Earliest visibility of the lunar crescent is an important calendrical element. It was needed in all early calendars and remains in use in some lunar calendars today. An astronomical criterion of earliest lunar visibility was therefore evolved quite early, using observations, right from the Babylonian era. In subsequent periods the Babylonian single factor ‘moonset lag’ criterion was used extensively, although gradually it was realized that it was rather simple. Recently, an improved and comprehensive global criterion of earliest visibility, developed by the author, has been used to generate an extensive inverted moonset lag data set. These data, as a function of latitude and season, all for the tirst time provide a useful comparison with the simple ancient criterion. It is found that the simple criterion is remarkably good for the latitude region where the Ancients collected their observational data, illustrating the care with which their data was gathered. At other latitudes, there are significant differences, as may be expected. Although the simple criterion may now be replaced by an accurate season and latitude dependent criterion, the former will continue to provide a useful basis. The paper discusses various related historical developments.