472004_13905538-math-book

Introduction

I recently reformulated the way I calculate experience in my D&D 3.5 campaign. [Actually, what happened was that my computer's power supply failed and I had nothing better to do with my time for a few hours. But anyway...] It took about a page and a half of 4 x 5½-inch notepaper, and consisted of 25 expressions and observations. When I showed it to others, they were mystified; it may as well have been written in Ancient Greek for all the meaning they took from it. So I set about re-creating the logic that had been distilled into those 21 statements.

The results aren’t for everyone, I’m the first to admit. They make sense to me, others may not find them so useful. But when the work was complete, I thought others might be interested; so I’m presenting them here as a Blog Post. Unfortunately, D&D 4th ed is completely different from 3.x Ed in this respect. (At least this observes the truism that nothing is completely understood until after it becomes outdated!) But for those who still use D&D 3.0 and 3.5, an alternative and mathematically-precise system for calculating XP awards might just hold value, so here it is.

This analysis was carried out to place XP awards in my D&D campaigns on a mathematically-defined basis and to achieve specific goals for the Xp awards system:

  • The system should be mathematically precise for any combination of party member character levels and encounter constituant CRs
  • The system should award bonus XP to party members of lower levels on the basis that they would have learnt more from the battle
  • The system should award reduced XP to NPCs relative to PCs
  • The system should award reduced XP to other participants [animals, intelligent swords, etc] relative to NPCs
  • System should award XP for non-combat encounters on a consistant basis with respect to combat encounters.

Party CR

By definition in the DMG it requires aprox 13 encounters of equivalent level to that of the party for each member to gain a level. What does “of equivalent level” actually mean? Assuming that it means an equal number of opponants, each of the same level as their counterpart within the party, we have a working definition, but not yet a functional one. The DMG also gives guidelines for determining a single number to reflect the capability level of any given opponant mix, in the form of a table. When that table is dissassembled, it becomes clear that the equiavelence of an encounter can be summed up as:

1. (2 x N) @ A = N @ (A+2) where N is the number of creatures of a given CR, and A=the CR of those creatures.

Thus an encounter with two creatures of CR 5 is the same thing as one encounter of CR 7. Mathematically, this is an exponential relationship in factors of root 2, so the following can also be stated:

2. N @ (A+1) = [sqr(2) x N] @ A.

These two calculations permit any combination of encounter CRs to be reduced to a single numeric variable by reducing the constituant CRs to a common base, totalling them, and then reconverting the total to an exact EL.

This permits a functional definition of “equivalent level”:

3. An encounter is of “equivalent level” if the total EL is equal to the total of the Party CRs expressed as an EL.

Base XP Award

Because this system awards bonus XP for skill rolls, ideas, roleplaying, etc in non-combat situations, whereas the base system does not, it seemed appropriate that the base award be reduced. As an initial value, a ratio of 16 encounters of equivalent CR to 1 level advancement has been chosen. This fraction can be altered as desired.

This means, in turn, that the experience earned for a single encounter of equivalent CR is equal to 1/16th of the XP difference between the current Character level and that of Character Level +1. Analysis of the table in Chapter three of the PHB shows that this, in turn, is equal to 1000/16 x (CR+1), or aprox 62.5 x (CR+1). This value is termed E1:

4. E1 = 62½ x (EL+1), where the EL is equal to the Party CR.

However it will actually be the case, more often than not, that the party will be confronted by encounters of an EL that does not precisely match the Party CR. It might be higher, or it might be lower. Using the principles stated in the DMG, and the analysis above, it can be determined that the actual XP award for a given EL, relative to the Party CR, is

5. E2 = E1 x 1.4^D1,
where D1 = EL – Party CR.

Negative ELs and CRs Less Than 1

6. A CR of ½ is assumed to be equivalent to a CR of -1 for the purposes of XP calculation.
7. A CR of ¼ is assumed to be equivalent to a CR of -2 for the purposes of XP calculation.
8. A CR of 1/10 is assumed to be equivalent to a CR of -3 for the purposes of XP calculation.

Party Size Adjustment

At first glance, it should make no difference how many characters make up the party. They have the same number of hit points, just spread amongst more characters. They have a smaller chance to perform a successful attack, but they have more attempts to do so because the party as a whole will get more actions in a turn than if they were fewer in number but of higher levels. They have less effect when successful, but this is balanced by…. nothing? Their opponants, being of higher level in comparison, get fewer attacks but they have a greater chance of success; and when they do succeed, they will do more damage….?

Clearly, there needs to be an adjustment for the number of participants in a battle. The problem is quantifying that adjustment, as it would seem to be different based on the CR value of individual participants. Perhaps this modifier should be determined as an individual adjustment to the amount of XP received?

According to the DMG, the theoretical basis of the XP tables provided assumes a party consisting of 4 characters of equal level. Using (1), it is clear that this gives a theoretical “quarter opponant” of the encounter taking place a level of EL-4. Thus, individual awards for each party member can be determined as:

9. E3 = 62½ x (EL-3) x 1.4 ^ (D2-3)
where D2 = (EL-4) – Individual Char Level
and
where D2 >=0, or,

10. E3 = -62½ x (EL-3) x 1.4 ^ (3-D2)
where D2 = (EL-4) – Individual Char Level
and
where D2 <0.

Member Level Bonuses

This seems to automatically achieve the second objective of the system, awarding more XP to characters of lower level, but it does NOT do so for the reason that (in theory) they would have learnt more from the encounter, it does so simply because it takes greater contributions from multiple characters of lower levels to achieve the same effect net effect in a battle. Furthermore, the ability to learn is often considered an attribute of INT, but basing the bonus on that stat would unfairly reward Mages and other characters whose class requires a high INT and penalise other classes.

Since there is no fundamental value on which to base these that is not inherantly unfair to one class or another, the only solution is an arbitrary and abstract one based on a relative value. Fortunately, on this basis, we have the ideal value already determined in D2:

11. D2 : bonus
-5 or worse : x 1/2, then x 1/3, x 1/4, etc.
-4 : -40%
-3 : -20%
-2 : -10%
-1 : -5%
+0 : +0%
+1 : +5%
+2 : +10%
+3 : +20%
+4 : +40%
+5 or more : x2, then x3, x4, x5, x6, etc.

Thus, for an EL 10 encounter, the basis of D2 is EL 10-4=6. A character of Character Level 5 would have a relative D2 of +1, and would receive +5% to his XP award. A first level character in the same party would receive x2 XP. An eighth level character would have a D2 of -2, and would receive -10% XP.

Significant Opposition / Weak Opposition

These are relatively straightforward, using this system: the GM can simply lower or raise the CRs of individual creatures, or of the party members, or both, to allow for relative strengths. As a rule of thumb:

12. Especially costly combat for PCs: EL+1
Especially easy combat for PCs: EL-1
Opposition has especially strong tactical position at start of combat: EL+1
Opposition has especially weak tactical position at start of combat: EL-1
Opposition has significantly greater resources (magic etc) relative to the PCs: EL+1
PCs have significantly greater resources (magic etc) relative to the enemy: EL-1

Non-PC Adjustments:

When I run combat for a party consisting of both PCs and NPCs, I let the PCs make the major decisions. The NPCs will act according to their natures and classes, unless told not to (a fighter will still attack, but won’t put any real thought into which opponant [attacking the closest or biggest or whatever], or – if he’s the thinking/tactical type – will hold his action until after all the other characters have acted so that he can pick his target appropriately; and so on). This lets me run the battle more easily and ensures the PCs a starring role. As a result of this relative lack of ‘initiative’, it does not seem fair for the NPCs to get the same rewards as the PCs.

However, not all GMs agree with this practice. That’s fine; the system so far has made no distinction between PCs and NPCs, so its easy to treat NPCs as PCs if that practice suits your campaign. There are arguments in favor of this interpretation as well, relating to keeping the game balance between NPCs and PCs. To implement this more standard arrangement, simply ignore steps 13 and 14, below.

It is also my practice to award animals XP so that they can learn and become more effective. This is just a quick and dirty method of simulating these things; each level brings an extra HD, better saves, etc, as though they had progressed on the appropriate character chart. This subsystem was originally created to give familiars a chance to survive and to have an impact as their owners gained levels, and the opposition became more lethal.

Furthermore, some magic items in my campaigns gain XP, increasing the magical bonus they confer over time. However, if the item ever goes to a new owner, the item starts again at 1st level with 0 XP. This represents a stronger bonding between the character and his equipment, as it becomes more focussed.

13. NPCs receive 1/2 the XP they would have received as a PC. This includes any characters whose player does not attend the game session.
14. Anything else which earns XP earns 1/4 the award they would have received as a PC.

1/4 was chosen for the magic items, animals, etc because it means that they will go above +5 at about the same time that their owners achieve epic levels. In a campaign not intended to reach epic levels (I don’t run any at the moment), I would limit them to +5 in bonuses, and perhaps make the ratio 1/3 instead of 1/4. ensuring that the PCs have time to enjoy their plus-five item for a while when they achieve the pinnacle of their powers. This is also a good rule of thumb for the power levels of treasure awarded, by the way!

1/2 was chosen because it’s twice as much as the animals get, and thus seems a reasonable number – and it’s easy to calculate.

Low/High Treasure Adjustments

It is assumed that each xp is matched by 10 GP of value in treasure. If this is not the case (and it rarely is!), the difference is divided by the number of characters and applied as a bonus or penalty AFTER all other adjustments. Animals and items are excluded from the ‘number of characters’ for this purpose, but Familiars and similar creatures are INcluded. Thus, in a low-magic campaign, where both sides have little in the way of magical goodies, the EL doesn’t change but the XP awarded increases significantly. If a low-magic party comes up against a high-magic opposition, the EL increases, but the party may get most of it’s reward as goodies after the battle.

15. Bonus XP = [TOTAL XP Awarded - Treasure (GP/10) ] / Number Elegible Characters

The resulting bonus xp is awarded to each character. However, if the bulk of the treasure comes in one or two discrete items, it may be better to reduce their bonuses and spread the balance amongst the characters who did not receive the items. Each item should be handled seperately. Where this is the case, the provisions of the section below on Uneven Distribution Of Treasure also come into effect.

Too Much Booty

It is possible – in fact, quite easy at low levels – to have the treasure be too high for the battle, resulting in the “Bonus” actually being a reduction in the XP awarded. This can cause problems in two ways: first, with a negative value so high that a character actually “loses” XP from the battle (in theory) and second, because sometimes the treasure is not evenly distributed, which advantages one character and penalises the others in calculations for future encounters. It is necessary to address both of these issues before proceeding further.

“Negative XP” from the battle: Deferred Penalties for Treasure

15a. Characters should always earn at least 1/2 the base xp reward (5) from a battle. This is designated the “Protected” XP award – because it’s protected from the effects of a negative bonus. This rule ensures that characters always get something for their trouble. However, by removing some of the xp from the calculation, it increases the likelyhood that a negative xp modifier will be greater than the allowed margin. When this happens, some of the xp “bonus” can be deferred to future battles. The “Treasure Penalty” first wipes out the Member Level Bonuses, then the Party Size Adjustments, and then up to half the base xp awarded. This should absorb the bulk of the penalty.

15b. When some penalty is deferred, it is simply added to that character’s next allotment of Bonus XP from Treasure. I should also comment on one aspect of this rule: why not track the ‘unpaid penalty’ at a party level, which would be much simpler for the DM than tracking it by character? The answer is that this unfairly penalises those low-level characters who earn enough xp from the encounter to fully pay off their “xp penalty”, in effect spreading the penalty of the high-level characters who don’t do so onto them when they have already paid their share.

But this is a contentious issue; it can be argued that because the High-level charaters increase the overall EL of the party, they permit the GM to increase the level of opposition, and hence the XP award for ALL party members. The low-level characters are, according to this line of arguement, riding on the coat-tails of the high-level members of the party, and this ‘burdon-sharing’ is a fair way for them to pay for that ride. This is a perfectly valid arguement, in my opinion; and one that deserves some consideration. Implementing this rule requires an alternative version of rule 15b.

15b(alternative): Total penalties deferred are added to the GP value of the next treasure bonus to be awarded.

For me, the big difference comes down to whether or not the highest-level member of the party is a PC or an NPC, especially one that’s been hired specifically for the purpose of “backstopping” the PCs if they bite off more than they can chew. If the highest level member of the party is a PC, then it’s not right that the low-level PCs ‘subsidise’ that character’s involvement, and I would use rule 15b as stated above. But when circumstances add a high-level NPC to the party, especially one that they aren’t paying for in gold, the value that they get from his presence should penalise them somewhat, in which case, the alternative form of 15b should be used.

Uneven Distribution Of Treasure

It will often be the case that much of the value of a treasure will be in the form of Magic Items, which can’t easily be distributed through the party. One person gets the big item, in fact (sometimes) one character will get the bulk of the items simply because his character class enables him to make use of such items. The disposition of treasure is completely up to the players, the GM should have no say in it beyond giving voice to the attitudes of any NPCs in the party. What we are concerned with here is the impact that uneven distribution should have on XP earnings.

What is the effect of a +1 item, in terms of character capability? Well, when a character gains a level, he gains +1 to hit. When he improves his STR (usually), his damage goes up, something that can be done every 4 levels. But the character gains other things with each of those levels: hit points, possibly an increase in the number of attacks that can be made, improved saves, skill points, one in four (or more) will give the character an additional feat, and probably one or more class abilities, none of which come with the +1 item. So a +1 longsword (or whatever) adds a fraction of 1 level, and a fraction of 4 levels. Assuming that each element of the level gain is to be equally-valued (any alternative just gets us in deeper trouble), let’s total up the total number of improvements that a character will get from a single generic level.

Single Generic Level:

  • HP
  • Skills
  • Saves
  • BAB
  • Total improvements = 4 per level.

plus, 4 generic levels:

  • stat increase
  • 4 in 5: number of attacks increase by 1, or 4 in 5 spell advancements and +1/2 of number attacks increse
  • 2 feats or 1 feat and 1 in 5 spell advancement
  • x class abilities (usually 2 in 4, but may be higher or lower. Assume that more frequent class abilties implies weaker individual class abilities, or the class is unbalanced.
  • Total improvements = 1 + 4/5 + 1 + 2 = 4.8 per 4 levels.

So the total value of a +1 item is 1 of 4 single level improvements, plus 1 of 4.8 four-level improvements, or
1/4 + 4 x 1/4.8 = 1.08333 levels worth of gain. Call it 1 level worth of improvement.

This gives us a basis for a ruling, based on the value of a +1 in the DMG. Everything in it can be related to the value of a +1 weapon by comparing the GP values. A quick glance at table 7-9 shows that the formula for value of plusses is
value = 2000 x (plus) x (plus).

15c. V1 = sqr [Value of magic item / 2000] = value in +1s.

This gives an adjustment to a character’s level based on the amount of magic items they have in excess of the usual. The adjustment is added to a character’s level for the purposes of calculating the experience they receive. If you over-power a party with too much treasure, the members who receive that treasure effectively take a CR “hit” on encounters.

XP for Non-combat encounters:

The average character who is good at something will have +2 or better in stat bonus to the relevant skill. This will increase by +1 every 5 levels, on average. They can also be assumed to allocate a skill rank into the ability for every character level (at least). It is thus a simple matter to assign an EL to any situation based on the DC to be overcome during the encounter. There are times when this can be determined in advance (traps, etc), and times when it can’t (interaction with NPCs/roleplaying). Note that roleplaying awards are optional, and up to the DM to award or modify based on circumstances at the time. I’ve even given roleplaying bonuses in combat if they seemed appropriate!

16. Base = 2 + int (char level / 5)
17. Encounter EL = ½(DC – base)
18. XP awarded = 1/10 x normal XP award.

XP for Skill Use:

There are two occasions when these awards are appropriate. One is when a character uses a skill in such a way that it solves a problem in a surprising or unexpected way. The other is when the character uses a skill to advance the plot in some significant way WITHOUT using the die roll to take the place of roleplaying.

19. Encounter EL = ½(Actual Die Roll)
20. XP awarded = 1/20th x normal XP award.
21. Maximum award = 5 x total rolled.

Note that this award completely disregards character levels, skill levels, and DCs required. That’s because the only way to rationally construct a system that takes account of these variables is to base the system on the margin of success, but players don’t always know the DC required and I don’t always want to take the time to perform the subtraction of total minus DC in my head. I’ve tried it, and it just bogs things down too much. This method is far simpler in game play; I can just draw up a rough table showing the PCs and jot down the actual rolls they make that qualify for the award, then perform all the calculations when time permits.

EXAMPLE OF USE:

A party consists of a 4th-level character, a 6th-level character, two 7th-level characters, and an 8th-level character.

They confront an enemy consisting of one CR8 creature, two CR6 creatures, two CR5 creatures, and fourteen CR½ creatures.

The enemy has marginally more magic at their disposal, and a distinct tactical advantage, and for a while look dominant, but the party eventually score a decisive victory through superior strategy and teamwork. How much experience should be awarded?

Step 1: Determine party CR:
One 8th-level character: 1 @ 8th = 2 @ 6th = 4 @ 4th, which is the lowest level within the party.
Two 7th-level characters: 2 @ 7th = 4 @ 5th = 4 x 1.4 @ 4th = 5.6 @ 4th.
One 6th-level character: 1 @ 6th = 2 @ 4th.
One 4th-level character: 1 @ 4th = 1 @ 4th.
TOTAL: 4 + 5.6 + 2 + 1
= 12.6 @ 4th
= 6.3 @ 6th
= 3.15 @ 8th
= 1.65 @ 10th
= 1.65 / 1.4 @ 11th
= 1.18 @ 11th level
= aprox 11th. So the party is equivalent to one 11th level character.

Step 2: Determine EL:
1 CR8 creature: 1 @ CR8 = 2 @ CR6 = 4 @ CR4 = 8 @ CR2 = 16 @ CR0.
2 CR6 creatures: 2 @ CR6 = 4 @ CR4 = 8 @ CR2 = 16 @ CR0.
2 CR5 creatures: 2 @ CR5 = 4 @ CR3 = 8 @ CR1 = 8 x 1.4 @ CR0 = 11.2 @ CR0.
14 CR½ creatures: 14 @ CR-1 = 7 @ CR1 = 7 x 1.4 @ CR0 = 10 @ CR0.
TOTAL: 16 + 16 + 11.2 + 10
= 53.2 @ CR0
= 26.6 @ CR2
= 13.3 @ CR4
= 6.65 @ CR6
= 3.325 @ CR8
= 1.6625 @ CR10
= 1.6625/1.4 @ CR11 = aprox EL11.
Allow +1 for the initial tactical position, gives EL12.

Step 3: Base XP:
D1 = 12 – 11 = 1.
Base XP = 62.5 x (12+1) x 1.4^1 = 62.5 x 13 x 1.4 = 1137.5; round up to 1,138 each.

Step 4: Individual Bonuses:
8th-level character:
D2 = EL – 4 – Char Level = 12 – 4 – 8 = 0. D2 = 0 , so use (9):
E3 = 62.5 x (12-3) x 1.4^0 = 62.5 x 9 x 1 = 562.5, round up to 563.
Member Level Bonuses increase the base award by 0%, so the 8th level character receives 1138+563 = 1701.
It would take 5.3 such encounters for the character to go from exactly 8th level to 9th level.

7th-level characters:
D2 = EL – 4 – Char Level = 12 – 4 – 7 = 1. D2 > 0 , so use (9):
E3 = 62.5 x (12-3) x 1.4^1 = 62.5 x 9 x 1.4 = 787.5, round up to 788.
Member Level Bonuses increase the base award by 5%, so the 7th level characters receive (1138+5%) +788 = 1194.9 + 788 = 1982.9, round up to 1983XP.
It would take 4.04 such encounters for the characters to go from exactly 7th level to 8th level.

6th-level character:
D2 = EL – 4 – Char Level = 12 – 4 – 6 = 2. D2 > 0 , so use (9):
E3 = 62.5 x (12-3) x 1.4^2 = 62.5 x 9 x 2 = 1125.
Member Level Bonuses increase the total awarded by 10%, so the 6th level character receives (1138+10%) +1125 = 1251.8 + 1125 = 2376.8, round up to 2377.
It would take 2.95 such encounters for the character to go from exactly 6th level to 7th level.

4th-level character:
D2 = EL – 4 – Char Level = 12 – 4 – 4 = 4. D2 > 0 , so use (9):
E3 = 62.5 x (12-3) x 1.4^4 = 62.5 x 9 x 4 = 2250.
Member Level Bonuses increase the total awarded by 40%, so the 4th level character receives (1138+40%) +2250 = 1593.2 + 2250 = 3843.2, round up to 3844.
It would take only 1.3 such encounters for the character to go from exactly 4th level to 5th level, so there is a very good chance that this encounter was enough for him to gain a level and close in on his colleagues!

That’s if they are all PCs. But what if the 6th level character and the 4th level character were both NPCs? Answer – they get exactly half of the XP, ie 2377/2=1188.5 (round to 1189) and 3844/2=1922 xp, respectively. Observe that the NPC factor is continually slowing their progress, producing “slippage” in character level relative to the PCs, but the greater this slippage becomes, the more bonus xp they receive for being of a lower level. There is very little difference between what the 7th level PC and the 4th level NPC received – but it takes a lot less XP (ie, fewer encounters) for the 4th level character to gain a level and reduce the slippage. These twin mechanisms combine to always keep NPCs weaker than their PC counterparts in a party, while not handicapping them to the point of helplessness; and also mean that any low-level characters that join the party will quickly close up ground on the party.

Step 5: Treasure Adjustments:
‘The enemy has marginally more magic at their disposal’ according to the encounter recap, but this is a relative assessment, comparing enemy with party; it tells us nothing with respect to the amount of loot the enemy actually have. According to tables in the DMG, the following would be reasonable for the encounter:

  • Coins: 13000 cp, 6000 sp, 3570 gp, 100 pp = 5300 gp value
  • 10 gems: 7 gp, 12 gp, 40 gp, 50 gp, 90gp, 100 gp, 300 gp, 600 gp, 1200gp, 3000 gp (total value = 5399gp)
  • 4 mundane items : masterwork greatsword (350gp); masterwork Dwarven Waraxe (330gp); full plate armour (1500 gp); Healer’s Kit (50gp) (total = 2230gp)
  • minor magic item: Arcane scroll, 2 spells: both 1st lvl spells, caster level 3: Protection from Good, Sleep (value 150gp)
  • minor magic item: Divine scroll, 3 spells: 1st @ 5th: Enduring Elements, 1st @ 5th: Obscuring Mist, 2nd @ 5th: Enthrall (1000gp)
  • minor magic item: Potion Enlarge Person (250 gp)
  • minor magic item: Ring Counterspells (4000gp)
  • medium magic item: Studded Leather Armour +1 (1175 gp)
  • medium magic item: Bastard Sword Flaming Ghost Touch +2 (32335 gp)
  • Grand Total: 51839gp

It is clear even from a passing glance that the Ring of Counterspells and the Bastard Sword are the picks of the treasure pile when it comes to magic. Between them, they account for just over 70% of the total value.

From (15): Bonus XP = (1701 + 1983 + 1983 + 1189 + 1922 – 5183.9) / 5 = (8778 – 5183.9) / 5 = 3594.1 / 5 = 718.82 each. Call it 719 xp.

However, the ring is worth 4000gp, or (4000/10) = 400 xp alone. One character gets that 400 xp worth of treasure, so the others should get the xp that goes with it. In other words, whoever gets the ring gets -400 to their xp bonus, and the other 4 characters get +100 each.

Similarly, the sword is worth 32,335gp, or 3233.5 xp. Call it 3234. One character gets that 3234 xp worth of treasure, so they should forego that much xp bonus and the others get 1/4 of that value extra, each, or +809 xp.

Let’s assume that the sword goes to the 2nd 7th level character, and the ring to the 8th level character, in which case:

8th-level character:
1701 xp + 719 – 400 (ring) + 809 (sword) = 2829 xp.

1st 7th-level character:
1983 xp + 719 + 100 (ring) + 809 (sword) = 3611 xp.

2nd 7th-level character:
1983 xp + 719 + 100 (ring) – 3234 (sword) = -432 xp.
half of 1138 xp is protected, ie the character gets 569 xp. This leaves a deficit of -432-569 = -1001 xp. This will be subtracted from future xp bonuses until paid off.

6th-level character:
1189 xp + 719 + 100 (ring) + 809 (sword) = 2817 xp.

4th-level character:
1922 xp + 719 + 100 (ring) + 809 (sword) = 3550 xp.

Step 6: Future CR Adjustments:
Until the deficit of character 3 is paid off, both characters 1 and 3 (who received a significant share of the treasure) receive an EL adjustment.

Character 1, 8th level:
From 15c: V1 = sqr [4000 / 2000] = sqr(2) = 1.4. The character is treated as having +1 level for the purposes of xp calculation until the deficit is paid.

Character 3, 7th level:
From 15c: V1 = sqr [32335 / 2000] = sqr(16.1675) = 4.02088. (This should not be a surprise to anyone who has examined the DMG table for melee weapon values). The character will be treated as having +4 levels for the purposes of xp calculation until the deficit is paid.

Step 7: Recalculate Party CR for planning future encounters:
Technically, this doesn’t have to be done now. But I find that it’s helpful to do it while the procedure is at hand. Before this can be done, the DM needs to know who has gone up a level. Based on the final xp awards, lets assume that characters 2, 4, and 5 all gain levels. So we now have:

Two 8th-level characters: 2 @ 8th = 4 @ 6th = 4 x 1.4 @ 5th, = 5.6 @ 5th.
Two 7th-level character: 2 @ 7th = 4 @ 5th.
One 5th-level character: 1 @ 5th = 1 @ 5th.
TOTAL: 5.6 + 4 + 1
= 10.6 @ 5th
= 5.3 @ 7th
= 2.65 @ 9th
= 1.325 @ 11th
= 1.325 / 1.4 @ 12th
= 0.95 @ 12th
= aprox 12th. So the party is considered equivalent to a 12th level character, one better than before.

This contrasts strongly with the values for xp calculation from the next encounter:
One “9th”-level character: 1 @ 9th = 2 @ 7th = 4 @ 5th, which is now the lowest level within the party.
One 8th-level character: 1 @ 8th = 2 @ 6th = 2 x 1.4 @ 5th = 2.8 @ 5th.
One “11th”=level character: 1 @ 11th = 2 @ 9th = 4 @ 7th = 8 @ 5th.
One 7th-level character: 1 @ 7th = 2 @ 5th.
One 5th-level character: 1 @ 5th = 1 @ 5th.
TOTAL: 4 + 2.8 + 8 + 2 + 1
= 17.8 @ 5th
= 8.9 @ 7th
= 4.45 @ 9th
= 2.225 @ 11th
= 1.1125 @ 13th
= aprox 13th. This means that base xp will be reduced, and bonus xp will be increased for most characters. The character who gets the least bonus xp will be the character with the deficit, even before that is taken into account. Most parties, under this circumstance, will make sure that any “tasty” items will find their way into the hands of the characters who missed out on the powerful goodies this time around, even without this xp prod to share the spoils; that will give the character with the deficit an extra xp bonus to help eradicate the deficit – assuming there’s something nice in the next treasure!

Real-Life Shorthand

handwritten-workings
Note that in actual play, I would not spell it out the way I have above, and would not show the workings; my calculations would be abbreviated, and would look more like the example to the left.

That’s about half-a-page of handwritten working. I would expect to use more space than that tracking hit point loss, Initiative, and spell effects during the combat!

Conclusion

So, there it is. In comparison to the rather unwieldy table arrangements in the 3.0 and 3.5 DMG, this is a simple and more useful alternative – at least for me.

It also has a huge side benefit in terms of balancing opposition levels with the party. If I know the effective level of the party, I can determine what size of encounter should give them difficulty. Since I adopted this system of matching enemy EL to party EL, the players have noticed a dramatic improvement in the encounters that I run for them (from their own statements). They no longer take even apprantly one-sided battles for granted, because they can never be sure of what’s lurking in the shadows – but they know that either I’m wasting everyone’s time with a fight they will inevitably win, or I’m setting them up for a sucker-punch, possibly drawing them into a weakened tactical position for a nastier opponant to come.

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