Vision Score is a recent addition to League of Legends and it is very useful if you are aware of what it tells you.
Vision Score is a number that is trying to actively represent how much you have contributed to your team's vision of the map. There are many ways to contribute to your vision score, including increasing your vision and decreasing the enemy's.
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League of Legends Vision Score
The main way to increase Vision Score is to have wards that stick around. You are awarded points towards your Vision Score based off of the lifetime of the wards you place. For every minute your ward is giving vision you get one point.
Your Vision Score will also increased based off of the lifetime of enemy wards you clear. The remaining lifetime of the ward gets added to your Vision Score. For every minute the ward had left on it before expiring you get one point. Permanent wards count as if they would have one and a half minutes left.
Additionally, some abilities as well as trinkets can gives points, but they are not as impactful on your Vision Score as placing and destroying wards.
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