In chess, a "match" is a series of games between two players. The correct term for an individual game is a "game".
"Plays per person" is known as simply "moves". If each player has made 37 moves, that's 74 half-moves, or 74 ply (in the context of lookahead in the game tree by a computer).
Most analysts, when studying performance, assign scores of 1 and 0 to White and Black when White wins, 0 and 1 when Black wins, and 1/2 point to each when there's a draw. It is unusual to not count draws when analyzing performance. Doing so would decrease White's apparent advantage. For example, I just checked all the 2013 games from Chessbase's Megabase and White scored 53.4% with draws counted as a half point for each side.
By the way, one of the reasons that draws have decreased in the last 30 years is probably the advent of faster time controls. I also suspect one reason that games have gotten longer is the death of adjournments.