Perhaps in single-player, but in multiplayer the noob-box is doomed against practically any army. While cavalry archers provide less missiles-per denari, the noob-box is notoriously bad at countering all armies. The is for multiple reasons, but just addressing your comment it is because for the noob-box to be affordable, the space inside it has to relatively small - making archers stacked on-top of each other. For whatever reason, Rome doesn't allow for stacked archers to fire at the same rate as they would if they were spread out, making them less effective. Furthermore, the fact that they are inside a small area means that the effects of enemy fire is even greater than it would be otherwise, meaning that almost every arrow will hit its target. In theory, if the enemy army did not include melee-cavalry one could counter this by having a few cavalry units operate independently outside of the noob-box. But assuming that your opponent is semi-intelligent, and includes a few cavalry units he will easily at the very least make them a non-issue by forcing them to run away from the box, or be forced into a fight with its flanks open to enemy charges.
For more info on why the noob-box is fundamentally flawed, take a look at the following comprehensive video by Cluny the Scourge.
Last edited by Mr Longbowman; September 04, 2016 at 07:09 PM.