Safety in Numbers – Correlation or Causation?

Correlation does not always equal causation

In a past life, I trained as a Scientist (a Chemist) and I’ve always been drawn to analysis of data. The son of a Pharmaceutical Researcher and a Public Health professional, I was brought up with “correlation =/= causation”. Sometimes, though, you have to say that a correlation is so strong, and seen so repeatedly in so many different circumstances independent of other factors that the link is almost certainly causative. Despite what people may tell you, science is never certain about anything – the scientific method means that something is always open to being disproved – e.g. the speed of light being the ‘fundamental speed limit’ is still open to being challenged by stray Neutrino’s travelling faster.  So it isn’t possible to say anything ‘for certain’, but here’s a great case study for you.

Safety in numbers (S/N)

I blogged about this here, but my argument was a bit weak and incomplete. I intend here to show the full weight of the argument, and why I think that S/N is ‘the real deal’ – by which I mean that, all other things being equal, more cycling will improve the safety per cyclist.

What is ‘Safety in Numbers’?

S/N is the idea that as you increase the numbers of a group of road users on the road (cyclists or pedestrians), that the safety per person using that mode improves – i.e. if you double the number of people cycling, you do not double the number of accidents – the number of accidents either rise very slightly, stay stable, or counter-intuitively, fall. I am most interested here in looking at the case for S/N in cycling as this is the evidence I’m most familiar with, and it’s easier just to use one example to keep the blog concise.

How does it work?

There are a number of possible mechanisms for S/N; it could be that increased numbers mean that other road users are more used to looking out for the more common road users and anticipating their movements; it could be because the infrastructure is built to better cater for the more common road users; finally, it could be that more people cycling, or walking, means less cars and therefore less interactions which could lead to a collision of enough severity to be recorded.

The evidence:

NB – it should be noted that there is a general trend of falling death rates on our roads, as we learn to keep people alive better and cars become more collision friendly.  The data below should be seen in that light.

1. Cycling in 14 European Countries, 1998:


There is a clear relationship here, showing that those countries with the highest levels of cycling have the lowest numbers of fatalaties per 100,000,000 km.

2.  Levels of cycling against fatality rates – UK 1950-99

Cycling in UK 50-99

a)  Between 1950-52, cycling levels rose and fatality rates fell

b) Between 1952-1972 there’s a pretty clear relationship showing that less cycling correlates with higher fatality rates.

c) Between 1973 and 1999 fatality rates fell despite cycling levels remaining roughly constant – I believe this to show a marked improvement in our ability to keep people alive, as a similar effect is seen in driving accidents.

3. Levels of cycling against fatality rates – Netherlands 1980-99

Cycling in NL 1980-98

It’s commonly thought that cycling was always common in the Netherlands.  Certainly, similar levels of cycling to the UK were common until the 60s (ie very high), but they then fell, and have been recovering since the late 70’s, as can be seen above.

This graph shows very clearly that as distance cycled per year increases, safety improves.  However, there is a major confounding factor here – the Dutch changed path in the late 70’s and went all-out to promote cycling.  This led to a program of cycle track building, closing of roads to cars but not cycles etc, building a fit-for-purpose, safe cycling network which will have also had an effect.  So are numbers of cyclists increasing because it’s getting safer to cycle?

Numbers from safety?

It is also commonly argued that it is ‘numbers from safety’ not ‘safety in numbers’; i.e. that more people cycle where conditions are safer to cycle and this accounts for the evidence usually put forward for the S/N effect rather than increasing numbers driving the improvement in safety. It is clearly true that the number one reason that people do not cycle currently in countries such as the UK is a perception of cycling as being dangerous, and the lack of infrastructure to allow people to cycle in safety and comfort. So, is it an increase in numbers cycling that improves safety, or the other way round?

The evidence above cannot differentiate between infrastructure being implemented leading to ‘numbers from safety’ and a true ‘Safety in Numbers’ effect.  What we need is an intervention which will affect cycling numbers in a short period of time without a change in levels of infrastructure.  A perfect example of this is introducing a helmet law and enforcing it – it’s well established that helmet compulsion laws lead to a collapse in numbers cycling.  What happens to safety in the immediate aftermath of these laws being brought in and enforced?

If safety is coming from numbers, independently of infrastructure, we would see that accident rates and deaths per cyclist increase as the number of cyclists decreased.  If this effect was observed over a short time period, where infrastructure cannot be expected to be implemented or taken away, then it is reasonable to assume that it is caused by the change in number of cyclists directly, by whatever mechanism.

1. NZ Helmet Compulsion Law – Introduced 1994

NZ helmetlawsafety

(Graph from here:

This is a fascinating set of data.  Over the course of 3 years, the number of people cycling halves, but the total accident rate stays roughly stable (meaning an increase in risk per person) – and then starts to increase further.  Safety in numbers in reverse – as the number of cyclists fall, the risk per cyclist rises.

2. Australia Helmet Compulsion Law – 1991

(Data lifted from here:


Again, numbers of injuries per cyclist rose as the amount of cycling decreased.  I believe that this is strong evidence that safety does come from numbers of cyclists, as well as infrastructure and other measures.

NB – you’ll note that the data in the two studies above is not in the same units as the graphs at the top.  Both final sets of data measure injuries, not fatalities.  However, I believe that to a good approximation injuries will be proportional to deaths over a short time period – over larger periods of time, as noted above, we are becoming better at keeping people alive; but all of these studies look at periods of time of a decade or less*.


1.  The ‘Safety in Numbers’ effect exists in cycling and as numbers increase, all other things being equal, safety per cyclist improve as shown repeatedly in different studies.

2. There may well be a ‘numbers from safety’ effect where good quality infrastructure and lower speed limits are in place, but safety in numbers exists independently of these measures.

3. The existence of this effect should not be taken as an excuse not to build infrastructure as this is likely to improve safety further.

4.  Helmet compulsion is a poorly considered idea which reduces levels of cycling with downstream public health effects from less people exercising and increases the risk of remaining cyclists having an accident.


My view of how science works is that it doesn’t matter who is making an argument; an argument should stand or fall on its own merits. So don’t take my word for what’s below – I’m happy to have my ideas challenged. Comment away!


*Fatalities may be slightly reduced by the increased wearing of helmets, but this would be a separate effect from looking into Safety in Numbers



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9 responses to “Safety in Numbers – Correlation or Causation?

  1. I wonder whether the people who advocate the safety in numbers effect as a cycle promotion policy perhaps confuse it with the critical mass effect, which I think is entirely different. Perhaps one follows from the other – that incremental increases produce incremental improvements until a tipping point is reached. Of course in nuclear physics, where the concept originates, the key engineering problem is how to control the transition – possibly not a useful allegory for cycling.

    You can see critical mass effect most obviously in the monthly rides of the same name, but in the real world it was also seen on a daily basis in factory towns as shifts changed. That scene is now pretty rare, but I remember in the 60s and 70s seeing the dockyard workers coming out of the Portsmouth Naval Dockyard literally in their thousands, on their bikes, and no motor vehicle could stand in their way. Portsmouth of course has a particular geography – very contained, quite small, flat and densely populated and built – which favoured cycling, indeed still does, although in those days another factor of course was the relative unaffordability of cars even for the skilled working class. The effect was in fact still visible when I paid a visit in 1988 (the day of the Lockerbie Bombing) to the Trident submarine yard in Barrow in Furness. By then I am sure every worker had his Mondeo outside his home, but it was useless for work as the shipyard wasn’t geared up for parking.

    I don’t think we will see cycle safety and cycle numbers working together in that virtuous circle again because the effect is too gradual, and safety in numbers ignores the thing which really holds back mass cycling – riding a bike in this country is actually, in rational objective terms, fairly safe, probably safer than walking, safer than playing football or tennis, or DIY. The problem is that it doesn’t feel it, either in terms of how it feels when a novice tries the road and is terrified, or from media treatment which treats cycling as somehow a daring, sporty, risk-taking pursuit, requiring the right clothes and the right equipment and, of course, head protection. You only have to look at the poster adverting the current Bike Show in London to see how the industry chooses to portray itself. I see absolutely nothing of myself in their image, and yet I probably ride far more miles than most of the types they portray just riding to and from work or the shops.

    • Thanks for commenting – I always find it fascinating to hear about how popular cycling was in the UK – I’ve heard of similar scenes to what you describe in Reading in the 50’s and60’s!

      I understand the way you’re describing the ‘critical mass effect’ as cycling levels hitting a level that suddenly causes a large improvement in safety.

      I would speculate that there are are several explanatory mechanisms for SIN working together: less aggressive driving and more care taken by drivers as they are more likely know a cyclist; drivers better able to predict cyclist behaviour through greater exposure; cyclists being more likely to be more experienced, and gaining from herd knowledge about cycling; and, over a longer timescale, town planners more likely to ride bikes and therefore better able to plan safe, usable infrastructure. You’d expect all of these factors to be a small incremental increase in cycling levels produces a small incremental improvement in safety.

      Critical mass effect as you describe above, I’d argue, is just safety in numbers at the extreme – where bikes dominate the road, safety for cyclists (and everyone else!) is assured..

  2. The functions look pretty much like 1/x, so it seems the decision to divide all by distance ridden swamps more interesting information in the data. Leaving aside the problem in estimating the total distance of km ridden in the county, would you mind to present the data in more meaningful units, like per person or per modal split share of bicycles for that time based on number of ways (I know that may be difficult to get)?

    • Hi Ingo;

      re 1/x; I agree, it looks like total numbers killed cycling are remaining fairly constant with increasing amounts of cycling – i.e. that risk per mile is inversely proportional to the number of miles cycled.

      I used deaths or injuries per mile here as the most relevant available statistic for this type of analysis – I merely wanted to prove the existence of Safety in Numbers as there’s been some discussion about this amonst cycle campaigners. All of the data I drew upon here was freely available on the internet – it should be relatively straightforward to find data for absolute numbers of deaths and present them per 100,000 of population if you were interested in doing that. Sorry, I don’t have time to do this for you, time is short 🙂 I would be interested to read any results of this kind of analysis.

      There was a famous case here in the UK where politicians presented the UK as being safer for cycling than the Netherlands, by presenting data of cycling deaths/100,000 population. It should be clear that there is an awful lot more cycling in the Netherlands – and many more older and younger (and therefore more vulnerable) people cycling in the Netherlands.


  3. Pingback: Road safety versus saving lives | movementsci

  4. Within the last year I changed my commute from one where I rode or drove about 10 miles out into a suburb (shared with few bicycles) to one where I ride (never drive) about 7 miles into an urb. Of the routes that I ride, one in particular has a high bicycle ride share during (summer) commute hours, perhaps as high as 33% at some intersections. I base my estimate on counts of people on bikes waiting to go, versus the length of the light — 48 seconds provides enough time for about 24 cars, versus the 12 people that I sometimes count waiting on bicycles.

    With that many people on bicycles, I see in-the-small effects for safety-in-numbers. Anyone wishing to turn right (in the US — corresponding in the UK would be left) was quite likely passed on the right by a bicycle while waiting in line at the current or previous light, and if they reached a bicycle-passing speed, passed several on the way to their turn. Most of the lights have a second or two of early walk signal to ensure that crossing pedestrians are clearly visible, and very many people on bikes also start their motion on the pedestrian walk signal or even as the cross-traffic goes red, thus making them more visible to left-turning (UK, right-turning) traffic. What I observe would not require any long-term learning; 15 seconds of heightened awareness is all that is required.

    Here’s a short video example:
    It ought to be abundantly clear to all the cars in that bunch (more than are likely to clear the light in one go) that there are bicycles on the right, not only did I pass them, so did the guy behind me.

    I have a good example of “early go” in slow motion here. By the time the light is green everyone is well underway, though not even the most aggressive cyclist in the bunch has reached the intersection-proper.

    But because we are in motion and because we are so many, we are more visible. Arguably, the guy in front is putting himself at somewhat greater risk from illegally-late-turning traffic, but he also provides greater protection for all of us behind; if each passed through the intersection alone, we would need to provide our own visibility.

    • Thanks for your comment – yes, I agree that ‘early go’ – either formal or informal – is a natural thing to have at lights where there are conflicting movements (although of course this only helps those who arrive at the light when it is red..).

      I agree that this kind of awareness change is likely a key component of the safety benefit of ‘Safety in Numbers’ – when I was in Copenhagen (where the streets are awash with cycles) I was astounded at how good drivers were at looking in their mirrors before turning right. Of course they also have legal differences to the UK (which is one of only a few countries in Europe not to have ‘Strict/Presumed Liability’ rules).

      There are various other factors likely to be at play – the worst driving I see can only be explained by drivers seeing those on bikes as some kind of deviant, lower forms of life that can be knocked down with impunity. This mindset cannot continue when people have close friends or family who cycle regularly on the roads.

  5. Thanks for the very useful analysis Ben, which confirms my own thoughts pretty much, both as to the existence of SiN and the way it works. I also like the micro example given in the comments. I see this for myself in the difference in driver behaviour between central London and Birmingham.

    One particular thought – doesn’t the rise in casualty rate in Britain from 1952 to 1972 pretty much confirm the theory that ‘pure’ SiN exists? As far as I’m aware (and I grew up in that period!) there was no mass removal of cycle infrastructure over that time.

    There was growth in motor traffic of course, but it should be easy to correct for that by simple division, to give Fatalities/bvkm ridden/bvkm driven. I’d be surprised if the graph didn’t still slope the same way.

    • Thanks Phil.

      I think the relationship is slightly more complicated than risk being directly proportional to motor vehicle mileage (Smeed’s Law says that each additional vehicle mile is less dangerous than the one before…so e.g. doubling the number of vehicle miles will increase KSI’s but won’t double them) but as you say it must be possible to correct for this..

      There is also the additional complication of improving healthcare..but again there surely must be a way to correct for this. When I get a chance I’ll chuck some numbers in a spreadsheet and see what pops out.

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