"The Red-Headed League" is a fairly typical Sherlock Holmes tale in which the narrator, Dr. Watson, sees everything the great detective sees but does not understand his friend's deductions, conclusions, or many of his actions until the end, at which point Holmes explains everything in detail. This explanation occurs in the last few pages of the story, beginning with these words:
"You see, Watson," he explained in the early hours of the morning as we sat over a glass of whisky and soda in Baker Street, "it was perfectly obvious from the first that the only possible object of this rather fantastic business of the advertisement of the League, and the copying of the 'Encyclopaedia,' must be to get this not over-bright pawnbroker out of the way for a number of hours every day."
The reader has been mystified along with Watson up to this point and is happy to learn about the detective's thought processes after having participated in imagination in the initial interview with Wilson, the resulting investigation, and the dramatic arrest of the master criminal.
Holmes explains that the assistant's fondness for photography made him suspect that he was up to something in the cellar. He made inquiries about the assistant and found that he was dealing with "one of the coolest and most daring criminals in London." The only thing he could imagine John Clay doing in the cellar was digging a tunnel. When he and Watson walked around the corner and saw a branch of the City and Suburban Bank, Holmes was sure that Clay was digging a tunnel from the pawnbroker's shop into the basement of that bank.
One of the most striking clues was the condition of "Spaulding's" trousers. Holmes called at the shop pretending to want directions to the Strand and observed that the assistant's trousers were "worn, wrinkled, and stained."
"And how could you tell that they would make their attempt to-night?"
"Well, when they closed their League offices that was a sign that they cared no longer about Mr. Jabez Wilson's presence--in other words, that they had completed their tunnel. But it was essential that they should use it soon, as it might be discovered, or the bullion might be removed."
The burglars chose Saturday night because they knew Wilson would be gone all day Sunday, and they would need a lot of time to move the gold through the tunnel into the pawnbroker's shop, then get a horse and wagon and load all those boxes as discreetly as possible and make their getaway. No doubt they would do the loading in broad daylight rather than trying to be secretive. After all, "Spaulding" was an employee of the pawnbroker and would be known to the neighbors and beat policeman.
When the Holmes and Watson are waiting with three other men in the dark vault for Clay and his partner to arrive, the bank director Mr. Merryweather explains that there are 30,000 napoleons in the crates.
"The crate upon which I sit contains 2,000 napoleons packed between layers of lead foil."
This means that there would be fifteen very heavy crates of gold to be dragged through the tunnel by the two men crawling on their hands and knees, with one of them pushing and the other pulling. The distance from the bank to the pawn shop was considerable. So Holmes was right in calculating that the burglars would almost certainly have to make their move on that Saturday night.