D&D 3E/3.5 3.5 XP Table

[andargor]

You may want to look at these threads:

Looking for experience speadsheet?

Excel party xp calculator for 3.5e!

These are discussions about the XP and EL formulas in excruciating detail

I've got the result of their work in an excel spreadsheet on my site (click on sig).

Andargor

 

[DarkWizard]

Thanks for the links to those threads, and your site, good stuff. It is just too bad that the XP table appears to have been eyeballed rather than use a formula. Ah well.

 

[Dr_Rictus]

At the risk of sounding like Pascal, there actually is a formula, it's just a little complicated and has some exceptions, such that I got bogged down in trying to express it correctly.

Bah.

 

[Lamoni]

I just simulated the entire table in Excel using the following formula. There are still a few caveats though. Experience for CR1 at levels 4 and 5 don't work (WotC just arbitrarily stuck 300 there when it doesn't belong). Everything else follows the formula. Unfortunately, I didn't see any way to do it without an IF statement.

=IF(Y-X<0,((X*(3-MOD((Y-X),2))*100)*(0.5^ROUNDDOWN((X-Y)/2,0))),
((X*(2+MOD((Y-X),2))*150)*(2^ROUNDDOWN((Y-X)/2,0))))

I just copied and pasted from excel and then replaced the cell references with X and Y.
X = character level
Y = CR

I hope this helps.

Edit: You also need to make sure you follow the table for things that don't give experience. Or you can just delete the values from any cell where the CR is 8 below the character's level. The table also doesn't show experience for CR's 8 greater than party level.

To further explain the formula, it calculates experience differently based on whether it is above or below the CR=Level line. It uses a different base value for odd increments and then multiplies the value by 2 as you move across. If you have any questions, feel free to ask. You might be able to reduce the formula so it looks better and is easier to read in case you want to do it by hand.

 

[Dr_Rictus]

WotC just arbitrarily stuck 300 there when it doesn't belong.

Basically true, except it's not entirely "arbitrary," and either it or 450 XP "belongs" if you're to keep the chart monotonically increasing with degree of challenge.

Obviously, there's an exception to the progression such that any character under level 3 is treated as being level 3, because otherwise it becomes non-monotonic (that is, XP decrease as the encounter becomes more challenging).

See, with base XP linear in character level, and doubling XP for every 2 levels' difference in challenge, the maximum XP for any given CR happens at level 3 (I believe it would be sqrt(2)+1), or about 2.4, if the function were continuous).

You can deal with that in one of two obvious ways. You can either base XP on MAX(3,Level) rather than Level (i.e., never consider level to be less than 3, since that would cause XP to go down) or you can set an XP cap at any given CR equal to what a 1st-level party would get.

In general, the table (obviously) takes the first approach. It just uses the second one for CR1. So, that decision is arbitrary in a sense, but the number 300 itself isn't; it's an artifact of the underlying formula.

 

[Dr_Rictus]

Actually, it might clarify things to just mention the following explicitly:

All of the irregularities in the table are the result (I claim) of two things:

1) XP awards must always increase as encounters become more challenging, but the underlying formula fails to have this property for a constant CR and character levels less than 3. Something must be done to correct for this.

2) In multiplying (or dividing) the XP award by 2 for every 2 CR difference, 1.5 is used as an approximation for the square root of 2. This approximation is only used for odd differences: the square root of 2 squared is still 2.

That's pretty much it. Two different methods are used to correct for point #1 depending on on whether CR=1 or not, which introduces two different irregularities into the table, but for the same underlying reason. See my post above for the two different methods.

Other than those things and the details of how they're applied, the formula is basically:

XP=300*X*2^((Y-X)/2)

using Lamoni's terminology for X and Y.

 

[Piratecat]

All of the irregularities in the table are the result (I claim) of two things:

Dang, you're smart. You're the kind of guy I'd want in my game.

(In other words, we miss you.)

 

[DarkWizard]

All these are things I have gone over, however as has been stated here all of these formulas inevitably produce irregularities at certain points. They work, with a bit of tweaking, but I am just hoping against hope that there might yet be a consistent formula to use without producing any variations from the values listed in the DMG. I am slowly beginning to believe there is no such formula.

 

[Lamoni]

The formula I gave does work, and I am sure it is the formula that WotC used. However as Dr_Rictus explained, if continuted for levels less than 3, you begin to get less experience. Since getting less experience for a more challenging encounter doesn't make sense, WotC inserted a few 300's in the first column. They could have stuck with 375, 400, and 450 in my opinion, but they chose not to. If you want a formula with zero exceptions, then I am afraid you won't find one... except in Excel where you can just include the formula in another IF statement. If you are happy with a formula with only those 3 exceptions, you can still be a happy camper.

Edit: Here is an excel formula that will give you the exact values as on the WotC table. Just put numbers from 3-20 for the level and numbers 1-20 for the CR.

=IF(AND(X<7,Y=1),300,
IF(ABS(X-Y)>7,"",
IF(Y-X<0,((X*(3-MOD((Y-X),2))*100)*(0.5^ROUNDDOWN((X-Y)/2,0))),
((X*(2+MOD((Y-X),2))*150)*(2^ROUNDDOWN((Y-X)/2,0))))))

 

[DarkWizard]

Actually, yes, I am looking for a formula with zero exceptions. However I am only looking for it just to see if it is actually possible. I am perfectly happy with what already works, but this is sort of like my own personal holy grail, that I will never find.