Studying CK2 base tech rate has been informative but not helpful. The tech rate that determines ahead/behind translates to a 10.35% chance per year of a tech increment (1/10th of a tech level). Which is quite a bit higher than the base 1.2% chance. So much higher that even with maxed out schools and universities, you can't match it without advisers on tech missions, demesne/neighbor bonuses or special bonus events. Unless you have state stats of 134 or better, you *will* fall behind. Tech level 5 is supposed to be Renaissance tech, so that's ok, I guess, except it makes the baseline tech curve kinda useless for our purposes. Especially since everybody gets the same ahead/behind curve once play starts. Everybody gets Western, yay! :/
Before play starts, however, not everyone is created equal. There are a couple CK2 cultural/religious groups with different starting techs, different "ending" techs, and as you change start date the game just linearly interpolates between them. This translates to a different average tech rate for different groups during non-played time, which may be what we're after. The groups and their average tech rate:
Firenze & neighbors: 10.336%/year for a 0.1 tech increment. Damn close to the 10.348% that is baseline tech growth
Catholic: 6.46%
Other(Pagans and non-Greek Orthodox): 6.46%
Iberian Catholic: 5.082% (better start due to muslim tech, same end, so lower rate)
Greek: 3.445%
Muslim: 2.412%
Note that the highest tech rate achievable without temporary factors is 1.2% * (1+30% from schools) * (1+80% from universities) = 2.808% Everybody gets Muslim, if they're lucky and work hard, yay! :/
Those CK2 tech group rates can also be expressed as a percentage of the baseline. If we applied those percentages to the max bonus achievable from buildings (134%, 1.3*1.8-1, learning score of 1.34 if I understand learning score correctly), we end up with hard standards for how many tech buildings you should build to get membership in a tech group. Unfortunately I do mean hard, as in extremely difficult to achieve. So I arbitrarily decided that 2 in 7 provinces should have fully upgraded schools and the rest none and that that average level of learning score (0.383) would be the gold standard instead of the maximum possible. So the new standards look like:
Muslim = CK2 Muslim, 23% of standard, < 0.0893 LS
Ottoman = average(greek, muslim), 28% of standard, < 0.1085 LS
Eastern = average(greek, other), 48% of standard, < 0.183 LS
Western = CK2 catholic, nominally 62.5% of standard, > 0.183 LS in practice
With this I get a roughly even Ottoman / Muslim split in 1300 and 1337 (so we got some modernizing/westernizing to do yet, ok), an even west/east split in 1418 with a few stragglers, and basically 2 to 1 west to east in 1453. It's hard to stay muslim or ottoman in this setup. Which, since nobody burns libraries or anything in CK2, I'm ok with. Once Old Gods lets us sack things this'll all need revisiting, assuming it even passes muster now, so test your saves vs these newer standards and let me know what you think.