Part 126: An explanation of growth rates and stat caps by Colon VAlso, I did the math, and looked into some of the characters' average end-stats, and such. Assuming that the game really does just do a simple 1-100 number for each stat, it's pretty simple to calculate. I mostly used early-game characters, because excepting one legendary little girl, most late-game characters come pre-promoted, and/or have horrible growths.
Assuming a character doesn't have the tactician's bonus, on average, their pre-promotion stats hitting the cap can only really be expected to happen if A) the stat's growth is absurd (Lyn/Guy's Speed, Oswin's Defense) and/or it's a stat that starts very high (Defense, Sain's Power, Lyn/Guy's Speed, Oswin's Defense). On average, a 50% growth or greater in a stat (not counting Luck or HP) that starts at about 7 or higher provides a reasonable chance of hitting the cap, while one of 60% or greater in a stat that starts at 8 or 9 will cap pre-promote as often as not.
Assuming that the 'ideal' growth rate is 40%, with a starting value of 7, said stat will, on average, end up at 14 or so, though variation in one direction or the other is entirely possible.
Post-promotion, things get a bit more complicated, because of the non-uniform caps. Generally speaking, however, FE7 seems to consider a "good" stat cap to be at about 30 (Hector's Power, Lyn's Skl/Spd, etc), 25 for "average" (Eliwood, Kent and Sain's everything, etc), and 20-22 for "poor" (Lyn & Guy's Def, Pretty much everyone's Res). That's, on average, about 5 points of "growing room" added onto the 15 or so from pre-promotion.
What does this mean in practical terms?
1) If a character hits their pre-promote caps, they are almost guaranteed to also hit the post-promote caps, especially when you factor in the stat boost from promoting.
2) Keeping with the "ideal average growth" of 40% and a starting stat of 7, with a final cap of 25, will end up hitting that cap about half of the time, so that holds water.
3) For a cap of 20-22, a 30% growth rate will turn out similar chances of hitting the cap, while for one of 30, 60% does the same thing.
4) For every 2 taken from the starting stat, you need an extra 5% growth to keep the chances of hitting. (A stat that starts at 3 instead of 7 would need a growth of 60% to have even chances of hitting a cap of 25) And vice-versa. (A stat starting at 9 only needs a 30% growth for even odds of hitting 25, or 50% for one of 30)
And for those of you playing along at home..
Average Max-Level Stat = Starting Stat (+ Promotion Bonus) + Growth * (Final Level - Starting Level)