Smeed's Law, named after R. J. Smeed, who first proposed the relationship in 1949, is an empirical rule relating traffic fatalities to traffic congestion as measured by the proxy of motor vehicle registrations and country population. The law proposes that increasing traffic volume (an increase in motor vehicle registrations) leads to an increase in fatalities per capita, but a decrease in fatalities per vehicle.
Smeed also predicted that the average speed of traffic in central London would always be nine miles per hour, because that is the minimum speed that people tolerate. He predicted that any intervention intended to speed traffic would only lead to more people driving at this "tolerable" speed unless there were any other disincentives against doing so.
His hypothesis in relation to road traffic safety has been disputed by several authors, who point out that fatalities per person have decreased, when the "Law" requires that they should increase as long as the number of vehicles per person continues to rise.
Smeed's formula is expressed as:
or, weighted per capita,
where D is annual road deaths, n is number of registered vehicles, and p is population.
Smeed published his research for twenty different countries, and, by his death in 1976, he had expanded this to 46 countries, all showing this result. Smeed became deputy director of the Road Research Laboratory and, later, Professor at University College London.
Smeed claimed his law expresses a hypothesis of group psychology: people take advantage of improvements in automobiles or infrastructure to drive ever more recklessly in the interests of speed until deaths rise to a socially unacceptable level, at which point, safety becomes more important, and recklessness less tolerated.
Freeman Dyson summarized his friend's view as:
Smeed had a fatalistic view of traffic flow. He said that the average speed of traffic in central London would always be nine miles per hour, because that is the minimum speed that people will tolerate. Intelligent use of traffic lights might increase the number of cars on the roads but would not increase their speed. As soon as the traffic flowed faster, more drivers would come to slow it down.....Smeed interpreted his law as a law of human nature. The number of deaths is determined mainly by psychological factors that are independent of material circumstances. People will drive recklessly until the number of deaths reaches the maximum they can tolerate. When the number exceeds that limit, they drive more carefully. Smeed's Law merely defines the number of deaths that we find psychologically tolerable.
Whilst in charge of the RRL's traffic and safety division, Smeed's views on speeds and accidents were well reported at the time of the introduction of a mandatory speed limit on UK roads: "If I wanted to stop all road accidents I would ban the car and introduce an overall speed limit, for there is no doubt that speed limits reduce accidents. Of course, roads with higher speeds often have lower accident rates. It is only on the safer, clear roads that you can drive fast - but that does not prove that you are driving more safely."
He recognised that few methods of reducing accidents were painless and thus preferred to report facts and not to make direct recommendations as: "political, social and economic factors come in - but the people who make the decisions must know what the facts are on a subject.".
Speeds on congested roads
At the opposite end of this theory was Smeed's observations of heavily congested networks. He noted that at some minimum speed, motorists would simply choose not to drive. If speeds fell below 9 mph (14.5 kph), then drivers would keep away; as speeds rose above this limit, it would draw more drivers out until the roads became congested again.
The validity of Smeed's "Law" is a matter of debate:
Smeed's Law is a classic example of a statistical fallacy caused by mathematical coupling wherein correlation is found between variables that share common factors. A series of random numbers for inputs would generate the same hyperbolic curve that Smeed's graphs show. The potential for this error was first described by Pearson in 1897  and has been restated elsewhere.
Powles (Oxford Textbook of Public Health) notes that the Australian state of Victoria which experienced deaths in excess of the Smeed formula until about 1970, subsequently adopted a range of interventions which took it from being a poor performer in terms of road safety to one of the best. Deaths fell in absolute terms from a peak of 1000 in 1970 to below 300 in 2009, despite strong growth in population and the number of vehicles.
Critics observe that fatality rates per vehicle are now decreasing faster than the formula would suggest, and that, in many cases, fatality rates per person are also falling, directly contrary to Smeed's prediction. They attribute this improvement to effective safety interventions. (see Andreassen, Broughton, Oppe, and Ameen & Naji)
However, John Adams of University College London argues that Smeed's law linking deaths, vehicle-miles and population was still valid for a variety of countries over time, claiming that the relationship held for 62 countries in a paper published in 1995. He noted an enormous difference in fatality rates across different parts of the world in spite of safety interventions, and suggested that Smeed's Law was still useful in establish general trends, especially when using a very long time period. Variations from the trend were normally better explained through economics, rather than claimed safety interventions. However, Adams found that Smeed's calculation of estimated deaths from vehicles per population was less successful than the calculation for vehicle-miles.
- R. J. Smeed (1949). "Some statistical aspects of road safety research". Journal of the Royal Statistical Society. Series A (General). Journal of the Royal Statistical Society. Series A (General), Vol. 112, No. 1. 112 (1): 1–34. doi:10.2307/2984177. JSTOR 2984177.
- Freeman Dyson (2006-12-05). "A failure of intelligence: operational research at RAF Bomber Command, 1943–1945 (Part II)". Technology Review.
- "Motorways Saving Deaths - Road Research View". The Times. 7 February 1964.
- Pearson, Karl (1897). "On a form of spurious correlation which may arise when indices are used in the measurement of organs". Proceedings of the Royal Society. 60: 489–498. doi:10.1098/rspl.1896.0076.
- Archie, Joseph (1981). "Mathematic coupling of data: a common source of error". Annals of Surgery. 193 (3): 296–303. doi:10.1097/00000658-198103000-00008 – via PubMed.
- D. C. Andreassen (1985). "Linking deaths with vehicles and population". Traffic Engineering and Control. 26 (11): 547–549.
- J. Broughton (1988). "Predictive models of road accident fatalities". Traffic Engineering and Control. 29 (5): 296–300.
- S. Oppe (1991). "The development of traffic and traffic safety in six developed countries". Accident Analysis and Prevention. 23 (5): 401–412. doi:10.1016/0001-4575(91)90059-E. PMID 1741895.
- J. R. M. Ameen and J. A. Naji (2001). "Causal models for road accident fatalities in Yemen". Accident Analysis and Prevention. 33 (4): 547–561. doi:10.1016/S0001-4575(00)00069-5. PMID 11426685.
- John Adams (1995). Risk. London: UCL Press.
- John Adams (1987). "Smeed's Law: some further thoughts" (PDF). Traffic Engineering and Control. 28 (2): 70–73.