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Message: <blockquote data-quote="Cheiromancer" data-source="post: 1647765" data-attributes="member: 141">Cool little thing I just realized:  The tables in chapter 14 of Grim Tales implicitly uses a definition of the power of the group that is tantalizingly similar to mine.  But it is one that breaks down for very diverse groups, while mine doesn't.  I thus argue that my definition is better.Recall that I use the sum of the square of the CRs of the members of a group as a measure of the group's power. Then if X is the sum of the squares of the CRs of the monsters, and Y is the sum of the squares of the CRs of the characters, then xp per level is given by xp = (X/Y)*300This is just the system I described in post 35 of this thread.  And X/Y is the fraction of the party's resources that should be used up.  It is quite different from what the Grim Tales/Immortal's Handbook system uses.The system described in Grim Tales, which Upper Krust refers to as version 5.1 of his IH appendix, implicitly uses a different system of determining the power of a group.  The formulas that follow are all approximate, since the tables use integer values for EL:  First, table 14-1 relates CR to EL using the formulaEL = 1+4*log2(x1+x2+..+xm)Where log2 is the logarithmic function to base 2, and x1...xm are the CRs of the monsters in the encounter.  And table 14-2 uses EL adjustment = -2*log2(m)Where m is the number of combatants in the group.  You add these two together, then subtract the analagous expression for the EL of the adventurers (whose CRs are y1...yn, and n is the number of characters).  This EL difference is converted to xp per character level according to table 14-4, which equivalent to the following formula:xp = 300*2^(1/2*EL)Algebraically this reduces to a formula which is a little hard to write on a message board; it will help if I can define two terms.  "P" is a measure of the power of the monsters, and "Q" is a measure of the power of the adventurers.  The definitions of P and Q follow:P = (1/m)*(x1+x2+...+xm)^2Q = (1/n)*(y1+y2+...+yn)^2And the xp per level is similar to what is given above:xp = (P/Q)*300Alert readers recall that my measure of the power of a group are X and Y.  They are defined as follows:X = (x1)^2 + (x2)^2 + ... (xm)^2Y = (y1)^2 + (y2)^2 + ... (yn)^2A little algebra will show that if the x terms are identical, P = X.  Similarly if the y terms are identical, Q = Y.  Adventuring groups are typically more uniform than the monsters in an encounter, so Q will usually be very close to Y; P and X will be a little further apart.  But even if the x terms are quite different, P and X are typically not *too* far apart.For example, consider an encounter consisting of a CR 10 hill giant, four CR 7 trolls and a CR 4 ogre.P = (1/6)*(10+7+7+7+7+4)^2  = (1/6)*(42)^2  = (1/6)*1764  = 294X = 100+49+49+49+49+16   = 312Only about a 6% difference, even though there is a fair spread among the CRs in the encounter.  Of course, if the spread is very wide, the difference will be quite extreme.  For example, in the case of a Red Wyrm (CR 62) and 600 human skeletons (CR 2/3- consider them to be 400 CR 1 critters), you get P = 532, while X = 4244.  The P (and X) value of a Red Wyrm all by itself is 3844; somehow the addition of the skeletons causes the P measure to falsely and drastically underestimate the power of the encounter.  Thus the caveat in Grim Tales and the IH appendices to avoid mixing low powered allies in with a high powered boss monster.  Obviously this lowering of the measure of a group's power cannot happen if the power is defined as in X; adding the squares of non-zero CRs can only make X increase.I submit that X is a better measure of a group's power than P is; adding creatures should not make the group weaker.  And, of course, when the monsters are all the same, X=P. ------Really this was a lot faster and more obvious as an intuition; writing it all out makes it seem quite a bit more complex than it is.</blockquote>

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