COLOGNE, Germany — In early December, the Cologne police made their New Year’s Eve preparations. Drawing on the previous year’s experience, they identified their biggest worry as pickpocketing and fireworks among the crowds. So they increased their holiday deployment, to 142 from 88, concentrating on the banks of the Rhine River, where revelers traditionally gather for a giant fireworks display.

As 2016 neared on Dec. 31, however, some 1,500 men, including some newly arrived asylum seekers and many other immigrants, had instead assembled around Cologne’s train station. Drunk and dismissive of the police, they took advantage of an overwhelmed force to sexually assault and rob hundreds of people, according to police reports, shocking Germany and stoking anxieties over absorbing refugees across Europe.

“We were just pressed on all sides by people,” recalled one victim, Johanna, 18, who agreed to speak by telephone from Lake Constance, Germany, where she lives, only if her last name was not used, fearing hostility, particularly over social media. “I was grabbed continually. I have never experienced such a thing in any German city.”

Much is still hazy about that night. But the police reports and the testimony of officials and victims suggest that the officers failed to anticipate the new realities of a Germany that is now host to up to a million asylum seekers, most from war-torn Muslim countries unfamiliar with its culture.