While Ball was best known as the commander of the First Fleet's HMS Supply, he was also notable for the exploration and the establishment of colonies around what is now Australia and New Zealand.

In October 1787 Ball was appointed to command HMS Supply and to join Captain Arthur Phillip's expedition to establish a penal colony in New South Wales.

In March 1796, Ball was given command of HMS Ariadne and joined Rear-Admiral Hugh Cloberry Christian's convoy to capture Dutch and French colonies in the Caribbean.

In March 1797, Ball was appointed to HMS Daedalus and was stationed off South Africa where she was involved in the capture of six vessels and the action of 9 February 1799.

Ball was commander of HMS Gibraltar at the Battle of the Basque Roads, and was called as a witness at the Court-martial of James, Lord Gambier, regarding those events.

Supply's armament was increased in 1786 from its original four small 3-pounder cannons and six 1⁄2-pounder swivel guns to include four additional twelve-pounder carronades.

[5] On 10 June they began their voyage across the Atlantic to Rio de Janeiro, Brazil, taking advantage of favourable trade winds and ocean currents.

[1] On 14 February Ball on Supply sailed with Lieutenant Philip Gidley King, who was to establish a subordinate settlement on Norfolk Island.

Ball discovered navigational and physical difficulties in approaching the island – challenges which were to affect future settlement there – but he managed to bring both people and supplies ashore by 6 March.

[11] On 19 March the weather cleared and Ball and Captain John Hunter of Sirius started to unload the remaining convicts and provisions.

[12] Ball noticed the current was pushing the ships toward the sunken rocks and signalled to Hunter before manoeuvring Supply away from the danger.

[11][12] Sirius was supposed to continue on to Canton (present-day Guangzhou), to pick up supplies, but with its loss at Norfolk Island, Supply sailed on 17 April to procure provisions from Batavia, Dutch East Indies, carrying Philip Gidley King, who was to continue on to England with the Governor's dispatches.

[13] Ball returned to Port Jackson on 18 October,[14] having chartered the Waaksamheyd to bring the rest of supplies, which arrived 17 December.

In March 1791 Ball sought leave to return to England both to recover his health and to attend to family affairs.

[17] In January 1808 it was noted that Ball applied for the governorship of New South Wales, but the request was turned down as no change in governor was intended at that point.

[3] With his health recovered, he returned to duty in December 1793 and was assigned command of the sloop HMS Fury, joining Rear-Admiral John MacBride's squadron in the Downs.

[3][19] In March 1796, Ball was given command of 24-gun sixth rate HMS Ariadne, and joined Rear-Admiral Hugh Cloberry Christian's convoy to the Leeward Islands Station, with the intention of capturing the Dutch and French colonies in the Caribbean.

With Lieutenant-General Sir Ralph Abercromby's forces, Christian sailed on 26 April, to invade St Lucia, which surrendered 25 May.

[21] On 14 August Daedalus and HMS Fox, which was on operations in the Red Sea, received information from trading vessels that Frenchmen were stationed at the town of Kosseir.

[27] With the death of Captain John Turnor in January 1801, Ball took command of the 64-gun third rate ship of the line HMS Trident.

[30] With Rowley appointed in April 1807 as Commander-in-Chief, the Downs, Ball was moved to the navy's list of reserve officers.

[42] A plaque commemorating Ball was added to the Johnston tomb on 20 October 2013 at a service attended by the Australian High Commissioner to the United Kingdom.