Determining Encounter Level

[Davin]

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

Yeah, since your constant worked I assumed that it had to be derived in some fashion like that. Personally, I prefer using the log2 to simplify that out and save myself some headaches.

As for a pure formula for the XP table--there isn't one.

Actually, I'm thinking there might be. I just spent a little while playing with a simple quadratic formula (though the constants make no sense yet) and came up with some pretty close column-matches (R=.99+).

Here's the trick... another major table from the book (load weights, STR>10) is based on a similar formula, but plugging in the values doesn't match the numbers exactly. The trick happens when you round the numbers off -- with a variable rounding factor! The larger the value, then the larger the rounding factor (in computable groups). I'm thinking this table might work out the same way -- using a formula to compute a raw number and then rounding it off with a variable factor based on the size of the number (or level) so that the values come out easy for a human to use.

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).

I don't think we have to cross power with XP here - the table crosses power with power to produce XP. If we convert power (both ways) to a linear scale (with POWER(2,L/2)), then I think that problem might disappear.

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

Actually, that one's pretty easy to handle -- just MAX(3,partylevel) before you start. You also have to chop off the top & bottom extremes, too. But those are pretty simple cleanup tasks -- fitting the body of the table into a formula is the tough part.

Have I sparked any other ideas for you?

 

[Joshua Randall]

Bumped to make it easier to find.

 

[nopantsyet]

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?

C'mon--now you've got to tell...

 

[Davin]

C'mon--now you've got to tell...

The language is an ancient one called APL. The code I can't show exactly due to a lack of appropriate character set, but it's close to:

2×2@+/2*C÷2

Nobody's got a shorter implementation?

 

[Davin]

Sorry for being delayed so long on this subject...

I handed this formula over to my DM and the first thing he did with it was check the EL for 4 Orcs (CR=0.5). This formula comes up with EL=4.5 when it should be EL=2. It follows the rule for {double number of monsters = EL + 2}, but that doesn't apply to cases at the low end of the table. How can we fix the formula to account for this?

I also did some more analysis on the table and found numerous places where they don't follow their own doubling rule. If this was a consistent pattern, I think I can see a way to calculate it, but it just doesn't follow their own rules at the "bottom" edge of the table. (The bottom edge varies depending on which version of the table orientation you're looking at, and this isn't restricted to low levels.)

 

[Davin]

*bump*

Has anyone figured out how to extend the EL formula to include CR's < 1 yet?

 

[Jadinna]

*bump* Has there been any further workings on this? I am looking for a way to accurately calculate an encounter level.

 

[Davin]

You and me, both! I've been spending some time lately working on the XP table with only slightly more success, so I'm rather frustrated on two computational fronts.

I'm thinking that maybe the formula here fails simply because the numbers are numerically less than 1 (rather than any special meaning that has). If that's the case, then I've been hoping that I could find a way to scale the starting CR's up so that they're no longer less than 1, then run the formula on them, and then somehow reverse the scaling process to bring them back to the normal range.

So far I haven't succeeded at this, but I've only had time to try a few different methods. I'm still hopeful that we can come up with something that we can use.

Does anyone else have any ideas we might try here?

 

[kingpaul]

I'm thinking that maybe the formula here fails simply because the numbers are numerically less than 1 (rather than any special meaning that has). If that's the case, then I've been hoping that I could find a way to scale the starting CR's up so that they're no longer less than 1, then run the formula on them, and then somehow reverse the scaling process to bring them back to the normal range.

So, for example, you have CRs of 1/8 and 1/3, you multiple all CRs by 24 to kill the fractions?

 

[Davin]

So, for example, you have CRs of 1/8 and 1/3, you multiple all CRs by 24 to kill the fractions?

Yes, something like that. But I don't think that a simple multiplication will do the trick. I think it may need to be based on an exponential system (to work better with the curent 'doubling' curve maybe??). Remember that it has to be something that you can reverse afterwards to get it back to it's original scale, and that's quite a trick when you're passing them through exponents, summations, and logarithms.