Sir Arthur Conan Doyle often has his narrator begin his stories with some description of Sherlock Holmes, but in the case of "The Red-Headed League" Watson says very little about Holmes at the beginning of the tale. This is evidently because Conan Doyle wanted to have Watson devote his full attention to a description of Holmes' red-headed visitor Jabez Wilson. The whole business of the Red-Headed League had to be made plausible. Later in the story, however, Watson devotes a full, long paragraph to a description of Sherlock Holmes.
My friend was an enthusiastic musician, being himself not only a very capable performer but a composer of no ordinary merit. All the afternoon he sat in the stalls wrapped in the most perfect happiness, gently waving his long, thin fingers in time to the music, while his gently smiling face and his languid, dreamy eyes were as unlike those of Holmes the sleuth-hound, Holmes the relentless, keen-witted, ready-handed criminal agent, as it was possible to conceive. In his singular character the dual nature alternately asserted itself, and his extreme exactness and astuteness represented, as I have often thought, the reaction against the poetic and contemplative mood which occasionally predominated in him. The swing of his nature took him from extreme languor to devouring energy; and, as I knew well, he was never so truly formidable as when, for days on end, he had been lounging in his armchair amid his improvisations and his black-letter editions. Then it was that the lust of the chase would suddenly come upon him, and that his brilliant reasoning power would rise to the level of intuition....
Sherlock Holmes enjoys comfort and leisure, but he can become a man of action when he is motivated to solve a challenging problem. No doubt many of Conan Doyle's armchair-detective readers liked to think of themselves in the same way. Holmes is able to enjoy his enviable lifestyle because he has become famous for what Watson calls "his brilliant reasoning power." Clients are more than willing to pay him large sums of money to solve their problems. And, since he is almost invariably able to solve the problems they bring him, he attracts more and more clients. He is known all over Europe and as far away as Russia. Yet because of the law of supply and demand, there being so many people with problems and only one Sherlock Holmes, he is able to pick and choose the cases he works on. And since he never has to worry about money, he is willing to help people like Jabez Wilson who are unable to pay his usual fees for services. Conan Doyle fashioned his great detective this way because it enabled the author to deal with a whole spectrum of characters and mysteries. Holmes is not confined to working for the sort of people who can pay him with bags of gold coins. Many of his most interesting cases deal with clients for whom he works on a "pro bono" basis. So his work and his leisure are both sources of enjoyment for the great detective. His readers all envy him and wish they could have his lifestyle with its mixture of luxury, adventure, and intellectual stimulation. It is possible to become addicted to Sherlock Holmes stories. Countless readers are familiar with his appearance, his crisp way of talking, his home at 221B Baker Street, his good and bad habits, his methods, his tastes, and everything else about him.