In a later post I will address the novel's themes and characters and compare them to those in Pride and Prejudice. For the time being I will use the historical record to evaluate Lady Russell's near-fatal judgment of Captain Wentworth's career prospects, which occurred six years before the novel begins.
As a preface, Jane Austen was well acquainted with the Navy and its officers. Two of her brothers were post captains who rose to become admiral after her death, and the description of naval occurrences, though not in the foreground, is done carefully by someone who knows what she's talking about.
Captain Wentworth was not born at a lucky time or at least, he didn't advance in his career at a lucky time. The best years for navy men were the early years of the revolutionary wars, the 1790's, when British dominance on the sea was less secure and there were ample prospects for distinguishing oneself in action and gaining a fortune in prize money (Austen's older brother Francis was made lieutenant in 1792, just as war was declared, and rose to become Admiral of the Fleet). Captain Wentworth was not a Captain in those 'lucky' years before Trafalgar, and was probably not a lieutenant for most of them. In 1806 he was a Master and Commander, an officer qualified to command small 'unrated' naval vessels such as sloops of war. He was promoted due to his role in the British Victory off Santo Domingo earlier that year. This victory was the last time British ships of the line met French ships of the line in a fleet action in open water. After Santo Domingo, the bulk of the French navy remained bottled up in Brest, Toulon and other ports, blockaded by British squadrons. While this was good for Britain it was bad for the careers of her sailors, who now had extremely limited opportunities to distinguish themselves.
The Battle of Santo Domingo by the great sailor/artist Nicholas Pocock. In the foreground the British Northumberland (74, right) engages the French Imperial (120!, left). The Imperial was driven aground and later burned.
This was made worse by the fact that there were more captains than ships for them to command, and in some ways the situation was even worse for Masters and Commanders. While full 'post' captains could theoretically command most ships in the navy, from a 32-gun Frigate to a 120 gun ship of the line, Masters and Commanders were restricted to a fairly small number of smaller warships. As NAM Rodger relates in pages 518 of his authoritative The Command of the Ocean, in 1805 only 51 percent of Commanders were employed, a number that dropped as the decade wore on to 44 percent in 1810 (the numbers for post captains were somewhat worse in this regard). Moreover, while promotion is automatic for those of 'post' rank or higher*, a Master and Commander has no guarantee that he will be promoted any further. As Rodger goes on to relate in page 519, it was typical for both commanders and post captains to have a period of unemployment after their promotion, which could be prolonged. This made one's time as a Master and Commander a dangerous period in one's career, where employment was hard to come by and further advancement uncertain.
This, then was Captain Wentworth's situation as he courted Anne Elliot. He was at an awkward time in his career at an unfavorable point in the war; he had no guarantee of anything better than a Master and Commander's half pay, which would seem paltry even to a family less snobbish than the Elliots.
Yet things were not all bad for Wentworth, and he had ample reason to hope. While the big ships of the line (commanded by more senior post captains) were stuck in boring an udnprofitable blockades of Toulon, Brest and other ports, sloops of war were able to raid shipping, fight French privateers and engage the small warships that slipped past the British blockade. These sorts of actions could bring both glory and prize money. The question would be weather he could get a command. But here his hopes had reason to be bright: his family connections through his sister, married to Admiral Croft. When the novel takes place (in 1814, after Napolean's exile to Elba, before the Hundred Days), Croft is rear admiral of the white -- the lowest rank of admiral, and of middling seniority among his peers. Given the sometimes slow pace of promotion through the list, he must have been either a senior post captain or a junior admiral in 1806**. In either case such connections were valuable to a man who needed a command, especially if his patron in turn had friends in high places.
Wentworth's prospects, then, were uncertain but promising. In the event he prospered, winning promotion to post rank for taking a frigate with a sloop, a fact that is briefly mentioned in the text, but which is quite an accomplishment, to say the least***, and going on to lucrative frigate commands in the especially lucrative West Indian station, which remained active for much of the war and which allowed Wentworth to make his fortune. He could not have known for sure that his career would turn out like this, but an informed observer could guess; had Lady Russell known more of the navy or esteemed it more highly she may not have advised Anne as she did.
A useful contrast to Wentworth's prospects in 1806 are those of Captain Benwick's in 1814. Like Wentworth was then, he is a Master and Commander, but unlike Wentworth he has no fortune, no guarantee of advancement and no means of distinguishing himself further -- he has no more wars to fight. Barring being called up in the brief mobilization during the Hundred Days (or called for transport duty to say, ferry the British Army to New Orleans and their doom), it is likely that Benwick will live on a Mater and Commander's half pay for the rest of his life. As Rodger repeatedly points out, age of birth and promotion were the critical factors in a sea officer's career; Wentworth belonged to the last generation of officers who could hope for much distinction or fortune.
*This is what the narrator means toward the end of the novel when she speaks of (post) Captain Wentworth having advanced as far in his career as he can based on his merits.
**The text says that he was in the Trafalgar action (almost certainly as a captain) and was then sent to the East indies sometime thereafter. It is likely that he was sent to the East Indies upon his promotion to Rear Admiral.
***Capturing a frigate with a sloop resembles Lord Cocrhane's taking of the frigate El Gamo with his sloop, the Speedy. This in turn was the basis of the fictional Sophie/Cacafuego action of Jack Aubrey, whose career resembles Cochrane's and whose character resembles a more comic and less constant Captain Wentworth.