It takes a streak of foolhardiness to answer the question “What are you optimistic about?” Because any response would seem to taunt the fates to prove one wrong. But in 2007 I took the bait and ventured that every form of violence, when measured objectively, was in decline – a claim I buttressed with 100 graphs in my 2011 book The Better Angels of Our Nature. Friends advised me I was setting myself up for embarrassment: a war with Iran, a contest over oil, or a nuclear terrorist attack could erupt any day. And wasn’t I even a bit superstitious about the impending centennial of the first world war?

Though I was documenting the past rather than prognosticating, a decade’s worth of new data provides a chance to calibrate our understanding of global trends. In the early 21st century did a bunch of undulating curves fortuitously scrape bottom? Or, as I argued, was something systematic going on?

To any headline-clicker, the answer is obvious. The year 2015 began with the Charlie Hebdo massacre and proceeded to a failed ceasefire in Ukraine, atrocities by Islamic State, and a human catastrophe in Syria that has spilled over Europe’s borders.

Graphic evidence: Steven Pinker's optimism on trial Read more

But headlines are a poor guide to history. People’s sense of danger is warped by the availability of memorable examples – which is why we are more afraid of getting eaten by a shark than falling down the stairs, though the latter is likelier to kill us. Peaceful territories, no matter how numerous, don’t make news, and people quickly forget the wars and atrocities of even the recent past. Only by tabulating violent incidents as a proportion of the opportunities and determining how that proportion changes over time can we overcome our cognitive biases and see which way the world is going.

In an annual exercise, I put my optimism on trial by updating my graphs to see whether the happy trends through the early 2000s have continued, backtracked or been erased altogether.

Let’s start with the bad news: civil war. The Uppsala Conflict Data Program (UCDP) defines it as a conflict between a government and a rebel force which verifiably kills at least a thousand soldiers and civilians a year. Discouragingly, the precipitous decline in the number of civil wars after the end of the cold war, from 26 in 1992 to four in 2007, has bent back up to 11 in 2014. The flip doesn’t come close to undoing the progress, but it raises the question: what went wrong? To answer it crudely: Putin and jihad. Of the 11 wars, two pitted Russian separatists against Ukraine; and eight involved radical Islamist forces enabled by local anarchy and inept or repressive governments.

One of these wars, in Syria, also caused a small bounce in the global rate of war deaths after a vertiginous six-decade plunge. From a high in the second world war of almost 300 battle deaths per 100,000 people per year, the rate rollercoasted downward, cresting at 22 during the Korean war, nine during Vietnam and five during the Iran-Iraq war before bobbing along the floor at fewer than 0.5 between 2001 and 2011. In 2014 it crept up to 1.4; again, upsetting, but a fraction of the previous highs. Newsreaders might expect the Syrian carnage to have undone the historic progress, but they fail to notice the many recent civil wars that ended without fanfare (in Chad, Peru, Iran, India, Sri Lanka, India and Angola), and have forgotten earlier ones (Greece, Tibet, Algeria, Sudan, Indonesia, Uganda, Ethiopia and Mozambique) that had massive death tolls.

The good news is that this is the only bad news: the rate of every other kind of violence has stuck to its recent low or declined even further. The most concentrated forms of destruction our sorry species has dreamed up are world war and nuclear war, and we have extended our streak of avoiding them to 70 years. Wars between great powers, also hugely destructive, have been absent for almost as long – 62 years. Wars between nation states, a constant of history for centuries, have continued their fall into obsolescence: no more than three in any year since 1945, none in most years since 1989, and none since the invasion of Iraq in 2003.

Mass killings of unarmed civilians can be as lethal as wars. During the second world war about 350 of every 100,000 civilians were slaughtered each year, but the rate has juddered down steeply ever since. Estimates from the Uppsala Conflict Data Programme (UCDP) begin at 0.3 in 1989, spike to 14.5 during the Rwanda genocide in 1994, and fall to 0.1 in 2008. They have fluctuated within the rounding error of that figure to 2013.

Wars (other than world wars) kill far fewer people than homicides, and here the news is downright heartening. The decline in homicide that many western nations enjoyed in the 1990s got a second wind in the past decade. In the US, the most violent first-world democracy, it fell from 10 per 100,000 in 1991 to 5.5 in 2000 and then to four in 2014. In England it dropped from 1.8 in 2003 to less than one in 2014. UN guesstimates for the world as a whole have declined from seven in 2003 to six in 2012. Many crime experts believe that a global reduction by 50% in 30 years is entirely feasible.

Are the recent crackdowns on dissent in Russia, Venezuela, Turkey and China signs of a worldwide retreat of democracy? No. Though the blastoff of democratisation from 1976 to 2007 could not continue indefinitely, the global democracy score calculated by the Polity Project has crept upward, not downward, since then.

Recent attention to campus rapes and viral footage of athletes smacking their wives may leave an impression that violence against women is on the upswing. Estimates are minutely sensitive to women’s willingness to report the crimes and to the way survey questions are worded. But, at least in the US,, where government statisticians use a constant yardstick, rates of sexual and domestic violence fell enormously from the 1970s to the mid-2000s, and have held steady since then.

What about the ultimate institutionalised violence, capital punishment? Believe it or not, the death penalty is on death row. In the past four decades, between two and three nations have abolished capital punishment every year (eight since 2010), and today fewer than a fifth of the world’s countries execute people. Even in the US, the outlier among democracies, seven states have repealed the death penalty since 2007, and the national rate of execution has fallen almost by half. If trends continue, the death penalty will vanish from the earth by 2026.

As for institutionalised violence against homosexuals, though some African countries have stepped up their persecution, the global trend toward decriminalisation has continued, from 25 countries in 1960 to 83 in 2009 and 90 in 2015. Even this year’s most widely denounced killing, the shooting of Cecil the lion in Zimbabwe by an American dentist, belies the trend: the popularity of hunting in the US has been in steady decline from 1976 to 2014.

Though I’m relieved that making myself a hostage to fortune eight years ago has not turned out badly, (at least so far), needless to say my greater relief is for the state of humanity. Despite the headlines, and with circumscribed exceptions, the world has continued its retreat from violence. We need invoke no mysterious arc of justice or end of history to explain it. As modernity widens our circle of cooperation, we come to recognise the futility of violence and apply our collective ingenuity to reducing it. Though a few narcissistic despots and atavistic zealots stand athwart this current, history does not appear to be on their side.

• Steven Pinker’s graphs can be seen in full here