The Rugby World Cup final and World Series went against the form book and most academics regard ‘the M word’ as a trick of the mind

“Never underestimate the value of momentum.” That’s what Sir Clive Woodward advised after England’s rugby players lacerated Australia a fortnight ago. And how wise those words seemed when New Zealand were also scattered and flayed, and it seemed England’s name was all but engraved on the Webb Ellis Cup. And then, without warning, the team’s hot hand turned Arctic and the World Cup was ripped from their grasp by South Africa.

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“Momentum is so important in football.” That’s what Dimitar Berbatov told us on Friday, before predicting Manchester United would win their fourth match on the bounce against a Bournemouth side without a victory since September. But whatever impetus Ole Gunnar Solskjaer’s side had beforehand vanished in the south-coast squalls as United lost 1-0.

The M word was also heard in baseball circles last week after the Washington Nationals recovered from a 19-31 start to the regular season to win a first World Series. How else to explain the victory without resorting to one of sport’s great articles of faith? But while it is hard to find a player or coach who doesn’t believe in momentum with the zeal of a 17th century puritan, most academics regard it as nothing more than a trick of the mind.

The hot hand in basketball? A famous study published by the psychologists Thomas Gilovich, Robert Vallone and Amos Tversky in 1985 tore that one to shreds. After examining Philadelphia 76ers’ shooting data, the academics showed successful streaks and failures were indistinguishable from the sequences of heads and tails one would expect from flipping a coin time and again. The hot hand was, they argued, “a powerful and widely shared cognitive illusion”. While the original 1985 research has recently been challenged, other studies have also found that our minds are often duped by patterns in randomness.

What about football? A few years ago the economists Stephen Dobson and John Goddard examined every English league match between 1970 and 2009 – 81,258 games – to see whether longer winning, unbeaten and losing runs were observed more often than would be expected by chance. After accounting for team and opposition strength they found that, on average, sequences of consecutive wins and matches without a win end sooner than expected. In other words the momentum effect was negative – perhaps because teams played differently to preserve an unbeaten record.

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Another study, published last year, looked at whether scoring a goal just before half-time benefited teams more than at other times. The results were again conclusive. “We do not find any evidence of an effect of timing toward the end of the half,” the researchers wrote. “The performance in the second half of teams scoring late in the first half is very similar to the performance of the teams scoring at other times in the half.”

Yet an intriguing new study by academics at Duke University in North Carolina suggests a momentum effect may be a factor in individual sports – if a player feels psychologically threatened by an opponent climbing the rankings. When researchers analysed nearly 60,000 tennis matches between 1992 and 2016, they found players typically won fewer points and matches than otherwise would be expected when facing an opponent who had recently shot up the ATP or WTA world rankings.

These players also committed more double faults than expected against players with upward momentum, which the researchers suggest shows they felt more mental pressure in such matches. When the academics sifted through data from 2.7m chess matches there were similar findings. Even when competitors were evenly matched, players performed worse against an opponent they knew had been climbing in Elo points.

How to explain it? According to Hemant Kakkar, an assistant professor of management and organisations at Duke University, “Our experiments suggest players do mental calculations about a competitor. They tend to think, yeah, this person will keep moving up. Because of this, they start feeling threatened and their performance tends to suffer.”

Facebook Twitter Pinterest Washington Nationals General Manager Mike Rizzo kisses the Commissioners Trophy in front of fans along the World Series victory parade. Photograph: Samuel Corum/EPA

It seems plausible enough. The researchers tested their theory with four non-sport studies on over 1,800 participants that measured how worried they felt in various scenarios. The results again showed that people were more threatened by upwardly mobile opponents than those with the same rank who lacked momentum.

There was an antidote, however. When a person found a reason to doubt an opponent’s momentum in the tests – or practised affirmations of their own abilities – they were less threatened and did better in the tests.

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But this is only study and finding proof of positive momentum in team sports remains elusive. The latest study I saw, published in July, looked at players who had made the last shot of an NBA match to take the game into overtime – and then tracked how they did after that, with surprising results.

Sporting wisdom would suggest those who scored the equaliser before the buzzer would be more confident, while those who missed the last shot before overtime would be more down. In fact the researchers found that after scoring the last shot in the fourth quarter, players’ field goal percentage dropped 12.14% points on average – whereas the field goal percentage of players who missed the last shot rose 10.09% points on average

In other words, individuals reacted with a drop in performance after success and an increase in performance after failure. This was probably because players who scored on the buzzer believed they had a hot hand and took relatively more shots in overtime from sub-optimal positions.

So much for the value and importance of momentum, then – whatever Woodward, Berbatov and the rest of sport may think.