factors are involved)

[Feantar]

Is the a formula for this anywhere, or is this derived from the tables? Because the two posters above seem to hint at one that is complex, but give approximations (which are useful) - but still, is there a formula one can run the numbers through?

[zlefin]

Is the a formula for this anywhere, or is this derived from the tables? Because the two posters above seem to hint at one that is complex, but give approximations (which are useful) - but still, is there a formula one can run the numbers through?

I'm not aware of a place with the explicit formula; only with the derivations from the tables, and the general principles.
I should be able to figure it out though; i'll use a style similar to the one I do for coding; note that this involves exponentiation and logarithms, I'll assume you're familiar with them.

for each character, take 2^(char_level/2)

add up all of those values for each character; this will create a new value, which i'll call Y for now.

Then calculate the logarithm of Y, using a logbase of 2; then double that value; then subtract 4; and that is the party level (if I got the formulae right)
if the final value is less than 1 then things get a bit weird because iirc pathfinder and 3.5 use slightly different rules for how some low crs work; and i'm not exactly sure how it'd all work, but a value of -1 should be treated as matching a cr of 1/2, and a value of -3 should be treated as matching a cr of 1/4. There might also be some irregularities if you're using some level 1 chars, as pathfinder and 3.5 have different ways of handling them.

[Feantar]

I'm not aware of a place with the explicit formula; only with the derivations from the tables, and the general principles.
I should be able to figure it out though; i'll use a style similar to the one I do for coding; note that this involves exponentiation and logarithms, I'll assume you're familiar with them.

for each character, take 2^(char_level/2)

add up all of those values for each character; this will create a new value, which i'll call Y for now.

Then calculate the logarithm of Y, using a logbase of 2; then double that value; then subtract 4; and that is the party level (if I got the formulae right)
if the final value is less than 1 then things get a bit weird because iirc pathfinder and 3.5 use slightly different rules for how some low crs work; and i'm not exactly sure how it'd all work, but a value of -1 should be treated as matching a cr of 1/2, and a value of -3 should be treated as matching a cr of 1/4. There might also be some irregularities if you're using some level 1 chars, as pathfinder and 3.5 have different ways of handling them.

Thank you! I generally have trouble trying to extract formulas from tables. This should be it:
http://bit.ly/2x6NnI5
n, is the number of characters in the party
Ci, is the ECL of character number i

I'm assuming I should round down(hence the floor brackets) for non integer results as is traditional in d20. If I remove the rounding down, the lower bound needs to be adjusted to Z <=0, and I have no idea what to do in the (0,1) space. Except enjoy the concept of infinite CR :smallbiggrin:.

Z=\lfloor 2\log_{2}(\sum_{i=1}^{n} 2^{\frac{C_{i} }{2}}) -4\rfloor ,
CR =\begin{cases}Z & Z \geq 1\\ \frac{1}{1-Z} & Z < 1\end{cases}

[zlefin]

I don't think rounding down should be down, round normally if you're going to round; in fact, i'd recommend against rounding at all, as long as you're doing the fancy calculation, you might as well use the full number to get a better sense of the party's power. There's a modest but real power difference between Z = 5 and Z = 5.5;
this would be especially relevant if you use an encounter builder table like pathfinder's one http://www.d20pfsrd.com/gamemastering/#Step-3-Build-the-Encounter


As a reminder, there's a difference between pathfinder adn 3.5 CR rules; in 3.5 iirc, 2 cr 1 creatures results in a cr 2. whereas in pathfinder, 2 cr 1 creatures results in a cr 3.

I'm not sure how to properly formulate the 0 < Z < 1 area myself. but at least you can know the boundaries of it, which should suffice with a little estimating.

and you're quite welcome :)