Heads or tails? It all depends on some key variables

Everyone knows the flip of a coin is a 50-50 proposition. alone it ‘s not. You can beat the odds. So says a three-person team of Stanford and UC-Santa Cruz researchers. They produced a provocative study that turns conventional wisdom, well, on its head for anyone who has always settled a minor dispute with a simple coin pass.

It besides could have profound implications in America ‘s favorite sport — pro football — because the coin flip plays an integral function in deciding games that go into overtime .
But first, here ‘s what the researchers concluded : Using a high-speed camera that photographed people flipping coins, the three researchers determined that a coin is more probably to land facing the same side on which it started. If tails is facing up when the coin is perched on your thumb, it is more likely to land tails up.

How much more probable ? At least 51 percentage of the time, the researchers claim, and possibly equally a lot as 55 percentage to 60 percentage — depending on the flipping motion of the individual .
In other words, more than random luck is at work .
The humble mint flip has been the discipline of considerable discipline by researchers exploring concepts such as probability and statistics. There even was an unscientific look by a prisoner who once flipped a coin 10,000 times inside his cell .
” But they ‘ve all been improper because people write down whether it comes up heads or tails, but they do n’t know how it started, ” said Susan Holmes, a Stanford University statistics professor who co-authored the study, which was published in 2007. “ You have to know how it starts. ”
And if you know that, the researchers believe, then you have a better chance of knowing how it will land .
The power of a coin flip
Tossing a coin long has been a option for deciding superficial matters — like a dinner-table spat over the last slice of pizza. But mint flips besides have played much more outstanding roles. The Oregon city of Portland got its name after a best two-out-of-three penny flip by two settlers. ( Boston was the lose identify. )
There was a black mint flip on Feb. 3, 1959, that allowed early rock ‘n ‘ wheel star Ritchie Valens to get a seat on a minor plane that was supposed to carry him, Buddy Holly and two others to their adjacent concert web site. The plane crashed shortly after parody, killing all four .

The mint somersault even is found in literature and film. Javier Bardem won an academy award for his character in the 2007 film version of Cormac McCarthy ‘s “ No Country for Old Men ” in which the villain tosses a coin to decide whether he should kill person or let them live .
But nowhere in modern company does the coin impudent loom larger than in sports — specifically the NFL .
A coin flip determines which team gets the football first in overtime if the sexual conquest is tied after regulation play. And heading into this season, the team winning the overtime flip had won 63.3 percentage of the games — and won the game 43.3 percentage of the time on its first possession, preventing the other team from evening touching the ball .
Consider the very first game of the temper, on Sept. 10, when Tennessee quarterback Kerry Collins called the overtime coin chuck and lost. Pittsburgh elected to receive the kickoff and marched down the field for the game-winning field finish. But before the coin flip, referee Bill Leavy, a former San Jose policeman and fireman, had held the silver dollar out on his hitchhike. It would have been distinctly visible to Collins if he had looked .
The Stanford and University of California-Santa Cruz researchers would suggest that Collins missed a golden opportunity to shade the odds in his privilege .
Although the learn ‘s results would seem to potentially tilt the NFL ‘s play field, the league office in New York does n’t believe it has a trouble. Officials were storm that anyone had bothered to conduct a cogitation examining coin-tossing odds .
They studied what ?
At the 49ers ‘ prepare adeptness in Santa Clara, players had two initial reactions :
1 ) Do n’t those eggheads have more crucial things to do ?
2 ) You ‘re pulling my branch .
But the more the 49er players listened, the more they became intrigued. They promptly saw how — if the report were accurate — they might be able to gain an advantage .
Center Eric Heitmann, a Stanford alumnus and 49ers captain, said : “ I ‘ve never heard anything like that before, but I guarantee that I will be thinking about it each clock time I ‘m out there for the coin flip. ”
A crafty smile even emerged on the face of linebacker Takeo Spikes, another 49ers captain .
” And if it works for us, I ‘ll be the first one to support that study, ” he said .
That, countered kicker Joe Nedney, is just plain absurd. He was n’t buying the study one morsel.

” There ‘s so much variation in how a coin is flipped, ” Nedney said. “ How could you possibly know how many rotations the coin makes ? ”
Researchers would say Nedney was not asking the properly question .
The determining factor is not how high a mint is flipped, according to the survey. Nor is it any early variable such as fart amphetamine, vent temperature or phase of the moon. It ‘s not the size or the slant of the mint, either. ( legendary football bus Vince Lombardi was said to be a “ heads ” man because he mistakenly believed more metallic on that side of the mint increased the odds of it landing up. )
It ‘s all in the flick .
” The way we flip coins creates a bias, and that makes it stay more time in the position it starts in, ” said Holmes, the Stanford professor .
Holmes co-authored the sketch with Persi Diaconis, her husband who is a magician-turned-Stanford-mathematician, and Richard Montgomery, a UC-Santa Cruz mathematics professor, in hopes of gaining a better agreement of the physics involved .
Using a television camera from the Stanford engineer department that snapped 1,000 frames per second, they determined that the laws of basic mechanics play a bombastic function. Coins flipped from a hitchhike do n’t merely rotate around their axis, but they besides spin like a Frisbee .
The degree of that Frisbee spin depends on the motion of the ovolo .
The more Frisbee spin, the longer the side facing up stays facing up when the mint is in the breeze .
And the longer the side facing up stays facing up, the better prospect it will land that direction .
” Some people flip in a more bias room than others, ” Holmes said. “ There ‘s always bias to the side that ‘s facing up, and the discrepancy depends on the gesticulate of the flipper. ”
A tauten landing open, like a wood postpone, changes the equality. But grass — or the synthetic FieldTurf used in some NFL stadiums — mirrors the land conditions used in the analyze and does not materially change the result .
If they had only known
That ‘s why the results might have been of interest in the NFL — if anyone had known about it. Titled “ dynamic Bias In The Coin Flip ” when published in 2007 in the Society for Industrial and Applied Mathematics Review, the paper drew a smattering of pastime. But it flew about entirely under the radar in the sports earth — where the impact could be the greatest .
” We got a shout from something called ‘ASPN, ‘ “ Holmes recalled .
She meant ESPN. And no, she ‘s not much of a sports winnow .
Fans much grouse about what they see as the built-in unfairness of the NFL overtime system — normally after their favorite team loses a mint flip, and then the game .
Ray Anderson, a former Stanford actor and the NFL ‘s executive vice president of operations, said the league is well mindful of the statistical boundary favoring the team that wins the overtime coin flip. Almost every offseason, the NFL contest committee discusses changing its overtime rules. But the players largely are oppose to change because they worry that extending the duration of the game would increase the risk of injury .
” so until there ‘s something more assure or seems to truly violate the integrity and intent of fairness, it credibly wo n’t change, ” Anderson said. “ There has n’t been anything dramatic enough to compel a change. ”
not even research that claims the coin flip is not a 50-50 suggestion ?
” I very ca n’t add anything on the study because I was a political skill major at Stanford, ” Anderson joked .
The 49ers kicker Nedney, with tongue firm planted in boldness, suggested that there could be other ways of determining who gets the ball first in overtime .
” We should start having it decided with Rock, Paper, Scissors, ” Nedney said. “ Have the two captains out there battling the best two out of three. Or the referee should stand between the captains and say, ‘ I ‘m thinking of a act between one and 10. ‘ “

(c) 2009, San Jose Mercury News (San Jose, Calif.).

Visit MercuryNews.com, the World Wide Web site of the Mercury News, at www.mercurynews.com
Distributed by McClatchy-Tribune Information Services.

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