To those who were wondering if Mycroft would be any good, since he just uses his “cold, logical brain”, someone has to put him in the loop. Real investigations are an information firehose. Dozens of police door knocking the neighbours, dozens identifying and collecting CCTV camera recordings, watching hours of footage, dealing with incoming calls from the public who heard that Betty had said that Fred wasn’t home that night.
Managing and distilling the firehose and sending the information up the line is a Systems issue, not a logic or an intelligence issue. They build in review processes so some underling’s missing something doesn’t wipe out the investigation. The logical, intelligent Mycroft would say “set up a system” just like we do already. One mind can’t do it alone.
There are 4 key problems with the enchanting idea that a brilliant amateur can do stuff the police can’t.
The first is that the process is not one of coldly logical deduction, as endless shows have trained us to think. It is called abduction (nothing to do with kidnapping) and it essentially means playing the odds. Google the concept. The notion that only the exceptional eccentric genius can do it is silly. Police are not the stupid plods this genre has to assume them to be.
The second is that fiction is populated with a finite number of “Clues”. The Chekhov’s Gun principle requires that each fact mentioned can have only a binary significance. It must be a Clue, or a Red Herring. If the writer tells us a Gaulois cigarette butt was found, then it can be nothing other than a clue to the offender, or a misdirection by the offender to cast blame on someone else. In a real investigation, the world is populated by random shit for the most part. Random cigarette butts left by someone who has nothing to do with it, random baseball cap blown in by the wind, and so on. The is no God-like author to predigest all of this into Clues for the police.
Third, remember that in the case of the vast majority of murders, it is pretty clear from the outset who did it. The argument is whether it was self-defence or provocation or the like. In many of these cases, the offender bolts, so the investigation is more about finding where the suspect is physically located.
Finally, there is no battle of wits between the detective and the offender. The criminal, no matter how smart, has to act in real time with imperfect information, and has to take a series of significant risks the outcome of each of which is not foreseeable. The police do not have to act in real time, and can take as long as they want to unpick all the bad decisions from the good ones made by the crim. The crim can only guess that the couple in the house next door are asleep, that there is no log in the security system of which he is unaware, and trying too hard to find out in advance is itself incriminating. As an example, a local criminal was found googling “pleading the fifth” on the night his wife disappeared, in circumstances where he was trying to say he had no idea what happened to her.
I would leave with a slightly tangential observation on a point someone made above, that perhaps Mycroft might not like stifling police procedures. Those procedures exist for a reason. The point of investigations is not to persuade the investigator, it is to persuade a jury, and all the detail of recording and paper trail confirmation is designed with that in mind. Anyone who does not get that does not have their head in the right place to be anywhere near investigations.
TD;DR. This genre of entertainment is undoubtedly appealing, but for reasons that have nothing to do with its closeness to reality. It is at its heart Scoobie-Doo for grown-ups.