Why does the case of the "Red-Headed League" interest Holmes?
What interests Holmes about the information given by Jabez Wilson is the strong possibility that Vincent Spaulding is a master criminal known to the detective as John Clay. The most significant details are contained in the following dialogue.
“What is he like, this Vincent Spaulding?”
“Small, stout-built, very quick in his ways, no hair on his face, though he's not short of thirty. Has a white splash of acid upon his forehead.”
Holmes sat up in his chair in considerable excitement. “I thought as much,” said he. “Have you ever observed that his ears are pierced for ear-rings?”
“Yes, sir. He told me that a gipsy had done it for him when he was a lad.”
Holmes has never seen Clay in person but knows of his description, especially that he has a white splash of acid on his forehead and his ears have been pierced for ear-rings. The other features match what Holmes knows about Clay's appearance. He is small, stout-built, and about thirty years old.
Later when Holmes sees Wilson's assistant on the pretext of asking for directions to the Strand he is sure of his man. He tells Watson:
“Smart fellow, that....He is, in my judgment, the fourth smartest man in London, and for daring I am not sure that he has not a claim to be third. I have known something of him before.”
Obviously Clay would not be working at that obscure little pawnshop unless he was planning to commit a serious crime. Holmes sees the branch bank a short distance away and deduces that Clay is digging a tunnel and wanted to get Wilson out of the way with the Red-Headed League hoax. Holmes deduces that Clay is doing a lot of digging from the moist and wrinkled condition of the knees of his trousers. Later when Holmes, Watson, Mr. Merryweather the banker, and a policeman are waiting to surprise Clay in the bank's basement, Jones the policeman tells Merryweather about Clay's character and history.
“John Clay, the murderer, thief, smasher, and forger. He's a young man, Mr. Merryweather, but he is at the head of his profession, and I would rather have my bracelets on him than on any criminal in London. He's a remarkable man, is young John Clay. His grandfather was a royal duke, and he himself has been to Eton and Oxford. His brain is as cunning as his fingers, and though we meet signs of him at every turn, we never know where to find the man himself. He'll crack a crib in Scotland one week, and be raising money to build an orphanage in Cornwall the next. I've been on his track for years and have never set eyes on him yet.”
Clay is arrested in the act of attempting to steal 30,000 gold Napoleons with a confederate. He is certain to be hanged for murder, but in Victorian times he could have been hanged for his other felonies, including the attempt to steal the French gold. Clay is associated with the infamous Dr. Moriarty, who is Sherlock Holmes' arch-enemy. They will later engage in a death struggle at Reichenbach Falls in Switzerland, which is described in "The Final Problem."
Sherlock Holmes made a lot of money from some of his cases, and therefore he was in a position to lead an enviable life of luxury and to accept only clients whose personalities or problems interested him. Often he would work on what lawyers call a pro bono publico basis, meaning they were expending their time and effort "for the public good" and not getting paid. Holmes always seemed deeply concerned about the security of his country. He felt there was a perpetual war of good against evil and that it was his duty to do what he could to protect the innocent against the hordes of wrongdoers who threatened civilization.
When Jabez Wilson comes to him with his petty complaint, it is obvious that there is little money involved. Wilson only earned a total of thirty-two pounds, and he is obviously looking for a pro bono relationship with Sherlock Holmes, since he is unlikely to want to part with any of those thirty-two pounds. Holmes takes the case because it is unusual and also because he is already suspecting that there is something serious behind it. As is often the case, he draws on his wide experience with crime and criminals to speculate whether John Clay might be the assistant willing to work for half wages. In a later story the reader will learn that the notorious Dr. Moriarty was himself deeply involved in the attempt to steal the French gold and that John Clay was only working for him.
Other stories in which Holmes is working on a pro bono basis are the one about the Six Napoleons, the one about the Speckled Band, and the one about the Solitary Cyclist. He frequently complains that he needs constant challenges to his analytical powers to keep him from becoming bored and depressed. His reputation as a great detective and also a humanitarian often attracts humble clients who could hardly afford to pay the fees to which a consultant of his stature is entitled.
Early in that story, Holmes remarks to Watson "“You will remember that I remarked the other day, just before we went into the very simple problem presented by Miss Mary Sutherland, that "for strange effects and extraordinary combinations we must go to life itself, which is always far more daring than any effort of the imagination.”
When he's presented with the actual announcement that led Wilson into the adventure, we're told "Holmes chuckled and wriggled in his chair, as was his habit when in high spirits. “It is a little off the beaten track, isn't it?” "
This is evidence that Holmes loves the strange, the odd, the bizarre, and the apparently irrational; he takes pride in showing the rational and logical reasons behind the absurd.
Holmes is extremely interested in "all that is bizarre" or unusual. The nature of this case and its clues are definitely unique, so the interest of Holmes and Watson is peaked. Because this case is so unusual, Holmes finds it intriguing.