Bild newspaper has seen a report from the Federal Criminal Police Office (BKA) which shows that 1,688 sexual offences were committed by a category of migrant which includes asylum seekers, refugees and illegal immigrants in 2015.
The figures did not include the sexual assaults reported on New Year's Eve in Cologne and other cities, which are still under investigation. Police have received reports of 433 sexual assaults on that night in Cologne alone.
Government figures show that at the start of of 2015 there were 629,000 refugees and asylum seekers in the country. By the end of the year this figure had risen to around 1.7 million.
In other words the refugee population of Germany rose from a January level 0.77 percent of the German population - which increased from 81.2 to 82 million through the year - to 2 percent at the end of the year.
Most sex crimes committed by men
When comparing the percentage of refugees in the German population to their representation in sex crime figures, at first glance the statistics don't look good.
At one extreme, migrants representing 2.0 percent of the total German population would have been responsible for 3.6 percent of sexual crimes - making them more likely to commit a sexual crime than someone outside this category.
At the other extreme, migrants representing 0.77 percent of the total German population would have been responsible for the same 3.6 percent of sex crimes - making the sexual crime rate among migrants even higher.
But it's not so simple. On top of the number of known refugees is an unknown number of illegal immigrants.
Figures from the federal government in June 2015 showed police had found around 82,000 people living in Germany illegally in 2014. But the actual number is likely much higher. No figures for 2015 are yet available.
Another factor which skews the figures is that sexual offences are overwhelmingly committed by men.
Government figures from 2015 suggest that almost two men are offered asylum for every one woman, and estimates throughout the year put the number of single men arriving in the country at anywhere up to 75 percent of all arrivals.
In other words it is not surprising that a population category predominantly made up of men is over-represented in a crime statistic which is essentially the domain of only one sex.
Police raid a property in the Maghrebi quarter in Düsseldorf. Photo: DPA
A further important footnote is that crime levels vary drastically within the category lumped together as refugees depending on what country they come from.
Police statistics indicate that migrants from North Africa are much more likely to be involved in crime than those from Syria, Iraq or Afghanistan.
Meanwhile a police report released on Wednesday shows people from Syria, Iraq or Afghanistan were increasingly likely to be victims of crime during the course of 2015.
The current state of investigations in Cologne over the New Year sex attacks also shows that the large majority of men under suspicion for those sex crimes come from Algeria and Morocco.
While 57 of the 73 suspects are from those two countries, 7 are from Iraq and Syria and none are from Afghanistan. Three meanwhile are from Germany.
The BKA would not confirm or deny the veracity of Bild's figures to The Local.
‘Vast majority don't commit crime'
In general, the publicly available summary of the report shows that criminality did rise throughout 2015, but not at a rate that corresponded to the large number of people arriving in the country.
The report specifically notes that crime rose most sharply in the first six months of the year before tailing off from July onwards - this is despite the fact that the majority of asylum seekers came to Germany after Merkel said “Wir schaffen das” in late August.
“The vast majority of asylum seekers did not commit crimes,” the report concludes.
In two-thirds of crimes against human life which involved an asylum seeker, the victim was of the same nationality as the perpetrator. In 28 cases the victim was killed - with one of the victims being a German national.
According to Bild's information 240 of this kind of crime - which includes murder and attempted murder - were committed in 2015.
One particularly steep rise in recorded crime was a 50 percent increase in physical violence in refugee housing throughout the year.