I had a private email pointing out that my method of assigning initiative would given an even application of skills, contrary to my post, and produce a general with an initiative of 4. Neither was what I intended. So it's time to do the old DM trick: choose different dice.
Average dice have a 2,3,3,4,4,5 and those tend to group in the middle. Low-average dice are similar, but produce numbers weighted for the low end. A typical one would be 1,2,2,3,3,4, but in this case I want a little more extreme, so let's use one that goes 1,1,2,2,3,4. Come to think about it, usually matches my die-rolling in a lot of games. If we only subtract one instead of two, we get a nice range of lower initiative generals.
So, that'll be the measure of the generals. And remember, we're rolling for "divisional" commanders and above. Think wing commanders and "column" commanders in this period as the division hadn't been invented until 1745, and then only in Maurice de Saxe's army in Flanders.
Now when one gets promoted through attrition, you get to roll his initiative all over again! This means the guy with the initiative of zero might turn out to have a three at the next level, and vice versa. There is such a thing as promoting beyond ones level. And there's historical justification for this. There are generals who got promoted simply because there wasn't anyone else available, who turned out to be great at the higher level.
One reader asked a bout "special promotions" where you promote someone due to valor. Not quite. Not in this period. Instead the worthy gets a promotion within the nobility. He might well be the model of a modern Major-General, but now, instead of being a Baron, he is a Duke. That makes for a less-expensive promotion from the monarch's point of view as that worthy has to maintain his social standing at his own expense. Expect peculation to increase. Another promotion might be to give him his own regiment (an already existing one, of course), but one he can rename after himself. At his own expense, of course; new gowns for the mistress and the wife are not cheap, and he has to purchase that regiment, and pay you. See? When you're the monarch, money-making opportunities abound (why do you think the new Elector of Hesse-Kassel, when he came into the title in 1760, doubled the number of regiments in his army by simply splitting all existing foot regiments in two? All of those new Colonel-Proprietors had to pay him the purchase price).
So now we go on to the armies.