THE IRISH were elated, and they had every right to be. Their victory on November 5th against New Zealand, rugby’s perennial overlords, was their first ever, after a winless run of 28 matches lasting 111 years. Aptly, they beat the mighty All Blacks at Chicago’s Soldier Field—where the game was being played in the hope of expanding the sport’s appeal in America—just five days after the Chicago Cubs had ended a 108-year wait of their own by prevailing in baseball’s World Series. But the significance of the result was not simply that the men in green had finally claimed rugby’s most-prized scalp. It was also that they had vanquished the most dominant All Blacks side of all time.

The Kiwis arrived in America on the back of 18 consecutive victories, a new record for a major international team and a streak that had included their triumph in the 2015 World Cup. Yet the length of such runs is not the best way to gauge the ability of a side, since these numbers do not account for the strength of the opposition. The all-time record for consecutive victories belongs to tiny Cyprus, who won 24 consecutive games between 2008 and 2014 against the likes of Azerbaijan and Latvia.

In contrast, the bulk of New Zealand’s matches are typically against Australia and South Africa, two giants of the sport and the only other countries to have won the World Cup more than once. The All Blacks’ recent purple patch, however, included World Cup fixtures against minnows Namibia, Georgia and Tonga, and a three-match home series against an ailing Wales. Rugby historians will also note that the Kiwis had previously strung together undefeated sequences of 20 games (from 2011 to 2012), 22 games (from 2013 to 2014) and 23 games (1987 to 1990), each of which was blemished by a single draw.

Ahead of the pack So how can we tell that New Zealand’s 2016 vintage was the strongest ever? The most reliable measure of team quality comes from Rugby Vision, a predictive model assembled by Niven Winchester, an economist at MIT who also researches rugby probabilities. The system forecasts the results and margins of victory for all major international and most domestic matches. Had you used the model to place $100 spread bets on the scores of each of the 48 games at last year’s World Cup, you would have earned a tidy profit of $548 (or 11.4%).

Mr Winchester’s predictions are based on team ratings, which are constructed by exchanging points between opponents after a match. Conquering a strong rival means that you gain a large number of their ratings points: Ireland took 1.68 of them from New Zealand in Chicago. Beating a weak team, however, will earn you little. The All Blacks collected no ratings boost at all for their 68-10 thrashing of lowly Italy on November 12th, and actually lost 0.16 points when they edged past Wales by 36-22 on June 18th, a smaller margin of victory than the model expected.

Rugby Vision’s system therefore rewards sides that consistently best high-quality opposition, while remaining unimpressed by those that beat up on weaklings. Crucially, the model provides historical probabilities of match outcomes. Mr Winchester has fed into his algorithm the result of every single international fixture since the second world war between teams from “tier one”— Argentina, Australia, England, France, Ireland, Italy, New Zealand, Scotland, South Africa and Wales. This can tell us what chances any given team would have of beating the All Blacks at a neutral venue at any point since 1950 (the model uses five years of training data, and accounts for home-field advantage).

The result is that, before this month’s batch of Autumn Internationals, the Kiwis were further ahead of their rivals than any other side in history (see chart). Their closest challenger, England, would have had just a 14.9% chance of vanquishing them. If you take the average probability of victory against New Zealand for South Africa, Australia, France and England—the only nations to have beaten them at least five times, and the only other teams to have appeared in a World Cup final—then that number stood at 10.1% at the start of November. Both measurements were the lowest ever seen.

Looking at the latter figure (marked by the black line), you can see that past incarnations of the All Blacks have approached this kind of supremacy before. The squad that won the World Cup on home turf in 1987 achieved an average loss expectancy against the sport’s best sides of 15.2% in 1989; and the version that repeated that feat in 2011 reached 14.5%. Surprisingly, the best-rated Kiwi cohort before the current crop was the class of 2007. In the lead-up to that year’s World Cup, the All Blacks annihilated a series of tier-one opponents on foreign soil: England by 21 points, South Africa by 27, Wales by 35, Scotland by 40, France by 44 and Italy by 62. At one stage, their average loss expectancy was just 11.2%. But a one-in-nine chance of defeat is not the same as a certain victory, and the Kiwis lost narrowly to France in the 2007 quarter-finals. That cohort will be forever remembered for choking on the biggest stage—proof, if ever one was needed, that statistical dominance and “greatness” are different things.

The 2016 side can lay claim to both. Many of the current squad contributed to the World Cup triumph of last year. After that tournament, however, New Zealanders worried that a golden era had drawn to an end, as several outstanding players retired. One was flanker and captain Richie McCaw, who was renowned for his fearless tackling and an uncanny ability to steal the ball from opponents. He was also a three-time winner and eight-time nominee for the World Rugby Player of the Year award. Equally revered was fly-half Dan Carter, the side’s playmaker and kicker, with three wins and five nominations for the same prize. Both are generally recognised as the best players ever at their positions.

Additionally, the tournament marked the final appearances of Ma’a Nonu and Conrad Smith, the two centres responsible for distributing the ball outside of Mr Carter. Also playing in black for the last time were burly front-rowers Keven Mealamu and Tony Woodcock. Between them, these six stalwarts had won 707 international caps. For comparison, the entire 31-man England squad for the same tournament could boast just 836.

Fears of a succession crisis have proved unfounded. If anything, the All Blacks have surged even further ahead of the chasing pack. Consider this: in 2015, New Zealand played South Africa twice, Argentina twice, and Australia three times, picking up six wins while scoring 206 points and conceding 129. This year, in exactly the same combination of fixtures, the revamped All Blacks have won all seven, totting up 299 points and allowing 94. The young pretenders have matured into world-beaters. The most notable example is Beauden Barrett, a 25-year-old fly-half who was named the 2016 World Rugby Player of the Year in his first season as a regular international starter. Mr Barrett and his teammates might have tasted the rare bitterness of defeat in Chicago. Nonetheless, they appear poised to reach even greater heights in time.

Zeal and zest All this leads inexorably to the question of how a nation of 4.7m people—roughly half the population of London or Paris—can consistently produce the world’s strongest side. Enthusiasm certainly plays its part. In 1905 the “Original” All Blacks toured Europe and America, the first time that they had travelled overseas, and won all but one of their 35 matches. The team’s success was a source of immense pride in a land that was still a British colony, and which did not gain complete self-governance until 1907. The sport has been something of a national obsession ever since. A lengthy piece in The Guardian before last year’s World Cup gives a flavour of how closely the game is woven into the fabric of Kiwi life: it is the pastime of every schoolchild, the yardstick by which rural villages measure themselves, the tide of the national mood. (Mr Winchester, a Kiwi himself, recalls rugby popping up in his economics exams.)

There is no greater honour in New Zealand than wearing the black jersey. Seven All Blacks have been knighted, compared with three Britons. To mark its 150th anniversary in 2013 the New Zealand Herald, the country’s most popular newspaper, selected Mr McCaw as one of the nation’s ten greatest people—alongside Edmund Hillary, the first man to climb Mount Everest, and Ernest Rutherford, who discovered the structure of the atom.

The All Blacks therefore get the pick of the islands’ athletes, though New Zealand does have strong rugby-league and cricket sides as well. By contrast, football is the chief sport in most European countries, and Australian-rules football and cricket dominate across the Tasman Sea. In spite of this selective advantage, there are just 150,000 registered players in New Zealand, far fewer than the 230,000 in Australia, 290,000 in France and 340,000 in both South Africa and England.

That smaller pool of talent is highly skilled. From the age of five, as “Small Blacks”, players are taught to focus on handling and spatial awareness. At schoolboy level, they are graded by size rather than age, to reward finesse, not physicality. In the professional tiers, brawn becomes more important: New Zealand is blessed with a large population of Pacific Islanders, whose physiques tend to combine pace and power in a way that makes them unstoppable with a ball in hand. But the mark of an All Black, vast or nimble, is the ability to take a pass from a teammate while darting through the tiniest of gaps.

This emphasis on movement and distribution would be unfamiliar in other countries. British rugby players grow up boshing into one another with all the subtlety of a herd of oxen. South Africans are equally known for their “direct” style of play. Perhaps only the Australians devote as much attention to creating space and slipping runners between defenders. In international matches, this skill is thought to matter most. But in order to test this belief—and to determine which ones actually do have the greatest impact on winning—we downloaded publicly available match reports on every game between tier-one international sides since 2010, and built a statistical model that measures which elements of a rugby match truly predict a team’s scoring.

Stat attack Our findings from these 348 fixtures run contrary to many common assumptions in rugby. Having more than half of the possession or “territory”—the amount of time spent in an opponent’s half—is often cited as proof that a team is in control. Yet these numbers bear little relationship to the outcome of games. In our six-year sample, the team with more possession was victorious precisely half the time, and the side with more territory just 47%. You would get just as much predictive power from a coin toss. The All Blacks, incidentally, have on average had 51% of possession and 52% of territory. The range for all nations on both metrics is between 47% and 53%.

In fact, just a handful of the twenty or so variables that appear in standard reports proved to be statistically significant predictors of how many points a team will score (see chart). “Clean breaks”—the number of times an attacker bursts through the defensive line—turned out to be the most important factor. Even when controlling for other offensive variables, such as the tally of passes completed and the count of tackles evaded, sneaking behind the opponents’ defence was correlated with greater attacking success. Specifically, improving your total of clean breaks by one standard deviation was associated with scoring 4.7 extra points. (Standard deviations are a measure of spread: in a normally distributed set of data, 68% of observations will fall within one standard deviation of the mean, and 95% within two. On average, a tier-one international team makes 5.6 clean breaks per game. Improving by one standard deviation would get them to 10 breaks, which would typically see their score rise by 4.7 points.)

Other widely cited events such as offloads, kicks from hand and rucks (impromptu scrimmages) won also wound up having little impact on scorelines. What mattered was penetrative running, as measured by clean breaks and metres run with the ball. In both of these aspects, the Kiwis are untouchable. Other sides usually “carry” for between 300 and 400 metres in a game. The All Blacks do so for 500 (see chart). On average, the New Zealanders make an impressive nine clean breaks per match.

The data also revealed the importance of the “dark arts”. After the ball is fumbled or ushered off the side of the pitch, the game is restarted among the hulking forwards. If your opponent has committed a handling error, you have the opportunity to put the ball into a scrum, with the hope that it will emerge on your side of the melee. If he has carried or propelled the ball over the sideline, you are awarded a “lineout”; that is, the chance to throw the ball into a jumping throng of players. The data confirm that losing possession in either of these scenarios is correlated with a decline in point-scoring. Such unglamorous elements of rugby are not generally associated with the swashbuckling All Blacks. Yet they are the most frugal side in both situations. They are also remarkably proficient at securing “turnovers”, by pinching the ball from their opponents, often from under a pile of bodies. That too is an indicator of a potent attack.

Our model cannot account for everything. It explains roughly half of the variance in rugby scorelines, and its projections for each team were within seven points (or a single converted try) 60% of the time. With better data, more comprehensive results might be possible. Nonetheless, they give a clear indication of why the Kiwis are rugby’s kings. They run incisively. And they excel at the dirty work.