> 1) What is the crime rate committed by Muslim immigrants, as compared to natives? (You suggest it's higher. How much higher?)

No, I don't suggest it's higher. I suggest that there is no obvious correlation between religion and crime rate. The lowest crime rate (by far, as in a factor of three or so below the average) is among Syrians (a predominantly Muslim country), then Iraqis (another predominantly Muslim country), then a mix of other countries (predominantly Balkan countries with a Christian majority, but also Afghanistan). Most criminals per capita come from Serbia, by a huge margin (and still make up a relatively small fraction of Serbian immigrants). The natural conclusion is that crime rate is correlated with other factors, not religion.

> 2) What's the crime rate for Muslim immigrants of low socio-economic status, compared to Germans of low socio-economic status?

Nobody has dug that deeply into the data yet. Partly because religion isn't something that's accurately known (even in Germany, only a minority of Muslims self-identified as Muslims in the most recent census, for whatever reasons; whether the rest acted out of privacy concerns or because they have been secularized, I do not know). I do know that one study (a couple of decades ago, mind you) that tried to adjust for social-economic factors between Turkish immigrants (predominantly Muslim, though you have to distinguish between Sunnis and Alevites) and Germans did not find any real measurable difference after that.

> 3) How many additional robberies/rapes/murders/etc will result from allowing in 1000 extra immigrants? (Compute by projecting from existing crime data.)

You cannot extrapolate, because so far the projection is not linear in the number of refugees. This probably has a number of reasons: for starters, violent crime appears to be concentrated within refugee reception centers as the result of people living close together with little room for privacy and under less than ideal conditions; but as the number of refugees grows, the number of refugees within reception centers doesn't. For another, other serious crime appears to be concentrated within criminal organizations that do not grow at the same rate as the number of refugees.

Most importantly, it's not like there's an actual policy option for allowing or not allowing them in. Not to put too fine a point on it, but the refugees are coming to Europe now because other countries are overflowing and can't take any more. Unlike America, Europe isn't surrounded by oceans to keep refugees out. Any credible attempt at controlling the influx of refugees has to begin with the border between Greece and Turkey, which is difficult for a number of reasons (starting with the quasi-cold war between Greece and Turkey and the fact that you cannot just let refugees drown). Even if the border could be controlled, there is no guarantee that refugees would not find a way through, say, Russia (which is already happening, after all, and it's not like Putin wouldn't have an incentive to show them the way). Any policy that assumes that you can make a major dent into the refugee influx is pure fantasy, IMO.

> Perhaps. But when the racist right points out this "botched response" (designed to hide the truth), surely you can understand why this gets them extra credibility with voters? And similarly, does anyone besides the racists have a plan to prevent another Cologne?

The racists don't have a plan to prevent another Cologne. Not a credible one, anyway. They live in a fantasyland where you can just push a button and immigration stops.

In the end, what happened in Cologne is like a mass shooting in the US: individually, a horrific event, but one for which there is no quick and easy public policy response, and in the end, does not pose a much bigger statistical risk than being hit by lightning. The best public policy response to Cologne is probably to recognize that the suspects primarily belong to existing organized crime groups and therefore to deal with these gangs. That, unfortunately, does not have an easy solution, but comes down to pretty traditional police work. The biggest problem in this area is that budget cuts have hit law enforcement pretty hard; Germany could definitely use quite a few more police officers.

In any event, the biggest public policy challenges lie in the civil sector right now: for example, teaching refugees the language and teaching them skills that make them employable is one of the biggest concerns, but there's a shortage of teachers.