Dana Mackenzie wrote a nice series of articles about opening statistics in 2015.
For the most drawish openings, he writes this:
The Exchange Slav (D14) dominates this category like no variation dominates any other category. It’s a unique ECO code, a variation that is more about the players’ psychology than about chess. According to Rob Weir’s tables, this variation results in a draw 79.9 percent of the time in master play, and usually quickly. (The average number of moves is 25, about 8 less than any other variation.) If anything, I think that Weir’s statistics understate the extent to which these six moves serve as a wordless draw proposal. Weir removed all games of 10 moves or shorter from his database. When I look this position up on ChessBase, it looks as if at least 90 percent of the games are draws.
The top five drawing variations:
D14 (Exchange Slav with … Nc6 and …Bf5): 79.9 percent draws
D79 (Symmetric Grunfeld, 1. d4 Nf6 2. c4 g6 3. g3 d5 4. Bg2 Bg7 5. Nf3 O-O 6. O-O c6 7. cd cd): 59.0
C92 (Ruy Lopez, Flohr-Zaitsev Variation 9. … Bb7): 57.5
D13 (Exchange Slav, not 5. Nc3 Nc6 6. Bf4 Bf5): 56.2
B36 (Maroczy Bind, side variations): 56.1
For the least drawish:
Unlike the last category, the Hall of Shame of chess openings, this category consists of the most honorable, “fightingest” opening variations in chess. And what better variation to start with than B89, the Velimirovic Attack in the Fischer-Sozin Variation of the Sicilian Defense? The above position arises after 1. e4 c5 2. Nf3 d6 3. d4 cd 4. Nxd4 Nf6 5. Nc3 e6 6. Bc4 Nc6 7. Be3 Be7. To get an idea of the fireworks that may ensue, take a look at the amazing game Fischer-Geller from Skopje 1967. This was one of the three losses that Fischer included in his My 60 Memorable Games, so you know it has to be a pretty special game.
The top five:
B89 (Sicilian Defense, Sozin-Fischer-Velimirovic Attack): 25.2 percent draws
A44 (Old Benoni, 1. d4 c5 2. d5 e5): 25.5
B00 (Uncommon 1. e4 openings, e.g. Nimzovich 1. … Nc6, Borg 1. … g5, etc.): 27.5
C05 (French Tarrasch, closed variation, including the pawn sac 1. e4 e6 2. d4 d5 3. Nd2 Nf6 4. e5 Nfd7 5. Bd3 c5 6. c3 Nc6 7. Ngf3 Qb6 8. O-O!?): 29.5
A60 (Main Variation Benoni, 1. d4 Nf6 2. c4 c5 3. d5 e6, side lines): 29.6