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<blockquote data-quote="Cheiromancer" data-source="post: 1643780" data-attributes="member: 141"><p>What do you mean I’m not using your system correctly? <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink ;)" data-smilie="2"data-shortname=";)" /></p><p></p><p>What I was doing was divide raw experience evenly, then divide by the character’s level. In your example I would divide the 101,400 raw xp evenly (so 25,350 per character), then divide either by 15 or 14. The 15th level characters would get 1690 xp (25350/15) and the 14th level characters get 1810 xp (25350/14). Which is, of course, the correct answer.</p><p></p><p>My only doubt about your system is that it makes the players have to divide their xp. That’s not something they do naturally. I mean, you can say “everybody get 120 xp per level” and they won’t forget to multiply, but if you tell them “everybody get 1200 raw xp” they might forget to divide. It’s just human nature. Though I could do it for them, of course.</p><p></p><p>As for me, I would calculate raw xp (101,400), divide by the total party level (58) and tell everyone they get 1748 xp (101,400/58). One problem with this is that folks who fall behind will never, ever, catch up. And I kinda think they should.</p><p></p><p>But the biggest problem with *my* method (one I've just now noticed) is that it makes the total xp from an encounter independent of the number of characters in the party; it is dependent only on their level. If I have twice as many characters (but the same level) the total party level doubles, so everyone gets half as much xp. But there are twice as many characters, so the total xp is the same.</p><p></p><p>(The same is true of your system, my friend. Twice as many characters means that the power factor is doubled, so everyone gets half as much xp. But since there are twice as many people, that means the total xp is the same.)</p><p></p><p>However, in the IH doubling a party will double the CR and double the number of combatants. This will increase the party EL by +4 for the increase in CR, and decrease the party EL by -2 for the increase in numbers (tables 2-1 and 2-5 in v4, or tables 2-1 and 2-2 in v5). A net increase of +2, which means the difference between the encounter level and the party level drops by +2, which means the *total* xp awarded is halved. (See table 2-8 in v4, or note that party size is counted twice in v5; once in table 2-2, and again in table 2-5).</p><p></p><p>So I think we need a new formula!</p><p></p><p>For 4 characters of level n, the formula for total xp is</p><p></p><p>xp = (CR^2)*300/n</p><p></p><p>Highlight to see the derivation of this formula (which we already know and accept):</p><p>[SPOILER]</p><p>First, we know from UK's tables that doubling a creatures CR increases its EL by +4, and that quadruples the xp awarded. So xp is proportionate to CR^2. The xp is also a function of the party's level (and maybe other things); call the function f<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f44e.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt="(n)" title="Thumbs down (n)" data-smilie="23"data-shortname="(n)" />. Then we want to figure out what f<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f44e.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt="(n)" title="Thumbs down (n)" data-smilie="23"data-shortname="(n)" /> is in the formula</p><p></p><p>xp = (CR^2)*f<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f44e.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt="(n)" title="Thumbs down (n)" data-smilie="23"data-shortname="(n)" /></p><p></p><p>Now, we know that 4 characters of level "n" need to face 13.3333 equal CR challenges to go up a level. For an nth level character to go up a level, he needs to get n*1000 xp. That's n*4000 xp for the group. Divide by 13.333 and that's n*300 xp per encounter. So if CR=n in the previous equation, then</p><p></p><p>xp = n*300 = (n^2)*f<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f44e.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt="(n)" title="Thumbs down (n)" data-smilie="23"data-shortname="(n)" /></p><p></p><p>and we can solve for f<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f44e.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt="(n)" title="Thumbs down (n)" data-smilie="23"data-shortname="(n)" />. In other words, when there are 4 characters of level n, </p><p></p><p>f<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f44e.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt="(n)" title="Thumbs down (n)" data-smilie="23"data-shortname="(n)" /> = 300/n</p><p></p><p>And so we conclude that, for a party of 4 nth level characters,</p><p></p><p>xp = (CR^2)*300/n</p><p>[/SPOILER]</p><p></p><p>Let p be the number of characters in the party. Then the total xp awarded is a function of p. Call this function g(p). g(4)=1, and, generally, g(2x)=1/2 * g(x). Clearly g(p)=4/p In other words, the total xp awarded for an encounter is</p><p></p><p>xp = (CR^2)*1200/(p*n)</p><p></p><p>The expression p*n is just the total level of the party.</p><p></p><p>----</p><p></p><p>Now, what to do when the members of the party are of different levels? What UK does is award people xp on a per level basis. In this case you divide the total xp into a number of shares equal to the total number of levels in the party. Each party member gets 1 share per level. In which case</p><p></p><p>xp per level = (CR^2)*1200/(total level^2)</p><p></p><p>Now since for characters I am using "level" when I really should be using CR (since ECL and CR is the same in UK's system) I can say something quite neat, namely that the xp award (per character level) is directly proportional to the sum of the squares of the CRs of the opponents, and inversely proportional to the square of the sum of the CRs of the characters. That is quite as elegant, imho, as the pythagorean theorm.</p><p></p><p>If you divide xp equally (as I am wont to do), you need to determine a power factor for the group, equal to the number of players times the total level. (Or you could say the number of characters squared times the average level of the character.) Now the raw xp is (CR^2)*1200, and you divide by the power factor to work out the individual awards.</p><p></p><p>To give more xp to lower level characters (as you seem to like), each character has a power factor equal to the number of characters squared times *that* character's level. </p><p></p><p></p><p></p><p>All this may be true, but your formula departs greatly from what UK has in the Immortal's Handbook whenever the party size is significantly larger (or smaller) than 4. So did mine, of course. Would you care to revise your statement of flawlessness, bugfreeness and balance, or would you prefer to argue that UK should change his system?</p></blockquote><p></p>
[QUOTE="Cheiromancer, post: 1643780, member: 141"] What do you mean I’m not using your system correctly? ;) What I was doing was divide raw experience evenly, then divide by the character’s level. In your example I would divide the 101,400 raw xp evenly (so 25,350 per character), then divide either by 15 or 14. The 15th level characters would get 1690 xp (25350/15) and the 14th level characters get 1810 xp (25350/14). Which is, of course, the correct answer. My only doubt about your system is that it makes the players have to divide their xp. That’s not something they do naturally. I mean, you can say “everybody get 120 xp per level” and they won’t forget to multiply, but if you tell them “everybody get 1200 raw xp” they might forget to divide. It’s just human nature. Though I could do it for them, of course. As for me, I would calculate raw xp (101,400), divide by the total party level (58) and tell everyone they get 1748 xp (101,400/58). One problem with this is that folks who fall behind will never, ever, catch up. And I kinda think they should. But the biggest problem with *my* method (one I've just now noticed) is that it makes the total xp from an encounter independent of the number of characters in the party; it is dependent only on their level. If I have twice as many characters (but the same level) the total party level doubles, so everyone gets half as much xp. But there are twice as many characters, so the total xp is the same. (The same is true of your system, my friend. Twice as many characters means that the power factor is doubled, so everyone gets half as much xp. But since there are twice as many people, that means the total xp is the same.) However, in the IH doubling a party will double the CR and double the number of combatants. This will increase the party EL by +4 for the increase in CR, and decrease the party EL by -2 for the increase in numbers (tables 2-1 and 2-5 in v4, or tables 2-1 and 2-2 in v5). A net increase of +2, which means the difference between the encounter level and the party level drops by +2, which means the *total* xp awarded is halved. (See table 2-8 in v4, or note that party size is counted twice in v5; once in table 2-2, and again in table 2-5). So I think we need a new formula! For 4 characters of level n, the formula for total xp is xp = (CR^2)*300/n Highlight to see the derivation of this formula (which we already know and accept): [SPOILER] First, we know from UK's tables that doubling a creatures CR increases its EL by +4, and that quadruples the xp awarded. So xp is proportionate to CR^2. The xp is also a function of the party's level (and maybe other things); call the function f(n). Then we want to figure out what f(n) is in the formula xp = (CR^2)*f(n) Now, we know that 4 characters of level "n" need to face 13.3333 equal CR challenges to go up a level. For an nth level character to go up a level, he needs to get n*1000 xp. That's n*4000 xp for the group. Divide by 13.333 and that's n*300 xp per encounter. So if CR=n in the previous equation, then xp = n*300 = (n^2)*f(n) and we can solve for f(n). In other words, when there are 4 characters of level n, f(n) = 300/n And so we conclude that, for a party of 4 nth level characters, xp = (CR^2)*300/n [/SPOILER] Let p be the number of characters in the party. Then the total xp awarded is a function of p. Call this function g(p). g(4)=1, and, generally, g(2x)=1/2 * g(x). Clearly g(p)=4/p In other words, the total xp awarded for an encounter is xp = (CR^2)*1200/(p*n) The expression p*n is just the total level of the party. ---- Now, what to do when the members of the party are of different levels? What UK does is award people xp on a per level basis. In this case you divide the total xp into a number of shares equal to the total number of levels in the party. Each party member gets 1 share per level. In which case xp per level = (CR^2)*1200/(total level^2) Now since for characters I am using "level" when I really should be using CR (since ECL and CR is the same in UK's system) I can say something quite neat, namely that the xp award (per character level) is directly proportional to the sum of the squares of the CRs of the opponents, and inversely proportional to the square of the sum of the CRs of the characters. That is quite as elegant, imho, as the pythagorean theorm. If you divide xp equally (as I am wont to do), you need to determine a power factor for the group, equal to the number of players times the total level. (Or you could say the number of characters squared times the average level of the character.) Now the raw xp is (CR^2)*1200, and you divide by the power factor to work out the individual awards. To give more xp to lower level characters (as you seem to like), each character has a power factor equal to the number of characters squared times *that* character's level. All this may be true, but your formula departs greatly from what UK has in the Immortal's Handbook whenever the party size is significantly larger (or smaller) than 4. So did mine, of course. Would you care to revise your statement of flawlessness, bugfreeness and balance, or would you prefer to argue that UK should change his system? [/QUOTE]
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