Players don't want to win that event, which has been staged since 1960, because no par 3 winner has gone on to wear the green jacket in that year.
A check back through the New Zealand Olympic history book revealed there have been 24 teams representing New Zealand, or Australasia.
Those teams turned out in a combined Antipodean force in 1908 in London and 1912 in Stockholm. New Zealand swimmer Malcolm Champion carried the flag at the latter Games, where he won a gold medal as part of the 4 x 200m freestyle team.
But from that point on, New Zealand flagbearers have gone on to win an Olympic medal after fulfilling their duties on opening day on just six other occasions.
Arthur Porritt won the bronze in the 100m sprint at Paris in 1924 - the race in which he was renamed Tom Watson for the classic film Chariots of Fire, whose stirring theme is heard at every medal ceremony during these Games.
Middle distance legend Jack Lovelock carried the flag at Berlin in 1936 before going on to win the 1500m title.
Adolf Hitler was there to see what Lovelock described as his perfect race.
Twenty eight years later, with a stunning gold in the 800m behind him from Rome in 1960, Peter Snell did the honours at Tokyo and went on to take the 800m-1500m double.
Fast forward another 24 years and kayaker Ian Ferguson won gold and silver medals at Seoul.
He teamed with Paul Macdonald to win the K2 500m, and finished second in the 1000m, again with Macdonald for company. That was four years after the pair and team mates Grant Bramwell and Alan Thompson stunned the paddling world with four gold medals.
Eventing great Mark Todd had a curious situation in 1992. He carried the flag and was part of the New Zealand team which won the silver medal in Barcelona.
However while Andrew Nicholson, Blyth Tait and Vicki Latta received medals, Todd's horse had been withdrawn with injury before the showjumping phase.
Barbara Kendall won silver in 1996 as flagbearer, while rower Mahe Drysdale took the bronze at Beijing when gold seemed to be his but for a debilitating illness in the days leading up to his single scull final.
And that's it, a small group of athletes who went on to stand on the dais having been the first New Zealander into the various Olympic stadiums.
Put it another way: 17 flagbearers have not found medal glory at "their" Games.
So what should be read into that? Very little, actually.
The reason flagbearers are chosen is not necessarily because they are rated a medal certainty. It helps, but those responsible for making that choice have their own criteria.
Willis certainly wasn't thinking curse after his final. His disappointment stemmed from his own lack of finish.
Bad luck? Bad judgments? Perhaps, just like trying to figure the disparity between New Zealand's gold and bronze medals, on one hand, and the far fewer silver, it's just one of those quirks of New Zealand's Games record.