I'm trying to figure out what calculations were used to generate the XP values required for level up. On Medium progression, it starts with 2,000, then 3,000 additional XP. It appears to follow a pattern of doubling the value every other level, but it doesn't seem to stick with this the entire way through.
Does anyone know what the formula is to determine the XP values or are they just arbitrary?
3.5 used a nice geometric sequence, but Wizards decided for some reason that couldn't be included in the SRD. So to play it extremely safe, Paizo used a different sequence, not quite the same as before.
Yeah, that sequence made a lot of sense and so does the PF one until about 9th level. 'Tis a shame about the XP chart not being included in the SRD.
To be honest I'm not convinced there is a nice equation that describes the pattern of increase. Looking at the numbers and how it increases in an excel spreadsheet show some weird jumps where it either jumps up by a lot more then it was or even decreases how much experience is required for the next level.
It kind of feels like someone was playing with an equation but wanted the numbers to look nicer so they manually adjusted them for various reason such as wanting them to be rounded off nice after the increases, but then needed to pull the increase back into line after doing that.
Being a math person I'm curious myself, but at least initially looking at it I'm not convinced there is an equation that will do what you want. Maybe an equation with a list of rules... maybe.
Honestly, XP are best left in the dust of history.
I'm not for certain. However, how I do XP is what the next level is multiply by 1000. So from 1st to 2nd you need 2000,2nd to 3rd you need 3000 (for a total of 5000), and ect.
I'm not for certain. However, how I do XP is what the next level is multiply by 1000. So from 1st to 2nd you need 2000,2nd to 3rd you need 3000 (for a total of 5000), and ect.
That's what it was in 3.0/3.5, but XP progression charts were left out the System Reference Document (as was pointed out earlier).
To be honest I'm not convinced there is a nice equation that describes the pattern of increase. Looking at the numbers and how it increases in an excel spreadsheet show some weird jumps where it either jumps up by a lot more then it was or even decreases how much experience is required for the next level.
It kind of feels like someone was playing with an equation but wanted the numbers to look nicer so they manually adjusted them for various reason such as wanting them to be rounded off nice after the increases, but then needed to pull the increase back into line after doing that.
Being a math person I'm curious myself, but at least initially looking at it I'm not convinced there is an equation that will do what you want. Maybe an equation with a list of rules... maybe.
I seem to remember something saying each level should be so many encounters of equivalent CR (13ish, 13.5 maybe?), but I don't know if that is PFRPG or previous.
Have you looked at the CR amounts to see if the levels are some multiple of that?
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I seem to remember something saying each level should be so many encounters of equivalent CR (13ish, 13.5 maybe?), but I don't know if that is PFRPG or previous.
Have you looked at the CR amounts to see if the levels are some multiple of that?
22 encounters per level for slow progression, 15 normal, 10 fast.
I think I have it figured out. To level 2, it is 2,000 XP. To level 3, it is 3,000 additional XP. From then on, the additional XP required is double what was required the level before. So, to get level 4, you double what it took to get to level 2, meaning an additional 4,000 XP. For level 5, it's 6,000 XP and so on. Following this logic, the medium progression would look like this:
1 - 0
2 - 2000
3 - 5000
4 - 9000
5 - 15000
6 - 23000
7 - 35000
8 - 51000
9 - 75000
10 - 107000
11 - 155000
12 - 219000
13 - 315000
14 - 443000
15 - 635000
16 - 891000
17 - 1275000
18 - 1787000
19 - 2555000
20 - 3579000
This chart almost perfectly lines up with the current Medium progression. My guess is that some of the XP totals were just rounded to nicer numbers after being calculated in this fashion. Specifically, this was done for 10th, 12th, 14th, 16th, 17th, 18th, and 20th levels.
Finally, the Gamemastering sections has this to say about play beyond 20th level:
Experience Points: To gain a level beyond 20th, a character must double the experience points needed to achieve the previous level. Thus, assuming the medium XP progression, a 20th-level character needs 2,100,000 XP to become 21st level, since he needed 1,050,000 XP to reach 20th level from 19th. He'd then need 4,200,000 XP to reach 22nd level, 8,400,000 XP to reach 23rd, and so on.
This falls in line with the "double the previous XP required" equation that was used above. There we go, mystery solved! Now, if only I could figure out how the Treasure Values per Encounter were determined.
Actually, what I posted above helped me discover a few more things. Specifically, how XP values were determined for a specific CR and the expected amount of encounters required for leveling up.
Following the double the XP logic above, here are the values required to reach the next level. That is, the amount of XP that must be earned, not the total XP a character will have at that level.
1 - 0
2 - 2000
3 - 3000
4 - 4000
5 - 6000
6 - 8000
7 - 12000
8 - 16000
9 - 24000
10 - 32000
11 - 48000
12 - 64000
13 - 96000
14 - 128000
15 - 192000
16 - 256000
17 - 384000
18 - 512000
19 - 768000
20 - 1024000
When lining those up with CR equivalent encounters (Level 1 PCs face CR 1 encounters, Level 2 vs. CR 2, etc.), I noticed that every CR value is one-fifth of what is required for the next level. CR 1 creatures grant 400 xp or one-fifth of the 2,000 XP required to reach level 2. CR 2's 600 XP is one-fifth of the 3,000 required. This continues on perfectly all the way down the line, even beyond 20th level, if you calculate past that.
As all XP is assumed to be divided evenly among the party and the average party is 4 PCs, this means that it takes 20 equal CR encounters for a PC to reach the next level, regardless of their current level. Thus, it seems that before all the rounding was done, the game was built with these XP values and number of encounters in mind. Of course, the game isn't meant to be played with CR equivalent encounters over and over again, but it's cool to see the math that was used to figure this stuff out. I hope this gives me some insight into the treasure values.
Off to the spreadsheets!