The useleness of absolute numbers

A few days ago, I was reading an article about accidents involving cyclists. Being an avid cyclist and dealing with data and numbers of all kinds every day, I immediately noticed this sentence: “The regions most affected by accidents are those where bicycles are a real tradition: Lombardy, Veneto, Emilia Romagna, and Tuscany. Incidents tend to occur on Saturdays and Sundays, between 10 AM and 12 PM, during the months of May to October, with a peak in August.”

What seems odd to you?

After reflecting for a moment, it’s clear that the regions, days, and times when accidents are most frequent are simply those when cyclists are most frequently on the road. This is a type of error or oversight that’s fairly common among journalists, who, being less familiar with numbers, often report data without critically analyzing it.

Saying that accidents happen more frequently on Saturdays and Sundays doesn’t provide any useful information, because those are the two days when cyclists are on the roads the most, and thus are also the days with the highest risk of accidents (the same logic applies to the most popular months and times of day). In this case, the raw data doesn’t make any sense unless it’s somehow “cleaned up.”

What needs to be done in such cases is to have a “benchmark” to compare the results (what’s referred to as a “benchmark” in English). In the case of our article, a simple benchmark could be the ratio between the number of accidents and the number of cyclists on the road that day. This means that, instead of looking at the absolute number of accidents, we look at the relative number. By doing this, we give each day of the week the same “probability” of being the most dangerous day, removing the natural advantage that days like Saturday or Sunday have due to the higher number of cyclists.

Let’s take a look at the table below (note that the numbers are fictional):

If we consider the absolute number of accidents, Sunday is the most dangerous day with 60 accidents. However, if we use the correct benchmark, dividing the number of accidents by the number of cyclists on the road, the most dangerous day in relative terms becomes Thursday, with a ratio of 1.5%.

A similar example of this concept is found in marketing: the effectiveness of an advertising campaign targeted at a certain group of people is evaluated not only by looking at the absolute value, but by comparing it to the results of a “control group” – a group of customers who are not exposed to the campaign. Only by “relativizing” the absolute results can we determine whether the campaign was effective or not.

So, when you come across statistics and conclusions like this, pay attention to the data and ask yourself whether they’ve been properly analyzed or not, because otherwise, they might not make any sense.

And anyway, to stay safe and avoid articles like this, when you go out cycling, be careful around cars!