Does combat width help in destroying a pocket?
I mean, if you have a one-tile pocket that you need to destroy as fast as possible, and it has a load of enemies (enough to fill any combat width), is it better to attack from one side for 80w, or should I try to widen the combat to 120/160/200w? Assuming that I can only fill that extra width with subpar attacking units such as infantry.
(Assume pre-NSB combat widths for simplicity.)
This depends on whether or not you can win the smaller combat without attacking from extra flanks. If you can do that, you can destroy all of the enemy formations while only fighting a small portion of them. If you can't do that, attacking, failing, and attacking again with fresh units allows the defender to put their own 'fresh' units at the top of the defense stack as well.
If you have a much better reinforce rate than the enemy (or larger formations), you can start the combat by attacking from 1 province, and then add the other provinces to expand the width afterwards of the initial combat starting, which will force all additional units to join through reinforcements. Through the combination of higher chances or needing less successful rolls to bring in more width than the enemy, you can enjoy a temporary advantage which hopefully tips the balance and allows you to win.
In more general terms, I'd say that more width is generally worse for time in combat than less width. My reasons for saying this has to do with the way that targeting works. More width generally means more formations on one side or the other. More formations on either side (or worse, both sides) means that attacks are going to be split a lot more evenly between all available targets. This has the effect of maximizing the amount of defense/breakthrough that gets activated, which is going to minimize your chances of overwhelming their defenses and dealing amplified damage. This means that even though our attacks are going up, less of them are being amplified which means our overall damage ratio is going down, while the enemy total org pool has increased in size.
If the duration of the combat is going to be particularly long either way, or the enemy has a very good reinforce rate such that reinforcements are going to be a concern, going up in width is a better idea. This is because the rate at which the enemy can bring org into the combat through reinforcements is more or less a fixed rate, while opening more width will generally always mean that more damage is being thrown back and forth. This means you have a better chance of dealing more damage than what they 'heal' over time, and you'll slowly drain their org pool and win the fight.