You don’t need Sherlock Holmes to figure out why there are more unsolved murders in the Big Apple these days.

The number of detectives in the NYPD has plunged from 5,531 to 4,992 in the past three years, a 10 percent decline.

At the same time, the citywide clearance rate for murders — cases that are considered solved — has fallen from around 74 percent in 2018 to just 56 percent this year through November, according to Colby Hamilton, a spokesman for the Mayor’s Office of Criminal Justice (MOCJ). He noted that the clearance rates keep cases tied to years; for example, a murder in 2020 being solved in 2021 keeps the case counted in 2020.

Brooklyn North investigators — who handle some of the most violent precincts in Gotham — have solved the fewest percentage of murder cases in the city this year through November, 47 percent, the MOCJ stats show.

“Dipping below 5,000 detectives is an extremely low staffing level that was last seen in the mid 1990s. Less detectives and more violent crime is definitely a dangerous combination. Per capita, detective case loads become unmanageable,” said Michael Palladino, former president of the NYPD Detectives’ Endowment Association who currently heads the National Police Defense Foundation.

“Technology is a great tool but chasing down and reviewing video footage is labor intensive, especially for short-staffed Detective Squads,” he added. “Complicating matters is the legislated revolving door of justice combined with prosecutors who’d rather be activists. It’s a complicated mess that embraces criminals and leaves innocent victims and the police stranded.”

NYC has recorded 454 murders this year through Dec. 12, NYPD data show. The department would not say how many remain unsolved.

Annual clearance rates for citywide shootings for the last three years also show an even more disturbing trend. And it comes amid another record year for gunplay — 1,795 reported shooting victims through Dec. 12.

In 2019, the figure was 47 percent. In 2020, amid the pandemic and riots in the aftermath of the George Floyd killing, the shootings clearance rate plunged to just 40%, stats show. This year, through November, that number has dropped further, to 36%.

The math is easy, experts say. Fewer detectives handling more cases amid surging crime means fewer cases get solved and more bad guys walk the streets.

“It’s a recipe for disaster,” said Joseph Giacalone, a John Jay College of Criminal Justice professor and ex-NYPD sergeant.

In April, the Post reported the mass exodus of more than 5,300 NYPD uniformed officers who retired or put in their papers to leave in 2020 — a 75 percent spike from the year before, according to department data. Many were detectives.

The exit — amid the pandemic, anti-cop hostility, riots and a skyrocketing number of NYC shootings — saw 2,600 officers say goodbye to the job and another 2,746 file for retirement.

Giacalone explained the trickle- down effect when a gumshoe hangs it up.

“When veteran detectives retire from the department, it leaves a wide knowledge and experience gap that can’t be fixed with training alone,” he said. “Every time one retires, their cases are distributed amongst the remaining detectives – increasing case loads. In 2020, we saw more homicides, more shootings, and policing riots. All of that drains resources and shelves cases. Criminals already emboldened by criminal justice reforms get a free pass to roam the streets.”

Said the NYPD on the clearance numbers: “Detectives across the NYPD work hard to achieve justice. They are often the voice of the voiceless. They never give up and never forget, no matter how much time passes. This is true no matter their overall numbers, which can fluctuate based on staffing, the department’s operational needs, crime patterns, attrition, promotion, and any number of other factors. Detectives are foundational to the NYPD’s successful intelligence-driven policing. Their ranks are renowned for the sustained credibility they establish with those they serve and for the unmatched expertise they employ in building strong, fact-based prosecutions.”