Adhika masa is inserted on an average about every 2.5 years in Indian calendar. The actual place of insertion may vary from 2 year and 3 months to up to 2 year and 10 months.
The gap between purely solar and purely lunar calendar increases by 10.88 (~11) days every year. Insertion of one Adhika masa, periodically adds 29.53 (on an average) days to the lunar calendar.
What this act of inserting ‘Adhika masa’ achieves is that the act aligns the specific point(s) of solar calendar (e.g. days of equinoxes, solstices, etc.) with that of ‘Median lunar Tithi’.
That is the best ‘an act of insertion of Adhika masa’ can do…but even more critical…it is the OPTIMUM it should do.
Anything else would result in over or under-correction.
This enables alignment between daily calendar that is lunar in nature (days, Tithi, Paksha, masa, which in turn are tracked easily with the visual observation of the phases and positions of the moon) with the key points of seasons (e.g. equinoxes and solstices).
The arrangement works like a magic for at least a century and even up to few centuries.
Eventually, the shift in position of equinoxes and solstices, due to the phenomenon of ‘precession of equinoxes’ would be finite enough (over a period of 1000-3000 years) and the calendar would require mega-correction(s), e.g. The status of ‘first nakshatra’ was changed as required.
Ancient Indian literature is full of these ‘mega-corrections’.