First, one must find another spell. As a general rule, we should stick to not re-inventing everything, since the balancing of spells is very diffult. As such, if your caster wants a new spell, you should look at already published spells, such as those found in the Tome of Magic, Complete Wizards Handbook and the like. You pick a spell, and treat it as something your character has "invented" and then proceed to research it. If/when you succeed, you can add it to your spellbook/spell-list. In the case of clerics and priests, most spells from Tome of Magic are from spheres they can not cast. Thus, if you want the spell on your list, you need to be able to fit it to one of the spheres to which you have access.
All research must take place in a laboratory, where the researcher must spend 8 hours for it to count as a day. It is possible to interrupt research during the day, but nothing lower than 1/2-days will count towards the time needed to finish the spell. Spell research is lengthy and expensive.
Buying your own laboratory is expensive. A lab normally costs between 1000 og 10.000 gold pieces. The bigger and better the lab, the better chance of researching the spell. It is sometimes possible to rent a lab, but usually only if you have a very close connection to the person renting it out. Casters usually do not let anyone snoop around their precious labs. If at all possible such renting comes at a cost as well, never less than 1/10th of the value of the lab per week.
Then you need to research the spell. The normal price of spell research is 200-500 gp/spell-level/week. A spell takes a minimum of 1 week + 1 week/spell-level to research. So a 1st level spell takes a minimum of 2 weeks at 200-500 gp/week (400-1.000 gp) and a 3rd level spell takes a minimum of 4 weeks at 200-500 gp/week (800-2.000 gp) to research. The price of research is rolled random at the beginning of each week.
You must be able to pay the weekly rate at the start of a week for it to count. If you run out of money, it is possible to take up the research once you have gathered enough money to continue.
When the time is up (for example, the 2 weeks for a 1st level spell), the you and the DM rolls to see if the caster has made the new spell.
The roll is based on several things, such as the INT or WIS (depending on class) of the caster, his level, the level of the spell and of course the laboratory.
Chance to research a new spell in %: Lab modifier + INT + LVL - 2 x spell level
Lab modifiers:
1.000 gp lab: 10%
2.000 gp lab: 15%
3.000 gp lab: 20%
4.000 gp lab: 25%
5.000 gp lab: 30%
6.000 gp lab: 35%
7.000 gp lab: 40%
8.000 gp lab: 45%
9.000 gp lab: 50%
10.000 gp lab: 55%
If you fail your roll, you need to research for another week, paying the additional cost, before you may attempt to complete your research.
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