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also if your line is too deep the time to rotate gunners to fire cuts in to your reload cycle which lowers your damage out put.
and yes the shape of your formation matters depends on what you are getting hit with(spells,cannons, and other missle units) while having a more ranks does stop a charge from going through, which lowers the impact damage of the change(when units change there is a hidden damage mod that is just base on mass and speed and if it doesn't run you over not all of your units is taking that damage) but most of the time if you get charged by mounted units you are ♥♥♥♥♥♥.
They also get a slight advantage in melee, as there will be less of them to be attacked at the same time, so they will last a little bit longer, although it's not going to matter that much.
Combined with a checkboard formation it can give your units a very stong advantage when defending from enemies with lots of fast units that can flank you easily (or if you want to cheese with an almost full ranged stack), but normally I wouldn't bother unless really necessary.
I'm not sure it has any effect on normal ranged attacks, but if it does, it's not much. Of course it has the disadvantage of making you much more vulnerable to artillery or certain spells, so if you are facing a dwarf army with half a dozen pieces of artillery, it's much better to use a wide formation, but overall I think narrower or square formations are far more effective.
in general squares are indeed better simply cause the extra rotation can come in clutch at times but dont discount more spread out formations when dealing with certain factions
But then a square formation can rotate much better than a wide formation.
Really their formation is more about how they handle getting shot at. Being dense makes it easier for collateral damage from artillery, and I imagine volleys of arrows kill off more archers when they're in square formation.
That said, I guess guns are better against wide formations and suck against squares? Since they can only hit the front row.
https://www.youtube.com/watch?v=3aGRzy_PzJQ
I recommend watching it even though it is for WH, not WH2.