Certain powerful races have a "level adjustment" (LA) applied to them to account for the extra powers that members of the race have. For example, a duergar or tiefling has a level adjustment of +1, and a drow has a level adjustment of +2. A member of such a race will have levels in character classes, defining her "class level" (CL), but, for the purpose of determining how much XP must be earned to advance, the level adjustment is added to the CL to get the "effective character level" (ECL).

Additionally, certain races start out with more than one "racial hit die". Each additional hit die also adds one to the ECL of the character.

Effectively, the ECL of any character is equal to the number of hit dice (from race or class) + the level adjustment.

The following table illustrates the effect of the level adjustment on earned experience. For this table, I am assuming that a level one character with an LA of +y starts out with the XP of a character with LA +0 and level y. That assumption appears to be consistent with what Wizards of the Coast has said about ECL and XP.

Effect of Level Adjustments

Level	Level Adjustment +0			Level Adjustment +1			Level Adjustment +2
	Earned XP	ECL	Next Level	Earned XP	ECL	Next Level	Earned XP	ECL	Next Level
1	0	1	+1,000	1,000	2	+2,000	3,000	3	+3,000
2	1,000	2	+2,000	3,000	3	+3,000	6,000	4	+4,000
3	3,000	3	+3,000	6,000	4	+4,000	10,000	5	+5,000
4	6,000	4	+4,000	10,000	5	+5,000	15,000	6	+6,000
5	10,000	5	+5,000	15,000	6	+6,000	21,000	7	+7,000
6	15,000	6	+6,000	21,000	7	+7,000	28,000	8	+8,000
7	21,000	7	+7,000	28,000	8	+8,000	36,000	9	+9,000
8	28,000	8	+8,000	36,000	9	+9,000	45,000	10	+10,000
9	36,000	9	+9,000	45,000	10	+10,000	55,000	11	+11,000
10	45,000	10	+10,000	55,000	11	+11,000	66,000	12	+12,000
11	55,000	11	+11,000	66,000	12	+12,000	78,000	13	+13,000
12	66,000	12	+12,000	78,000	13	+13,000	91,000	14	+14,000
13	78,000	13	+13,000	91,000	14	+14,000	105,000	15	+15,000
14	91,000	14	+14,000	105,000	15	+15,000	120,000	16	+16,000
15	105,000	15	+15,000	120,000	16	+16,000	136,000	17	+17,000
16	120,000	16	+16,000	136,000	17	+17,000	153,000	18	+18,000
17	136,000	17	+17,000	153,000	18	+18,000	171,000	19	+19,000
18	153,000	18	+18,000	171,000	19	+19,000	190,000	20	+20,000
19	171,000	19	+19,000	190,000	20	+20,000	210,000	21	+21,000
20	190,000	20	+20,000	210,000	21	+21,000	231,000	22	+22,000

We can derive a number of useful formulae from the data in this table.

The formula for how much XP one must earn to be at the beginning of level x with LA +0 is simple:

XP_LA+0(x) = 500 x (x - 1)

A character with LA +1 needs to earn an extra 1,000 XP to advance each level:

XP_LA+1(x) = 500 (x + 1) x

A character with LA +2 needs to earn an extra 2,000 XP to advance each level:

XP_LA+2(x) = 500 (x + 2) (x + 1)

Generalizing:

XP(x,y) = 500 (x + y) (x + y - 1)

XP(x,y) = 500 (x² + 2xy - x + y² - y)

Let us calculate what the XP difference is imposed by having LA y.

XP(x+1,y) - XP(x,y) = 500 ((x+1)² + 2(x+1)y - (x+1) + y² - y) - 500 (x² + 2xy - x + y² - y)

XP(x+1,y) - XP(x,y) = 500 (x² + 2x + 1 + 2xy + 2y - x - 1 + y² - y) - 500 (x² + 2xy - x + y² - y)

XP(x+1,y) - XP(x,y) = 500 (x² + 2x + 1 + 2xy + 2y - x - 1 + y² - y - x² - 2xy + x - y² + y)

XP(x+1,y) - XP(x,y) = 500 (2x + 2y)

XP(x+1,y) - XP(x,y) = 1000 (x + y)

Every level gained requires additional XP to be earned equal to 1000 times the LA: 1000 XP for LA +1, 2000 XP for LA +2, etc.

Let us calculate what the XP difference is between LA y+1 and LA y.

XP(x,y+1) - XP(x,y) = 500 (x² + 2x(y+1) - x + (y+1)² - (y+1)) - 500 (x² + 2xy - x + y² - y)

XP(x,y+1) - XP(x,y) = 500 (x² + 2xy + 2x - x + y² + 2y + 1 - y - 1) - 500 (x² + 2xy - x + y² - y)

XP(x,y+1) - XP(x,y) = 500 (x² + 2xy + x + y² + y) - 500 (x² + 2xy - x + y² - y)

XP(x,y+1) - XP(x,y) = 500 (x² + 2xy + x + y² + y - x² - 2xy + x - y² + y)

XP(x,y+1) - XP(x,y) = 500 (2x + 2y)

XP(x,y+1) - XP(x,y) = 1000 (x + y)

Just as we'd expect, this formula is identical to that which we derived for adding one to a class level with the same Level Adjustment: either adds one to the character's ECL.

Reducing Level Adjustment using the Unearthed Arcana rule

We've now quantified the cost of having a level adjustment. But what is the value of being in a race that requires that you pay that cost?

The recent V3.5 rule book from Wizards of the Coast, Unearthed Arcana brings up that very question and argues that the benefits of being a member of a powerful race that requires a level adjustment taper off as the character advances in level. In effect, they argue that eventually class benefits outweigh racial benefits, and that a level adjustment required by the race becomes increasingly burdensome. They proposed a mechanism by which a character could reduce her level adjustment by paying an XP cost at specific levels. The XP cost to be paid is 1000 times (<current ECL> - 1). Which level(s) to pay that cost at depended on the LA required by the character's race. After paying that XP cost, you also reduce the character's ECL by one.

Note that the XP price paid depends on ECL, which includes racial hit dice, but the level at which to pay depends only on the level adjustment, which is the other factor that can increase ECL compared to CL.

Algebraically, what is the effect of paying that XP cost? If a character has just advanced from CL x to CL x+1 with LA +y, the XP she needed to do this was calculated above.

XP(x+1,y) - XP(x,y) = 1000 (x + y)

Additionally, since we calculated the effect of a single point of LA as

XP(x,y+1) - XP(x,y) = 1000 (x + y)

In other words, doing this level adjustment doesn't cost the character anything now: she paid the price in the past for being a member of a powerful race by spending more XP to get to her current level, but after performing the level adjustment reduction, her CL remains the same with a lower ECL, which will allow her to advance more quickly in the future.

To help visualize this, consider the duergar (LA +1) and the drow (LA +2). Neither has a racial hit die, so in both cases, ECL = CL + LA. LA +1 allows an ECL reduction at Level 3. LA +2 allows an ECL reduction at Level 6 and again at Level 9. Let's see what this would look like for the first ten levels of a character using the Unearthed Arcana rule.

Effect of Reducing Level Adjustments using the Unearthed Arcana rule

Level	Level Adjustment +0				Level Adjustment +1				Level Adjustment +2
	Earned XP	"Book" XP	ECL	Next Level	Earned XP	"Book" XP	ECL	Next Level	Earned XP	"Book" XP	ECL	Next Level
1	0	0	1	+1,000	1,000	1,000	2	+2,000	3,000	3,000	3	+3,000
2	1,000	1,000	2	+2,000	3,000	3,000	3	+3,000	6,000	6,000	4	+4,000
3	3,000	3,000	3	+3,000	6,000	3,000	3	+3,000	10,000	10,000	5	+5,000
4	6,000	6,000	4	+4,000	9,000	6,000	4	+4,000	15,000	15,000	6	+6,000
5	10,000	10,000	5	+5,000	13,000	10,000	5	+5,000	21,000	21,000	7	+7,000
6	15,000	15,000	6	+6,000	18,000	15,000	6	+6,000	28,000	21,000	7	+7,000
7	21,000	21,000	7	+7,000	24,000	21,000	7	+7,000	35,000	28,000	8	+8,000
8	28,000	28,000	8	+8,000	31,000	28,000	8	+8,000	43,000	36,000	9	+9,000
9	36,000	36,000	9	+9,000	39,000	36,000	9	+9,000	52,000	36,000	9	+9,000
10	45,000	45,000	10	+10,000	48,000	45,000	10	+10,000	61,000	45,000	10	+10,000

Observe that the LA +1 character has Earned XP exceeding his "Book" XP by 3,000 - the "buy out" cost.

Similarly, the LA +2 character has Earned XP exceeding her "Book" XP by 16,000 - the sum of the two "buy out" costs.

In both cases, after reducing the Level Adjustment, the "Book" XP is exactly the same as a character that had started out with Level Adjustment +0.

In play, the way you'd look at this is that the advancement of a member of a powerful race is slower than normal, requiring extra XP to be earned because of her Level Adjustment, but gradually speeds up to a normal pace as the Level Adjustment is gradually reduced and the characters ECL shrinks to equal her CL. The character would have earned more XP to get to the same place as her companions, but would have had the benefit of her racial abilities along the way.

Delaying Level Adjustment Reduction

The Unearthed Arcana says that a character using this technique must do it at the designated levels. But is that really necessary?

As we can see from the chart, doing so is very neat: the character spends precisely the right amount of XP at the right time to be at the beginning of the same class level, but with ECL decreased by one.

If a character delays reducing her Level Adjustment, she'll probably earn less XP than she would have otherwise, assuming she is having encounters appropriate to her old ECL: the amount of XP earned by a character depends on the relationship between the Challenge Rating of the encounter and the ECL of the character. Therefore, it is in the character's best interest to reduce her Level Adjustment at the first opportunity.

If the character were to deduct the same amount of XP at a later time, while decreasing her ECL, she would not be at the beginning of a level. In fact, if she waited long enough, she could actually end up at a higher class level.

Mechanically, there is nothing inherently wrong with this: the character advanced more slowly because of her level adjustment and then finally "pays" for it with the appropriate amount of XP.

But, from a role-playing viewpoint, in a campaign where the character had adventured using the V3 experience rules since level one, it makes no sense: the character would have advanced at a slow pace and then would suddenly be advancing at a normal rate while seemingly gaining (part of) a level.

In such a campaign, there'd be no role-playing harm in letting a character reduce points of Level Adjustment at the beginning of any level, as long as the level is at least as high as the designated level for doing so: she'd end up paying more XP for the privilege, but would maintain class level continuity.

Retrofitting Level Adjustment Reduction into Dargas

How can we retrofit this rule "after the fact" into Dargas? Our characters of races with Level Adjustments are all well above the class levels at which they would have paid the XP cost and reduced their ECL. They all have XP totals which are correctly within the range of their Level Adjusted ECL.

The characters which started out as V1 or V2 characters were converted using the rules suggested in the "Conversion Guide": their old class levels were converted to a combined V3 Character Level, which the player then split up as appropriate among character classes.

Three drow and one duergar were converted. There was nothing especially "powerful" about those races in V2: they simply took the "Drow Kit" or "Duergar Kit" from Skills and Powers. But, in V3, those are "powerful races" and have a Level Adjustment.

Rightly or wrongly, when we converted these characters to V3, we gave them class levels as prescribed by the Conversion Guide. Then, the Level Adjustment appropriate to their race was applied, giving them an ECL higher than their CL, and an XP total was given to them appropriate to their ECL.

The DM could have said "If Hazen was a Level 15 duergar thief in V2, in V3, he is still ECL 15 but must be a Level 14 rogue, since being a duergar effectively adds a level to him." Instead, he said "Hazen was a Level 15 duergar thief in V2 and is now a Level 15 duergar rogue in V3, and his ECL is now 16," and assigned Hazen XP based on his ECL of 16.

Since then, the characters have adventured for an entire year, and have accrued XP based on their (elevated) ECL. Therefore, rightly or wrongly, the XP total we have been given is our correct earned XP: we are "used to" operating at those levels. And therefore it follows that if we were to retroactively apply the Unearthed Arcana method to our high-level characters, we should simply subtract 3,000 (for a LA +1 race) or 16,000 (for a LA +2 race) from the current XP totals and just see where it leaves the characters.

It has been proposed that the "correct" way to do this is instead to first subtract out the ECL adjustment and then subtract the 3,000 or 16,000 XP. But, as you can see by looking at the chart, that can't be right: it is the subtracting of the XP that performs the ECL adjustment: you never subtract the XP from an unadjusted XP total.

Perhaps the DM should have assigned a certain amount of XP to each character at conversion time, and said "This is your XP, which corresponds to an ECL of such and such. Your race has a Level Adjustment of +1 or +2, and therefore your CL must be less than your ECL by that amount, unless you spend 3,000 or 16,000 to reduce your ECL. If you do so, spend your remaining XP to buy class levels with no level adjustment." But he didn't.

So, if a CL 15 character had LA +2, making her ECL 17, had accrued 6,000 XP towards ECL 18, she is now adjusted to be ECL 15 with 6,000 XP accrued towards ECL 16. She ends up not only being closer to advancement, but will advance faster, since her ECL is reduced.