Anyone interested in the precise calculations done should contact Ian Miller by e-mail as I have no intention of writing it up properly. You are welcome to the program source used, but note that it is in LISP with very few comments.
Characters in Ars Magica have a number of types of score. For each of these the rules for improvement are different. There are order of increasing ease of advancement:-
Characteristics are not of direct interest here, as there is no defined method
of improvement. Each of the others can gain experience points by a different
set of methods. The methods applicable to each are as follows:-
| Talent | Skill | Other Knowledge | Casual Knowledge | Magic Theory | Magical Art | |
|---|---|---|---|---|---|---|
| Story/Role play | Yes | Yes | Yes | Yes | Yes | Yes |
| Practice | Yes | Yes | ||||
| Training | Yes | Yes | Yes | Yes | ||
| Exposure | Yes | |||||
| Lectio | Yes | Yes | Yes | |||
| Disputatio | Yes | Yes | Yes | Yes | ||
| Book Learning | Yes | Yes | Yes | Yes | ||
| Studying Vis | Yes | Yes | ||||
| Lab. Work | Yes |
Whereas Casual Knowledges can be improved by Exposure this is capped at level 4, so will not have any impact on maximum scores. Accordingly Casual and other Knowledges can be consider together.
Talents and skills are especially important as they can significantly affect the rate of progress in Knowledges and Arts. Notably the Talent Concentration affects the rate of book learning and the Skill Scribe affects the Quality of books which in turn affects book learning.
The only systematic way to improve Talents is to practise them. (Precisely what activities count as 'Practice' is open to Story-Guide interpretation.) The game mechanics is one stress die per season. The number of x.p. awarded is <stress die score>/<current level>(round down) with a maximum of 3 per season. Accordingly the rate of x.p. accumulation tails off as level rises. The effects are tabulated below. As there are complications associated with zero level talents (which you are not allowed to practise), the calculations are all based on starting from level one (with one experience point).
The columns in the table are as follows:-
The final five columns tabulate number of sessions to achieve the given level, on five different assumptions:-
| Seasons practice to achieve Level | |||||||
|---|---|---|---|---|---|---|---|
| Talent Level | Expected x.p. | Expected seasons to next level | 1% | 10% | Median (50%) | 90% | 99% |
| 1 | 2.6 | 0.77 | 0 | 0 | 0 | 0 | 0 |
| 2 | 2.09 | 1.44 | 1 | 1 | 1 | 1 | 2 |
| 3 | 1.459 | 2.74 | 2 | 2 | 2 | 3 | 5 |
| 4 | 1.039 | 4.81 | 3 | 4 | 5 | 7 | 9 |
| 5 | 0.697 | 8.61 | 6 | 7 | 9 | 13 | 16 |
| 6 | 0.5759 | 12.15 | 11 | 14 | 18 | 23 | 28 |
| 7 | 0.4339 | 18.44 | 19 | 23 | 30 | 37 | 45 |
| 8 | 0.3239 | 27.79 | 32 | 38 | 48 | 59 | 70 |
| 9 | 0.2007 | 49.83 | 51 | 61 | 76 | 93 | 108 |
| 10 | 0.0897 | 122.63 | 84 | 101 | 125 | 154 | 182 |
| 11 | 0.06759 | 177.54 | 154 | 190 | 246 | 315 | 384 |
| 12 | 0.06759 | 192.34 | 272 | 333 | 421 | 526 | 624 |
| 13 | 0.05449 | 256.93 | 417 | 498 | 613 | 745 | 866 |
| 14 | 0.05339 | 280.95 | 614 | 721 | 869 | 1036 | 1187 |
| 15 | 0.04239 | 377.45 | 842 | 972 | 1149 | 1346 | 1522 |
| 16 | 0.04239 | 401.04 | 1147 | 1308 | 1526 | 1766 | 1979 |
Given the numbers of seasons practice that are plausible it can be see that scores of 6 or 7 can be quite common, but scores above 10 will be exceptionally rare. As the Ars Magica book rightly says "scores of 9 or higher suggest folk who are approaching the pinnacle of human knowledge and achievement".
Skills may be improved by practice in precisely the same way as Talents. In addition, they may be learnt by training. This (with able students and teachers) can sustain 3 x.p. per season improvement up to the level of the teacher. A level 10 skill is achievable with 19 seasons of training with a suitable teacher.
Whereas this can significantly increase the level of the average practitioner, it has very little effect on the highest levels achievable. The enormous numbers of seasons required for a single level improvement above 10 means that a student is unlikely ever to rise even a single level above his teacher. It is possible where there is a very long established school of excellence for a skill that has regularly taught masters of a skill to the level of the greatest Grand-master that higher levels may be found. The existence of such schools seems unlikely to me but Story Guides must decide.
Knowledges have a wider variety of options for improvement. At low levels the rate of improvement (although typically not the methods) are likely to be broadly in-line with skill improvement. The main difference is that there is no ceiling beyond which the experience point acquisition collapses. With an adequate supply of Tractatus, book learning can continue indefinitely. A dedicated book learner is likely to develop a Concentration Talent of about 7. A student with Intelligence +3 and the Book Learner virtue (+2 to book Quality), may have 12 points to add to the books Quality to calculate study total. Such a student would gain 3 x.p. from the poorest Tractatus and 5 x.p. from a particular excellent one.
The main ceiling on progression would seem to be the supply of Tractatus. As such it is hard to place a clear limit outside the context of a specific subject and a specific Saga. Subject will be very important is popular subjects will not only have more dedicated students, but more Tractatus available.
In general, maximum scores in the range of 10 to 15 seem most likely.
As noted above Magic Theory is a knowledge, but there are a couple of extra methods of advancing in it. These are learning from Vis, and experience (effectively practice; see p191).
Experimentation with Vis has the problem of being dangerous, and at high
levels slow. The following table indicates the expected x.p. gain from a
seasons experimentation with Vis according to current level and number of
Pawns expended. An Aura of 5 is assumed.
| Level | 1 Pawn | 2 Pawns | 3 Pawns | Level | 1 Pawn | 2 Pawns | 3 Pawns | |
|---|---|---|---|---|---|---|---|---|
| 1: | 2.700 | 2.700 | 2.700 | 9: | 0.754 | 1.339 | 1.770 | |
| 2: | 2.700 | 2.700 | 2.700 | 10: | 0.633 | 1.128 | 1.659 | |
| 3: | 2.500 | 2.700 | 2.700 | 11: | 0.522 | 1.017 | 1.459 | |
| 4: | 2.080 | 2.500 | 2.600 | 12: | 0.401 | 0.807 | 1.239 | |
| 5: | 1.559 | 2.290 | 2.500 | 13: | 0.289 | 0.786 | 1.239 | |
| 6: | 1.328 | 1.980 | 2.290 | 14: | 0.177 | 0.666 | 1.128 | |
| 7: | 1.107 | 1.770 | 2.190 | 15: | 0.075 | 0.655 | 0.917 | |
| 8: | 0.876 | 1.459 | 1.980 | 16: | 0.064 | 0.544 | 0.907 |
Given the alternative of safely obtaining an experience point by, for example, inventing a spell; it seems ill advised to attempt learning Magic Theory fromVis where there is less than one point of expected gain. Accordingly I do not think the possibility of Vis research will have any effect on maximum Magic Theory scores.
Experience brings in only one x.p. per season, albeit in a season when other goals may be achieved as well. As such experience will boost general levels of the Knowledge. Whereas this is not fast, it does allow reliable improvement without dedicating seasons to just improving Magic Theory. Hence it is economic in terms of seasons spent. However, Tractatus book-learning remains faster, and more likely to control the level ceiling.
In practice a more important factor may be the likely level of dedication. Magi especially of House Bonisagus, will place far more effort into achieving high scores than they will for most knowledges. (House Criamon may make similar efforts for Enigmatic Wisdom.) The amount of time dedicated to this Knowledge will be greater than any other. Accordingly as scores in the 20 to 30 range might be achieved, according to your assumptions. Scores at the higher end of this range would require Magi that pursue excellence in Magic Theory nearly to exclusion of the ability to practise it.
Arts can be improved far faster than any Ability. In general it is exceptional to gain more than 3 x.p. for an ability in a season. However it is quite achievable to gain 15 x.p. for an Art in a season. Further it is possible (after gaining "Increased Understanding" in temporary twilight) to write Summae of a level better than half the author's level. Accordingly there does not seem any ceiling on book learning for Arts. With an adequate accumulation of books on the Arts being studied a senior Magus might have up to about 3000 xp.s[1] in Arts. This could give:-
The last of these is the least likely as would require hundreds of Tractatus or equivalent in the single Art. Nevertheless it might be possible, for example, that House Flambeau has accumulated sufficient books on Ignem.
After a study (and simulation) on the interaction of Art scores and Longevity Potions, I came to the conclusion that there is no sane maximum score for Arts. A magus, with the necessary vast supply of books, who dedicates two seasons a year to studying Corpus, Intéllego and Magic Theory, can continue to design Longevity potions that provide themselves with Aging Immunity at well over 500 years old.
The practical limit is survival to about 350 with about 90 in each of Corpus and Intéllego. The only hard limit is that after 460 years on Longevity potions you automatically go into Final Twilight by the time this happens they could have scores of about 120 in the two Arts. To study this much requires about 400 Tractatus in each Art.
Story-Guides: Take this as a warning of the potential consequences of allowing your players to have too many books.
