How does gaming performance affect the rarity of potions I get?

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I often get Common Potions in agar.io, sometimes I get Rare Potions, and seldom I get some higher level potion. The rarity of the potion seems to be connected to my gaming performance.
How are they related?
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History of Potions in Gaming
Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.
Images: Mikhail Nilov, Mikhail Nilov, Yan Krukov, Riccardo