Reply to thread

Message

<blockquote data-quote="Davin" data-source="post: 1293170" data-attributes="member: 1183">Yes, how did you come up with this?&nbsp; Part of it looks like it's empirically derived.&nbsp; (And yes, I believe it works.)I can see how &amp; why the part in parenthesis works, but I got completely lost when I got to the &quot;6.6439 log&quot; part.&nbsp; 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 &quot;should&quot; be the correct formula ... the same, except the log should be to the base 2 and the constant multiplier should be simply 2.&nbsp; So, if you're using a language that supports a base-2 log, then the first part of that formula should just become:[CODE]2 * log2 ( ... )[/CODE]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:&nbsp; Another formula simplification is also possible.&nbsp; 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.&nbsp; However, when using computers you may often simply have a list of all the individual CR's without having them pre-counted.&nbsp; If this is the case, then you can simplify the summation by removing the &quot;N(i)&quot; term entirely and just have &quot;C(i)&quot; be each monster's CR (for &quot;k&quot; monsters).&nbsp; 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.&nbsp; Can anyone else's beat that?</blockquote>

[QUOTE="Davin, post: 1293170, member: 1183"] Yes, how [u]did[/u] 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: [CODE]2 * log2 ( ... )[/CODE] 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. [I]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?[/I] [/QUOTE]

Verification