Fine, I missread your post for 3 seasons instead of the 2 you suggested, so Teaching score of 2 it is, still not too likely. The speciality is a fair point again, but with scores that good your apprentice must be close to the gauntlet right?
Well getting latin 4 and MT 1 are the most important thing for the apprentice, since that's when they start being useful. Add to that the Arts Libs at 1, that's the first 4 years of the apprenticeship (using the average 15/yr), Teaching 2 is year 5. MT 2 can be reached before the end of year 6, meaning that the first tractatus could be produced year 6 or 7. From then on, they can start churning tracttii out, if they are not needed in the lab.
The model get taught in the spring, write an essay to show how well you understood the topic (summer), make it better (autumn) and even better (winter) makes a nice loop.
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But you could already do this with a com score of one higher and a good teacher. How often did this happen in your games?
So far, never. Not only do we not have that house rule, but we prefer to play with the gifted being rare, so rather than having a large selection of potential apprentices to choose from, who will have all these optimal this and that, you are stuck with what you find. Either you make do with this Int +1 apprentice or you can cross half of Europe to find another one who won't speak your language and might not be better anyway and you might annoy the local mages whose pond you are fishing in anyway.
Not a "true" House Rule per say, but my group uses an OR and Integration tracker. Our SG maintains two copies, one full and one redacted. It has proven extremely useful for a long running game since it allows changing and developing Hermetic Magic Theory.
The redacted version is the one that the PCs can see. While it mostly only contains the research that has been completed or that we are working on, it is also somewhere that we can post ideas to.
The full version list out a massive range of OR and Integration that are currently being worked on, groups working on it, current points each has earned (if some PC manages to steal the research), and when it will be completed (if ever). There are some completed research as well which has an extremely small distribution so that it is not known.
For each completed research there is a ranking in "Spread". These are: Total, Common, Uncommon, Rare, Very Rare, Isolated, and None. This determines how much of the Order knows the effect and how common books that would teach it are. Below is the breakdown for each level.
Spread - % Order Knows - % New Books - Notes
Total - 100% - 100% - A change to MT that effects and is known by the whole Order
Common - 75% - 60% - Widely spread and on the way to being the norm. Useful effects reach this in a long time. Very useful effects reach this in a moderate time. Niche effects rarely if ever reach this level.
Uncommon - 50% - 30% - Something niche that has been around for a long time, something useful that has been around a moderate time, or something very useful that has been around a short time.
Rare - 25% - 10% - Very useful things will reach this in a span of a few years to a decade. Useful things will reach this in a short time. Niche will reach this in a moderate time and might not become wider spread based on just how niche it is.
Very Rare - 10% - 1% - Something along the lines of a House Mystery in its spread. All discoveries start at this level once book(s) on them are released to the Order at large.
Isolated - 1% - 0% - Something only known by a single Covenant
None - 0% - 0% - This is only known by its inventor
A short time is a decade or two, a moderate time is two decades to a century, and a long time is greater than a century.
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By default the Gift is only one in every 10k people. That is only about 6,000 alive in all of Mystic Europe (plus any in the outer Tribunals). While the Order is only about 20% of that total, there is a lot of competition for Gifted individuals with the varies hedge traditions and also a large percentage of loss which are not found until they are to old to apprentice (if found at all).
If we are looking at just the people in the age range acceptable to be apprenticed, there is a total of only about 1,200 of them in Mystic Europe. This means that at any given time there is only roughly one child in the age range to become an apprentice for every Hermetic Magus. And even then, some of them will be older than what a Magus would want or younger than 5.
In an older thread I did the math on how far and wide you would have to search to find someone with the Gift, as well as how far you would have to search to find someone in the age range to become an apprentice. They were massive enough that if the Order did not form groups who systematically searched out those with the Gift and age range required, they would have already become larger in size than could be supported.
I will try to dig up the thread and link it in this post since it does a better job of the breakdown.
EDIT Found it, this is my first post on the subject though you might have to backtrack a touch to find all of it.
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I think that I remember that thread. In the game that I will end next week, the mages learned the Sight range In spell to detect gifted people and then they walked from the Rhine Valley all the way to the slave market in Prague and back, by a different route. They got lucky in a brewery in Bamberg so they found a Vengeful tween girl who set fire to the brewery where she worked to cover her escape...
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Absolutely none.
Or maybe just one, copying books treat art levels and ability levels as equal, while original authoring has three points for an ability equating one point for an art. The same conversion should be used in both, but this is clearly correcting a misprint IMHO, and not overruling the design.
By and large I think ArM works well, and house rules tend to create more problems than they solve. Particularly, it is difficult to keep them consistent, and once you start house ruling you may be forced to rule more.
That said, it would be delighted to see more complete house rule sets posted, simply because when the rule sets are complete, it is possible to gauge their consistency. Fragmented rules remain ideas only ... one cannot know how they work without knowledge of the other house rules in play.
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I have one simple house rule that helps a lot: experience from botches and 1s is limited by Warping just as all other experience is with Sympathy Traits.
I would really love to see how your SG has these lists set up. Using a spreadsheet or something else?
This is something I could see adding on to the spate of worldbuilding I've done for our saga the past couple of weeks.
Yes they are spreadsheets. The redacted one we have access to has several of the tabs removed and then the remaining data cut down or replaced with "???". For example the only OR and Integrations we know of at VR, I, or N level of spread are ones we have created ourselves.
Many of the ones we know are being researched are through House Bonisagus politics. There is also the assumption that many of the Hermetic Virtues are being studied for Full Integration (especially ones that can easily be explained by a refinement of Hermetic Theory like 'Adept Lab Student'). The varies example OR scattered throughout the line are also on the redacted version (Parma Folds, Aristotle/Plato Magic Theory, LR w/ Fertility). Several of the Supernatural Ability granting Virtues are being studied for Integration. SG said all the non-Core Spell Mastery abilities we use should be on the list, but we added them to the game before the list was created. I am sure he has a few being studied on his full list.
There are a few completed ones on the list that have caused interesting changes in the game. The LR w/ Fertility is one (though its spread is only Rare) and Refined Arcane Connections is Common (it reduces the time to ~ a week, you can produce your MT total in a season).
There are also the ones we have created or are working on. My Magus permanent version of "Awaken Plants" is Rare (it is niche). Our "Blood of Hermes" OR/Integration is also on our list, though it is currently only being researched.
This is very cool and I may steal it. Would you or your SG be willing to share a copy of the spreadsheet as it stands, so I can see the form fields involved? 
The redacted copy is fairly simple, since it only has things that the PCs know. It list the Subject, Success Total Needed (which will of course vary by game), PC total (if any of us are researching it), NPC Name & totals (which are all '?' for totals since we have not done any espionage), Source location (book & page), Description (which covers a rough description of its effect), and Notes (odds and ends, like that the Aristotle and Plato research is being done by groups). It is split out between an OR tab and an Integration tab, with related things grouped. There is also a tab which defines the Spread levels (which I posted earlier in the thread).
I don't think my SG would give me a copy of the full version to share. He is an EB and has things in it which I am sure he does not want any of us seeing.
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You can change an Ability speciality when it increases a level.
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Ironically, I thought that wasn't a house rule 
Oh, I just remembered another rule I have as an automatic.
You can add levels of Complexity to spells instead of having them require a Finesse roll. This super applies to Creo but can also sometimes apply to other Arts as well for all that its mostly focused on Creo.
Basically, you conjure something with levels of Complexity and the magic works, no need for what I consider to be bad design Finesse roll.
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Excluding combat situations, right?
My group specifically allows added Complexity to reduce the time modifier. We also allow Creo ritual creation effects to take a number instead of rolling, which when combined with enough Complexity to reduce the time modifier to 0 lets it always succeed with a Standard result. This allows several Core spells to be used as written.
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Are you talking about Spontaneous Magic here? Cause if so I don't assume that Complexity can be added out of nowhere in order to bypass Finesse there.
This is mostly in terms of creating things out of nowhere or using magic to craft things, and it mostly applies to formulaic spells. Basically, in my view, the magus does the research ahead of time, and puts that research in the spell's laboratory text and so when it comes to casting they don't have to do things on the fly.
But if you are doing things on the fly then yeah, Finesse as an ability makes perfect sense.