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IS SMEED’S LAW STILL VALID?
A WORLD-WIDE ANALYSIS OF THE TRENDS IN FATALITY RATES
Abstract: Professor R J Smeed published his famous formula for predicting road deaths in 1949. Later
on, other authors tried to validate or update the formula based on newer data. Most of these
publications emphasized the encouraging finding that the increase of vehicle ownership leads to a
decrease in fatalities per vehicle. Less attention was paid to the other and less encouraging –
interpretation of Smeed’s formula, namely that the increase of vehicle ownership leads to an increase
in fatalities per population and in the total number of fatalities. Fortunately, the increasing trend of the
total number of fatalities started to change towards a decreasing trend in some countries from the 60’s.
The paper analyses GDP, vehicle ownership, population and road fatality data from 139 countries.
Relationships between these variables are shown. Using cluster analysis, countries are grouped
according to their safety performance trends.
Key Words: Smeed, road safety, vehicle ownership, fatality rate, cluster analysis
1. INTRODUCTION
In his famous paper, Smeed published his
formula for predicting road deaths as an
empirical rule relating traffic fatalities to motor
vehicle registrations and population (Smeed,
1949).
D = 0.0003 (N·P2)1/3 (1)
where D is the number of annual road deaths,
N is number of registered vehicles and P is
population. His paper is mostly cited
emphasizing that the increase of vehicle
ownership leads to a decrease in fatalities per
vehicle (Figure 1).
D/N = 0.0003 (N/P)-2/3 (2)
Csaba KOREN
Professor, PhD
Department of Transport Infrastructure and
Municipal Engineering
Faculty of Engineering
Szechenyi Istvan University
Egyetem ter 1.
9026 Gyor, Hungary
Fax: +36-96-503-451
E-mail: koren@sze.hu
Attila BORSOS
Junior lecturer, PhD Student
Department of Transport Infrastructure and
Municipal Engineering
Faculty of Engineering
Szechenyi Istvan University
Egyetem ter 1.
9026 Gyor, Hungary
Fax: +36-96-503-451
E-mail: borsosa@sze.hu
Journal of Society for Transportation and Traffic Studies (JSTS) Vol.1
65
Figure 1. Relation between number of deaths per 10 000 registered motor vehicles and number
of vehicles per 1 000 population for 1938
Less attention was paid to the other – and less
encouraging – interpretation of Smeed’s formula,
namely that the increase of vehicle ownership
leads to an increase in fatalities per population
and in the total number of fatalities (Figure 2).
D/P = 0.0003 (N/P)1/3 (3)
Figure 2. Relation between number of fatalities per 100 000 population and number of registered
vehicles per 1 000 population for 1938
Later on, other authors tried to validate or
update the formula based on newer data. The law
was found to be valid with some changes in
parameters (e.g. Adams, 1987). Fortunately, the
increasing trend of the total number of fatalities
started to change towards a decreasing trend in
some countries from the 60’s. For the UK, the
Smeed prediction was moving correctly and had
approximately the right magnitude until about
1966. Since 1966 the Smeed prediction continues
to rise, while the real road deaths have fallen
quite reliably. By 2000, the Smeed prediction
was about 4 times too high (Safe Speed, 2004).
The models describing the changes in road
fatalities are using among others vehicle
Koren, et al.
66
kilometres travelled and Gross Domestic
Product.
Research carried out by Oppe (Oppe, 1991
cited in Elvik & Vaa, 2004, p. 38) found that the
long-term development of traffic fatalities in the
highly motorised countries follows a law-like
pattern determined by the growth of motorisation
and the decline of the fatality rate per vehicle
kilometre of driving.
The change from the increasing to the
decreasing trend could be observed in several
countries. Kopits and Cropper have found that
the income level at which traffic fatality risk
(F/P) first declines is $8600 (1985 international
prices), regardless of how the time trends are
specified. This is the approximate income level
attained by countries such as Belgium, the
United Kingdom, and Austria in the early 1970s,
South Korea in 1994, and New Zealand in 1968
(Kopits, Cropper, 2005).
2. SCOPE OF THE PAPER
This paper presents a world-wide analysis that
addresses the verification of Smeed’s law.
Chapter 3 gives an overview of the data used
during the analysis. Chapter 4 and Chapter 5
focus on the validation as well as the review of
the two interpretations of Smeed’s law. In
Chapter 5 the authors propose a new function
that better describes the evolution of fatality rate
per population in the function of level of
motorization. In Chapter 6 countries are grouped
into 6 clusters according to their GDP, vehicle
ownership rate and fatality rate per population
based on their 2007 data. In Chapter 7 a detailed
investigation of Asian data is provided and
finally Chapter 8 summarizes the conclusions.
3. DATA USED IN THE ANALYSIS
For our analyses we used fatality, population,
vehicle ownership and GDP figures. The data
used in Chapter 4 and Chapter 5 of this paper,
namely the number of fatalities, number of
registered motor vehicles and population stem
from a global report on road safety for the year
2007 (WHO, 2009). Those countries that have
less than 100 road deaths were excluded from the
analysis, thus 139 countries were considered.
In Chapter 6 dealing with the cluster analysis
along with the previously mentioned data the
GDP per capita was added. The gross domestic
product based on purchasing-power-parity (PPP)
per capita was derived from the World Economic
Outlook Database of International Monetary
Fund (IMF, 2009).
In Chapter 7 focusing on Asia the data come
from various sources. These were the online
database of United Nations Economic and Social
Commission for Asia and the Pacific
(UNESCAP, 2009), the global report on road
safety for the year 2007 (WHO, 2009), the
ASEAN Statistical Yearbook (ASEAN, 2005) as
well as data rows for China and Thailand from
the NICE on RoadS EU-Asia project (Koren &
Borsos, 2006).
4. FATALITIES PER VEHICLES
Figure 3 and Figure 4 contain fatality rates per
vehicle as well as vehicle ownership rates for the
139 countries in 2007, together with Smeed’s
relationships. Looking at Figure 3, we see that
the number of fatalities per vehicles fits well into
the trend Smeed found. This is remarkable,
considering that the vehicle ownership rates at
the time of his study were between 0.01 and
0.23, while some of these figures exceed 0.8
now.
Is Smeed’s Law Still Valid? A World-Wide Analysis of the Trends in Fatality Rate
67
Figure 3. Vehicle ownership and fatality rate per vehicles in 2007 compared with Smeed
However, if we have a closer look of the area
below 10 fatalities per 10 000 vehicles (Figure 4,
log scale), we see that almost all data lie below
the curve, especially for vehicle ownership rates
higher than 0.2 which are well out of the range of
Smeed’s data from 1938. Also the logarithmic
scale contributes to the visibility of the
differences from the curve.
Figure 4. Vehicle ownership and fatality rate per vehicles in 2007 compared with Smeed
(log scale)
5. FATALITIES PER POPULATION
As an overall strategic indicator, the most widely
used variable to describe the road safety level of
a country is the fatalities per population. As it is
shown in Figure 5, these data are very much
dispersed, the ratio of the highest and lowest
values being up to 7:1 for a given vehicle
ownership level in 2007. This dispersion is
apparently much higher than it was in 1938, with
the ratio of about 3:1 between the highest and
lowest fatality rates for ownership levels of 0.02
and 0.04. The increase in dispersion is most
probably due to the difference in the set of
countries studied: Smeed’s survey covered a
relatively homogenous group of the most
developed 20 countries of the world, while the
2007 data come from 139 countries in five
Koren, et al.
68
continents with huge differences in their
economic power, vehicle fleet, road network,
social attitude, education and enforcement
culture.
Looking at the dispersed “cloud of points” of
Figure 5, or trying to find usual regression curves
and correlation coefficients, one might come to
the conclusion that there is no relationship
between vehicle ownership and fatality rates.
This is certainly true if we follow the “try several
curves until the best fit and then find an
explanation” method.
Figure 5. Vehicle ownership and fatality rate per population in 2007 compared with the Smeed
formula
The authors followed a different approach:
find a formula which explains the phenomenon
and then try to fit it. For the description of the
relation between vehicle ownership rate and
fatalities per population the following formula
was used here:
D/P = a·N/P·e-b·N/P (4)
The term a·N/P is expressing the growing
exposure with the increase of the vehicle
numbers. While N/P is very low, e-b·N/P is about
1, so the first part of the formula, i.e. the growth
in vehicle numbers is dominant.
The second part of the formula, e-b·N/P is a
negative exponential function, expressing that
the growth of vehicle ownership generally goes
together with the increase in vehicle and
infrastructure safety as well as with an
improvement in education and enforcement.
The formula was fitted to the 2007 data of 139
countries, finding a and b to minimise the square
of differences between actual and expected D/P.
From the data, “a” was found to be around
230, which means that for the ownership figure
of 0.1 vehicles per person 0.1·230= 23 fatalities
per 100 000 population are expected.
From the data, “b” was found to be around 4.4,
which means that for the ownership figure of 0.1
vehicles per person the impact of safety
improvements is a correction factor of e-4.4·0.1 =
0.64, for 0.3 vehicles per person e-4.4·0.3 = 0.27,
while for 0.6 vehicles per person e-4.4·0.6 = 0.07.
Thus, with higher motorisation rates the second
term of the formula becomes dominant.
Though the least square method was used to
find the best fit, the curve should not be
considered as a regression line and therefore no
correlation coefficients are given here.
Is Smeed’s Law Still Valid? A World-Wide Analysis of the Trends in Fatality Rate
69
The formula used is appropriate to describe
the phenomenon that with low motorization the
number of fatalities is increasing. Once reaching
a certain threshold, the society will devote and
can afford more efforts to turn the previous
trends in road safety. The turning point of the
fitted curve is about 0.20-0.25 vehicles per
person and 20 fatalities per 100 000 population
(Figure 6). Apparently there are huge differences
among countries. These differences are mainly
due to the considerable variations between
countries’ characteristics such as geographical
features, economic and political background.
Figure 6. Relationship between vehicle ownership and fatality rate per population for 2007
Although the above data represent a cross-
section from one year, the relationship between
vehicle ownership and fatalities can be also
explained as a change over time (see also section
7.3).
The change in the number of fatalities per
population is influenced by the following driving
forces:
• Increase in vehicle ownership rate goes
together with an increase in accident
exposure.
• Increase in vehicle ownership rate goes
together with economic growth and
technological development (better
infrastructure, better equipped cars, better
emergency services etc.).
• Social attitude against road safety
changes (evaluation of accident costs,
acceptance of restrictions etc.).
The combined impact of the three driving forces
leads to three stages of development:
• Declining road safety situation
Increasing fatality rate per population dominates
due to growing traffic volume and exposure, the
economy is weak, and there is no social attention
to road safety.
• Turning point
The road safety situation is quite bad; however,
the economic performance makes the change
possible, if there is adequate social and political
will.
• Long-lasting improvement
The pace of economic and technological
development as well as the change in social
attitude is higher than the growth in traffic
volume.
It has to be mentioned here that the number of
vehicles is far from being a perfect measure of
accident exposure. Vehicle kilometers travelled
on a countries road network would describe the
exposure much better. In the above explanations
the term “vehicles” could be replaced by
Koren, et al.
70
“vehicle kilometers” as well. Probably the
dispersion of the points in the figures would be
considerably less. Similar studies were
performed earlier for cases when there is a good
data set of vehicle kilometers. This is usually
possible for individual countries with consistent
vehicle kilometer data over the years (e.g. Safe
Speed, 2004). Unfortunately, the international
statistical data collections contain vehicle
kilometer data only for a very limited number of
countries and even for those countries which
provide such data, the difference in definitions
and calculation methods reduces the possibility
of international analyses.
6. CLUSTER ANALYSIS
In order to arrange countries by their 2007 data
into clusters, three variables were chosen: GDP
per population, vehicles per population and
fatalities per population. Because of their
different magnitudes, all variables were
normalized, i.e. their values were divided by
their respective means. Then the countries as
cases were clustered according to the three
variables using K-Means Cluster Analysis in
SPSS software. Among others tables of cluster
membership and distance from cluster centre
were produced as outputs. After several runs it
was found that the choice of 7 clusters gives a
reasonable description of each cluster. The
number of cases (countries) in each cluster and
the cluster means of the three variables are
shown in Table 1. Clusters were numbered
according to their growing GDP/P means. Except
for Clusters 5 and 6, the Vehicles/P means are
growing parallel to the GDP/P means. The
Fatalities/P means generally follow the findings
before; they are low at low and high vehicle
ownership rates, while the highest fatality rates
were found for medium ownership figures. In
Figure 7 clusters are illustrated with different
markers in the vehicle ownership – fatality rate
coordinate system.
Table 1. Main data of the clusters
Is Smeed’s Law Still Valid? A World-Wide Analysis of the Trends in Fatality Rate
71
Figure 7. Clusters of countries according their GDP, ownership and fatality rates
Cluster 1 contains the poorest countries. Their
vehicle fleet is similarly low. Fatalities per
person in these countries are half of the average
of all countries. Most of these countries are in
Africa but other countries like Tajikistan and
Afghanistan belong also to this group.
In Cluster 2 the average GDP is higher but still
only half of the average of all countries. Their
vehicle fleet is closely proportional to their
income. Despite their relatively low vehicle fleet,
fatalities per person in these countries are 1.2
times the average of all countries. Countries in
this cluster are distributed on 4 continents.
Only 12 countries belong to Cluster 3 which
contains the most dangerous ones. Their GDP
and vehicle fleet is around the average of all
countries, but their fatalities per person figure is
2.2 times more than the average of all countries.
Also 4 continents are represented in this group
and in several of these countries a large number
of population is exposed to a high risk (Russia,
Kazakhstan, Iran, Mexico, South Africa,
Venezuela).
Cluster 4 contains countries with slightly
higher income than the average. Their vehicle
fleet is higher than it would be expected from the
GDP figures. Fatalities per person in these
countries are around the average of all countries.
Besides some new EU member states (Bulgaria,
Hungary, Poland, Slovakia) countries like
Argentina, Korea, Thailand, Uruguay belong to
this group.
Cluster 5 is an outlier in some sense. Here the
average GDP is 1.7 times higher than the average
of all countries and their vehicle fleet is much
higher in proportion to their income (or the other
way round: their GDP is lower than it would be
expected from their vehicle fleet). Probably this
discrepancy leads to the result that fatalities per
person in these countries are 1.2 times of the
average of all countries. Countries in this cluster
are the lower income old EU member states
(Greece, Portugal) some higher income new
member states (Czech Republic, Estonia,
Slovenia) as well as three other countries from
three continents.
Cluster 6 contains the 20 most developed
countries with a GDP three times than the
average. Their vehicle fleet is slightly lower than
it would be expected from the GDP figures.
Fatalities per person in these countries are only
about 70% of the average of all countries. Most
of the old EU member states as well as Australia,
Canada, Japan and the USA belong to this group.
Cluster 7 has only one element, this outlier is
Qatar with its very high GDP and moderately
high fatality rate.
Table 2 shows the first ten countries in each
cluster closest to the cluster centre
Koren, et al.
72
Table 2. The first 12 countries in each cluster closest to the cluster centre
7. ANALYSIS OF ASIAN TRENDS
7.1 Fatalities per vehicles – 2007 data
In order to have a better view on Asia we
collected the 2007 data for the Asian countries.
As far as the fatalities per vehicles are
concerned, the countries are quite dispersed
along the Smeed curve due to their different
vehicle ownership rates.
Figure 8. Relationship between vehicle ownership and fatality rate per vehicles for Asia
7.2 Fatalities per population – 2007 data
From the point of view of the fatalities per
population even stronger differences can be
perceived among Asian countries. Most of them
are still in the upward trend, but the downward
section is also significant (Figure 9). The high
dispersion of fatality rates between countries is
Is Smeed’s Law Still Valid? A World-Wide Analysis of the Trends in Fatality Rate
73
due to the fact that Asia is the most divergent
continent: countries with low, medium and high
income, with widely different geographic
conditions, road networks, vehicle fleets and
social systems can be found here.
Figure 9. Relationship between vehicle ownership and fatality rate per population for Asia
Unfortunately, in some countries the fatality
rate is over 30 per 100 000 inhabitants. Oman,
Kazakhstan, Iran are the worst-performing
countries with a motorization level of 200~300
and a fatality rate higher than 30 fatalities per
100 000 population. On the contrary there are
some well-performing countries, such as
Singapore (4,82 fatalities per 100 000
population, 191 vehicles per 1 000 population) or
Japan with quite high level of motorization (5,18
fatalities per 100 000 population, 714 vehicles
per 1 000 population).
The difference in fatality rates between
countries is quite high, and also the ownership
levels have a very wide range. The latter is due
to the high share of two-wheelers in several
countries.
7.3 Fatalities per population – time series
For some Asian countries time series of cars per
population and fatalities per population were
analyzed. For seven out of eight countries the
number of registered vehicles (ASEAN, 2005),
in case of Japan the passenger cars in use
(UNESCAP, 2009) were used. Owing to lack of
data the length of these time series differs, the
following list gives an overview of the years
included in the analysis:
• China: 1994-2003, 2007
• Malaysia: 1997-2003, 2007
• Myanmar: 1997-2000, 2007
• Philippines: 2003, 2007
• Singapore: 1997-2003, 2007
• Thailand: 1994-2003, 2007
• Lao People’s Democratic Republic:
1997-1999, 2007
• Japan: 1990-2002, 2007
The overall picture is similar to the previous
cross sectional figures but in Figure 10 the
changes for each country can be observe.
Koren, et al.
74
Figure 10. Changes of fatality rates versus vehicle ownership in some Asian countries
Some countries in the lower motorization
phase have low fatality numbers but these figures
have steadily been increasing in the last decade
(China, Myanmar, Philippines, Lao PDR). Some
others (Malaysia, Thailand) suffer from much
higher fatality rates but these rates are
decreasing, especially in Thailand. The low
Japan fatality rates show a further decrease.
Fatalities of low vehicle ownership countries
(e.g. China, Philippines, Myanmar) are still low
but unfortunately rapidly increasing. Countries
with medium vehicle ownership (like Thailand,
Malaysia) have quite high fatality rates but these
are decreasing remarkably. In these countries,
the high share of two-wheelers contributes to the
high fatality figures. Japan’s data are very much
similar to that of the high income countries in
Cluster 6.
8. CONCLUSIONS
It was found that Smeed’s formula is describing
reasonably well the changes (increase) in
fatalities up to the 0.2-0.3 vehicles/person
ownership level, whereas above this level the
formula is too pessimistic, the fatalities are
fortunately tending to decrease in reality.
For the description of the relation between
vehicle ownership rate and fatalities per
population a new formula was found combining
a linear function showing the growth of vehicle
ownership with a negative exponential function
explaining the improvements in safety level. The
formula can be used both for cross sectional data
of a given year to describe difference between
countries and for time series of given countries.
In terms of road safety, three stages of
development can be identified all over the world.
In the first phase the road safety situation is
declining. At a second phase, countries come to a
turning point. The third phase can be a lasting
improvement.
The range of fatality figures between countries
for a given car ownership level is quite large.
These differences underline the fact, that the
trends found are not like laws of nature. A
country will not automatically follow the trend,
but a lot has to be done to follow it; it is a result
of many efforts in vehicle design, infrastructure
safety, enforcement and education.
The cluster analysis identified six clusters of
countries with similar fatality rates, car
ownership and GDP levels within each cluster
but huge differences between clusters. Countries
within the same cluster should preferably follow
similar road safety strategies.
Is Smeed’s Law Still Valid? A World-Wide Analysis of the Trends in Fatality Rate
75
The Asian countries show a very much
dispersed picture in terms of fatality rates and
their trends.
Many of them are in a declining road safety
situation, where an increasing fatality rate per
population due to growing traffic volume
dominates, and there is not enough social
attention to road safety.
Some other countries are around the turning
point, their road safety situation is quite bad, and
however, the economic performance makes the
change possible, if there is adequate social and
political will. There is also the chance for a long-
lasting improvement, if the pace of economic and
technological development as well as the change
in social attitude is higher than the growth in
traffic volume.
Koren, et al.
76
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Is Smeed’s Law Still Valid? A World-Wide Analysis of the Trends in Fatality Rate