Europe is on high alert. Soldiers are on patrol in metro stations, security has been tightened at big public events and, almost every week, police somewhere on the continent report having thwarted a terrorist attack. A widespread feeling of insecurity, fed by a spate of recent atrocities in France, Belgium and Turkey, has hardened over the course of a violent summer.

In just two weeks in July, 86 people were killed in Nice when a lorry drove through Bastille Day crowds on the promenade; a knife-wielding 17-year-old attacked passengers on a train in Würzburg; a gunman shot dead nine civilians in Munich; a bomb went off at a wine bar in Ansbach; and two men slit the throat of an elderly priest in his church in a quiet Normandy town.

Even before the past year brought unsettling proof of the reach of Islamic State, Europeans had been growing increasingly anxious.

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In March 2015, when 28,000 of them were asked by Eurobarometer what they saw as the most important challenge to the security of EU citizens, by far the most common answer was terrorism, mentioned by half of the respondents (up from one-third in 2011).

All other concerns – organised crime, climate change, wars, economic crises or nuclear disasters – were marginal by comparison. Eighteen months later, that concern is no doubt even more pronounced.

Yet terrorism and perceptions of the risk it poses are rarely aligned. That’s the point of psychological warfare: a single event can have effects disproportionate to its scale or lethality, through the fear it creates or the response it provokes.

So how likely is a westerner to be killed by terrorists? Since 2014, the number of people who died in terror attacks in the West has been on the rise. Last year the figure for western Europe was 161, according to the US state department. However, because the overall numbers for the West are low, single events with high casualty rates, such as the co-ordinated attacks that claimed 136 lives in Paris in November 2015, can cause significant shifts in the overall pattern.

Such spectacular atrocities, and the extensive media coverage they receive, can also mask some broader trends.

Terrorism database

The Global Terrorism Database (GTD), a vast repository of information on almost every attack since 1970, maintained by the University of Maryland, shows that terrorism today is killing far fewer westerners than it did in the 1970s and 1980s. In 1979, by one measure, there were more than 1,000 individual terrorist attacks in western Europe alone, compared to just over 350 last year.

The death rate in western Europe peaked in the mid-1970s, when the IRA campaign was at its height, and rose again in the early 1980s, when attacks by the Basque separatist group Eta peaked (the activity of left-wing groups such as the German Red Army Faction, Italy's Red Brigades and the Weather Underground Organisation in the US was also a factor).

Ever since, with the exception of relatively isolated deadly attacks – the Lockerbie bombing in 1988, for example, or the Madrid bombing in 2004 – terrorism in Europe has been in decline.

In the US, the threat is even smaller. With the exceptions of 9/11 and the Oklahoma bombing in 1995, there has been no year since 1970 when terrorism claimed the lives of more than 50 people on US soil. About the same number die from lightning strikes. Earlier this year, president Barack Obama was criticised for saying, correctly, that the danger of drowning in a bath was greater than that of being killed by terrorists. The GTD shows that terrorism is heavily concentrated in a handful of countries, none of them in the West (which accounted for just 5 per cent of total deaths last year).

In the past five years, more than three-quarters of all the deaths catalogued by the team at the University of Maryland have been recorded in just six countries: Afghanistan, Iraq, Nigeria, Pakistan, Syria and Yemen. The database does not yet include figures for 2016, but an analysis of news reports shows that in July this year – the month of the Nice attacks – at least 842 people were killed in terror attacks in Iraq, including 346 who died when a car bomb exploded in the middle of a busy market in Baghdad on July 3rd.

"People commonly say, 'that's different, Iraq and Afghanistan are war zones', but from a humanitarian perspective it is exactly the same – an attack on a civilian population there is the same as an attack on a civilian population in Paris or London or New York City, " says Erin Miller, programme manager at the GTD.

Graphic news coverage

So if westerners are among the least likely to be affected by terrorism, why do they fear it so much? The cognitive psychologist Daniel Kahneman suggested that the human mind uses a shortcut to estimating risk that he and his collaborator

Amos Tversky

called the availability heuristic: the easier it is to imagine an event, the more common we think it is.

"We use the ranking in our mental search engines as a shortcut to estimating probability," says Steven Pinker, an experimental psychologist at Harvard University, in an email interview. "With more intense and graphic news coverage, and more blanket coverage through cable TV, the internet and social media, we are bombarded with images and descriptions of terrorist attacks, but rarely of ordinary police-desk homicides, so we think the terrorist attacks are more likely. Which is exactly what terrorists anticipate: attract the greatest publicity, and the most fear, with a bit of violence."

In his latest book, The Better Angels of Our Nature, Pinker draws on data and statistical analyses to argue that violence is in long – and short-term decline and that today is probably the most peaceful time in the history of mankind.

Despite that trend, he says, people are hyper-alert to the risk of death by violence. He points out that the coverage of terrorism is personalised – through vigils, individualised stories about the victims and other ways of expressing our grief and shock – in a way that “would have been unthinkable in times of war, when hundreds of times as many victims were reported tersely”.

The nature of the Islamist threat is also a factor, Pinker believes. “Most of the terrorism in Western Europe of the 1960s, 1970s and 1980s was motivated by Marxism and nationalism, which intellectuals and many journalists tended to sympathise with, so the terrorism was indulged as going too far in a not-so-bad cause. Not so for the ideology of Isis [as Islamic State is also known].”

Politicians who warn of “existential threats” and security services that exaggerate terrorists’ capabilities may contribute to the heightened anxiety, but so do shifts in the nature of terrorism itself. The GTD data suggests that attacks in the West have declined in frequency but become more lethal.

In other words, a decline in volume has been offset by the greater determination of today’s terrorists, especially those inspired by radical Islam, to kill in quantity. In the 1970s and 1980s, symbolism and property damage were more common features. “Certainly there were many, many people killed, but on an attack-by-attack basis, there were not as many extremely deadly attacks, where you’re finding more than 20, 50 or 100 people killed in a single event,” says Miller.

An analysis of the database by the think-tank Rand earlier this year showed that between 1970-2002 in the West, terrorism occurred in clusters – likely a reflection of the relatively localised activities of groups such as the IRA and ETA operated. Since 2002, however, the distribution of events has been statistically random.

That could offer reassurance. It suggests that cancelling a holiday in Nice this summer was not the most rational response to the Bastille Day horror.

Yet randomness, by widening the number of potential targets, also leaves more people feeling they have reason to fear for their lives.