Speed Cameras, Causality and Chance

Features

  • Author: Dr Jennifer Rogers
  • Date: 17 Feb 2015
  • Copyright: Image appears courtesy of iStock Photo

A town in the UK was worried about the number of accidents that they were experiencing on the roads. The local council offered to install some speed cameras, but the important decision of where to place the speed cameras needed careful consideration.

thumbnail image: Speed Cameras, Causality and Chance

A sensible strategy for choosing the locations of the speed cameras was proposed as follows: looking at a number of candidate sites over a year and monitoring the number of accidents at each. Those sites with the highest number of accidents would then be assumed to be accident hotspots and speed cameras would be placed there. Table 1 shows the number of accidents in Year 1 at the 30 candidate locations and we can see that the highest number of accidents in any one location was 9 and that this occurred in 4 different places: locations 7, 18, 21 and 23, with the total number of accidents over the year being 151.

Location Number of Accidents (Year 1) Number of Accidents (Year 2)
1 7 2
2 7 9
3 8 0
4 1 6
5 8 8
6 6 9
7 9 2
8 0 4
9 4 9
10 4 0
11 6 4
12 3 5
13 1 4
14 1 8
15 0 0
16 4 0
17 6 0
18 9 5
19 3 0
20 6 0
21 9 4
22 6 1
23 9 6
24 3 6
25 5 1
26 8 4
27 0 2
28 7 4
29 3 8
30 8 5
Total 151 116

 Table 1. Number of accidents in each candidate location in Year 1 and Year 2.

Speed cameras were subsequently installed in these locations and then the number of accidents over the year that followed was monitored to measure performance. Looking at Table 1 again, we see that every location where a speed camera was installed saw a reduction in the number of accidents and additionally, the total number of accidents in the town also came down. This would seem to suggest that the speed cameras have been successful in driving down the number of road traffic accidents.

But here is where I tell you that this demonstration has been done completely using random numbers and so all of the numbers in Table 1 have been generated by chance. A random number generator was used to generate a number between 0 and 9 independently for ‘Year 1’ and ‘Year 2’ for each of the ‘candidate locations’. Those locations with more accidents in Year 1 didn’t have a higher probability which was then reduced after putting speed cameras in place, there were no speed cameras! And herein lies the dangers of mixing up causality and chance. Being presented with just the data in Table 1, it was straightforward to draw the conclusion that there was a causal relationship between speed cameras and the number of road accidents in a given location and we concluded that the speed cameras were the cause of the observed reduction in accidents. In fact, this apparent causal effect was all just driven by chance and can be explained by something called regression to the mean [1,2].

Regression to the mean is the technical term for things evening out and says that, on average, every observation is likely to be somewhat close to the expected value. That is, the ordinary and expected is what happens more often than not and the extraordinary is just a rare, random fluctuation. The principle of regression to the mean is that luck fluctuates, but over time it evens out. Consequently, if we have something that is extreme, either high or low, the first time round, it will tend to be closer to the average the second time round. Similarly, if something is extreme the second time round, then most likely it will have been close to the average the first time, which we do also see in Table 1. We will sometimes just observe random highs and random lows and so when these do happen, we shouldn’t necessarily put too much undue emphasis on them.

We see regression to the mean frequently in sport and one of the best examples is called the Sports Illustrated curse [3]. This so called curse says that a player or team featured on the cover of Sports Illustrated is likely to then have a disappointing week or even season after. But let’s think about this in more detail for a moment. A player or team is only likely to feature on the cover of Sports Illustrated when they are at the very pinnacle of their game. They are only likely to make the cover after exceptionally good performance, which is a combination of both skill and luck being on their side. After this high, we would expect – by regression to the mean – that their performance return back down towards their personal average. So what could be interpreted as a dip in performance, is actually just their performance returning back to normal following a random high.

We generally are surprised by unusually good or bad performances in sport. We start to wonder what’s going on when a pretty average team unexpectantly wins a few games in row or a supposedly good team all of a sudden go on a losing streak. But let’s think about when sports teams have bad patches more closely. There does tend to be pretty major casualty in these scenarios and that’s the coaches/managers. Bad patches tend to be the time when teams sack their managers, with the new manager then seeing a short-term bounce back and improvement in performance. But this can be misleading as research has shown that you typically see the same pattern of bounce back if you don’t change the manager [4]. This improvement in form can be attributed to regression to the mean and the bounce back is simply a random low moving back to the average which, importantly, would have been seen irrespective of the manager being replaced. These short term-dips in performance are expected and then the return to ordinary performance is what makes the new managers look good.

It should be said that the purpose of this article is not to say that speed cameras don’t work or that sports teams should never sack their managers. Not all extreme observations, whether high or low, are merely random fluctuations caused only by chance. But I do hope that this article will make you take a step back and think about the underlying processes next time you do see something that appears shocking and unexpected.

[1] Barnet AG, Pols JC and Dobson AJ. “Regression to the mean: what is it and how to deal with it.” Int. J. Epidemiol. 2005; 34 (1):215-220. doi: 10.1093/ije/dyh299
[2] Galton F. “Regression Towards Mediocrity in Hereditary Stature.” The Journal of the Anthropological Institute of Great Britain and Ireland 1886; 15:246-263.
[3] http://www.sicurse.com/
[4] Ter Weel B, “Does manager turnover improve firm performance? Evidence from Dutch soccer, 1986-2004,” De Economist 2011; 159(3):279-303.

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