I don't agree. I think Holmes' reasoning is realistic, only he has been placed by Conan Doyle in situations where strong evidence is available for him to detect. He's not a superhero, but the game is fixed in his favour. Moreover, I think it is only on rare occasions that Holmes' conclusions are based on secret evidence.
Conan Doyle himself satirised Holmes' deductions. (I should say abductions: Holmes' primary mode of reasoning is abductive: from evidence to explanatory theory.) In the little-known satire, How Watson Learned The Trick (hat-tip), Conan Doyle has a bit of fun at Watson's expense. Watson tried to deploy Holmes' famous trick of abducting explanatory facts about his interlocutors from their appearance. However, Watson's effort go awry as he fails to work out the correct causes for the traits he sees: Holmes has not failed to shave because he is preoccupied, as Watson thinks, but because his razor is being sharpened.
Does this go to show that Conan Doyle was satirising the way he gave Holmes unrealistically accurate powers of reason?
Consider the locus classicus of Holmes' personality abductions, with Watson himself as his subject in A Study in Scarlet:
“... I knew you came from Afghanistan. From long habit the train of thoughts ran so swiftly through my mind that I arrived at the conclusion without being conscious of intermediate steps. There were such steps, however. The train of reasoning ran, ‘Here is a gentleman of a medical type, but with the air of a military man. Clearly an army doctor, then. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair. He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured. He holds it in a stiff and unnatural manner. Where in the tropics could an English army doctor have seen much hardship and got his arm wounded? Clearly in Afghanistan.’ The whole train of thought did not occupy a second. I then remarked that you came from Afghanistan, and you were astonished.”There is nothing miraculous about Holmes' logic. He observes a heavily suntanned man who presents as both doctorly and soldierly, nursing an injury and looking drawn. Provided that Afghan wars were the most prominent recent British military adventure at the time in a sunny part of the world, it was not a great leap. Conan Doyle's trick here is not to make Holmes a superhero of reason, but to provide him with lots of clues to work, and some not explicitly described.
As an example of Holmes' reasoning, I find it atypical only in the opacity of the clues, Conan Doyle giving less decriptive detail than he tended to do, taking the canon as a whole.
More typical is Holmes' assessment of Miss Mary Sutherland in A Case of Identity, after Watson characteristically fails to miss all the salient clues:
"'Pon my word, Watson, you are coming along wonderfully. You have really done very well indeed. It is true that you have missed everything of importance, but you have hit upon the method, and you have a quick eye for color. Never trust to general impressions, my boy, but concentrate yourself upon details. My first glance is always at a woman's sleeve. In a man it is perhaps better first to take the knee of the trouser. As you observe, this woman had plush upon her sleeves, which is a most useful material for showing traces. The double line a little above the wrist, where the typewritist presses against the table, was beautifully defined. The sewing-machine, of the hand type, leaves a similar mark, but only on the left arm, and on the side of it farthest from the thumb, instead of being right across the broadest part, as this was. I then glanced at her face, and, observing the dint of a pince-nez at either side of her nose, I ventured a remark upon short sight and typewriting, which seemed to surprise her."
"It surprised me."
"But, surely, it was obvious. I was then much surprised and interested on glancing down to observe that, though the boots which she was wearing were not unlike each other, they were really odd ones; the one having a slightly decorated toe-cap, and the other a plain one. One was buttoned only in the two lower buttons out of five, and the other at the first, third, and fifth. Now, when you see that a young lady, otherwise neatly dressed, has come away from home with odd boots, half-buttoned, it is no great deduction to say that she came away in a hurry."
"And what else?" I asked, keenly interested, as I always was, by my friend's incisive reasoning.
"I noted, in passing, that she had written a note before leaving home but after being fully dressed. You observed that her right glove was torn at the forefinger, but you did not apparently see that both glove and finger were stained with violet ink. She had written in a hurry and dipped her pen too deep. It must have been this morning, or the mark would not remain clear upon the finger. All this is amusing, though rather elementary, but I must go back to business, Watson.Conan Doyle, typically as here, provides plenty of detailed evidence for Holmes' abductions, and furthermore these abductions are generally solid. Holmes works out a theory that provides a strong explanation for the evidence.
To be more precise and speak in Bayesian terms, Holmes' theories are causal hypotheses that would be highly likely to produce as a consequence the evidence he detects. The trick is that Conan Doyle provides Holmes with evidence that, when considered abductively, naturally produces a single, highly probable theory.
Graham Moore, in his article, argues that what Conan Doyle was doing in his satirical humiliation of Watson was this:
Conan Doyle has stacked the deck in Holmes’s favor, so to speak. Anyone in Holmes’ shoes — any reader, even someone just as brilliant as Holmes — could make any number of similar inferences that have equal chances of being correct. All Conan Doyle has to do, as the God of this fictional universe, is to slip Holmes the right ones underneath the table.I don't think that's right. It's not that Conan Doyle gives Holmes difficult clues open to multiple theoretical interpretations, then miraculously vouchsafes the correct interpretation to Holmes, while satirically putting the wrong ones in Watson's mouth. The trick is that Conan Doyle gives Holmes evidence to work with which points strongly in a single direction (or at least ends up doing so after further investigation), but to Watson he amusingly gave multivalent evidence and let Watson embarrass himself by treating it as if it pointed plainly in one direction.
Since Conan Doyle's trick is in the explanatory power of the clues he provides, rather than in the powers he affords Holmes, and since these clues are generally presented in detail to the reader, it should in general be possible for the reader to reach Holmes' conclusions. To do this can be difficult, but that is not the same as impossible.
For example (SPOILER ALERT) in The Adventure of the Three Students, Holmes identifies the student who has stolen a look at the exam paper as the only student who is tall enough to have seen the paper on the professor's desk from outside the study window:
"... it seemed an unthinkable coincidence that a man should dare to enter the room [days before the exam], and that by chance on that very day the papers were on the table. I dismissed that. The man who entered knew that the papers were there. How did he know?
"When I approached your room I examined the window. You amused me by supposing that I was contemplating the possibility of someone having in broad daylight, under the eyes of all these opposite rooms, forced himself through it. Such an idea was absurd. I was measuring how tall a man would need to be in order to see as he passed what papers were on the central table. I am six feet high, and I could do it with an effort. No one less than that would have a chance. Already you see I had reason to think that if one of your three students was a man of unusual height he was the most worth watching of the three..."Allowing Holmes his low assessment of the probability of a student entering the study on spec, there is nothing supernatural about his realising he was seeking a tall culprit. And Conan Doyle did not hide Holmes' thinking as he investigated the window:
Holmes halted and looked earnestly at the window. Then he approached it, and, standing on tiptoe with his neck craned, he looked into the room.
"He must have entered through the door. There is no opening except the one pane," said our learned guide [the professor].
"Dear me!" said Holmes, and he smiled in a singular way as he glanced at our companion.
"Well, if there is nothing to be learned here we had best go inside."Rather than hiding the key evidence, it is more like Conan Doyle is saying to his readers: "He who has ears to hear, let him hear." The trick is not to conceal the evidence but (as in Poe's most famous detective story, which influenced Conan Doyle) to hide the evidence in plain sight.
As you read the Holmes stories, don't imagine that you are enjoying a cheap trick. The reader really can solve almost all the crimes by the application of observation and reason. One's enjoyment of the stories is heightened all the more because, not only are they not tricks, but they are on the contrary and most often games set up precisely in order to be solvable!
Holmes isn't a superhero. Within the world of powerful evidence in which Conan Doyle places him, Holmes is simply solving the puzzles he is set.