EXPANDED CALCULATIONS IN
ENCHANTMENTS

Last update: Mon. January 11 2021

Introduction

GURPS Magic , P.21-22 says to us how to figure out the cost of magic items. It is not good, however, to compute the actual prices. This is the way to solve the problem in Quick and Dirty Enchantments with a few more assumptions.

Various Skill Level and Mean Salary

In GURPS Magic , P.21, it is assumed, that a journeyman enchanter (Enchant-15) makes an Average salary, and that a master (Enchant-20) is a Comfortable job. In real, however, the skill level may vary, and superior enchanters earn more. To estimate this, we begin by assuming that every two levels exceeds 20 in Enchant improve the job's Wealth level by one, for +2 overqualification exactly negates one level difference of the job's Status level in finding jobs (see GURPS Basic Set , P.518). This enables us to make the list (see below) that says the master's skill level, size of circle and mean salary.

Mean Salary in Enchantment (Effective Skill of 15)
A: A Master's Skill LevelB: A Master's SalaryC: Circle SizeD: Mean Salary
15E (Journeyman's Salary)1E
161.2 × E21.10 × E
171.4 × E31.13 × E
181.6 × E41.15 × E
191.8 × E51.16 × E
202 × E61.16 × E
213.5 × E71.21 × E
225 × E81.50 × E
2312.5 × E92.27 × E
2420 × E102.90 × E
2560 × E116.36 × E
26100 × E129.25 × E
27550 × E1343.2 × E
281,000 × E1472.3 × E
295,500 × E15367 × E
3010,000 × E16625 × E
3155,000 × E173,230 × E
32100,000 × E185,550 × E
33550,000 × E1928,900 × E
341,000,000 × E2050,000 × E

Note that this list is under these assumptions.

1. E is the typical monthly pay for Average job, and may vary in the world's TL (see GURPS Basic Set , P.517).
2. A that cannot be obtained directly is obtained by using linear interpolation.
3. Mean salary is calculated to three significant figures as D = (B + (C - 1) × E) / C and all "fractions" are dropped off.

Enchantment Cycles

According to GURPS Magic , P.22, average enchanters contribute 10 FP in a Quick and Dirty Enchantment and 50 minutes to regain them, for they have Recover Energy-15. Thus, one-hour enchantment has 60 + 5 × 10 = 110 minutes of cycle, or about 4.4 cycles in an eight-hour workday. It does not consider, however, two very important factors -mealtime and variable rest time. Every day, most humans spend 90 minutes in eating (see GURPS Basic Set , P.155), which allows recovering an extra FP while resting (see GURPS Basic Set , P.427). In addition, time used for meals is not counted in daily work (see Time Use Sheet or GURPS Basic Set , P.569). So, it is natural that professional enchanters schedule nicely and gain 36 FP (Recover Energy-15+) or 90 FP (Recover Energy-20+; suitable for masters with Enchant-19+) as "free recovery" every day. With this assumption, four one-hour enchantments (each mage contributes 10 FP), 1.5 hours mealtime, and 20 minutes rest make four cycles. In an eight-hour workday, the rest is 220 minutes, in which additional two cycles can be done. Things are somewhat complicated when we think about variable rest time. Let us consider 34-energy enchantment with a master (Enchant-19 and Recover Energy-20) and three journeymen (Enchant-15 and Recover Energy-15). In this case, mages lose 8.5 FP in average, and does not have to rest for 50 minutes, which is enough to recover 10 FP. To produce magic items efficiently, every journeyman should put 8 FP, while a master loses 10 FP in every casting. (Not to contradict the setting in GURPS Magic , we assume that each mage contributes no more than 10 FP.) To estimate the rest time and cycles, use the table below.

FP Contribution and Cycles (Recover Energy-15; One-hour Enchantment)
F: FP ContributionG: Rest Time without MealH: Number of Cycles
15 minutes8
210 minutes8
315 minutes8
420 minutes8
525 minutes8
630 minutes7 1/3
735 minutes7
840 minutes6.6
945 minutes6 2/11
1050 minutes6

Note that enchanters gain 36 FP for "free" and eight hour of labor may have no more than eight enchantments. In real enchantment cycles, enchanters must pace to the slowest recovery, which is listed as below.

Total FP Contribution and Cycles
(One-hour Enchantment)
I: Total FP ContributionACDHNotes
1-4151E8
5151E8[1]
6151E7 1/3
7151E7[1]
8151E6.6
9151E6 2/11
10151E6
11-121621.10 × E7 1/3
13-141621.10 × E7[1]
15-161621.10 × E6.6
17-181621.10 × E6 2/11
19-201621.10 × E6
211731.13 × E7[1]
22-241731.13 × E6.6
25-271731.13 × E6 2/11
28-301731.13 × E6
31-321841.15 × E6.6
33-341941.20 × E6.6[2, 3]
35-361841.15 × E6 2/11
37-401841.15 × E6
41-421951.16 × E6.6[2]
43-461951.16 × E6 2/11[2]
47-501951.16 × E6[2]
51-552061.16 × E6 2/11[2]
56-602061.16 × E6[2]
61-642171.21 × E6 2/11[2]
65-702171.21 × E6[2]
71-732281.50 × E6 2/11[2]
74-802281.50 × E6[2]
81-842392.90 × E8[2, 4]
852392.90 × E8[1, 2, 4]
86-902392.98 × E8[2, 4]
91-9424103.54 × E8[2, 4]
9524103.54 × E8[1, 2, 4]
96-10024103.62 × E8[2, 4]

Notes

[1]: Some enchanters are tired at the end of the day. (4 or less FP are not recovered in time.)
[2]: The master has Recover Energy at 20+. (Otherwise, the master have Recover Energy at 15-19.)
[3]: Enchantment power of 16, which is the most efficient. (Otherwise, power 15 makes the cheapest.)
[4]: Some journeymen are skilled (Recover Energy-20 and Enchant-19). (Otherwise, least skilled journeymen (Recover Energy-15 and Enchant-15) make the cheapest.)

Longer Enchantments make things easier; they are only done four or less times in an eight-hour workday, and enchanters do not need rest time other than "free recovery". (Two-hours ceremonies might make mages tired (4 or less FP are not recovered in time), but it is not crippling.) So, number of cycles are obtained as H = 8 / (J: casting time in hour).

Staffs for Enchantment

GURPS Magic ignores the effect from Powerstones completely. In fact, however, they give a few points, especially when long ceremonies are done in (very) high mana area. Imagine a six-foot length wooden pole with two Powerstones attached to each end. When Staff spell is enchanted on it, its Powerstones become dedicated (see GURPS Magic , P.70) and give double energy but no penalty in use for enchanting. Note that these Powerstones recharges at normal rate, because they are apart from two yards! It makes sense that most enchanters have one (or more) and use them as very useful items in enchantments. To think about the matter, weekly supply is important -even if mages work only five days in a week, Powerstones do not have holidays. So, K (energy contributed by staffs) is calculated as K = (7 / 5 × 2 × 2 × L / H) = 5.6 × L / H, where L is given by L = (stones' recovery rate (points/day)) × (number of staffs). Do not round down the fractions -it is possible that some tap their stones but some do not. To reflect this, space for the staffs must be considered. Even a large wardrobe (4'3" × 4'3" × 8'6") may hold up to three staffs without ill effects, while rooms surrounding the workplace are good to have dozens of staffs. (There should not be anyone but enchanters within ten yards from the center of enchantment.)

Enchantment Cost

We have checked factors that influence the labor cost. But anyway, how can we calculate the actual cost? GURPS Magic , P.22 describes about calculations to gain M (the labor cost) from N (energy cost). It seems very confusing, but is actually simple. Here are the formulae.

Quick and Dirty:
M = N × C × D / 22 / ((I + K) × H) / 0.9547 = N × (B + (C-1) × E) / (I × H × 21.0034 + L × 117.61904)

Slow and Sure:
M = N × E / 22 / 0.9547 = N × E / 21.0034

Note that C, H, I and L are determined from B, E, N, mana level and number of staffs, which are all given.

More Things to be Thought about

1. Charge Powerstone (see GURPS Magic , P.126):
Charge Powerstone seems to improve Powerstones' recovery rate dramatically. It has some risk, however, to break the stone and its cost must be added to M. Do not forget the rabor cost to cast the spell (see Non-Assistant Mages ). Charge Powerstone-enchanted Powerstones must be considered again: Their recovery rate are doubled but increase the risk to break the stones. Note that they shall be very expensive!

2. Draw Power (see GURPS Magic , P.180):
We ignore Draw Power spell in the article for some reasons written below. First, Draw Power needs vast amount of energy and its supply must be prepared. But their cost are too complicated and various to be considered. Furthermore, energy contribution by Draw Power depends on the caster's Magery level and health, which are hard to assume the "average". To use Draw Power, each GM must set these factors and modify the costs. Do not forget the penalty caused by the spell.

3. Higher Power:
In the article, we assume almost all enchantment are done at power 15, which makes labor cost lowest. In fact, however, higher power makes most efficient in some cases, for effective skill 16+ in Quick and Dirty Enchantments doubles the mergin of critical success, which increase the item's power and value. Especially for minor magic items that need 50 or less energy, labor cost increases little. In such a case, many enchantment groups may try "gambles", and there might be many high-powered items. Note that variable bonuses from Visualization or Symbol Drawing enable the group to "gamble" with little risk.

4. Mana Level:
We have considered enchantment only in normal or high mana. Very high mana makes enchantments much easier. It grants so much energy to mages and powerstones that it increases H and L. On the other hand, low mana is major disadvantage. Even staffs for enchantment give little energy and Recover Energy will not work. Furthermore, five-point penalty turns talented masters into journeymen. Note that enchanters in low mana area may regain FP almost as fast as they are in higher mana area, if mages may recover fatigue by Breath Control skill.

5. Manastone (see GURPS Magic , P.70):
Manastone may improve stones' effective recovery rate just like Charge Powerstone . Its risk is also like those of Charge Powerstone . (The risk may be higher, though.) There are some differences, however, between the two. First, the time to create a Manastone is much longer than those to cast Charge Powerstone. Second, Manastones may improve not only the rate but also maximum energy given by the stone.

6. Non-Assistant Mages:
Helps from non-assistant mages make the enchantment more efficiently. Lend Energy allows the enchanters having less rest. Wisdom or Bless does not increase the skill directly, but gives great bonuses to the mages with Visualization or Symbol Drawing. Furthermore, a mage with Share Energy and Telecast can provide up to five points of energy (Usually. It depends on Magery.) without any ill effects! Note that helping mages recover their FP during the ceremony and do not affect the enchantment cycle. Of cource, pays to these mages must be calculated on M.

7. Powerstone (see GURPS Magic , P.69):
No other magic items are more difficult to calculate their price than Powerstones. Their energy cost is determined by the value of the material, and many enchantments and the "bargain" of quirked stones make harder to know O (the effective probability that the process sucseeds). In some cases, however, the cost may be obtained easily, for Powerstone spell can be enchanted anything valuable at normal cost. A 1-point Powerstone worth \$120 (= 10 × 22 + 40 × 2) is a good material for a 2-points Powerstone, even if its "raw material" is not worth \$50 (= 10 × 12 + 40 × 1). To make the problems simple, we only consider 20-points enchantments. (Quadrupled energy seems nonsense in most cases.) O is 0.9547 + 0.9 × 6 / 216 or about 0.98, for a quirk reduces the stone's price by 10%. (Ignoring the effect from multiple quirks; it gives a little bonus to large Powerstones.) At normal process in making Powerstones, two enchanters work 22 days, try 132( = 22 × 6) enchantments and earn 2.2 × E in a month. Thus, if (10 × P2 + 40 × P) + E / 60 / O < 10 × P2 + 60 × P + 50 or (P - 51)2 < 502 + 366 - 53 / 588 × E, where P is the stone's power, there are appropriate P-points Powerstones that costs \$(10 × P2 + 60 × P + 50) or the cheapest to make (P + 1)-points stones. In this case, the price of (P + 1)-point stone is obtaind as one 20-points enchantment cast on the material that costs \$(10 × P2 + 60 × P + 50).

8. Skill Modifiers:
Bonuses to the spell have little problem. Simply increase C and recalculate. B and E might be decreased, though, because less skilled enchanters may contribute energy. Penalties make things more complicated, for mages with effective skill 14 or less cannot provide energy at all. To solve the matter, find the appropriate skill level of journeyman enchanters and obtain B, C and E. Do not forget modifiers to Recover Energy -bonuses may increase recovery rate dramatically (and vice versa).

9. Wealth Level:
This article sets a journeyman enchanter as an Average job and a master enchanter as a Comfortable job. This setting might not apply, of course, in some worlds. In such a case, B and E must be determined with proper assumptions.