Formula for experience

[Asmor]

This may be old news to some of you, but I just noticed it when I was looking at the exp tables in the DMG.

Anyways, the exp is based on a fairly simple system based on the difference between the party's level and the CR.

Let X = CR - APL

 X | Base experience
----------------------
 7 | 3600
 6 | 2400
 5 | 1800
 4 | 1200
 3 | 900
 2 | 600
 1 | 450
[b] 0 | 300[/b]
-1 | 200
-2 | 150
-3 | 100
-4 | 75
-5 | 50
-6 | 37.5
-7 | 25

Now, take that base experience and multiply by the APL to get the actual experience.

Example: A APL 15 party defeats a CR 20 creature. 20-15=5, or 1800 exp. Multiply by APL (15) to get 27,000.

Example 2: APL 12 party defeats a CR 6 creature. 6-12=-6, or 37.5. Multiply by APL (12) to get 450.

There's also a relatively easy way to make up the table from memory... Just remember this progression of multipliers:

1, 1.5, 2, 3, 4, 6, 8, 12

Base exp is APL x 300. Whether X (the difference between APL and CR) is positive or negative, count up the progression X steps starting with 0 (so X=1 or X=-1 is actually 1.5). If X is positive (i.e. the CR is higher than the APL) you'll multiply. Otherwise, if X is negative, divide.

APL x 300 (x or ÷) multiplier

 

[Infiniti2000]

I'm not going to check the numbers, but just remember that XP is awarded per 'each character' . Average Party Level doesn't apply. So, use "each character's level" instead of APL in your analysis.

 

[Delta]

I use this:

CD = challengeRating – partyLevel
award = partyLevel * 2 ^ (CD / 2) * 300

CD here (what Asmor calls X) stands for "Challenge Difference". Now, this formula is exactly on target for even CD, a bit of an approximation for odd CD (another line of formula can correct for that, but I actually don't bother, it's close enough). I also play 3.0, and don't bother with the per-character variation under 3.5.

 

[Asmor]

That's really a remarkable fit, way too close to be a coincidence.

CD      D&D     Formula
7	12	11.31
6	8	8
5	6	5.66
4	4	4
3	3	2.83
2	2	2
1	1.5	1.41
0	1	1
-1	0.67	0.71
-2	0.5	0.5
-3	0.33	0.35
-4	0.25	0.25
-5	0.17	0.18
-6	0.13	0.13
-7	0.08	0.09

This leads me to think that your formula is the actual basis for D&D's exp system. It fits identically at every even CD, and it's extremely close at the odd ones which have ugly decimal representations and were presumably rounded.

So... Thanks for posting that so much! Definitely a lot simpler to remember than the actual system.

 

[kigmatzomat]

The XP reward for an encounter of equivalent level is approximately equal to the XP required to reach the next level multiplied by the assumed 4-person party divided by the assumed 13 encounters/level. Which is essentially Level x 300 as a party reward or Level x75 for inidividual reward for CR=Level.

The reward adjustment for CR!=level follows the CR threat calc, doubling with each +2 to CR, halving with each -2 CR. Mid points are 1.5x for +1 CR, 0.75 at -1 CR. There's really very little difference between giving XP based on encounter CR and for the individual creatures, once you remove any situational modifiers.

 

[Flynn]

You might be interested in the Chi-Rho method of calculating XP, as it takes the above just one step further. You can get the basics here:
http://www.enworld.org/showpost.php?p=1662559&postcount=70

The rest of the thread makes for an interesting read, if you are into that sort of thing, and if I'm not mistaken, your posts above make it seem as if you might be.

Enjoy,
Flynn

 

[Asmor]

Ah, that does look interesting. Thanks!

Kigmatzomat: Regarding each difference in CR doubling/halving, that is basically the definition of the formula posted by Delta... Increase the difference by 2 and you add another full power of 2. Decrease the difference by 2 and you add another full power of 1/2.

 

[Delta]

This leads me to think that your formula is the actual basis for D&D's exp system. It fits identically at every even CD, and it's extremely close at the odd ones which have ugly decimal representations and were presumably rounded.

So... Thanks for posting that so much! Definitely a lot simpler to remember than the actual system.

Actually, I bet the designers were more likely literally thinking what you put in your original post. I think they were probably making the table so if CR = APL, you get APL * 300. If CR & APL differ, you get times or division by 2 for 2 steps; for a single step difference you get times or division by about half as much, or 1.5 (which in a perfectly smooth formula should really be sqrt(2) ~ 1.4).

The formula is just the mathematically most concise way I could find to say basically the same thing. (And I suppose has an advantage in not being license-encumbered, now that I think of it.)