Plus playing those arena games takes time, and if you're just interested in constructed, you might as well buy packs. I blew ?20 or so on packs one night because I wanted to kickstart my collection and have the ability to make some basic decks without missing 15 commons. I've also bought a few packs with gold since I've gone more than break-even from arena. It's nice for having something to play against friends, since we can't use arena decks for that (BLIZZ PLZ).
But yeah, if you want to spend as little as possible, and have fun playing arena, saving all your gold for arena is better value for money.