Determining Encounter Level

Has anyone seen a program or know of an algorithm for determining the encounter level for an arbitrary group of creatures with different challenge ratings?

The table in the DMG gives specific combos of creatures such as the "mixed pair" or the rule for doubling the number of creatures of a specific CR adds 2 to the encounter level. But is there a set procedure for determining EL when you have numerous creatures of various CRs?

If you have k sets of creatures with different CRs, and set them up as ordered pairs (Ni, Ci), where for each i, N is the number of creatures with CR C, then the formula you seek is:

gravyboat said:

Has anyone seen a program or know of an algorithm for determining the encounter level for an arbitrary group of creatures with different challenge ratings?

The table in the DMG gives specific combos of creatures such as the "mixed pair" or the rule for doubling the number of creatures of a specific CR adds 2 to the encounter level. But is there a set procedure for determining EL when you have numerous creatures of various CRs?

Click to expand...

Here are links to two different online generators that might help.

http://www.enworld.org/cc/fiend_factory/elc/encounter_calculator.htm
http://www.wizards.com/default.asp?x=dnd/dnd/20010320b

Later...

LazarusLong42 said:

If you have k sets of creatures with different CRs, and set them up as ordered pairs (Ni, Ci), where for each i, N is the number of creatures with CR C, then the formula you seek is:

Click to expand...

Sweet! I'm going to run through a couple of examples to numericaly check the formula. Did you derive this formula yourself?

LazarusLong42 said:

Click to expand...

Yes, how did you come up with this? Part of it looks like it's empirically derived. (And yes, I believe it works.)

I can see how & why the part in parenthesis works, but I got completely lost when I got to the "6.6439 log" part. The 6.6439 doesn't look like a constant that should be in any rational formula, and the base-10 log doesn't look like it belongs either.

After puzzling it out a bit, I discovered what I think "should" be the correct formula ... the same, except the log should be to the base 2 and the constant multiplier should be simply 2. So, if you're using a language that supports a base-2 log, then the first part of that formula should just become:
Both the multiplier and the log's base make much more sense in context this way.

Of course, if you don't have a base-2 log in your programming language or calculator, then the above constant gives you the same answer (plenty close enough) when using a base-10 log.

FYI: Another formula simplification is also possible. If you're doing this by hand, it's easy to count up how many creatures of each CR to plug into the list in the formula. However, when using computers you may often simply have a list of all the individual CR's without having them pre-counted. If this is the case, then you can simplify the summation by removing the "N(i)" term entirely and just have "C(i)" be each monster's CR (for "k" monsters). It produces the same result and you don't have to count up matching CR's in advance.



Just as a crazy curiosity, in my favorite programming language the above formula is coded using just 11 characters. Can anyone else's beat that?

Thanks to both of you...

EL is the encounter level of a list of k creatures, where the ith creature in the list has challeng rating Ci.

Here's a basic excel encounter sheet I used the formula in.

FYI - I've also figured out the equivalent formula for computing a composite party level, normalized to the standard 4-member party. It's the same formula except that you divide the summation by 4 just before taking the Log2.

Now for a tougher (semi-related) question... If it's not an infraction of IP, what's the (pure) formula for the XP award table?

I've got a formula that's close, but it's too linear in places where it should be logarithmic (I think). But it's the wrong time of day (night) to see where I'm going wrong.

Davin said:

FYI - I've also figured out the equivalent formula for computing a composite party level, normalized to the standard 4-member party. It's the same formula except that you divide the summation by 4 just before taking the Log2.

Now for a tougher (semi-related) question... If it's not an infraction of IP, what's the (pure) formula for the XP award table?

I've got a formula that's close, but it's too linear in places where it should be logarithmic (I think). But it's the wrong time of day (night) to see where I'm going wrong.

Click to expand...

Thanks Davin. I just realized that I need to consider how EL gets adjusted for more or less than 4 party members. I'll try your suggestion.

I do remember also trying to derive a closed (pure) formula for the experience table but could not get it close enough. I'll try to work on the problem again this afternoon and hopefully there will be progress. Let us know if you make any progress.

Thanks again.

I actually derived the formula from an online calculator; after looking over it, this sort of formula was the only thing that made sense.

As far as the log base--what the EL/CR system works in is actually base SQRT(2). You double in power every two CR, so for one level you increase in power by SQRT(2). The 6.6... is (log(sqrt(2))^-1


As for a pure formula for the XP table--there isn't one. It simply doesn't exist. The table in its current form has been fudged in several directions. This is because while power increases exponentially (power is proportional to (sqrt(2))^L), XP increases with the square (the midpoint XP for any given level is 500*L^2).

The major fudges in the table are at the top (levels 1-3) and vs CR 1 and 2 monsters.