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Sivir's Boomerang Blade returns to her after reaching the max range, so you can shift position to hit enemies who would otherwise have evaded it.
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Ricochet resets Sivir's basic attack timer on activation, so activating this immediately after landing a normal basic attack will maximize damage output.
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Try saving Spell Shield for enemy abilities that can disable you such as stuns and roots.
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Boomerang Blade costs a lot of mana to cast, so dodging it sets Sivir back. If it hits you on the way out, avoid its path on the way back.
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Sivir is a powerful pushing champion, so leaving her unattended in a lane for too long will often result in your turrets being destroyed.
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When laning against Sivir, it is possible to throw off the timing of her Spell Shield by faking an advance, then backing off.