Regarding UK’s “glaring error in my Encounter Level Breakdowns” (UK’s words for it). I did not like Cheiromancer’s insulting attitude toward UK. But I understood why he was upset, and I was similarly upset until I understood the solution to the problem. The reason he was upset is that UK’s new method seemed to preclude using the Grim Tales “Chi/Rho” method to determine XP.
Basically, the way the Chi/Rho method works is, that you can find the power of each opponent by squaring its power. So, for a (single) monster, power equal CR squared. The power of all opponents faced in a particular encounter, is Chi. You calculate Chi by simply adding the power of all opponents together (ignore the power of any creature with a CR than is less than the highest CR creature by 18 or more—for example, if the highest CR is 30, ignore any creature with a CR of 12 or less for purposes of calculating power).
Similarly, to figure out the power of a party member, you either square the CR or the ECL of the party member (ignore any party member whose CR is less than the highest CR party member by 18 or more). (Here it gets tricky with UK’s method, because I would say that the best approach would be the square the ECL of the party member, rather than the CR. In fact, Grim Axe also uses this. However, UK uses ECL differently than how WOTC or Grim Tales uses ECL, so if you use “ECL” the way UK uses it, then you should CR squared for power of a party member; otherwise, use ECL squared.) The total power of the party, Rho, is equal to the sum of the power of each party member.
The experience reward for each PC is: 300 * (Chi/Rho) * level. For level, you can either use the average party level, or the level the particular PC receiving the award. I would recommend using average party level, except for those party members who are simply too low level to contribute fully, in which case you should use that party member’s actual level—this prevents the anomaly of, say, a level 5 character in a level 15 party gaining massive XP against a group of CR 15 opponents where the level 5 character contributed very little to the encounter. But normally I just use average party level, so, each party member receives 300* (Chi/Rho) * (averagePartyLevel). Total XP earned by the entire party is 300 * (Chi/Rho) * sumOfAllPartyLevels, so you can actually divide that total however you want if you want to divvy it up based on how much each party member contributed.
You can also calculate EL with the Chi/Rho method, although you don’t have to calculate the ECL to calculate XP in the Chi/Rho method. To find the EL, use EL = 1 + (2 * log2 (Chi)). You can figure out party EL by replacing Chi with Rho. For my calculator, it’s simpler to use the equivalent expression EL = 1 + (2* ln(Chi)/ln(2)). If you want to map CR to EL, for a single creature, that would be EL = 1 + (2*ln(CR^2)/ln(2)). (In v5, UK has a chart mapping CR to ECL, which gives the same result as the equation I just gave).
UK has a system in v5 that doesn’t require the use of the calculator, and basically comes up with the same result as the Chi/Rho system. However, UK’s system gives you less accurate results than Chi/Rho when you use mixed CRs—and the more mixed they are, the worse result you get. In fact, with the v5 system, adding creature with a CR lower than the average CR to an encounter can in some cases actually decrease the XP award that you would get if that creature wasn’t present, which obviously isn’t right. The v5 system works pretty well when the CRs are pretty close. It doesn’t matter of the party’s CRs are close to the monster’s CRs—rather, each party member should have a CR close to the CR of each other party member, and each monster should have a monster close to the CR of each other monster—in this case, you can use the v5 system to good results. But I often use mixed CR encounters, sometimes very mixed, and I don’t mind using a calculator, so I use the Chi/Rho method, which is a system that is also “very elegant”, as Cheiromancer had stated.
OK, this has all been pre “glaring error”. Post “glaring error”, I could see that it didn’t work. Unfortunately, I used to be a math whiz, but I’m anywhere near as sharp at math as I used to be, so as far as I could tell there was no way for the Chi/Rho method to work anymore. I tried changing EL expression so that instead of log base 2 you used log base 3 or log base 3.2, but that didn’t make any difference. This is what Cheiromancer was so upset about—the seeming inability to use the Chi/Rho system any more.
I would also note that of course you can’t really use v5 either with the method, at least not as is, the tables would have to be adjusted to reflect the change, etc. But it seemed that UK’s method in v5 could simply be changed by updating the tables and such, where the Chi/Rho method appeared to be gone forever.
However, after working with the numbers a little bit, I discovered a solution. The previous method made the assumption that two (N) characters of equal level L are an equal challenge to one character of level 1.5*L (and that N^2=4 character of equal level L are an equal challenge to one character of level 2*L). Now, UK instead assumes that N=3.1623 (square root of ten) characters of equal L are an equal challenge of one character of level 1.5*L (and that N^2=10 characters of equal level L are an equal challenge to one character of level 2*L).
The solution is—instead of squaring CR to calculate power, or power=CR^2, you use CR^N, where N is the number of character of equal level L that are an equal challenge of one character of level 1.5*L. Previously, UK assumed that N=2, so we had power=CR^N=CR^2. Now, UK assumes that N=the square root of 10, so you can just use that number for N to calculate power. The Chi/Rho method still works.
Where all of this comes from, for those who don’t entirely understand UK’s system—which is most of us, including perhaps UK himself
. UK came up with his new system by challenging three assumptions that he believes are inaccurate, and fixing those problems. I agree with him on two of the points.
If I may quote from
http://www.immortalshandbook.com/sermon3.htm:
• Firstly, that Challenge Rating parallels Effective Class Level on a 1:1 basis - which simply isn't the case.
• Secondly, that Encounter Levels parallel Challenge Rating on a 1:1 basis - again, this isn't the case.
• Thirdly, that the discrepancy between PC and NPC wealth is too often ignored.
The first point is the one that I disagree with. The Grim Tales document seems to understand what WOTC means by Effective Class Level (ECL) and how WOTC uses it, but UK does not appear to. UK seems to mean something else by ECL that is not what WOTC or Grim Tales mean when they talk about it. Also, WOTC most certainly does not assume that Challenge Rating necessarily parallels Effective Class Level on a 1:1 basis.
Also, UK’s approach of “Challenge Rating 2/3rds Effective Class Level” is really bizarre, but again the problem is that it’s based on some false assumptions.
The second point is an excellent one. Well, there’s actually two points to parse out here. First of all, WOTC uses Encounter Level to basically be the combined total CR of an encounter. For example, if you have 4 CR 3 monsters, that’s equivalent to a single monster having what CR? Whatever that CR is, that’s the EL (Encounter Level). But WOTC also makes the assumption that CR (and, by logical extension, EL), have the following relationship—two monsters of CR=M is an equivalent challenge to a single monster of CR=M+2. I think this actually works very well at low and mid levels. In fact, for monsters of CR 17 or less, I use that assumption. But for CR 18 or greater, I think UK’s system is far more accurate. I mean, it’s just common sense really—it’s abundantly clear that two level 33 fighters are not an equal challenge to one level 35 fighter, nor are two level 33 wizards an equal challenge to one level 35 wizard. The two level 33s are clearly far more challenging than the single level 35.
Really, noticing this discrepancy, there are two ways that we could define EL. One would be to say, EL is simply something that represents, the combined encounter is equivalent to a single monster of what CR, and that is EL. The other would be to say—WOTC assumes that EL, like CR, is defined by, adding two to it doubles the challenge. But let’s de-couple CR from EL. We’ll keep CR to be the same thing it’s always meant. But let’s define EL as a number for the encounter which, when you add two to it, represents an encounter that is twice is challenging. And let’s realize that CR doesn’t necessarily have the same property, especially as the CR gets higher. An EL 42 encounter is, by definition, twice as tough as an EL 40 encounter. But a CR 42 is not twice as tough as a CR 40. The WOTC method is even worse as you expand the numbers—according to the WOTC CR*2=EL*2, you have 1 CR 42=2 CR 40s=4 CR 38s=8 CR 36s. I think it’s easy to see that a single level 42 PC is nowhere near as powerful as 8 level 36 PCs.
Of course, this begs the question, if a CR 42 is not twice as tough as a CR 40, how much tougher than a CR 40 is it? How do we calculate XP to reflect this CR/EL difference? Well, this was discussed above. You can use and Chi/Rho method, or an equivalent method which doesn’t require a calculator. But that still leaves the question what the proper value of N should be. The question is, for example, N level 30 characters is an equivalent challenge to a single level 45 character? (Or, more generally, N level L characters is an equivalent challenge to a single level 1.5*L characters). WOTC makes the assumption that CR*2=EL*2. UK originally went with the assumption that, instead of CR*2=EL*2, CR*2=EL+4, but now uses CR*2=EL+6 (actually, he uses CR*2=EL+2*10^.5). Using my N above, with the Chi/Rho method, we’re talking about CR*2=EL+2*N.
Personally, I simply use the WOTC assumption that CR*2=EL*2, so that a CR 7 is an equivalent challenge to two CR 5 monsters, or four CR 3 monsters, but only for CRs of 17 or less. For CR 18 or more, I use CR*2=EL+10. This is based on the assumption that, for example 5 level 30 characters is an equivalent challenge to a single level 45 character. This is simply my best estimate. I think that the UK’s current value of N=square root of ten is low, and 5 is my best estimate. Ideally, the determination of N should be playtested thoroughly. But it should be playtested at higher levels (level 21 and higher)—I know that N=5 with the Chi/Rho method would not be accurate for low and mid levels, but I personally feel that the geometric scale is more accurate than Chi/Rho at low and mid levels anyway (that is, I believe that at low and mid levels, the equation should be of the form CR*2=EL*X rather than CR*2=EL+X, where I believe that an equation of the form CR*2=EL+X is more accurate at a certain CR and above).
The third point is another excellent one. The official rules assume that a level 20 PC with PC wealth is equivalent to a level 20 NPC with NPC wealth. That clearly is an inaccuracy. I think that UK’s v5 rules address this discrepancy pretty well. The way it works is, each character level, ignoring wealth, is .8 CR. Each level of PC wealth counts as .2 CR. Each level of NPC wealth counts are .125 CR. So a level 20 PC is CR 20, and a level 20 NPC is 20*.8+20+.125=18.25, which rounds down to CR 18.
Or, for a less accurate but simpler method, UK has also recommended simply using, for an NPC with NPC wealth, using 5/6 the CR than if it were a PC, to account for the lesser wealth (or is this actually a more accurate method based on findings since v5?)
UK also has come up with, in v5, an outstanding version of calculating CR, and I expect it to be even further improved in v6. For example, you can look at a monster’s various abilities, and use that to determine its CR in v5. However, I believe that every CR needs to be individually playtested. I think that UK’s system is an outstanding tool, and one that could massively save playtesting time when determining accurate CRs of creatures. Basically, you would use UK’s system to assign a tentative CR, playtest that CR, and work from there to determine actual CR. UK’s system gives you an excellent starting point for estimating about where it’s CR should be, and would save you a lot of time versus just taking a look at the monster and making your best guess as the initial estimate to being playtesting, or trying to use some other CR estimation that is less accurate that UK’s system. But I don’t think you can simply take for granted that the CR of any given monster is exactly that using UK’s system. It only gives you a very accurately starting point, which will definitely save playtesting time, but which will not eliminate the need for playtesting entirely.
I would take the Balor as one example. It’s a CR 33 (using v5, silver rule). Now, the official CR of the Balor is 20, which I believe is a little bit low. I said a little bit low. CR 20 is way, way, closer than 33, which unfortunately, is nowhere close to being accurate. Also, a white dragon great wyrm in UK’s system comes out to a whopping CR 52—now they’re tough, don’t get me wrong, and the official CR is definitely too low, but it’s no CR 52! I’m not even faulting UK’s system here; I’m saying that a system that can completely accurately determine CR without individual playtesting is impossible. UK’s system is outstanding, but it simply cannot be used as a complete substitute for playtesting CRs.
