November 2013 saw an exceptional number of people killed while riding a bicycle on London's roads. In the space of two weeks, six people were killed in incidents involving coaches, buses or trucks. This unusual concentration of tragedy prompted inevitable media attention and calls for action ranging from banning HGVs from peak time travel to compulsory helmets and high-vis clothing to segregation of bicycle and motorised traffic. The rhetoric surrounding discussion referred to 'carnage on the streets', warnings to 'be careful out there' and even calls to stop cycling entirely. More level-headed commentators were urging campaigners to "raise awareness of cycle safety".

So what is a greater awareness of cycle safety? And does visualization have a role to play? A start point perhaps might be to convey a realistic sense of the risks involved in cycling. This is important because cycling is by and large a discretionary activity and the consequences of not-cycling can be significant. Indeed, most studies that have investigated life-long risks associated with cycling suggest that premature death is more likely to result from not cycling regularly than from doing so.

So how do we understand the risk associated with travelling on roads when on a bike? And from a visualization design point of view, how do we show it? Can we do so in a way that reflects the true rarity of incidents while also recognising the tragic consequences for those directly affected by collisions on the road?

One approach might be to examine how risk changes over time:

Here we show, in a conventional manner, the number of serious injuries (blue) and deaths (orange) of people riding bicycles in the Greater London area, broken down year by year. Collectively known as KSI statistics (killed and seriously injured), these types of figures are routinely used by transport authorities to assess the danger of transport networks both geographically and over time.

Of course this isn't risk, but rather the number of incidents involving people riding bicycles. It needs to be compared with the total number of trips and riders to understand the likelihood that any given journey might involve some serious incident:

By comparing the number of trips involving serious injury or death with the total number of trips, perhaps we have a better sense of how risk changes (risk of death has been declining steadily over the last two decades, but can change by a large proportion due to low absolute numbers). Risk of serious injury had remained broadly static since 2004 but has shown a slight increase in the last couple of years. At the time of writing, 2013 figures for injuries are not yet available.

If our focus is on injury to cyclists or fatal incidents, than such graphics quite reasonably draw our attention to the fact. But do they convey risk adequately? As indicated by the vertical axis label, the bar heights are scaled between 0 and 4 incidents per million trips. Perhaps we can read those historic probabilities with sufficient accuracy for the chart to be informative, but are we left with a realistic view of the risks involved?

The chart, and hundreds like it, suffer from what is, in the medical literature, referred to as denominator neglect. That is, when considering a risk of 1 / 1,000,000, we focus on the 1 and not the million bit of the fraction. The salient elements of the chart represent the injuries (blue bars) or deaths (orange bars). All those other incident-free journeys are implicitly referenced only in the title and small text of the vertical axis label. Not only is this 'denominator' virtually invisible in the chart, it is many many orders of magnitude greater than the figures we can see. If you work in a transport authority wishing to assess and mitigate serious road incidents then maybe the incident-free journeys are not your primary concern. If you have been affected by a road death or serious injury the invisible bits of the chart are likely to be the least of concerns. But for those trying to assess whether we are 'safe' riding bicycle on the road, the denominator is crucial.

So how do we give greater prominence to the denominator? One solution might be to show the incident-free journeys on the same chart:

So the largely 'safe' journeys are now a little more prominent as a green line superimposed on the 'dangerous' bars. But their magnitude is so much greater than the incident bars that we are forced to use a different vertical scaling indicated by a secondary axis on the right of our chart. To fit both sets of the figures on the same chart we have hugely compressed the safe journeys in comparison to the dangerous ones. More denominator neglect.

A human scale of representation

If it's an intuitive sense of risk we wish to convey, perhaps a more human-centred approach might be more applicable. Borrowing from the early 20th century isotype design, we could represent a journey made by someone on a bicycle in a more pictorial fashion:

We could use a bicycle as a symbol, but we care about people here and informing people's perception of risk. It also seems fitting, when considering the road deaths with tragic consequences for family and friends that we are reminded that this is something that affects real individuals.

In 2013 in London, 14 people who were riding bicycles at the time, were killed on the road. This is exactly the same number of people who were killed in 2012, also riding bicycles. You can read these figures from the right hand orange bars in the charts above. But at a more human scale, we might choose to represent those incidents using an array of pictograms:

This gives us a basis for representing larger groups of people. Here, for example are 100 individuals:

In 2012 in the greater London area, 657 people were seriously injured when riding bicycles. Let's represent them with a blue colour so we can distinguish them from those who were killed and those who made incident-free journeys:

657 serious injuries to people riding bicycles in London in 2012

If we are going to show all the journeys made in London including those 14 fatalities, we are going to have to squeeze many more people onto the page. In the graphics that follow, the each of the figures will be coloured either black (incident free), blue (journey where the rider is seriously injured) or orange (person killed while cycling). They will be coloured in proportion to the best estimates for 2012 incidents and trip data.

On average, 25,000 trips on a bicycle were made every hour in Greater London. That average includes the night-time, snowy Sundays in January as well as busier rush hour riding in June. Here are those 25,000 people making a journey within a one hour period. It's now looking like quite a large crowd:

If you are looking for blue or orange figures in that crowd, you won't find any, because the number of serious injuries per 25,000 journeys is way less than 1. In fact, in 2012, the year that saw the largest number of serious injuries to people riding bicycles in the last two decades, one third of a million incident-free journeys were made for every one involving a serious injury. So here are those 0.3m journeys, one of which is coloured blue to represent that single serious incident:

324,999 incident free journeys and 1 involving serious injury

Each block represents 25,000 incident-free journeys, as we did in the previous figure. So 13 blocks represents 325,000 journeys. Did you spot the single serious injury in blue? It was in the bottom-right block, three rows of people down about half way along (if you really want to find it, here is a high-resolution version of the graphic).

So if you were taking a typical bicycle journey, riding in an average fashion in average conditions, the chances of ending up in hospital with a serious injury are about the same as randomly selecting that one blue pixel in among all the grey ones in that image (1 in 333,330); or in English: unlikely.

But we're not finished yet. What about the chances of being killed on London's road when riding a bike? This is certainly what has occupied the minds of many in response to recent fatalities and media coverage. We can represent all bicycle journeys made in 2012 using the same approach, this time representing the 14 fatal incidents in orange. To help navigating round this graphic, we will group the figures in blocks of 13 as above, each representing 0.3m journeys. Spotting the 14 orange figures and the 657 blue figures is left as an exercise for the reader.