Across 1,091 ranked games on patch 16.21 in Master and above, Vladimir mains win 53.4% of their games in the mid lane.
Their most common build appears in 63.3% of those games and wins 54.3% of its 691 games.
It starts 
Doran's Ring and 
two Health Potions, completes 
Stormsurge, 
Liandry's Torment, 
Void Staff and 
Rabadon's Deathcap in that order, and takes 
Sorcerer's Shoes.
Two other builds are played often enough in the mid lane to be measured on their own.
In the mid lane, Vladimir mains fare best against 
Katarina (won 71.4% of 28 games), 
Ahri (won 60.5% of 38 games) and 
Jayce (won 72.7% of 11 games).
Their hardest matchups, the champions that counter Vladimir, are 
Zoe (won 26.7% of 15 games), 
Ryze (won 35.0% of 20 games) and 
Yasuo (won 41.9% of 31 games).