The "Usual Intelligence score for Magi ... is +3" is a quote taken from HoH:S rather than something that seems to hold true in most of the games commented about in this thread.
The template Magi in the Core ArM5 book average just over +3 Int, with 25% having Great Characteristic (only two in Int) and 33% having Improved Characteristics.
The template Magi in 4th do not include Characteristics. However it has the wonky XP rules which make Int a priority for many things, which most likely resulted in a spike of high Int Magi. It is the only edition with this type of XP setup.
The template Magi in 3rd edition average under +2.5 Int (if you ignore Mercere at Int -1 who is an Ungifted Redcap).
2nd edition does not have template Magi or even Houses in the core book. The Houses were added by the "Order of Hermes" supplement.
of course logically most mystagogues should be Jerbiton with the gentle gift and high presence... but clearly that isn't how it happens since most mystagogues are in the mystery houses (which might, therefore, frequently favor presence over stamina or intelligence)
That inference immediately sounded bizarre to me, but it took quite some thinking to realise why it would be bizzare.
The connection is probabilistic rather than deterministic. Gifted people with -3 Int exist, but they are rare. CharGen rules which capture that statistical correlation would have two problems. Firstly, they would be over-complex and unplayable. Secondly, players should be encouraged to play the statistical outliers. Therefore, this is left out of the rules, and the troupe can populate the world as they please.
The rules arent created in such a way that if you used them to create a character sheet for every person in ME then you would get the population average. Thus the rules dont force people with the Gift to have higher intelligence even though it is stated that these two correlate.
The rules exist to make the creation of a character as easy an enjoyable as possible often cutting corners or ignoring things that are "generally true" in the world if favor of achieving the aims of the game.
Thus we cannot assume that the rules always predict information about how the game world functions.
If they are, say, Int 0-1, they probably join House Jerbiton, for which you don't need to be clever, you need to be fun to have around and have some skill in arts.
Generally, though? They don't exist.
The point of making the Gift rare, and setting it so that all people with it are desirable to the Order is to lower the implicit infanticide rate caused by the Gift.
The discussions seems to have moved a bit, to how smart is the average mage.
Int is all about the lab total. Having 1 or 2 more points on the lab total, nice. Having +3 stamina, meaning the spell succeeds instead of failing, and means the difference between life and death, that's important.
Back to the OP, I admit nearly all magi will throw a token +1 towards Int at least, as +1 is a low cost, and having a negative int is surprising.
The question is, what does Int represent? In Ars majica, I'd suggest int is a large part about education. A naturally smart child who gets no education, would likely have an int of 0, or if lucky +1. A child not naturally smart, but going through the 15 year apprenticeship, would arguably justify the +1 or +2 int.
If one thinks int is purely natural, and education can't help those true potato intellects out there, I don't know where the -3 Int people go.
-4 or -5 is an exceptional stat. Mental and Social stats so low, if played correctly and not just seen as a dump stat, would be nearly impossible to play in a RPG setting without infuriating every other player.
-4 or -5 physical stats have other limits. -5 strength, would have problems going in cold areas, as they'd struggle to carry the wool cloak. -5 stamina wheezed after climbing 3 steps, or going up a slight incline.
Int is not only about the lab total, although that is an important part. It also helps with many Finesse rolls - and various other ability rolls depending on what you are doing, and helps to comprehend Twilight.
I agree with your supposition that Intelligence in ArM, and indeed characteristics in general are not purely inherited characteristics but derived ones too. Thus that the high average intelligence of magi is explained by the fact that the study of magic requires, and thus promotes, higher intelligence.
Which would imply that often what happens to the low-Int Gifted children who are found by magi become magi with non-low Intelligence scores.
I like to think magi who aren't desperate for an apprentice tend to pass over the negative int ones, and they get left for the other traditions. From Rival Magic - Amazons, Virgillians and Soqotrans all rely on Com to cast spells so may prioritise that. Muspelli have all sorts of magical abilities that use different stats, and huge strength is useful if you focus on having the etin-mod of a really strong giant.
Hedge Magic - Elementalists use different characteristics for their four different powers (which is annoying when trying to generate one as a character), so unless you want to maximise your refining score you don't need int.
Hedge Witches - they use int for lab totals (and therefore potion brewing) but not for any of their day-to-day magical ability uses. Stamina (for Flight, Healing and Shapeshifter and resisting Witches' moon) or Per (for Second Sight and Dowsing) would be more useful if you're not a dedicated potion-brewer.
Gruagachan - cast using Sta, research spells using Int, initiate non-Gifted into their powers with Pre - so really there's a range.
Learned Magicians - as the name suggests, Int is likely to be important, and one of their great powers is creating Amulets and Chartae which uses Int and relies on casting horoscopes (Int again). Unless you are going to specialise in casting Charms and using Com, you are likely to want high Int. (Even then, searching for charms in a book uses Int+Language so you may want a reasonable Int)
Vitkir - Int and Sta are both important, but you may find that Sta is slightly more useful as it also helps with Nat-thel avoidance.
So really there's a good range of options for low Int non-hermetic Gifted magical characters. (This is before you take into consideration Divine, Faerie and Infernal powers - the Rings of Solomon from the Divine can boost your characteristics and is suggested for Gifted non-magi, Infernal powers use Com and Sta if I remember correctly)
Not a bad idea, but the advancement rules, and in particular the childhood rules from Apprentices do not support that. In particular, there is nothing the parens can do to stimulate the development of a particular characteristics, barring magic.
Likewise, it is not unreasonable to say that a character with negative Int could not possibly complete the apprenticeship and gauntlet. However, the advancement rules say otherwise. Even with Int -5, you get the same xp as everybody else. Only learning spells is harder, but if spells are taught, it will only reduce the max level of spells learnt. Sure, one would fail a gauntlet of Bonisagus or Guernicus, but probably not of Flambeau.
I agree. In the Ars Magica cosmology, a lot of what you are is "hard-wired" in you: see e.g. "Genetic Memory" in Lords of Men, p.25. However, childhood education can "yield" Virtues, such as Improved Characteristics or Great Characteristic, and those can boost Int.
That is unambiguously true for certain Hermetic and Supernatural virtues, including mysteries and some House virtues. For most virtues, and certainly the characteristics improvements, it is ambiguous at best. These virtues develop and change naturally, notably replacing child virtues, even in the absence of education. While there is no objection to using education as a narrative justification, there is no mechanics to tailor the education to create such virtues.
Well, the parents could always take them on pilgrimage to raise their stats, but there is a distinct lack of rules regarding the random distribution of stats- in principle if both magi nd grogs have 7 points in abilities then so would the typical person in ME, which, as noted changes the distribution such that the average stat would be between 0 and +1.
By RAW the answer is best expressed as a shrug with YSMV stamped in 40 foot high letters. I guess poor characteristics is very common flaw?
This looks like an inconsistency brought into 4ed and reinforced in 5ed.
The random method of 3ed gave zero mean characteristics, and I think there is no doubt that zero was considered to be the population mean.
The points system came in as an alternative in 4ed. As we know, players tend to make more characters than they play, and with random mechanics will probably discard those with submean stats. Thus it makes sense that the points system gives a higher average. There is no inconsistency yet, since it is generally assumed that players play exceptional characters.
The problem appears when we use the same mechanics for the heroic PCs as for Tom, Dick, and Harry. That seems to be the assumption in 5ed. Same rules for PCs and NPCs, generally speaking, and same rules for major antagonists and John Average. Judging from The Medieval Tapestry that may have been the case also in 4ed.
... I was referring to actually making several characters for each slot, not really discarding rolled stats before making the characters¹ ...
but ok, using the bad stats for grogs is not a bad idea.
¹ not that I have never done that, but it is one of those things I got increasingly uncomfortable with over the years, until I converged to systems with non-random chargen.
I don't really mind systems with random character generation mechanics, as long as they include some system to keep it from getting out of hand on the "bad" side. Even the older versions of AM I have played (2nd and 3rd) have this, in which there is a virtue which allows you to swap a Characteristic to a positive range.
Ones that combine selection and random elements tend to be my favored. Traveller is an example, since while you make choices and direct the character creation you do not always get what you want. Sometimes you get better, sometimes worse. The "Mindjammer" setting which uses the Traveller rules is great, I actually like it far more than the version of Mindjammer using its own rules.