Smeed's formula is expressed as:
where D is annual road deaths, n is number of registered vehicles, and p is population.
Smeed published his research for 20 different countries, and by his death 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.
The relationship was revisited by John Adams who held that it was valid for a variety of countries over time, for example in Great Britain from 1909 to 1973. In 1995 Adams further showed the relationship worked for the data of 62 countries. He noted the enormous difference in fatality rates across different parts of the world even though vehicles may be built to approximately similar standards, which, according to the theory, is "explained by myriad behavioural adjustments in response to perceived increases in the threat of traffic".
However, the validity of Smeed's Law has also been disputed by several other authors (for example Andreassen, Broughton, Oppe, Ameen & Naji).
Smeed himself took his law as expressing a truth about group psychology: people would take advantage of improvements in automobiles or infrastructure to drive ever more recklessly in the interests of speed until deaths rose to a socially unacceptable level, at which point safety would become 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..
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 then drivers would keep away; as speeds rose above this limit it would draw more drivers out, until the roads became congested again.