The Volokh Conspiracy
[David Post, December 8, 2006 at 1:55pm] Trackbacks
You Think You've Got Bad Luck?:

Some of you may recall the weird story of a few years ago, when one of the giant balloons at the Macy's Thanksgiving Day parade in New York (the 60-foot tall "Cat in the Hat," in fact) came loose, crashed into a streetlamp, and fractured the skull of one of the onlookers below. And most of you surely recall that last October a small plane co-piloted by Yankees pitcher Cory Lidle slammed into an apartment in a building on New York's Upper East Side. What you may not know (and what I didn't know until recently) is that these accidents both happened to the same woman. (I was pretty sure this must be one of those silly urban legends that make the rounds from time to time, but according to the NY Daily News, MSNBC, and others, it is in fact true). It truly boggles the mind -- making the front page of the New York Times twice for falling victim to two of the most freakish, random, and improbable events one can imagine. The likelihood of this happening to the same person? Obviously, not zero (since it happened), but surely about as close to zero as one gets; what odds would you have given someone in 1998 if someone had been willing to bet on its occurrence? It's like . . . well, I can't really think of what it's like; I can't come up, off the top of my head at least, with anything remotely like it.

DavidBernstein (mail):
My recollection is that some woman, I think in New Jersey, won the lottery twice in one year a while back.
12.8.2006 1:59pm
Duncan Frissell (mail):

The likelihood of this happening to the same person? Obviously, not zero (since it happened), but surely about as close to zero as one gets;

But like persons who win the Lotto twice, the odds that some one person out of the large category of Lotto winners/freak accident victims will win the Lotto/suffer a freak accident again are much higher.

In the case of the Lotto, I've heard that it happens every 18 months or so.
12.8.2006 2:04pm
Glenn W. Bowen (mail):
My brother-in-law's father-in-law performed the surgery on the woman after she was hit by the balloon.

And he was in the Army.

Did anyone besides me notice that the term "Knights of Malta" was never mentioned in either article?
12.8.2006 2:04pm
doubled (mail):


The guy on Johnny Carson years ago who had been struck by lightning 7 times comes to mind.

Not an individual accomplishment, but how about in the NFL , the longest play in the history of the 80 year old league happenned in back to back years to the same team (Chicago Bears) on a play that happenns maybe once a decade(return for touchdown of a missed field goal).
12.8.2006 2:31pm
GMS (mail):
This reminds me of the story about Wilmer McLean, of whom it was said the Civil War started in his back yard and ended in his front parlor. The first Battle of Bull Run was fought on his farm, and his house was used as Beauregard's headquarters. He later moved to Appomattox, and Lee surrendered to Grant in his parlor. As far as coincidences go, it's not in the Cat in the Hat's league, but it's not bad.
12.8.2006 2:38pm
CardinalXimenes:
It's worth remembering, though, that we perceive the coincidence retrospectively and within an arbitrarily-chosen context. For example, the American Civil War ended with Lee's surrender to Grant in Wilmer McLean's parlor at Appomattox. McLean had moved to Appomattox after his house had been commandeered by Confederates and destroyed in the fighting of the first battle of Bull Run at the very beginning of the war. What are the odds that a war would practically start and end in the same man's house?

Not so bad, really, if we're the ones who get to decide what we're looking for. The real question being asked is, "What are the odds that the same person would be involved in two individually unlikely events?" Phrased that way, in a country of 300 million people it seems pretty likely that somebody's going to be in the same odd situation twice. As bizzare as this coincidence may seem, it's really a function of our human instinct to see retrospective patterns in our environment.
12.8.2006 2:45pm
CardinalXimenes:
And for an example, I now point to two totally unconnected posters simultaneously using an obscure piece of Civil War trivia to demonstrate the unlikeliness of the event.
12.8.2006 2:46pm
Malvolio:
My recollection is that some woman, I think in New Jersey, won the lottery twice in one year a while back.
Three times, but once was for a comparatively small amount of money, a few thousand. I thought it was very suspicious that she owned the 7-Eleven where she bought the tickets, but I can't see how it really would have helped her cheat.
12.8.2006 2:49pm
Rufus (mail):
Anopther striking coincidence (pun semi-intended) -- if I recall correctly, in 1957 a woman named Alice Roth was hit twice by foul balls during the same at bat at a baseball game in Philadelphia. She was struck the first time at her seat, and a second time as paramedics were carrying her out of the stadium.
12.8.2006 2:53pm
TomHynes (mail):
The odds aren't astronomical - about 1 in the population of Manhattan, and that is assuming that there only two really random events happen.
12.8.2006 2:58pm
PersonFromPorlock:

...I now point to two totally unconnected posters simultaneously using an obscure piece of Civil War trivia to demonstrate the unlikeliness of the event.

Oh, that just proves the existence of telepathy. ;^)
12.8.2006 3:13pm
Sarah (mail) (www):
If I were her, I'd move to Minnesota or something. And invest in great quantities of life insurance.
12.8.2006 3:19pm
John Burgess (mail) (www):
If something happens with a "one in a million" chance, it's happened to 300 Americans and 6,562 other world citizens, with the odds growing shorter as I type....

Population:

U.S. 300,364,051
World 6,562,011,787
12.8.2006 3:21pm
Waldensian (mail):

these accidents both happened to the same woman.

Yes, but only sort of. Recall that she wasn't injured in the crash of Lidle's plane, it simply hit her apartment. (Demonstrating once again why terrorists haven't ever used small general aviation aircraft -- such aircraft are perfectly lousy weapons of mass destruction.)

If she had actually been injured by a falling aircraft without being on the aircraft, that would have been a REALLY astounding thing, as this happens very, very, very rarely. Note that nobody but the occupants was injured in the crash of Lidle's plane, despite the fact that it crashed into freakin' Manhattan. There's just a lot of space down there.

Of course, I recognize that it only has to happen once if it's you....
12.8.2006 3:24pm
ed in texas (mail):
On an alternate note, there was a woman from Oklahoma with Multiple Schlerosis who took a hit from a lightning bolt, which apparently cause her symptoms to go away. She went to L.A. for a talk show appearance, and missed her appointment with Social Security about her disabilty benefits at the Murrah Federal Bldg., on the day that Timothy McVeigh came calling.
12.8.2006 3:26pm
arthur (mail):
Beat this one: Until recently, Hank Aaron was first on the list of all professional baseball players in alphabetical order, and also first in order of career home runs. In the same time period, Kereem Abdul-Jabbar was first on the list of all professional basketball players in alphabetical order, and also first in order of points scored.
12.8.2006 3:30pm
DJR:
This is not really related, but an interesting lottery story:

A man a few years back played the same "Pick 5" numbers in Virginia every week. "Pick 5" is (or was) a game that pays a $100,000 jackpot if you pick all five numbers, which is not shared if there are multiple winners. One week a clerk accidentally printed five tickets with the man's numbers, rather than one. The man only wanted one ticket, so the clerk kept the extras and gave them to the next four people who asked for a randomly selected Pick 5 ticket.

Of course, the numbers hit, and all five received the $100,000 prize.
12.8.2006 3:31pm
Apodaca:
T.S Garp:
We'll take the house. Honey, the chances of another plane hitting this house are astronomical. It's been pre-disastered. We're going to be safe here.
12.8.2006 3:35pm
Evelyn Blaine (mail):
I am not an expert on probability, so I invite correction, but it is my understanding that events of (in a certain sense) zero probability happen all the time. Whenever, for example, a process randomly picks out one state from continuum-many equipossible values, the ex ante objective chance of the outcome is zero, in the sense that the measure of the outcome over the probability space is zero. ("Throwing darts at the real line" is the expression I once heard a mathematician use.) Something analogous, I believe, occurs with every wave-function collapse (although of course all the outcomes are not equipossible). I think that some philosophers of science have been very bothered by this and have proposed using non-standard analysis to avoid having to accept actual events with zero ex ante objective probability.

It does rather call to mind the Infinite Improbability Machine in one of the Douglas Adams novels, I can't remember which ...
12.8.2006 3:54pm
Waldensian (mail):

Something analogous, I believe, occurs with every wave-function collapse (although of course all the outcomes are not equipossible).

Let me be the first to admit that I have no idea what this means. Although it sounds pretty interesting.
12.8.2006 4:00pm
CJColucci:
The hell with reality, I'm going back to fiction. Fiction has to be believable.
12.8.2006 4:10pm
andy (mail) (www):
The commentators here are no fun.

I find this anecdote cool.
12.8.2006 4:20pm
Duncan Frissell (mail):
Improbable events happen all the time.

Drop back 1000 years and calculate the odds of your own birth. Pretty small.
12.8.2006 4:23pm
bornyesterday (mail) (www):
Improbable events happen all the time.

Drop back 1000 years and calculate the odds of your own birth. Pretty small.


Drop back 15 billion years and calculate the odds of intelligent life evolving.

ps. I am an evolutionist, so please don't read too much into that statement.

pps. The surrender that ceased all hostilities of the Civil War was of a Confederate warship that sailed around for another year after the official peace was declared.

ppps. The surrender of the land armies that most significantly (with regard to strength of armies) signaled the end of the Civil War was Johnston's surrender to Sherman in a little farmhouse outside the neighborhood I grew up in in Durham, NC. Sidenote - a historical marker for the birthplace of Gen. Johnston in Virginia incorrectly refers to the site of the surrender as occurring at Bentonville, as opposed to Bennett Place.
12.8.2006 4:43pm
KeithK (mail):
[callous, self-centered]
I remember the parade incident quite well. I am still annoyed that it happened because it prompted changes in the rules governing the balloons in the parade. These days balloons need to have a certain compactness and must be carried low to ground when it is windy. Anyone who watched this year may remember the M&M ballon (which depicted a hot air balloon ridden by the red and yellow candies) being carried nearly horizontal due to the wind. Back in the day, one of the most fun parts of the parade was watching the handlers struggle terribly as the big balloon swung all over the place in the wind. Oh, to have the old Superman balloon back!!!
[/callous, self-centered]
12.8.2006 5:00pm
Glenn W. Bowen (mail):

The commentators here are no fun.

I find this anecdote cool.


That was fun.
12.8.2006 5:04pm
Marcus1 (mail) (www):
what odds would you have given someone in 1998 if someone had been willing to bet on its occurrence?

There's actually a logical fallacy named for this.

The more correct, if lamer question, I think: "What would the odds have been that she or anyone else who was recently involved in a well-known rare occurrence would be involved in another slightly similar well-known rare occurrence within a few years?"

Maybe the baseball fan who stole the homerun ends up in the brawl with the basketball player, or one of the guys who took Britney's crotch shot sold a cassette tape to Paris Hilton, or who knows...
12.8.2006 5:17pm
Speaking The Obvious:
Improbable events happen all the time.
Drop back 1000 years and calculate the odds of your own birth. Pretty small.
Drop back 15 billion years and calculate the odds of intelligent life evolving.
------
As one reads the papers these days, one is still waiting...
12.8.2006 5:21pm
Christopher M (mail):
DUDE, LINCOLN had a secretary named KENNEDY and KENNEDY had a secretary named LINCOLN. WEEERD. And the performance at the Ford theatre the night Lincoln was shot was a DEAD KENNEDYS CONCERT!!!!!
12.8.2006 5:30pm
Glenn W. Bowen (mail):
my wife is having dinner this evening with a person whose mother was J. Robert Oppenheimer's secretary.
12.8.2006 5:32pm
David Chesler (mail) (www):
Oh yeah, I was just reading a blog comment by the husband of somebody who was having dinner with Oppenheimer's secretary's child...

Meanwhile, today's Boston Globe reports on a woman name Beth Israel who recently gave birth at the maternity ward at Beth Israel Hospital.
12.8.2006 5:42pm
David Matthews (mail):
I remember, one day, in a northern Twin Cities suburb, I was driving along Nathan Lane, and just at that time a story came on the radio about Nathan Lane. I thought, "What are the odds?" Then, I thought again. Pretty good, given that at just about any hour of any day, someone's driving on Nathan Lane, and whenever a story about Nathan Lane comes on the radio, assuming they have their radio tuned to the right station, they probably say, "Wow. What a strange coincidence."
12.8.2006 5:50pm
Glenn W. Bowen (mail):

Meanwhile, today's Boston Globe reports on a woman name Beth Israel who recently gave birth at the maternity ward at Beth Israel Hospital.


if you were taking a shower, would that be "Bath Israel"? as the say at Marineland of the Pacific, what's the porpoise?
12.8.2006 6:19pm
David Matthews (mail):
As a good example of perspective in coincidence, I always challenge my statistics students (class size about 40) with the following:

I'm willing to bet that two of you share the same birthday. Each student, thinking, "the odds are about 1 in 365 that any student shares MY birthday," is thinking along the lines of 40/365 or a little better than 10%.

In fact, the probability that any two people in the class share a birthday is almost 90%

(To see this, first ignore Leap Year Day, since it doesn't change things much and is a pain in the ass to deal with. Then fix one student's birthday. Proceed to the next student. Her chances of not sharing a birthday with student #1 are 364/365. The chances of student #3 not sharing a birthday with either of the first two is 363/365. Continue for all of the 39 students selected after student #1. The chances that no two students share a common birthday is:

(364*363*362*...*327*326)/(365^39), or about 10.8%

Therefore, the probability that some two students do share a common birthday is about 89.2%

I've run this test every semester for about 15 years, and only missed once, so I'm beating the odds, somewhat.)
12.8.2006 6:59pm
Syd Henderson (mail):
Rufus (mail):
Anopther striking coincidence (pun semi-intended) — if I recall correctly, in 1957 a woman named Alice Roth was hit twice by foul balls during the same at bat at a baseball game in Philadelphia. She was struck the first time at her seat, and a second time as paramedics were carrying her out of the stadium.

The player was Richie Ashburn. Apparently he visited her in the hospital and corresponded with her for the rest of their lives.
12.8.2006 7:04pm
albarello (mail) (www):
I've run this test every semester for about 15 years, and only missed once, so I'm beating the odds, somewhat

Not really. Birthdays are not evenly distributed throughout the year.
12.8.2006 8:20pm
bornyesterday (mail) (www):

I remember, one day, in a northern Twin Cities suburb, I was driving along Nathan Lane, and just at that time a story came on the radio about Nathan Lane. I thought, "What are the odds?" Then, I thought again. Pretty good, given that at just about any hour of any day, someone's driving on Nathan Lane, and whenever a story about Nathan Lane comes on the radio, assuming they have their radio tuned to the right station, they probably say, "Wow. What a strange coincidence."


OMG OMG OMG

I was just rereading this post and the Dave Matthews Band came on the radio!
12.8.2006 8:44pm
David Matthews (mail):
"Not really. Birthdays are not evenly distributed throughout the year."

Actually, that would mean that I'm beating the odds even more, since if certain days are significantly more likely than others, it increases the chances of shared birthdays. (Take it to the extreme -- suppose everyone was born on January 1....)
12.8.2006 9:06pm
David Matthews (mail):
bornyesterday:

I'm a walking freaking coincidence....

and to make matters worse, earlier tonight I was talking to my teen daughter, and I said: "I wasn't born yesterday!!!!" What are the odds?
12.8.2006 9:09pm
hashofet:
This reminds me of a story from the 1970s. A man who had heard that the probability of a bomb being brought onto an airplane was 1 in 23,000, while the probability of there being two bombs on the same plane was astronomically low, something like 1 in 3 billion. After that, whenever he traveled, he carried a bomb in his luggage.
12.8.2006 9:58pm
Dave Hardy (mail) (www):
DUDE, LINCOLN had a secretary named KENNEDY and KENNEDY had a secretary named LINCOLN. WEEERD. And the performance at the Ford theatre the night Lincoln was shot was a DEAD KENNEDYS CONCERT!!!!!

That's total BS! The play at Ford's Theater was Oswald's American Cousin.
12.8.2006 10:10pm
Edd (mail):

"Not really. Birthdays are not evenly distributed throughout the year."

Actually, that would mean that I'm beating the odds even more, since if certain days are significantly more likely than others, it increases the chances of shared birthdays. (Take it to the extreme -- suppose everyone was born on January 1....)


Huh? I thought your money was on the event "at least 2 people share a birthday" coming out true.

Anyway, the probability of all this crazy stuff happening conditioned on the fact that it happened is 1. For that reason, I've never really understood the appeal of this kind of story.

Also, all the stories about people winning the lottery twice, that's just the birthday "paradox" in practice. Instead of birthdays from a set, you're choosing lotto players from a set.

Bottom line is that bizarre things happen all the time. To quote "Magnolia,"


And there is the account of the hanging of three men, and a scuba diver, and a suicide. There are stories of coincidence and chance, and intersections and strange things told, and which is which and who only knows? And we generally say, "Well, if that was in a movie, I wouldn't believe it." Someone's so-and-so met someone else's so-and-so and so on. And it is in the humble opinion of this narrator that strange things happen all the time. And so it goes, and so it goes.
12.8.2006 10:19pm
David Matthews (mail):
Hashofet, that is hillarious. And, fair warning, I'm most likely going to steal that story, in one form or another, and I'm not likely to credit you nor anyone else. There are such amazingly cool variations on that logic....My students already have enough difficulty with conditional probability....
12.8.2006 10:21pm
David Matthews (mail):
"I thought your money was on the event "at least 2 people share a birthday" coming out true"

Umm, never mind, you're both right. I'm wrong. Somehow I thought I was arguing for why I usually win, and not whether I'm beating the odds when I do win. Aaargh.
12.8.2006 10:33pm
Anthony A (mail):
A little more seriously: Let us assume that there is some sort of freak accident which ends up on the front page of the NYT about three days a week. Given the NYT's regional biases, it is likely that one of the three happens to a non-resident of New York, one happens to someone from the outer boroughs, and one to a Manhattanite. So approximately 50 times a year, a freak accident which ends up on the front page of the NYT happens to a Manhattanite. Assume the average number of people involved in said freak accident is 2.

Each week, each Manhattanite has a 1:1,000,000 chance of being in a FAWEUFPNYT. (Population of Manhattan is about 2 million.)

Assume that the average Manhattan resident lives in Manhattan for 30 years. This means that each Manhattanite has 1500 opportunities to be involved in a FAWEUFPNYT. This means that there is a roughly 1:668 chance that any particular Manhattanite will be involved in a FAWEUFPNYT while (s)he lives in Manhattan. The odds that any given Manhattanite will be involved in a FAWEUFPNYT twice are thus about 1:445408. In a population of two million, that means that about 4.5 Manhattanites will have this experience.
12.9.2006 12:14pm
skeptic (mail):
May I add, for the record, another surprising sidelight to October's Cory Lidle incident? (Forgive me for not tracking down the details.) According to a small account I read in the New York Daily News (or possibly the NY Post), some friend of Lidle's had been about to accompany him and Lidle's instructor on that doomed flight but for some reason did not; let's say he was ill or something. He apparently told a number of people how lucky he was not to have been on that plane. Well, just a month or two later, that man was killed in a small-plane crash somewhere on the West Coast.
12.9.2006 3:50pm
Harold Hamblet (mail):
My personal theroy of luck:

Lucky people are lucky. Unlucky people aren't,

She sounds like one of the latter.

On a personal note, after 23 years of marriage, we were driving by St. Joseph's Hospital in Syracuse and I mentioned to my wife that I was born at St. Joseph's. Turns out she was, too. At St. Joseph's in Baltimore.
12.9.2006 7:21pm
Lively:
The article says she sued Macy's and the city of NY for $395 million, but settled for undisclosed. Yet when her apartment was hit by the plane, family members said "she has no where to go." Sounds like the settlement was for very little.
12.9.2006 8:29pm
godfodder (mail):
Lively:
Ah! But that doesn't take into account the lawsuit she is no doubt filing against Cory Lidel's estate. Which will garner her enough cash to live on once the Macy's money runs out.

Making her the luckiest woman in NYC!
12.10.2006 12:01pm
Jeff S.:
Albarello,

It doesn't matter. Dave Matthews is beating the odds. http://www.maa.org/mathland/mathtrek_11_23_98.html.
12.10.2006 2:26pm
Bored Lawyer:

DUDE, LINCOLN had a secretary named KENNEDY and KENNEDY had a secretary named LINCOLN. WEEERD. And the performance at the Ford theatre the night Lincoln was shot was a DEAD KENNEDYS CONCERT!!!!!

That's total BS! The play at Ford's Theater was Oswald's American Cousin


The first part is still true.

And, to round out the coincidence, while Lincoln was shot in Ford's theatre, Kennedy was shot in a Ford automobile. Or so I heard.
12.10.2006 7:58pm
Daniel San:
Illinois requires a DNA profile of anyone convicted of a felony. The Illinois Department of Corrections has a database of 200,000 DNA profiles of inmates. Despite the fact that, for any individual, there a a 1:bazillion chance of a match, the database contains 971 matches. This is actually pretty close to the number that calculations would predict.
12.11.2006 10:02am
staghounds (mail) (www):
Owning the lottery store wouldn't help her cheat. It would help her steal. How many people hhand over tickets and ask thhe person behind the counter if they won? How many ask for them back?

And TWICE, years apart, I've had trees fall, from natural causes, on my car. While I was driving it.
12.11.2006 10:59pm
Mike Owens (mail):
I was once on a bus reading Sterne's "A Sentimental Journey Through Italy and France," and had just finished reading an aside about mating birds. Looking up at the end of the passage, I saw out the bus window --- mating birds.

And once I randomly poured nine sequential yellow M&Ms out of a bag of mixed colors - while studying for my Statistical Mechanics finals!
12.12.2006 5:32pm

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