yes, the formulas are a bit complex, it's linear plus a second linear thing.
I think something like +2000 times lvl-1 + 1000 for every fives levels.
It's really unbelievable that WOTC could own the rights to a linear exp progression.
They probably don't and PF is just cautious.
RPG Superstar 2010 Top 16
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It's a little bit strange.
The distinction between slow, medium, and fast progression is straightforward. Let's define some variables.
F(n) = (the amount of experience to reach Level n in fast track, in thousands)
M(n) = (the amount of experience to reach Level n on medium track, in thousands)
S(n) = (the amount of experience to reach Level n on slow track, in thousands)
f(n) = (the amount of experience a character at the beginning of Level n needs to rise to the next level, on the fast track, in thousands)
m(n) = (the amount of experience a character at the beginning of Level n needs to rise to the next level, on the medium track, in thousands)
s(n) = (the amount of experience a character at the beginning of Level n needs to rise to the next level, on the slow track, in thousands)
F(n) = M(n) * 0.67, rounded to a pretty number
S(n) = M(n) * 1.5, rounded to a pretty number
So, we'll restrict our analysis to M(n).
M(2) = 2
M(3) = 5
M(4) = 9
M(5) = 15
M(6) = 23
M(7) = 35
M(8) = 51
M(9) = 75
M(10) = 105
M(11) = 155
M(12) = 220
M(13) = 315
M(14) = 445
M(15) = 635
M(16) = 890
M(17) = 1300
M(18) = 1800
M(19) = 2550
M(20) = 3600
Subtracting M(n+1) - M(n), we find m(n):
m(2) = 2
m(3) = 3
m(4) = 4
m(5) = 6
m(6) = 8
m(7) = 12
m(8) = 16
m(9) = 24
m(10) = 30
m(11) = 50
m(12) = 65
m(13) = 95
m(14) = 130
m(15) = 190
m(16) = 255
m(17) = 410
m(18) = 500
m(19) = 750
m(20) = 1050
So, it might be profitable to see if there's any patterns there. Let's compare the ratio m(n):m(n-1). That is, if it took x amount of experience to rise from n-1 to n, what fraction of that will it take to rise from Level n to n+1?
m(3)/m(2) = 1.5
m(4)/m(3) = 1.3333
m(5)/m(4) = 1.5
m(6)/m(5) = 1.3333
m(7)/m(6) = 1.5
m(8)/m(7) = 1.3333
m(9)/m(8) = 1.5
m(10)/m(9) = 1.25
m(11)/m(10) = 1.6667
m(12)/m(11) = 1.3
m(13)/m(12) = 1.4615
m(14)/m(13) = 1.3684
m(15)/m(14) = 1.4615
m(16)/m(15) = 1.3421
m(17)/m(16) = 1.6078
m(18)/m(17) = 1.2195
m(19)/m(18) = 1.5
m(20)/m(19) = 1.4
At lower levels, this looks regular. From even levels to odd levels, the ratio is 3:2, and from odd levels to even level, the ratio is 4:3. You could make some justification that most classes get better new toys at odd levels, so the cost of rising to them is a little steeper, or you could say that the difference is there to make the levels break at prettier numbers.
But after 10th Level, the pattern breaks down. If there's a reason for m(10) to be 30,000, rather than 32,000, or for m(11) to be 50,000 rather than 48,000, I don't see it. The most I can get out of the charts is the intention that m(n+2) should be about twice m(n), so m(n+1):m(n) should stay around sqrt (2) = 1.414.
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RPG Superstar 2010 Top 16
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PFS makes it even simpler. Every module you complete you get 1 XP. Every 3 XP you level up.
Very true, but then you have to define "module" as a unit of experience. That works in Organized Play, when an adventure is a well-defined set of 5 encounters (one might be optional), within a tight parameter of difficulty. I'm not sure it translates well to the typical sandbox home campaign.
One problem with the PFS OP system, for example, is that a character who misses a few sessions never catches up to the rest of the PCs. Under both the 3rd Edition experience tables (where lower-level characters received more experience for the same encounter, thus narrowing the gap in real XP totals) and to a lesser extent the Pathfinder tables (where m(n) increases, so a gap of 7000 XP doesn't matter as much at higher levels), characters who are behind their peers can eventually match levels.
As someone who played in a home campaign using OP rules, I can tell you that being 4 levels behind the rest of the party, forever, isn't much fun.
The math behind it follows the the rule for monster xp.
Rules
1) For slow/normal/fast advancement, you should level up after 7.5/5/3.25 encounters with a CR of your respective level
2) Two monsters with the same CR give together the same XP as one monster with CR+2. By this we defined the even and odd levels separately, but have not tied them together. Every two levels, you need the double amount of xp to advance, for level 2 -> 2000, lvl 4 -> 2*2000, lvl 6 -> 2*2*2000 etc.
3) To have nice numbers, they rounded the entries in the tables, both for level advancement and xp for an encounter. Therefore the used pattern does not hold strictly. Furthermore, instead of tying the even and odd levels together by a factor of 1.41..., they used 1.5 alternated by 1.3333.
Therefore the xp needed for a level is
1000 * sum(n=1;n=level)[1.41^n]
(which is a geometric progression), plus some rounding.
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RPG Superstar 2010 Top 16
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I don't know about you guys, but I prefer the scheme that has a direct mathematical relationship, even if it does use sqrt(2).
Well, If you'd be satisfied with the idea of alternating between 1.5 and 1.3333, as the lower levels do, and continuing that procedure, then we'd have:
m'(1) = 0
m'(2) = 2000
m'(3) = 3000
m'(4) = 4000
m'(5) = 6000
m'(6) = 8000
m'(7) = 12,000
m'(8) = 16,000
m'(9) = 24,000
m'(10) = 32,000
m'(11) = 48,000
m'(12) = 64,000
m'(13) = 96,000
m'(14) = 128,000
m'(15) = 192,000
m'(16) = 256,000
m'(17) = 384,000
m'(18) = 512,000
m'(19) = 768,000
m'(20) = 1,024,000
and therefore:
M'(1) = 0
M'(2) = 2000
M'(3) = 5000
M'(4) = 9000
M'(5) = 15,000
M'(6) = 23,000
M'(7) = 35,000
M'(8) = 51,000
M'(9) = 75,000
M'(10) = 107,000
M'(11) = 155,000
M'(12) = 219,000
M'(13) = 315,000
M'(14) = 443,000
M'(15) = 635,000
M'(16) = 891,000
M'(17) = 1,275,000
M'(18) = 1,787,000
M'(19) = 2,555,000
M'(20) = 3,579,000
If you wanted to stick with a common ratio of square root of 2, then the experience chart would look like:
M''(1) = 0
M''(2) = 2000
M''(3) = 4829
M''(4) = 8829
M''(5) = 14,486
M''(6) = 22,486
M''(7) = 33,799
M''(8) = 49,799
M''(9) = 72,427
M''(10) = 104,427
M''(11) = 149,682
M''(12) = 213,682
M''(13) = 304,191
M''(14) = 432,191
M''(15) = 613,211
M''(16) = 869,211
M''(17) = 1,231,249
M''(18) = 1,743,249
M''(19) = 2,467,327
M''(20) = 3,491,327
FWIW, sCoreGen has this Excel formula to compute Medium Pathfinder XP/Level progression (broken down by me):
Main formula to reach level L:
c = m*(2^a-1) + n*(2^b-1)
Where...
a = L / 2, rounded down to the nearest integer
b = (L-1) / 2, rounded down
m = XP value for level 2 (2000)
n = XP value for level 3 (5000) - m
Now for some rounding (for levels 11+):
d = square root of (L-1), rounded down
e = (10^d) / 0.2
f = c / e, rounded
Final value = f * e
This has the added effect of computing XP values for Epic levels.
EDIT: these formulas aren't 100% exact for some levels of the Slow and Fast progression.
It's really unbelievable that WOTC could own the rights to a linear exp progression.
They probably don't and PF is just cautious.
You're making a common misconception that comes up when people talk about the OGL. The OGL has nothing to do with copyrights, trade marks, trade dress, patents, trade secrets, or anything else to do with intellectual property.
The OGL is a license... in fact, it's best if you think about it for these purposes as a contract. (It should be noted for sake of completion that, in American jurisprudence, the OGL is not a traditional contract from a definitional perspective; but in terms of its interpretation, and - most importantly - enforceability, it functions as a contract. It's a very specific type of specialized contract.) That contract allows you to do certain things (basically, to publish, use, and retool all material that WotC has declared to be "open game content"). If you go outside of that contract, and start to publish and utilize things that fall squarely outside of the OGL, you are then in breach of contract. And may owe WotC some kind of liability.
Now it's that last statement that's in question - what would you owe WotC? There's other legal issues to be explored, but the major legal disincentive to crossing WotC* is the unknown liability one faces. They could ask for monetary compensation, they could ask that you cease all operation.
These licenses have not been fully tested within the gauntlets of a trial court. Those licenses that have been challenged in courts have been upheld. So the signs aren't good for anyone wishing to brave those untamed waters.
So please, don't conflate issues of intellectual property with issues of licensing. They are, from a legalistic perspective, completely different things.
*And here I am singling out WotC for the sake of simplicity. More properly, it should be the Original Publisher, as Paizo is putting out its own OGL stuff. Paizo is just being more lenient about its mechanics, essentially saying that all mechanics are free to use and spread.
Woo! Math and some psuedo-coding!
Just what I needed as a break from studying for a physics degree! :p
Actually this was very interesting.
I wonder if wealth per level has a simpler progression, it seems to triple every four levels or so.
I much prefer the old 3.5 experience progression; it was very simple and elegant. While I can appreciate the xp budget approach, I have no trouble with the old EL design system (and the background math of encounter design is much the same in both anyway).
But, what I do like in Pathfinder's experience rules is the medium and slow progression. I have raised many an adventure party to the heights of power far too quickly for any hope of verisimilitude. Although in the "old days" the level advancement was glacially slow after 9th (and that's after we sped up xp gain), there was something wonderful about PCs taking 20 years to gain 20 levels. I no longer want to do that, but hitting 20th after 18 months of game time with an average party age of 19 is just wrong!
Anyway, I think the easiest and most elegant way to achieve the slower advancement, while retaining the simplicity of 3.5 xp charts, is to simply give fractional xp rewards based on your preferred advancement speed.
I think many people would be surprised to hear that the "fast" advancement track in PF is the standard rate in 3.x. It works out to around 14 encounters (13.33 officially). The "medium" rate is about 1.5 times that many, or around 20 encounters per level. And the "slow" rate is about 1.5 times as fast as medium, or around 30 encounters per level.
SO....you use the old EL xp generation method (or ad hoc, or whatever tickles your fancy), but in the final calculation of xp you simply multiply the "normal" award by 1.0(fast), 0.666(medium), or 0.444(slow), depending on your preferred rate.
Cheers
Medium XP for a specific level (n) is related to the XP award of the former level in this way:
(5 x (XP award for CR of (n) - 1) + total XP for (n - 1))
Medium XP for level 4 is then, five times CR 3 award plus the xp total to reach level 3: (5 x 800 + 5000) = 9000.
The next XP total, level 5, is then (5 x 1200 + 9000) = 15000.
For Slow XP, multiply Medium XP with 1.5 (the slow progression is arbitrarily rounded to nearest 1000 (at first, but to nearest 5000 at 9th, and so forth).
Also PC cash seems based on Fast treasure in this way for a specific level (n): ((n - 1) x 2.5 + total treasure at (n - 1)).
For example at level 4: (800 x 2.5 + 1000) = 3000
These formulas can be put in tables in excel and show epic level cash per level and XP totals.
It's really unbelievable that WOTC could own the rights to a linear exp progression.
They probably don't and PF is just cautious.You're making a common misconception that comes up when people talk about the OGL. The OGL has nothing to do with copyrights, trade marks, trade dress, patents, trade secrets, or anything else to do with intellectual property.
The OGL is a license... in fact, it's best if you think about it for these purposes as a contract. (It should be noted for sake of completion that, in American jurisprudence, the OGL is not a traditional contract from a definitional perspective; but in terms of its interpretation, and - most importantly - enforceability, it functions as a contract. It's a very specific type of specialized contract.) That contract allows you to do certain things (basically, to publish, use, and retool all material that WotC has declared to be "open game content"). If you go outside of that contract, and start to publish and utilize things that fall squarely outside of the OGL, you are then in breach of contract. And may owe WotC some kind of liability.
Now it's that last statement that's in question - what would you owe WotC? There's other legal issues to be explored, but the major legal disincentive to crossing WotC* is the unknown liability one faces. They could ask for monetary compensation, they could ask that you cease all operation.
These licenses have not been fully tested within the gauntlets of a trial court. Those licenses that have been challenged in courts have been upheld. So the signs aren't good for anyone wishing to brave those untamed waters.
So please, don't conflate issues of intellectual property with issues of licensing. They are, from a legalistic perspective, completely different things.
*And here I am singling out WotC for the sake of simplicity. More properly, it should be the Original Publisher, as Paizo is putting out its own OGL stuff. Paizo is just being more...
I find it exceedingly unlikely that WotC does or even can own the rights to a mathematical progression table.
Even if they inexplicably do, I don't see the need for the crazy complicated Pathfinder tables. Perhaps the argument that, explicitly, 500(x-1) as an experience table could be legally claimed might work if you pay your lawyers enough (which I imagine Hasbro does), but I doubt that covers any table that works on the principle y(x-1) where y != 500.
Now it is very easy to calculate monster xp. It does double every other level (only checked CR 1-20).
In the medium progression until level 10, the difference in exp between levels doubles every other level until after level 10; from there leveling is slightly slower from the math.
Compare the growth in additional exp required to reach the level:
Math:
11 45000
12 60000
13 90000
14 120000
15 180000
16 240000
17 360000
18 480000
19 640000
20 960000
Actual:
11 50000
12 65000
13 95000
14 130000
15 190000
16 255000
17 410000
18 500000
19 650000
20 1050000
So Paizo caused it to sometimes be slower to reach higher levels. It is important to note that reaching level 12 is quicker than reaching level 11, same is true for reaching levels 18 and 19 assuming that you are fighting on level monsters. It is especially important to note that level 18 will flyby considering monster xp goes up by a factor of 1.5 and the required xp only goes up by 1.3. I haven't done any analysis of the fast and slow progressions yet.
Chief Technical Officer
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I find it exceedingly unlikely that WotC does or even can own the rights to a mathematical progression table.
Archmage_Atrus's point it that it doesn't *matter* if they own it, or even if it's legally possible to own it.
All that matters is this: If you want to use the OGL, you cannot use Wizards' XP tables, or anything else they specified as Product Identity under the OGL.
Precisely, thank you Vic.
I much prefer the old 3.5 experience progression; it was very simple and elegant. While I can appreciate the xp budget approach, I have no trouble with the old EL design system (and the backround math of encounter design is much the same in both anyway).The reason I like the Pathfinder progression is that all the s***-crazy maths to determine how many XP a 14th level character gets for stepping on a goblin is already done for you; you add the static XP for the goblin, then realise you still need to do that a few thousand times.
Why hell, the math for that one is easy in 3.x, the 14th fighter doesn't get anything for "stepping on a goblin" (unless the goblin is more than 5th level).....
.....I couldn't resist.
I definitely agree that it is nice to just add up dead guys, but the wacky math involved in the xp tables is too high a price for that simplicity for me. I can just reference the xp by CR table. I do think its crazy to worry about individually accurate xp by level awards; average party level is good enough for anyone.
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hahahahahhahahhahahahhaaaa, ohh that hurts some of my players have a hard time adding up dice for attacks and damage..
"What is 7 plus 14? hmmm. Uhh 20 right so the Ac was 21 I miss."
Hmmm me thinks
"nooooo 7+14 is 21"
"Alright so 6+ str of 3 + 4 cold damage issssss,,, hmmmm 15!"
Hmmmm me thinks.
"Nope sorry you rolled a ten, really you did"
"Oh ok."
Really I find pathfinders system pretty easy and since I use the handy dandy DM screen the xp table is right there staring at me just daring me to do something crazy like throw the players an arbitrary 17xp in from the lands of chaos...
Nooooooo, and yes.
Here's the information for OOCalc. I'll post more info later (it's 2:15 AM right now!)
A1=1; A2=2; A3=3; ... A20=20
B1=0; B2=<XP for level 2 in chosen track>
B3=B$2*(POWER(2,INT($A3/2))+3*(POWER(2,INT(($A3-1)/2))-1)/2-1)Then you can fill B4 to B20 using the equation in B3. Then you need to round the values as I described above.
You can also do fun stuff with this, like calculating fractional levels.
For what it's worth, the Excel formula I came up with a couple years ago for the Medium chart was:
=ROUND((2000 * (2^FLOOR(A1/2;1) - 1) + 3000 * (2^FLOOR((A1-1)/2;1) - 1))/10^(FLOOR(SQRT(A1-1);1)+1)*2)/2*10^(FLOOR(SQRT(A1-1);1)+1)
Ok, so... kind of an odd place for my first post on these forums, but as I'm highly interested in expanding Pathfinder into Epic Levels as seamlessly as possible, I figured I'd give this a go.
I'll warn right now though that this may be rather long and rambling...
Sorcerer's formulas are quite good, but as noted, the exp is slightly off for a few levels, and there didn't seem to be a discernible pattern for the levels at which the rounding multiplier increased.
I... think I've ironed most of the bugs out of it, by approaching it from a slightly different angle. Nobbs mentioned that with the Fast progression a character is intended to level every 3.25 encounters. This got me thinking, with all this effort being put into extending the leveling chart past 20, what about extending the exp given by monsters past CR 25? Thankfully, exp based on CR is a much simpler calculation. In Open Office Calc, assuming B1 is the exp for a CR1 monster (400) the exp is calculated as B2=B1*(3/2), B3=B2*(4/3), repeating.
You then calculate the exp to level based on monster exp*(3.25) + (EXP required for previous level) rounded up to the current rounding multiple.
For example: C2=ROUNDUP((C1+B1*(13/4))/100;0)*100
Where the /100 *100 business is the amount to which the equation is rounded.
The rounding modifier and type change as well, as noted in Sorcerer's method, though thankfully there is actually a pattern now.
At level 7, and every six levels thereafter, you round to the nearest multiple, rather than rounding upwards. (ROUND instead of ROUNDUP in the OOC equation)
At Lvl 2+ round up to the nearest 100.
At Lvl 4+ round up to then nearest 500.
At Lvl 6+ round up to the nearest 1000.
At Lvl 11+ round up to the nearest 5000.
At Lvl 16+ round up to the nearest 50000.
At Lvl 21+ round up to the nearest 100000.
(I think I could continue to extrapolate this using the "Method of Finite Differences" but I really don't feel like trying to bludgeon my way through polynomial equations at the moment...)
Using this formula, the ONLY level where the calculated exp differs from the actual exp table is level 15 (420,000 instead of 425,000) so it's possible that an additional modifier of some sort may have to be applied every 15 levels to keep the formula exactly perfect, but since we don't have an official chart up to level 30, I have no idea what that might be.
Ok, I hate to double-post, but I may have just had a ridiculous breakthrough. Monster exp rewards by CR follow a completely linear formula, increasing by 1.5x/1.333x/1.5x/1.333x etc. all the way up the chart. Except at CR22, where they round up to the nearest 1000, and 24, where they just plain round to the nearest 1000. If you round down to the nearest 10000 at CR26, a CR26 monster gives 2,400,000 exp. From this point, up to CR41 every CR monster gives exp exactly 1000 times that of a monster at it's CR-20, at which point you can repeat the rounding.
Similarly, if I can figure out the math from level 21 to level 26 to make level 26 occur at 15,000,000 exp, then the exp required to level follows the exact same formula and multipliers, times 1000, as the formula from level 6 to level 20.
I'll see if I can't finish figuring this thing out tomorrow. I've been tinkering with this thing on-and-off for hours, and frankly, it's getting a bit too late in the evening for me to be dealing with higher math.
The Chart actually builds on the awards given at specific level (the one below).
Medium XP for a specific level (n) is related to the XP award of the former level in this way:
(5 x (XP award for CR of (n) - 1) + total XP for (n - 1))
Medium XP for level 4 is then, five times CR 3 award plus the xp total to reach level 3: (5 x 800 + 5000) = 9000.
For n= 2 to 20
2 000
5 000
9 000
15 000
23 000
35 000
51 000
75 000
107 000
155 000
219 000
315 000
443 000
635 000
891 000
1 275 000
1 787 000
2 555 000
3 579 000
For n= 21 to 40 (epic levels)
5 115 000
7 163 000
10 235 000
14 331 000
20 475 000
28 667 000
40 955 000
57 339 000
81 915 000
114 683 000
163 835 000
229 371 000
327 675 000
458 747 000
655 355 000
917 499 000
1 310 715 000
1 835 003 000
2 621 435 000
Paizo rounded the numbers neatly. These are raw values.
Note: Also note that PC cash seems based on Fast treasure in this way for a specific level (n): ((n - 1) x 2.5 + total treasure at (n - 1))
That's even more insane than mine! It's more closely related to the alternating recursion method I described above ... At least mine only has one magic number (at Lvl = 2) :)Here's the information for OOCalc. I'll post more info later (it's 2:15 AM right now!)
A1=1; A2=2; A3=3; ... A20=20
B1=0; B2=<XP for level 2 in chosen track>
B3=B$2*(POWER(2,INT($A3/2))+3*(POWER(2,INT(($A3-1)/2))-1)/2-1)Then you can fill B4 to B20 using the equation in B3. Then you need to round the values as I described above.
You can also do fun stuff with this, like calculating fractional levels.
For what it's worth, the Excel formula I came up with a couple years ago for the Medium chart was:
=ROUND((2000 * (2^FLOOR(A1/2;1) - 1) + 3000 * (2^FLOOR((A1-1)/2;1) - 1))/10^(FLOOR(SQRT(A1-1);1)+1)*2)/2*10^(FLOOR(SQRT(A1-1);1)+1)
The only reason it's so ugly looking is to get the rounding correct. Your formula doesn't have rounding, so of course it's going to look much neater!