Dota 2 is ultimately a battle for strategic resources.
How well a team does depends largely on how well they can control these resources. Anyone who has ever seen a match replay, whether pro matches or pubs, will notice an ever-present gold advantage pointer next to the teams' kill score. A team's power tends to be proportionate to their XP and Gold lead.
Gold in Dota 2 helps players buy key items, especially cores, to give them the edge they need to close the game. Thus, building this gold advantage faster will always increase a team's win probability.
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Items in Dota 2 that help accelerate farm directly
There are two types of gold in a Dota 2 match. Reliable gold is a passive per-tick income of gold every active player gets, as well as gold from bounty runes. The bigger part of a core hero's GPM (gold per minute) is, however, is earned through getting last hit on creeps.
In the initial minutes of laning, the key to getting higher net worth is a mind game of creep-score. From the mid-game of Dota 2, however, creep-clearing is the only way for a carry to get the upper hand without joining fights. To fasten this, there are four items that double as 'farming' items.
1) Battlefury
Battlefury gives a melee hero 'cleave', i.e. attack damage spreads as splash damage to an area behind the initial target. On carries like Phantom Assassin and Anti-Mage, this is a godsend because of their innate mobility and attack speed.
Exemplary Dota 2 hero that commonly builds Battlefury: Anti-Mage (50.74% winrate in Dota 2 7.29 with this item).
2) Maelstrom
Maelstrom gives a hero - whether melee or ranged - a chance to proc chain lightning, an effect which basically functions like a semi-reliable nuke in clearing creeps. Unlike Battlefury, Maelstrom itself is far more useful as a fighting item, making it the safer option in games where playing passively is not a choice.
Exemplary Dota 2 hero that commonly builds Maelstrom: Windranger (49.62% winrate in Dota 2 7.29 with this item).
3) Radiance
Radiance adds sustained magic damage in an area-of-effect form around the hero. In principle, this is like Maelstorm in terms of creep clearing. There are two key differences. Firstly, this works on illusions in Dota 2, making it a good purchase on heroes like Naga Siren. Secondly, a hero does not need to actively right click to damage other heroes with Radiance. Thus Radiance is a good purchase on Dota 2 cores that are durable, as the damage really adds up over time.
Exemplary Dota 2 hero that commonly builds Radiance: Wraith King (59.94% winrate in Dota 2 7.29 with this item).
4) Hand of Midas
Unlike the other 'farming' items, Midas gives the player a flat 160 GPM ramp from its active usage without the need to clear creepwaves. Thanks to the additional XP multiplier on the unit targetted by Hand of Midas, the item is a god-send for heroes like Invoker who need to farm, but cannot afford to take their step off the pedal in terms of ganks.
Exemplary Dota 2 hero that commonly builds Hand of Midas: Invoker (47.43% winrate in Dota 2 7.29 with this item).
5) Mask of Madness
Dota 2 heroes that have some innate way to clear creeps at a rapid rate, e.g. Sven, can make it even more rapid with mask of madness. The lifesteal also adds some further utility for these heroes, and the item also can be later disassembled to build something else in the late game.
Exemplary Dota 2 hero that commonly builds Mask of Madness: Luna (46.04% winrate in Dota 2 7.29 with this item).
Many items also indirectly add to farming speed. Movement speed is indispensable in Dota 2 for a carry, as it allows them to move faster around the map to clear camps and shove waves faster. Another example is stat items, which help illusion heroes like Terrorblade - making the illusions both tankier and more capable of clearing creepwaves on their own.
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