from The Numbers Guy blog at WSJ (many more links in article there):
May 17, 2007, 5:21 pm
A Most Unlikely Collection of Holes in One
Jacqueline Gagne, a 46-year-old Rancho Mirage, Calif., resident, has hit 10 holes in one in the last four months, over a stretch of just 75 rounds of golf. My column this week examines her improbable feat ? and estimates of just how improbable it is.
Jacqueline Gagne at the 18th hole of the Pete Dye Challenge Course of the Mission Hills Country Club in Rancho Mirage, Calif. Ms. Gagne has struck seven of her holes in one at Mission Hills, three of them on Pete Dye?s par-3 11th hole. (Photo by Peter A. Hogg) Ms. Gagne?s local paper, the Desert Sun, asked College of the Desert mathematician Michael McJilton, to estimate the odds against her feat, back when it stood at a mere seven aces. His estimate: 1 in 113.5 quadrillion, or 113,500 followed by 12 more zeroes (I?m using quadrillion in the U.S. sense of the word for a very big number; for more on the names of big numbers, see this Numbers Guy column).
As I explain in the column, tweaking various assumptions Mr. McJilton used yields a less astronomical number. But his basic procedure for the calculation is sensible and was also suggested by several other mathematicians I contacted. He used the formula for something called the Poisson distribution, which is explained on this page from Wolfram MathWorld. It may look daunting initially, but if you substitute the numbers Mr. McJilton used ? seven holes in one in 65 rounds, with a probability of one in 5,000 per round ? it should become clearer. An exclamation point after a whole number means that number multiplied by every whole number below it, to 1; so 4! = 4*3*2*1. (Strictly speaking, we?re interested in how likely it is for Ms. Gagne to have hit seven or more holes in one in 65 rounds, but the probability of her hitting more than seven is so small as to have no major impact.)
Some mathematicians I contacted were skeptical about such calculations. ?Golfers are not coins,? Kenneth Ribet said ? meaning that people can get on hot streaks, while the above calculation assumes each hole in one is independent. Streakiness in sports is controversial. Texas Tech professor Alan Reifman tracks news and research in the area at his blog, The Hot Hand in Sports.
Meanwhile, Berkeley mathematician George M. Bergman warned of a ?subtle fallacy?: We focus on the unlikely events that do happen, but there are many other events that would be equally impressive but don?t happen. We don?t hear about the millions of golfers who play 75 rounds without a hole in one. (I made a similar point about improbable sports events in a column last fall.) And since Ms. Gagne did accomplish her feat ? corroborated by witnesses ? the only justifiable probability is 100%, ?since the event happened,? Stanford?s Keith Devlin told me.
?I?m not a mathematician,? Robert Barnes, director of golf at Mission Hills Country Club, where Ms. Gagne usually plays, told me. ?I know that the odds of this being able to happen are astronomical.? To wit: In more than 70,000 rounds since the beginning of this year, there have been only eight or nine other holes in one not hit by Ms. Gagne, making the feat much rarer for her fellow golfers at the club than the national average.
Ms. Gagne seems to be taking it all in stride. She hadn?t hardly golfed before moving to Rancho Mirage from Rhode Island six years ago. ?If you?ve ever been out here to the desert, that?s pretty much what everyone does out here,? she said. ?I figured I would give it a try, and I fell in love.? She?s a lifelong athlete ?with a really good eye? who wishes she?d taken up golf sooner, ?because, who knows?? At this point, though, she has no expectations of going pro, instead happy to play recreationally five or six days a week in her retirement. When I asked if she?d get another ace, Ms. Gagne also said, ?Who knows??
Mancil Davis, director of golf operations for National Hole in One Association, which insures promotions awarding prizes for aces, wasn?t sure he?d get another himself when he was stuck on 50 holes in one from 1996 until last month (his email handle is ACES50).
In the mysterious arena of holes in one, Mr. Davis?s joking explanation for his 11-year drought makes as much sense as any: the Sports Illustrated cover jinx. Except, of course, as Mr. Davis notes, the week SI featured him, ?I wasn?t on the cover.? (Noted recreational golfer Michael Jordan was.)
May 17, 2007, 5:21 pm
A Most Unlikely Collection of Holes in One
Jacqueline Gagne, a 46-year-old Rancho Mirage, Calif., resident, has hit 10 holes in one in the last four months, over a stretch of just 75 rounds of golf. My column this week examines her improbable feat ? and estimates of just how improbable it is.
Jacqueline Gagne at the 18th hole of the Pete Dye Challenge Course of the Mission Hills Country Club in Rancho Mirage, Calif. Ms. Gagne has struck seven of her holes in one at Mission Hills, three of them on Pete Dye?s par-3 11th hole. (Photo by Peter A. Hogg) Ms. Gagne?s local paper, the Desert Sun, asked College of the Desert mathematician Michael McJilton, to estimate the odds against her feat, back when it stood at a mere seven aces. His estimate: 1 in 113.5 quadrillion, or 113,500 followed by 12 more zeroes (I?m using quadrillion in the U.S. sense of the word for a very big number; for more on the names of big numbers, see this Numbers Guy column).
As I explain in the column, tweaking various assumptions Mr. McJilton used yields a less astronomical number. But his basic procedure for the calculation is sensible and was also suggested by several other mathematicians I contacted. He used the formula for something called the Poisson distribution, which is explained on this page from Wolfram MathWorld. It may look daunting initially, but if you substitute the numbers Mr. McJilton used ? seven holes in one in 65 rounds, with a probability of one in 5,000 per round ? it should become clearer. An exclamation point after a whole number means that number multiplied by every whole number below it, to 1; so 4! = 4*3*2*1. (Strictly speaking, we?re interested in how likely it is for Ms. Gagne to have hit seven or more holes in one in 65 rounds, but the probability of her hitting more than seven is so small as to have no major impact.)
Some mathematicians I contacted were skeptical about such calculations. ?Golfers are not coins,? Kenneth Ribet said ? meaning that people can get on hot streaks, while the above calculation assumes each hole in one is independent. Streakiness in sports is controversial. Texas Tech professor Alan Reifman tracks news and research in the area at his blog, The Hot Hand in Sports.
Meanwhile, Berkeley mathematician George M. Bergman warned of a ?subtle fallacy?: We focus on the unlikely events that do happen, but there are many other events that would be equally impressive but don?t happen. We don?t hear about the millions of golfers who play 75 rounds without a hole in one. (I made a similar point about improbable sports events in a column last fall.) And since Ms. Gagne did accomplish her feat ? corroborated by witnesses ? the only justifiable probability is 100%, ?since the event happened,? Stanford?s Keith Devlin told me.
?I?m not a mathematician,? Robert Barnes, director of golf at Mission Hills Country Club, where Ms. Gagne usually plays, told me. ?I know that the odds of this being able to happen are astronomical.? To wit: In more than 70,000 rounds since the beginning of this year, there have been only eight or nine other holes in one not hit by Ms. Gagne, making the feat much rarer for her fellow golfers at the club than the national average.
Ms. Gagne seems to be taking it all in stride. She hadn?t hardly golfed before moving to Rancho Mirage from Rhode Island six years ago. ?If you?ve ever been out here to the desert, that?s pretty much what everyone does out here,? she said. ?I figured I would give it a try, and I fell in love.? She?s a lifelong athlete ?with a really good eye? who wishes she?d taken up golf sooner, ?because, who knows?? At this point, though, she has no expectations of going pro, instead happy to play recreationally five or six days a week in her retirement. When I asked if she?d get another ace, Ms. Gagne also said, ?Who knows??
Mancil Davis, director of golf operations for National Hole in One Association, which insures promotions awarding prizes for aces, wasn?t sure he?d get another himself when he was stuck on 50 holes in one from 1996 until last month (his email handle is ACES50).
In the mysterious arena of holes in one, Mr. Davis?s joking explanation for his 11-year drought makes as much sense as any: the Sports Illustrated cover jinx. Except, of course, as Mr. Davis notes, the week SI featured him, ?I wasn?t on the cover.? (Noted recreational golfer Michael Jordan was.)
