Level Independent XP Awards

[Kavon]

Yes, I believe I'm seeing the up side to that as well.. (note my second edit in my earlier post).
In order for the hobbits to catch up to the ranger a bit more, they'd have to fight their own fights independantly (which have to be tough fights at that).
If that is good or bad depends on the person.
I do think I prefer slightly lower level characters to be able to catch up (at least a bit) to their slightly higher level companions.

 

[Wulf Ratbane]

I do think I prefer slightly lower level characters to be able to catch up (at least a bit) to their slightly higher level companions.

I can see the necessity for this, at times; but there are better ways to do this than monkeying with the CR system.

(Story Awards: "You hobbits made it through that fight valiantly, staying on against the wraiths when all logic says you should have fled. You each get another +500 XP.")

Wulf

 

[Cheiromancer]

Personally, I think it's silly to give the hobbits a greater proportion of the XP than their own proportional contribution to the fight...

I do think I prefer slightly lower level characters to be able to catch up (at least a bit) to their slightly higher level companions.

I can see the necessity for this, at times; but there are better ways to do this than monkeying with the CR system.

(Story Awards: "You hobbits made it through that fight valiantly, staying on against the wraiths when all logic says you should have fled. You each get another +500 XP.")

I agree- the system is designed to award xp for situations which challenge you, and in proportion to how much it challenged you. If the hobbits make a small contribution (were challenged only slightly), they should get a small proportion of the xp. And if they were to make a contribution disproportionate to what this formula predicted, the DM could make a bonus award. Or not- for every time they make a big contribution, there are undoubtably other times when they fall short even of the modest contribution the formula expects, and occasionally may make the situation worse. On average the formula should be pretty close.

Like Kavon, I would like it if a character who ends up a level behind due to raising (or to making magic items for party use) would eventually catch up, but attempts to implement this seem to have disproportionate effect on lower level characters. That's my worry with the method Anubis uses.

I think that the "catching up" effect, though desirable in small amounts, can't be a feature of the CR/xp system. It has to be up to DMs.

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Incidentally, "CHI" and "RHO" are greek letters that look like X and P respectively. The CHI sound is the first sound in Challenge, and the RHO sound is the first sound in Rating. A -mancer is a kind of wizard, especially one who obtains information. So, simply by my handle I have an affinity for discussions regarding how to understand the relationship between XP and CRs. Nifty, huh?

 

[Wulf Ratbane]

Incidentally, "CHI" and "RHO" are greek letters that look like X and P respectively. The CHI sound is the first sound in Challenge, and the RHO sound is the first sound in Rating. A -mancer is a kind of wizard, especially one who obtains information. So, simply by my handle I have an affinity for discussions regarding how to understand the relationship between XP and CRs. Nifty, huh?

Damn, you're nifty. I am green with envy.

Incidentally, "wulf" is the sound you make when you inhale and gulp real hard, realizing you've made a stupid math error... (Gah! Just doesn't work for me.)

Email me and I'll pass along the spreadsheet that I just finished (working your commentary in).

Wulf

 

[Cheiromancer]

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)*300

This 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 formula

EL = 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)^2
Q = (1/n)*(y1+y2+...+yn)^2

And the xp per level is similar to what is given above:

xp = (P/Q)*300

Alert 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)^2
Y = (y1)^2 + (y2)^2 + ... (yn)^2

A 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
= 294

X = 100+49+49+49+49+16
= 312

Only 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.

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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.

 

[Wulf Ratbane]

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.

This is exactly the argument that was made to me by CRGreathouse. I've come to believe your definition IS better, because you don't get the odd results you get with the large "chunks" of CR/EL/Group Size groupings.

The only place where I differ is that, as far as using a table in a book goes... Well, folks prefer tables to exponential/logarithmic math. For the vast majority of encounters, the tables are more facile.

Being a stickler for accuracy and just enough of a computer geek to make a difference, I prefer the accurate formulas and a spreadsheet-- which I will make available to like-minded GMs as soon as I feel they are ready for prime time.


Wulf

 

[Wulf Ratbane]

Let's break it right down.

A given creature's Power is equal to its (CR)^2.

A group of creatures will have a Power equal to (CR1)^2 + (CR2)^2 + (CR3)^2 + ... + (CRn)^2.

We'll call the monster or encounter power X.

The party power is Y.

The relative difficulty of any encounter is simply X/Y. This result of this expression is the percentage of expected resources spent.

The relative XP award of an encounter is thus (X/Y)*300 per character level.

Two camps will diverge here:

For individual XP, multiply the relative XP award by each character's level.

For group XP, total all party levels and multiply by the relative XP award, then divide evenly among the party.

And as a final benchmark, the "win rate" of an encounter (expressed as a percentage) is 100 - (1/2 resources used).

Very cool, Chi-Rho.

I've attached a quick spreadsheet.

EDIT: Quick edit. For creatures with fractional CRs, you'll need to set up the worksheet a little differently. The power equation is CR^IF(CR<1,1,2).

In other words, for CR<1, do not square. I've updated the spreadsheet.


Wulf

 

[BryonD]

Never Mind, I'll retract the question.

 

[Cheiromancer]

The only place where I differ is that, as far as using a table in a book goes... Well, folks prefer tables to exponential/logarithmic math. For the vast majority of encounters, the tables are more facile.

Logarithmic tables were invented so that people could multiply, divide and take roots/powers easily. To multiply numbers you add the logarithms; to divide, you subtract. Adding and subtracting is easier than multiplying and dividing even if you have to look up the logarithm in the beginning and the anti-logarithm in the end.

If you decide to use a formula, though, you wouldn't bother with logarithms and exponents. You would let your calculator/spreadsheet handle the squaring, multiplying and dividing.

Wulf, I take off my hat to your spreadsheet fu. Very nice!

What makes these statements true?

Hopefully that's not a philosophical question. My brain shudders to consider the epistemology of DnD xp calculations. Here's a somewhat vague explanation:

The whole system of levels, sp, CRs, ELs and the like are related abstractions that are related in various ways. Their relationships can be reflected by certain formulas and equations which have properties that are desirable. For instance, we want the addition of monsters to increase the EL of an encounter, not decrease it. We want higher CR monsters to provide more xp. 13.333 moderate encounters should provide enough experience to advance a level. And so on.

A lot of the features of these equations cannot be proven theoretically to correspond to what goes on in a DnD session; they have to be justified by play-testing, pragmatically. If an encounter which your system predicts will be an easy encounter slaughters the party, then something has gone wrong- if it *is* an easy encounter, then the system has at least some value. The system that Wulf, UK, CRGreathouse and others have worked out has proven its value; this is just a little refinement of it.

It's possible (though I think unlikely) that there is a radically different method of how to calculate XP based on CR. I thought my system was radically different, but it turns out the difference is merely notational, and that I use a slightly different definiton of power than the Grim Tales system uses.

 

[Wulf Ratbane]

So this goes back to the idea that fighting 2 CR2 creatures at the same time has the same XP value as fighting 1 CR2 creature and then fighting another CR2 creature later. Correct?

Hmm... Yes. This of course is the core method. I don't know what you mean by "Goes back to..." as this is the goal I've always shot for.

Instead of multiplying the relative XP award by the character level, I suppose you could devise an alternate method to multiply it by the monster CR. That would scale it up proportionately.


Wulf