Hi,
I kind of realized that you're trying to put actual numbers to this, and my last post offered loose and useful thresholds. So less useful.
Ok. So no need to talk about apprentices or even journeymen, only masters and grand masters.
Although a character can be optimized so that he can take an apprentice right out of character creation, he is going to be a terrible master. He can open an apprentice's Arts, sure, but he won't be able to marshal the awesome totals needed to teach Arts efficiently, let alone preserve or transform an apprentice's supernatural virtues.
So let's say that most magi will wait 20-30 years before starting on his first apprentice. This isn't set in stone; some magi might start early, others might wait 30 or even 50 years, and some might live centuries without training anyone. But ok, 25 years.
Using the core rules for advancement, that represents 750 xps or spell levels post-Gauntlet. Those rules also recommend 2wp/year, for 50wp or a Warping Score of 4. No Twilight effects, either good or bad, RAW; no initiations. Very vanilla.
In 15 years, his apprentice will pass his Gauntlet, making him a real master.
Unfortunately, those rules encourage you to take 'lab seasons' in groups of 1 year, which does not quite account for 15 years of which 1 season is spent teaching. It's not quite RAW, but I recommend (and maybe one of the later sourcebooks recommends similarly) to advance the character 11 years, and 'waste' four years (16 seasons) on the apprentice. That's 330 more xps or levels, and +30wp, for a score of 5(+5pts).
So, the magus is now 40 years past Gauntlet. He has 880 points of stuff.
As for becoming an archmagus? Many magi never bother, having better things to do than play games. Other magi have extensive collections of dice. Different strokes. It should also be noted that a non-archmagus the same Hermetic age as an archmagus might actually be more powerful, because he did not blow seasons meeting some obscure challenge, and is more likely to pull out a nasty surprise, because fewer people know his secrets.
We can still put number to this, but need to make a decision. We know that the oldest magi are the most powerful, when they are not in Twilight, but are these magi past the age of bothering with such things? I'd think yes; that magi try to become archmagi while they are powerful but before long or final Twilights become a real possibility. Worse, an archmagus often has to take risks when other magi challenge him, which is not a game for magi teetering on the edge of eternity. Finally, ambitious magi will want to have time to enjoy and exploit their status, not simply put it on their tombstone.
So I'm thinking that magi usually achieve their goal between 60 and 100 years past Gauntlet, or never manage it for one reason or another, including being dead. I like to think of 60-75 as the sweet spot, something to enjoy before one's centenary (given that magi tend to pass Gauntlet at 20-30 years of age.)
We can put numbers to this too, the usual 30 points per year. We can also put Warping Points to this: 100 years past Gauntlet is 200wp, or a score of 8! That's kind of pushing it close.
Of course, all this is for NPCs, and will produce results in line with published characters.
PCs usually do quite a bit better at this in all respects, except for becoming an archmage: Such ambitions are usually crushed by the premature ending of a campaign. :)/2
Anyway,
Ken