Unmixed wine tended to be strong, with an alcohol content as much as 15 or 16 percent (at which point the yeast is killed by the alcohol it produces) and was considered unhealthy by the ancient Greeks, who customarily diluted it with three or four parts of water. Indeed, Athenaeus has Dionysus say
"Three bowls only do I mix for the temperate--one to health, which they empty first, the second to love and pleasure, the third to sleep. When this is drunk up wise guests go home. The fourth bowl is ours no longer, but belongs to violence; the fifth to uproar, the sixth to drunken revel, the seventh to black eyes. The eighth is the policeman's, the ninth belongs to biliousness, and the tenth to madness and hurling the furniture. Too much wine, poured into one little vessel, easily knocks the legs from under the drinkers."
The Deipnosophists (II.36)
The wine always was added to the water, usually in a large mixing bowl or crater, such as illustrated here (a calyx crater from the Metropolitan Museum of Art), then to be poured by a young slave from an oinochoë into the cylix of the guests. 
Reference: Athenaeus: The Deipnosophists (1927) translated by Charles Burton Gulick (Loeb Classical Library).
