Catch A thief With Pencil and Ruler

You don't need a PhD in math to figure out where the criminals live:

When a number of crimes, for instance burglaries, can be linked to the same offender, police often plot the locations on a map. The art of finding the location of the criminal’s home based on the crime sites is a key objective in what is known as geographical profiling.

Snook, Zito, Bennell and Taylor (2005) ran a competition between 11 techniques for locating offender residences. All techniques took as input the x-y coordinates of crimes (all committed by the same crook) on a map and made predictions of the criminal’s home location. There are many ways to turn these sets of coordinates into a point prediction. One stands out as exceptionally simple, so much so that it can be carried out with a pencil and ruler:

Center-of-the-circle heuristic: Predict that the offender lives at the mid-point of the line connecting the two farthest apart crime locations.

The figure up top shows the heuristic applied to a set of crime locations. Note that the midpoint is the center of the smallest circle encompassing all the crimes. Ten other methods for profiling were tested, including other “spatial distribution strategies” such as finding the centroid, harmonic mean, geometric mean, or point of minimum distance. Also investigated were computationally intensive “probability distance strategies” that involve fitting probability distributions such as the negative exponential, normal and lognormal and zooming in on maximally likely cells.

The 11 methods were applied to the crime locations of 16 UK residential burglars who had committed at least 10 crimes. Interestingly, all the strategies were run on a computer except for the center-of-the-circle heuristic, which was applied manually. We don’t know if that is because the crime-fighting software used is not clued into the power of the simple heuristic.

[T]he center-of-the-circle heuristic made the most accurate forecasts of where the criminals lived. In another study (Snook, Taylor and Bennell, 2004), laypeople who were trained with heuristic methods were as accurate at predicting home locations as a computerized geographic profiling system.

Now what would Charlie Eppes say?