It is always easyer to move block-like groups of units.
In your Roman example you should make:
(1) Velites and missle one group because they are probably wider spread than the rest of the infantry.
(2) Hastati, Principes, Triarii together in one group. Add to this the general, if he is placed behind the Triarii
(3 + 4) Cavalry of each wing a seperate group.
Move the Velites first, move the block with the heavy infantry behind them and arrange the groups with cavalry on the wings. This has the advantage that your blocks can always be placed with the first man in the up right corner (otherwise this position would be where your cavalry would be standing if it would be in the first line, even though it is in the third or fourth line).
It also allows to quickly re-arrange the groups of your army, for example placing all cavalry double quick on the right wing while moving all missle units to the left wing without touching the center block or re-grouping the entire army. Also usefull when your cavalry should be further to the front or more behind depending on the enemy's reaction to your missle units (cavalry charge, own missle fire or attack with spearmen; all would require different behaviour from the cavalry support)
Otherwise the army would go back to your starting formation when you move it again. This again can in fact be disered, for example when you are facing several AI armies as reinforcements. After fighting down the first enemy army your formation will be messed up. So moving the entire army as a group to the position where it has to fight the next enemy will place them in the correct formation again.
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