my knowledge of the rules is still very elementary but this is how i see it(sorry for any mistakes)
let's say i am trying to break the limit of energy. let's assume 55 points needed. as in one of the books.
i have a creo corpus(the most likely combo to be used in an experiment) lab total of 50 . i make a spell of the 5th magnitude.
either on the first season or later i will roll a discovery. let's assume i do so after a year. but the specific spell took a season to be made.
then i make the stabilisation. most of the things i roll on the extraordinary results chart are beneficial for this purpose. but let's say i am unlucky and gain 2 successes(5 breakthrough points each) every year. so the breakthrough is made in 6 years and a half.
ok,twilight may be a problem but it's only 5 points minus a simple die. so chances are on my side. plus i can stil rol to avoid it. at most i could have invented a weaker spel if i wanted to be safer. the point is that it's still easy.
now i suppose botches might be a problem but(especially if i added a +1 or more risk modifier) it's rather unlikely. at any rate i have magical memory or im just not stupid and i keep copies of my lab taxts or i just don't have them with me inside the lab.
Simple. In Metagame terms, you are playing the game so YOU can do things. We don't want to watch as NPCs do the cool stuff, do we? (And heck, if you, as ST, need someone to have a breakthrough, just do it! Why would you worry about math no one is going to see?). Second, the NPCs haven't read all the books, and don't have access to the ST. I would imagine, in canon, many "breakthroughs" are made, only to find out that it's already been done, and many never happen because of greed. Why waste your time, why warp the heck out of yourself, for a new parameter, when you could be breaking the Ageing limit, or the Limit of Creation? (Alas, there was no ST to laugh at them, so they ended their life a warped, hot mess, and a reputation as a fool.....)
Breakthroughs are hard, period. They seem easy, but it presumes that you can do exactly what you want, all of the time. In actual play, this rarely happens. Covenant service is often a problem, some covenants require 1 season a year, or some other interval. Story Flaws, Covenant hooks are also things that draw one out. Then there is the general advancement of one's Arts, inventing spells, making magic items.
Ars is a game of choice, and consequence of those choices. You can choose to pursue a breakthrough, if you like, but you have to give up something in the process. And you have to deal with the risks of it, which while aren't insurmountable are significant.
if i gain a failure on the chart and no brk points i can still use it right?? until i gain a breakthrough.
essentially it's empirical research right? dice aside i assume from an in game perspective it would work like this"first im researching the corpus spell that can transfer energy (it's on the corebook i think) from me to someone else to restore his fatigue i try to gain an insight about how this fridge spell manipulates energy and compare it with current magic theory. then i maytey the spell that removes fatigue trying to connect this with what im trying to do.
There is no "right" answer here - you should choose how to do things for your character/saga. But for my money - no, it's nothing like empirical research. It's more like deep yoga or Buddhist meditation, a mystical experience. You gain "Insight" into deeper magic, rather than scientific knowledge of how magic works. When you stabilize the magic you ingrain this insight into human terms, into ideas such as natural resonances and metaphors such as those of Greek myth or alchemy - but these are but words that are trying to convey what cannot be uttered, these are conceptions your feeble mind comes up with to get a grip of what cannot be truly comprehended.
Your mileage may vary. Choose your own style.
Either way, I think the best approach to the Original Research rules is that they're an add-on system that should be tailored to the saga. The troupe should determine the number of Breakthrough Points needed and adjudicate the advancement so as to best serve the game - which can certainly include very high point totals needed. I personally recommend basically abandoning the system in favor of the SG-controlled and story-driven system of integrating Ancient Magic and/or Hedge Magic.
I feel like the easiest way to answer the original question is to address the mathematics. What are the chances you get a discovery when inventing your 5th magnitude spell in one season? Let's keep this general for the moment. Let's say your probability is P[sub]1[/sub]. So, on average, you get a discovery after 1/P[sub]1[/sub] seasons inventing such spells. After that discovery you want to stabilize it. Let's say your probability is P[sub]2[/sub]. It then takes 1/P[sub]2[/sub] to stability it. So those 5 points take 1/P[sub]1[/sub]+1/P[sub]2[/sub] seasons on average, assuming no super-bad results (like your lab blowing up) happen in those other, less successful seasons. To reach 55, you'll need to pull this off 11 times. And we'll put this in years by dividing by 4. So that's 11(1/P[sub]1[/sub]+1/P[sub]2[/sub])/4 years.
If both P[sub]1[/sub] and P[sub]2[/sub] are 0.1, that would be 55 years of continuous work. But that's not the typical probability. If you get up to Magic Theory 11, you can use up to +3. Then every roll from 7 to 13 will work. That's 7, 8, 9, 2x4, 2x5, 2x6, and 2x2x3. P[sub]1[/sub]=0.331 instead, at best. What about P[sub]2[/sub]? Unfortunately, your opportunity to choose goes with the first one. Basically, you need to not get one of two rolls and not botch. You must have used -2 (0.011 odds), 0 (0.01 odds), +1 (0.1 odds), +2 (0.11 odds), or +3 (0.1 odds) to have gotten the discovery. That gives, neglecting botches P[sub]2[/sub]=1-0.203655589=0.796344411. That gives us roughly 11.76 years on average, or roughly 47 seasons, if you can manage to avoid botching (yay, Holy Methods & Powers).
Still, that's a while. That's 11.76 years in the lab on average (again, discounting any of the possible bad results that would extend this). Have you done anything else over those years?
Next, if botches become possible, how bad does this get? Plus what about the Warping?
My general conclusion is similar to others. The Breakthrough rules are there for players to use not to reflect the reality of the game world.
The rules are written so a character that is well built, well played, and sacrifices an appropriate amount of time and energy to Original Research has a reasonably good chance of getting a Breakthrough. Further they should be able to do it over the span of an average saga with time left to bask in the glory and/or suffer the fallout.
If the rules were written to simulate the no Hermetic Breakthroughs in over 4 centuries the setting presents then IMOHO no one would bother trying Original Research.
That being said it's still up to story guides to adjust the difficulty for whats appropriate to their sagas. As the the Errata for HoH:TL actually makes the base odds a lot better then what Callen figured. Since the errata lets you double dip your modifier first adding it then adjusting up or down if necessary. So with a +3 it's every roll between 4 and 10 (with the exclusion of 5 probably*) that results in a discovery and roll agains happen on any roll 9+. So a character with a MT11 and no chance to botch seems to have a better then 50% chance of getting a discovery and a better then 80% chance of stabilizing. That drops you down into it taking 30-40 seasons to get 11 stabilized breakthroughs. You will also suck up a royal ton of warping and have to play through 4 or more story events.
*It is even arguable that by a strict reading of the errata you can still get a Discovery "in addition to" a Complete Failure result (5+3 in this case) on your initial experiment. This raises the odds for the above mentioned character getting a discovery to almost 70%. So on average it would take less than 30 seasons to make 11 stabilized discoveries
My issue with the Breakthrough mechanics is that they exist.
Are they good? Are they bad? For me, that's beside the point.
The game is (precariously) balanced around Hermetic Magic being able to do certain things and not being able to do others.
Changing that balance changes the game.
Deciding upon whether to do so ought therefore to occur outside of the context of the game world: Hey, are we open to changing the game? What kind of stories do we want to tell about realizing that change? What kind of stories do we want to tell about the consequences and impact of that change? Will we need to resort to GM thunderbolts from on high to 'balance' things should some players find themselves marginalized? Will we find ourselves having to fudge or rewrite rules should a Breakthrough occur 'too early' due to good dice?
I don't see this kind of thing best served by accumulating Breakthrough points. A mythic/folklore approach seems more satisfying to me, involving achieving difficult, even apparently impossible goals through stories. A conversation among game participants (players and GM, not characters!!!) to decide whether a Breakthrough can even be achieved is also helpful, because the conversation is really about what kind of game the group wants to play.