Determining Encounter Level

[dcollins]

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

My solution has been to convert fractional CR's into negative integer CR's thus:
1/2=-1, 1/3=-2, 1/4=-3, 1/6=-4, 1/8=-5, 1/10=-6.

Then the doubling rule and the logarithmic formulas work out fine.

My D&D "Math Formulas" download with this and other equations can be found on this page: http://www.superdan.net/dnd3.html

 

[Davin]

My solution has been to convert fractional CR's into negative integer CR's thus:
1/2=-1, 1/3=-2, 1/4=-3, 1/6=-4, 1/8=-5, 1/10=-6.

THAT'S the kind of thing I'm looking for! Very interesting!

I'm having a bit of trouble, though, when interpreting an apparent discontinuity in your conversion. For instance, what's a CR of 0 mean? If you compute for four CR 1/3 (-2) creatures, it gives you a result of 0. If I'm guessing right, this might also be questionable for any resulting (or source?) values (converted) between 1 and -1. How do you interpret such situations? (I'll see if I can come up with a fractional conversion formula to see if that answers my question.)

As an aside, the formula on your web page only calculates for multiples of a single CR. I think it's better to be able to do it for a combination of different CRs so you can handle complicated encounters. The formulas discussed earlier in this thread can get around this problem (at least for CRs >= 1), and they seem to produce the same results as yours.

My D&D "Math Formulas" download with this and other equations can be found on this page: http://www.superdan.net/dnd3.html

You've got some very interesting and reasoned technical discussions here. I'm going to have to come back to visit sometime when I can read through it all in more detail.

I'm rather surprised by your Encumbrance Level formula, as you're the only other person I've seen (besides me) that actually calculates it with a variable rounding factor.

I notice that you also include a formula for calculating XPs, but you've failed to take into account the variances that are actually present in the printed chart. See a discussion on this subject at http://www.enworld.org/forums/showthread.php?t=75766 for more details.

 

[Davin]

(I'll see if I can come up with a fractional conversion formula to see if that answers my question.)

I think I've come up with an answer for myself...

The formula for converting from fractional CRs to negative Pseudo-CRs is:

PCR=Log2(CR)*2+1

and the inverse formula to convert it back is therefore:

CR=2^((PCR-1)/2)

So, your table contains some rounded values (which is perfectly fine) that could have been more closely listed as:

1/3  -2.169925001
1/6  -4.169925001
1/10 -5.643856190

And the answer to my own question about PCR=0 is that it represents CR=0.7071067812 ((2^.5)/2). Also, PCR=0.5 is CR=0.8408964153 and PCR=-0.5 is CR=0.5946035575, demonstrating that we've got a continuous (smooth) curve here. PCR=CR=1 too, so it joins seamlessly. However, it does not apply to CRs>1, so we still have to conditionally convert values.

I guess my next step is to check out how accurate we are when combining these numbers together into a composite EL. I assume the basic quantity multipliers have already been checked, but I'd like to also check for combinations between different CRs. Does anyone know of any semi-official combined-EL references where I can check my computations (other than the simplified calculator on WotC's site)?

Does anyone have any questions, comments, suggestions, or other feedback about any of this?

 

[andargor]

I've been watching this thread with interest. Our DM needs to have some guidance with determining encounter strengths. Our party is at about 15th level, and the encounters range from "walk in the park" to "downright deadly".

So I thought I'd hack up my own Excel with your formulas. I haven't covered the low CR stuff, because, well, we don't meet any.

Also, I'd like to extend the table past CL/CR 20. I looked at dcollins' formulas, but I can't make them stick. Any chance to have an extended table that goes to 30 in both directions? I'd rather look up than calculate.

Excel attached.

Andargor

 

[Davin]

Also, I'd like to extend the table past CL/CR 20. I looked at dcollins' formulas, but I can't make them stick. Any chance to have an extended table that goes to 30 in both directions? I'd rather look up than calculate.

Are you just looking for a larger XP lookup table (that matches the books)? If so, check your email. (And that's just why I'd rather have a formula that works to any level rather than a fixed lookup table.)

Other than that, I'm not quite sure what you're having trouble with. You seem to have implemented the EL calculations (& XP lookup). Am I missing something?

 

[andargor]

Are you just looking for a larger XP lookup table (that matches the books)? If so, check your email. (And that's just why I'd rather have a formula that works to any level rather than a fixed lookup table.)

Other than that, I'm not quite sure what you're having trouble with. You seem to have implemented the EL calculations (& XP lookup). Am I missing something?

Thanks for the email. Sorry for not being clearer. Yes, I used the formula for the EL as a guideline for our DM, but for XP lookup I was wondering how you calculated the "red areas" in your spreadsheet posted here. The areas not covered by the DMG.

We decided to award XP anyway for those "areas" and I would need those numbers.

Andargor

 

[Davin]

Yes, I used the formula for the EL as a guideline for our DM, but for XP lookup I was wondering how you calculated the "red areas" in your spreadsheet posted here. The areas not covered by the DMG.

Actually, that wasn't my spreadsheet that got posted. But what I sent you does include that area by extending the pattern according to the DMG-specified rules (doubling each value from two levels below). The Epic Level Handbook also has numbers and formulas for levels above 20, but the patterns vary slightly from those in the DMG. If you hadn't noticed the (rather long) discussion we had over in the thread http://www.enworld.org/forums/showthread.php?t=75766, and you're interested in the exact patterns involved, then you should check it out.

Hmmm... I just noticed that while I'd declared that level 20 used the same pattern as level 21 (in the tables), in fact that one level is indeterminate from the table and could be arbitrarily extended using either pattern. (It should most likely follow the same pattern as all the other levels in the DMG [except 4], which is actually different from the stated formula.) I'd better drop over there and make a note of that.

 

[andargor]

Ok, I read the thread, and used morpheous1777's table and extended it.

Since we are not calculating the precise coordinates for a hyperspace jump, even with the slight variance it will do.

I'm attaching my updated version, if anyone wants it.

Andargor

 

[Davin]

Ok, I read the thread, and used morpheous1777's table and extended it.

FYI - I just added a note to that thread on how I'm proposing to "standardize" that Level=20 extension. I hope that's the same way you did it. (And I hope you used his second table instead of the first one.)

Since we are not calculating the precise coordinates for a hyperspace jump, even with the slight variance it will do.

Right - this is more like dusting crops.

 

[andargor]

Fixed some bugs in the Excel. Attached. I removed the other ones.

Andargor