Part 1 - The Hot Spot Randomness Trap.

Tell me if you've heard this one before:

Your agency's crime analyst detects an uptick in crime in a few block radius over the past few weeks and presents it at your Compstat meeting. Your agency likes to jump on these quickly, so the area gets flagged as a "Hot Spot" and patrol officers are directed to make patrols of the area throughout their shift. And you make sure the officers document their patrols in the hot spot patrol file so you can have some good stats to report to city council.

The result a week or so later? You check the file and see that the patrol officers did a lot of patrols. And what do you know, crime in the area is down. The hot spot has been extinguished. Proof that your hot spot patrol strategy was effective, right?

Wrong.

While some crimes can be linked to specific locations, a lot of other crime has a degree of geographical randomness(1) to it. That randomness means that sometimes there will be groupings of crimes that have absolutely no connection to each other. If you randomly threw 100 darts at a map of your city, sometimes you would get a few darts that would land very close together. That grouping would be the result of pure randomness. Just like a crime heat map can sometimes show a spike of crime in a certain area even though the crimes are not actually connected.

I know what you're thinking - if the crime spike was just the result of a random distribution, then why would it disappear when you targetted it for patrols? Well, probably because the hot spot wasn't even a real hot spot, and the random distribution of crimes just happened to land somewhere else the next week. That "spike" in crime would have disappeared if you had made patrols or not.

This is called regression to the mean, which is a statistical phenomenon where, if a random process results in an outlier, then the next time that process happens the result will probably be closer to the average. We see this effect everywhere.

For example, if the weather is colder this week than the average temperature this time of year, then next week it will probably closer to the average temperature. If it is hotter than average this week, then next week will probably be closer to the normal average temperature. That's exactly why averages exist - over long periods of time the temperature in a certain month is usually about the same. We don't claim to have any influence over the weather from week to week, but when regression to the mean is observed in something we think we have influence over, we love to construct narratives to explain how we caused it.

As described by Nobel prize winning economist Daniel Kahneman in his book, "Thinking, Fast and Slow", humans like to create stories to explain what we are seeing. Imagine a firearms instructor dealing with recruits on the range. The instructor might think that the recruit who performed very well on the first shooting test but did worse on the second test must have "choked" because the instructor's praise put too much pressure on him to continue his high performance. And the instructor might think that her chastising of the recruit who did poorly on the first shooting test must have been effective because the recruit did much better on the second test. Should the instructor conclude that her praising good students makes them worse and chastising poor students make them better? Or were these two recruits actually just both average shooters who got lucky/unlucky on the first test and regressed to the mean on the second test?

So the stories that we like to tell ourselves (and probably the mayor, the police board, and the community) about how our hot spot patrols reduce crime could be just that - stories. It is very possible there wasn't a hot spot at all. It could have been just a random collection of crime that would have gone away if we had done nothing. We could be literally chasing ghosts and congratulating ourselves on our "intelligence-led policing" (which is slightly ironic).

I'm not saying that targeting hot spots doesn't work. It has been proven to work (macro study linked below). But that only matters if what you are targeting is an actual hot spot. And for that you need enough data set over a long enough period of time and within a tightly contained geographical area that you are not looking at a random outlier.

Does this mean there is no such thing as legitimate hot spots that develop rapidly? Of course not. But if you are looking at a small data set over a short period of time, then you have to be sure that the crime spike is not the result of randomness. Small, randomly generated data sets can be vulnerable to extreme outcomes. If you toss a coin 5 times and it comes up heads each time, you probably shouldn't conclude that you have a rigged coin. Toss a coin 100 times and if it comes up heads each time, then you almost certainly have a rigged coin. The smaller the data set, the more likely your conclusion is wrong.

Likewise, searching for an obligatory monthly hot spot by using weekly fluctuations in the geographic distribution of crime and varying how big your "hot spot" is so that it captures enough crime to qualify as a hot spot, and then making officers mindlessly patrol that area is probably a waste of resources, at least most of the time.

PART II - What are effective intervention strategies in hot spots? (Spoiler alert: it isn't just random patrols).

Note 1: Yes, I know 'random' isn't the technically correct word, but it works for the purpose at hand.