I've been interested recently in Original Research, and whether it is possible to actually achieve. I therefore created an individual-based model (written in the programming language C) that simulates a large number of magi pursuing breakthroughs, and reports on their individual (and more interestingly, median) behaviour. Since this is the sort of thing debated here in the past, I thought you might be interested in the results.
[At the moment I am unable to share the code; it employs various libraries which are IP-protected within our workgroup (in real life I use these sorts of models to predict marmoset populations, wildlife diseases, and human epidemics, amongst others). However, if I have the time I will strip out such dependences and post it.]
Assumptions:
* The rules from HoH:TL are followed to the letter (no house rules)
* The magus works on his original research on average 2 seasons per year, spending the other two seasons increasing applicable Arts.
* Lab total has a power relationship with age, rising steeply from 45 and levelling off to about 100 over a 60-year span. This is a simplification, but probably reasonable.
* The magus creates spells at half his lab total. The actual magnitude is drawn from a right-skewed triangular distribution (min=1, peak=LT/10, max=LT/10), thus is more likely to generate the higher magnitude effects. He is more concerned with speed rather than warping
* The magus lives through all botches, and does not die or enter Final Twilight during his research. He does not need to spend any time recovering from disaster-inflicted wounds, rebuilding his lab, playing out story events, or in Temporary Twilight. Just add a few seasons or years for these things.
Results:
~~~~~
The model keeps track of the number of seasons resulting in discoveries, botches, or useless research (from a breakthrough point of view). It also simulates the number of seasons spent stabilising discoveries, and the warping points acquired during this process.
I looked at all three breakthrough types and Risk Factors. I've presented a full range of stats because the median result isn’t always the most meaningful (50% of magi take this long or longer to complete their research). Sometimes it is useful to look at the lucky or unlucky magus. In the tables below, all figures are for number of seasons taken in total. Q1 is the lower quartile, 75% of magi take this long or longer (i.e. this might be the time taken by a lucky magus). Q3 is the upper quartile, 25% or magi take this long or longer (i.e. an unlucky magus)
[sorry about the tables in the Code field, allows me to get them to line up better]
A. Minor Breakthrough, 30 breakthrough points
—————————————————————————
The number of separate discoveries is independent of Risk; it works out at about 12 unique spells, and about 5 warping points.
(all numbers are seasons taken)
[code]Risk Median Min Q1 Q3 Max
+1 92 33 75 116 257
+2 55 25 46 64 111
+3 43 21 36 49 89
[/code]
So, at Risk +2, the median magus takes 55 seasons to achieve a breakthrough, but a lucky magus might do it in only 46 seasons (and a very lucky magus might be done in 25). Note that the overall time should be doubled, to allow for my initial assumption of 2 seasons work on the discovery each year. Thus the median magus using a Risk +3 might take 21-22 years to complete his minor breakthrough
B. Major Breakthrough, 45 breakthrough points
—————————————————————————
The number of separate discoveries is independent of Risk; it works out at about 15 unique spells, and about 10 warping points.
(all numbers are seasons taken)
[code]Risk Median Min Q1 Q3 Max
+1 134 56 112 158 323
+2 78 35 65 89 171
+3 60 32 52 67 106
[/code]
C. Hermetic Breakthrough, 60 breakthrough points
———————————————————————————
The number of separate discoveries is independent of Risk; it works out at about 20 unique spells, and about 14 warping points.
(all numbers are seasons taken)
[code]Risk Median Min Q1 Q3 Max
+1 167 74 142 201 363
+2 96 51 83 110 174
+3 75 43 66 85 144
[/code]
So, a Hermetic discovery using a +3 risk modifier takes on average 37-38 years (allowing for study in between). However, it should be noted that the maximum number of warping points gained was 29 (which surely included several Twilights), and the maximum number of laboratory botches was 9 during this research (2 botches over the course of the experimentation is more common, however).
However, I would have thought that some Bonisagi would have succeeded in a Hermetic breakthrough since Notatus. Perhaps my algorithm for determining Art score increases is optimistic, and I should take into account time taken to repair a lab after a botch, time spent in Twilight, and story events resulting from experimentation. It may also be the fact that I deliberately went for a fast development with the right-triangle distribution, which biases things towards big spells. A more cautious magus might go for lower magnitude effects (when I go for a more symmetrical distribution, a magus takes a median of 98 seasons to complete a Hermetic Breakthrough at Risk +3, invents 26 unique spells on average, and takes only 9 warping points)
The overall outcome is that Original Research is very much possible, but as expected, it takes a long time. One cannot necessarily count on a PC completing it in a hurry, since most sagas are shorter than the time needed to complete these events.
Food for thought: who is preventing magi from completing those Hermetic Breakthroughs? Perhaps an extremist cadre of The Lycaeum (see Art & Academe) is preventing anyone from spoiling the purity of Bonisagus's theory? Or perhaps it is just humility which prevents magi from embarking on such an audacious scheme as to rewrite Bonisagus*?
* Yeah, right.
Mark
So using these rules as a 'how the rest of the Order does' formula results in serious problems. Either Hermetic Theory needs to be evolving constantly like modern science, with new insights and revisions in most Folios or the OR rules need to be made much harder for the NPCs.
