Most Ball families in North America have heard that they were related to President George Washington. Highly likely the six brothers legend was created to provide a way for a New England Ball descendant to have a shot at making that connection. By the time of the fable's appearance in the Union Record in 1902 there had been very little New England "Ball" genealogy published (Bradley with his Coat of Arms theory relating Alling Ball to William of VA, Nicholas Ball for the Block Island clan, and some other general compendiums like Bond for Watertown MA and Savage and Farmer summarizing a wider New England area, for example), so the proposition was quite plausible at the time.
From “The Union Record”, published by Ball International Union and Keuka College, George H. Ball editor, Vol. 1, No. 2, April 1902, page 38:
“William Ball, of Wiltshire, Eng., had six sons, who came to America in 1635 on the ship Planter, namely: Alling, Francis, John, Samuel, Richard, and William. They first landed at Boston, and thence went to various parts. Alling went with the Tuttle family to New Haven, Conn., in 1638, and managed the Davenport farm in East New Haven until 1650.”…and further…”William, son of William, of Wiltshire, Eng., and brother of the first Alling, became a merchant, and is so styled in the first extant record of him in Virginia. As such, he naturally visited England often, and also the several American colonies, in the fur trade then, which was very remunerative.”
This fabled story made “fact” in the “Union Record”, but possibly having been around before that, is undoubtedly a fabrication, since there has never been any documentation presented to support it in the last hundred years. The first clue about the fable is that the Union Record only referred to the proof being in the hands of Mrs. Samuel Edgecome, of Mystic CT, rather than outlining the proof. For a journal that came into being to promote research into Ball family history, detailing the proof of the six brothers should have been front page news. To be fair, there was a Samuel and Elizabeth Edgcome living at Groton CT for the 1900 census and at Mystic CT for the 1910 census. Could be that Elizabeth Edgcombe did send the story to "The Union Record", but whether she created the myth or just passed it on is unknown and she kept the "proof" to herself.
The ship did exist: the “PLANTER of London, Nicholas Trerice, Master. She sailed from London April 1635 and arrived at Boston on Sunday, June 7, 1635.” Lists of her passengers for that voyage have been transcribed and are available on several ship passenger list websites. There is no “Ball” or any name that could be construed as “Ball” on that sailing. There are no other sailings noted for 1635, although, of course, there might have been another, since a round trip only took a bit over 4 months.
Then there is the problem of records of "first appearance" not supporting 1635 as a common arrival date for the known heads of the various New England Ball families with the names of the supposed brothers. John Ball of Watertown and Concord MA shows up in Watertown records in 1650 as “freeman”' his purported son John married and had a son John b. 1644, presumably in Watertown. Alling Ball first shows up in CT in 1643 (although he is proposed by some to have arrived as early as 1637). William Ball of New Haven CT, suggested but not proven brother of Alling, is first recorded in 1644 in CT. Records of Francis Ball start 1640 in Springfield MA and the Francis Ball noted in Dorchester shows up in 1639. There was a Richard Ball noted in Salisbury MA in 1650, but little is known about him. I am not aware of any early Samuel Ball records in New England. As for Col. William Ball of Millenbeck VA, I bow to others with more expertise, but I believe that he is thought to have arrived in VA about 1650.
Of course the first cold water to be thrown on this fable was the proof by the highly respected genealogist Donald Lines Jacobus that Alling Ball of New Haven CT was the son of an Alling Ball of London, England (see "The American Genealogist", Vol. 10, pp. 208-212). The real clincher is DNA testing; see the Project DNA study (also see FamilyTreeDNA Ball Study). There have been DNA tests completed for descendants of Alling Ball of New Haven CT, Francis Ball of Springfield MA and Francis Ball of Dorchester MA and both purported sons of John Ball of Watertown and those DNA results are different from both and William Ball of VA, as well as from each other. None of the early Ball immigrants to New England are genetically related to William Ball of VA or, for that matter, to each other.
Today the on-line access to the trees done by others just means that the legend has spread with computer speed and, because there are so many that want to believe they are related to President Washington, the myth will never die. Enjoy the fable, but please don't put it into your family tree and expect anyone to be impressed.