Earlygame vs late the #'s are different. The "x ratio" doesn't hold up very well. For example, I have attacked 15:1 in the early game on a level 2 fort and lost. However, by the mid-late game I can and frequently do assault fort levels 4 and down with 50 infantry regiments and take them easily (5 is a bit dicey without more troops). Morale seems to be a factor, I'm not sure what else is (leader pips were not as of 1.7 when I tested a good 10 assaults each with 6/6 vs no general and got the same outcomes...not perfectly scientific but if shock/fire matters in that context it's marginal).
As for when you do it, the answer is in the mid-late game to speed up wars. The losses are overblown at that point; the cost of an assault is less than a month's worth of manpower.
As for when you do it, the answer is in the mid-late game to speed up wars. The losses are overblown at that point; the cost of an assault is less than a month's worth of manpower.