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MOBA is the acronym of the genre given to games inspired by a MOD called Dota Allstars that became popular in WC3 The Frozen Throne a game released by Blizzard Entertainment. Usually MOBA's consist of elements of action, strategy and role playing into their game play styles. They usually do not consist of base building and micro-management of units and structures but instead concentrate the user to control one or a few units with various spells and combos much like an action or arcade game.
Currently there are many MOBA's under development such as League of Legends-Clash of Fates, Heroes of Newerth and Bloodline Champions.
Already existing MOBA's include Dota Allstars and Demigod.
Recently Icefrog, the current developer of the infamous MOD Defence of the Ancients Allstars signed a lucrative deal with Valve Corporation for his own team and speculation is a rift that he will start development on his own standalone MOBA based off of Dota.