# Smeed's law

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

Smeed's formula is expressed as:

${\displaystyle D=.0003(np^{2})^{1 \over 3}}$

or, weighted per capita,

${\displaystyle {D \over p}=.0003\times {\sqrt[{3}]{n \over p}}}$

where D is annual road deaths, n is number of registered vehicles, and p is population.

Smeed published his research for twenty different countries,[1] 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's interpretation

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.[2]

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.".[3]

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.

## Current applications

Even as of 2018, Smeed's Law is still applied in its raw form to get a basis of projected motor deaths to help plan for other utilities that may need to be nearby for safety reasons.[4] Although it may not be the most accurate of formulas, it can still be safely used a general rule of them due to its few number of factors that it actually takes into account.

## Studies

Since Smeed’s original interpretation 1960s interpretation of Smeed’s Law for motor vehicle deaths, it has since been interpreted in different way and applied to a number of studies. In 2011, the Federal Aviation Administration (FAA) applied Smeed’s Law to estimate the number of bird strikes as a function of aircraft departures and bird populations.[5] To test how Smeed’s Law would hold up in this different application, the population was kept small and the number of planes was kept to Utah; this application worked very accurately; the estimated number of bird strikes according to the modified Smeed’s Law was within 11% of the actual value. The study was found to be accurate enough to be used on a larger scale.

## Other research

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 [6] and has been restated elsewhere.[7]

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,[8] Broughton,[9] Oppe,[10] and Ameen & Naji[11])

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,[12] 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.[13]

Since Smeed’s original hypothesis and interpretation of his own equation, more research has been done to try to prove or disprove this theory. In 2007, Volume 1 of the Journal of Society for Transportation and Traffic Studies was published; this study was conducted to analyze motor vehicle fatality rates in many different countries to find whether or not Smeed’s Law is still applicable in modern times. This study used a population of 139 different countries; while Smeed originally sampled 20 of the most developed countries. With a more diversified sample, the modern study is further likely presently credible that is more applicable in current years. This study concluded that Smeed’s Law is still applicable in fatalities in countries with a 0.2 - 0.3 vehicle per person ratio, but countries with a higher ratio, the number of fatalities decreases greatly. This may be that Smeed’s Law does not take into account any cultural differences nor laws that may decrease the number of fatalities.

Other researchers have tried to find a way to describe the trends in countries with a higher vehicle per person ratio. “As traffic increases, attitudes toward risk and road user behavior both change in a way that maintains the levels of risk that individuals collectively are prepared to tolerate”.[14] One of the authors claims that although Smeed’s Law does apply at lower ratios, at higher ratios, a collective psychology is formed where people are more aware of the risk of motor vehicle related deaths and are inherently more careful in their driving. Since the 1940s, when Smeed’s Law was first created, the number of motor vehicles has greatly increased, but so have the number of laws, stricter speed limits, and more car safety factors and features. Education on motor vehicles and safe driving habits are more common, but have no place in Smeed’s Law. High-income countries typically are able to invest in their road infrastructure, maintenance of such infrastructure, traffic safety research and maintenance, vehicle development, and driver education, it would seem that high-income countries would do a lot better in terms of traffic related deaths, but since high-income countries also have a higher number of younger and more inexperienced drivers, this leads to an 8.3% increase in fatalities per 10% increase of young drivers.[15] Exposure at a younger age increases the probability of a traffic related death. Even so, high-income countries commonly have a lower number of traffic related deaths when compared to low-income countries.

John Adams, another researcher, found that Smeed’s Law is not applicable over a wide range of population, he believes that Smeed’s Law “should not be used as a basis for comparing road accident death rates for different countries at different levels of motorization”.[13][16] Data is shown how Smeed’s Law becomes less and less applicable over time. Adams suggests that deaths by motor vehicle should instead be the ratio of deaths by motor vehicle and vehicle mileage; this would allows Smeed’s Law to apply in an overall smaller way and average out follow modern trends more closely. This is not a new finding regarding Smeed’s Law. Both modern and older studies seem to find that Smeed’s Law is too outdated and because it only takes such a small number of factors into play, its not very accurate. For example, a study published to Applied Economics in 1999, compares death by foot or bicycle to death by motorized vehicles per capita. In this case, the deaths by foot or bicycle as the chosen mode of transportation is significantly higher than the motorized vehicle transportation. In fact, the results “suggest that motor vehicle use is inversely associated with deaths on the roads across”.[17]

## References

1. ^ 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.
2. ^
3. ^ "Motorways Saving Deaths - Road Research View". The Times. 7 February 1964.
4. ^ Lu, Yueh-Tzu; Fukushige, Mototsugu (2018-08-29). "Smeed's law and the role of hospitals in modeling traffic accidents and fatalities in Japan". Asia-Pacific Journal of Regional Science. doi:10.1007/s41685-018-0097-x. ISSN 2509-7946.
5. ^ Cottrell, Wayne D. (January 2011). "Using Smeed's Law to Estimate Number of Bird Strikes in Utah". Transportation Research Record: Journal of the Transportation Research Board. 2214 (1): 27–33. doi:10.3141/2214-04. ISSN 0361-1981.
6. ^ 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 (359–367): 489–498. doi:10.1098/rspl.1896.0076.
7. ^ 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. PMID 7212790.
8. ^ D. C. Andreassen (1985). "Linking deaths with vehicles and population". Traffic Engineering and Control. 26 (11): 547–549.
9. ^ J. Broughton (1988). "Predictive models of road accident fatalities". Traffic Engineering and Control. 29 (5): 296–300.
10. ^ 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.
11. ^ 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.
12. ^ John Adams (1995). Risk. London: UCL Press.
13. ^ a b John Adams (1987). "Smeed's Law: some further thoughts" (PDF). Traffic Engineering and Control. 28 (2): 70–73.
14. ^ Ross, Hugh Laurence (1985), Evans, Leonard; Schwing, Richard C. (eds.), "Smeed's Law, Seat Belts, and the Emperor's New Clothes", Human Behavior and Traffic Safety, Springer US, pp. 193–257, doi:10.1007/978-1-4613-2173-6_11, ISBN 9781461292807
15. ^ Porter, Bryan E., ed. (2011). Handbook of Traffic Psychology. Academic Press. doi:10.1016/c2009-0-01975-8. ISBN 9780123819840.
16. ^ Shimizu, H.; Davison, E.J. (February 1994). "108 Traffic congestion control of traffic network". Control Engineering Practice. 2 (1): 167. doi:10.1016/0967-0661(94)90690-4.
17. ^ Smith, Ian (April 1999). "Road fatalities, modal split and Smeed's Law". Applied Economics Letters. 6 (4): 215–217. doi:10.1080/135048599353366. ISSN 1350-4851.