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harlequin
2005-Dec-14, 02:55 AM
This AP story (http://www.washingtonpost.com/wp-dyn/content/article/2005/12/13/AR2005121301386.html)


The odds of the same Oklahoma Pick-3 lottery numbers coming up two nights in a row are a million to one, but that's just what happened last weekend.

The numbers 1-7-5 were selected at random both Saturday and Sunday night.

[snip]

University of Central Oklahoma mathematician Larry Lucas says that on any given day, the odds of choosing the correct three numbers in the order drawn is one in 1,000. Those who select the numbers in order get a cash prize of $500.

The odds are what? The odds of today's Pick-3 being the same as yesterday's is a thousand to one. The odds that 1-7-5 will come up two days in a row is a million-to-one.

HenrikOlsen
2005-Dec-14, 04:31 AM
Typical example of bad statistics.
Good catch.

SirBlack
2005-Dec-14, 04:53 AM
The odds are what? The odds of today's Pick-3 being the same as yesterday's is a thousand to one. The odds that 1-7-5 will come up two days in a row is a million-to-one.

Actually, if I'm reading it right, the article is correct.

The mathematician is saying that the probability of a particular combination of numbers appearing on any single day is 1 in 1000.

HenrikOlsen
2005-Dec-14, 05:01 AM
The mathematician was right about the one in a thousand odd for one day, but the journalists subsequent attempt at figuring the odd for the same numbers showing up two days in a row was way off. I doubt the mathematician had anything to do with that part of the calculation.

In order for the same combination to come up two days in a row, it doesn't matter which combination it is the first day, it's only the second day that's constrained, which makes it one in a thousand to get the same combination two days in a row.

Matthew
2005-Dec-14, 06:56 AM
But a million to one sounds so much better. Had it been three nights in a row it could have been considered rigged and would also have been a million to one chance.

Hawk one
2005-Dec-14, 07:57 AM
Slight tangent: This reminds me about a news story that I remember seeing about how Nokia was such a faulty brand, and how 70% of all cell phones in Norway being brought in for repair or replacement is a Nokia. And the salesmen would advice against buying one and it was all so terrible and crap and worst of the bunch...

And at the end of the story, this line came up: "Up until now, 7 out of 10 cell phones sold is a Nokia."

NEOWatcher
2005-Dec-14, 01:57 PM
Just another example of the media not understanding the statement. My guess is the mathemeticion explained the odds of choosing the number that comes up two days in a row is 1M:1. Just like he said choosing the number on any given day.

Fram
2005-Dec-14, 02:28 PM
Not exactly math, but numbers anyway.
When the record for highest hot air ballon flight was broken recently, the newspaper I read had an illustration, showing:
current highest flight: 18000m
new highest flight: 21000m
communications satellites: 23000m
:D

jumbo
2005-Dec-14, 02:29 PM
Bad depending upon how it is phrased.
1/1000 chance for each day is correct.
1 in a million chance is correct beofre the first draw if you require both subsequent draws to have the same numbers.
Once the first draw has happened the odds of the second being the same are 1/1000 as this type of game has no memory.
The odds of the numbers coming up twice depends upon when you ask the question.

NEOWatcher
2005-Dec-14, 02:35 PM
Bad depending upon how it is phrased.
1/1000 chance for each day is correct.
1 in a million chance is correct beofre the first draw if you require both subsequent draws to have the same numbers.
Once the first draw has happened the odds of the second being the same are 1/1000 as this type of game has no memory.
The odds of the numbers coming up twice depends upon when you ask the question.
Time is not as important as the what. Your 1:1M statement is missing the all important "the same as what". Same as a particular number? same as each other? I think that's where the clarity breaks down.
I've heard of trick questions before, but this is a trick answer.:doh:

jadebox
2005-Dec-14, 03:09 PM
Bad depending upon how it is phrased.
1/1000 chance for each day is correct.
1 in a million chance is correct beofre the first draw if you require both subsequent draws to have the same numbers.
Once the first draw has happened the odds of the second being the same are 1/1000 as this type of game has no memory.
The odds of the numbers coming up twice depends upon when you ask the question.

Phrased the way it is in the article ("The odds of the same Oklahoma Pick-3 lottery numbers coming up two nights in a row"), the correct answer is "1000 to 1" not "a million to one."

This is basically the same problem people had when, a few years ago, "9-1-1" was selected by the New York lottery on September 11. Some people tried to claim the chances were a million to one (or more) against that happening. Actually, the odds were better than one in 500 since they picked numbers twice that day.

-- Roger

HenrikOlsen
2005-Dec-14, 03:31 PM
Another way to look at the problem is to look at the total solutionspace.
For any two days there's a million different combinations, 1000 of these have the same combination both days.
Therefore the chance of the same combination happening two days in a row is 1000/1000000 or 1/1000.

SeanF
2005-Dec-14, 03:44 PM
Slight tangent: This reminds me about a news story that I remember seeing about how Nokia was such a faulty brand, and how 70% of all cell phones in Norway being brought in for repair or replacement is a Nokia. And the salesmen would advice against buying one and it was all so terrible and crap and worst of the bunch...

And at the end of the story, this line came up: "Up until now, 7 out of 10 cell phones sold is a Nokia."
That reminds me of a Dilbert cartoon where Catbert gets the Boss concerned that his workers are taking long weekends by pointing out that 40% of sick days taken are Mondays and Fridays.

jadebox
2005-Dec-14, 05:17 PM
It's only a million to one in a special case ....

You did notice the "beating my head against the wall" smiley at the end of my post, didn't you?

-- Roger

jadebox
2005-Dec-14, 05:22 PM
..... and the government gets to keep all the interest they earn off the money that they don't pay out immediately.

This may be just a different way of saying what you said .... but, at least here in Florida, they use a specific percentage of the money collected to purchase an annuity, the total value of which (over 20 years) is advertised as the grand prize. It's an advertising gimmick which allows them to make it seem that the prize is larger than it really is.

-- Roger

jumbo
2005-Dec-14, 05:28 PM
I see now.
Its 1 in a million if you require before the draw for the results to be both a given number combination. Its then 1/1000 for the second draw if that first combination comes up.

In this case though the first draw is irrelevant as it can be any combination the only requirement is that the second set of numbers be the same as the first whatever they may have been. So its then 1/1000. I think!

HenrikOlsen
2005-Dec-14, 06:46 PM
You got it.

Matherly
2005-Dec-14, 06:49 PM
That reminds me of a Dilbert cartoon where Catbert gets the Boss concerned that his workers are taking long weekends by pointing out that 40% of sick days taken are Mondays and Fridays.

If memory serves, the conversation continues with the Pointy-Haired Boss saying "What kind of idiot do they take me for?!?!" And Dilbert responding "Well, not an Idiot Savant. They can do math." :D

Gruesome
2005-Dec-14, 07:17 PM
The big mistake is the payout.

$500 if you win a 1000-1 bet??

Ooooh, sign me up.

HenrikOlsen
2005-Dec-14, 07:19 PM
That's only a mistake if you pay less then .5$ to play.
If you pay more, the mistake is in playing.:)

Chuck
2005-Dec-14, 07:26 PM
I should play the previous day's number every day. Then when I win I
can tell all my friends that I hacked into a lottery computer and set
the system date back a day. Then I'll offer to do it again if they'll
pay me $10,000 in advance. Then I'll change my name, move, make new
friends, and do it again. I could be rich.

It would cost me $1.00 per day about every thousand days and I'd get
back $500 when I won so my profit would be about $9,500. I'd win only
about once every 2.74 years though. Maybe I could play several state
lotteries at once so I could win more often. Or get richer friends
who could raise more money. Or dumber ones who would mortgage or pawn
everything they owned.

SeanF
2005-Dec-14, 08:21 PM
The big mistake is the payout.

$500 if you win a 1000-1 bet??

Ooooh, sign me up.
All lotteries are like that, aren't they?

After all, if they payed out equal to the odds, they wouldn't make any money.

LurchGS
2005-Dec-14, 08:25 PM
absolutely - after all, there's a reason we say "lotteries are a tax on people who can't do math"

jadebox
2005-Dec-14, 08:44 PM
The latest version of the AP story says "Mathematicians figure the odds of the same numbers coming up twice in a row are a million to one." :wall:

-- Roger

turbo-1
2005-Dec-14, 08:47 PM
It's even worse when you do the math for the payouts for the big state and multi-state lotteries. Typically, their payout is around 50% of the take, but if and only if you take your winnings in annuitized payments over 20 years or some such. If you want your money now, they essentially give you the amount that they would have had to pay to buy that annuity (less taxes). Start playing with the numbers, and a $1 lottery ticket looks like about a $0.25 value.

turbo-1
2005-Dec-14, 08:54 PM
The latest version of the AP story says "Mathematicians figure the odds of the same numbers coming up twice in a row are a million to one." :wall:

-- RogerIt's only a million to one in a special case - you preselect the number before the first drawing and figure the odds of the six individual picks coming up as 1-7-5-1-7-5 in sequence. That's a million-to-one shot, but it is not equivalent to saying "the same numbers coming up two days in a row".

There are only 3 numbers drawn each day, and since 3 numbers yields 1000 possible solutions, the odds of today's pick being exactly the same as yesterday's are one in 1000. Apparently, AP's "mathemeticians" skipped middle school.

Certassar
2005-Dec-14, 09:57 PM
Actually, if you think about it, the odds of the same 3 numbers coming up two days in a row are 50%. Either they do or they don't, right? Simple math.



(Just kidding, btw)

TheBlackCat
2005-Dec-14, 10:41 PM
It's even worse when you do the math for the payouts for the big state and multi-state lotteries. Typically, their payout is around 50% of the take, but if and only if you take your winnings in annuitized payments over 20 years or some such. If you want your money now, they essentially give you the amount that they would have had to pay to buy that annuity (less taxes). Start playing with the numbers, and a $1 lottery ticket looks like about a $0.25 value.
That is a really good deal for the government. Not only do they get the money that does not go into the payout, but the actual value of the money they have to pay the winner shrinks thanks to inflation as the 20 years progresses and the government gets to keep all the interest they earn off the money that they don't pay out immediately.

Gas Giant
2005-Dec-16, 02:33 PM
absolutely - after all, there's a reason we say "lotteries are a tax on people who can't do math"
Or "prole tax" as it's sometimes (cruelly) put over here.

Fram
2005-Dec-16, 03:11 PM
The chances of anything coming from Mars are a million to one - but still they
come!
Sorry, couldn't resist :shifty:

Dr Nigel
2005-Dec-16, 07:51 PM
Then again, million-to-one chances come out nine times in ten, right?

SeanF
2005-Dec-16, 08:10 PM
Then again, million-to-one chances come out nine times in ten, right?
"The doctors say he has a fifty-fifty chance of making it, though there's only a twenty percent chance of that."
-The Naked Gun

ZaphodBeeblebrox
2005-Dec-16, 08:13 PM
"The doctors say he has a fifty-fifty chance of making it, though there's only a twenty percent chance of that."
-The Naked Gun
Hmmm ...

So, That'd Be, 10% ...

RIIGHT?

:think:

Fram
2005-Dec-16, 09:45 PM
Hmmm ...

So, That'd Be, 10% ...

RIIGHT?

:think:

Well, not necessarily. If the other 80 % was a 60-40 chance that he'ld survive, then he would have a 52% chance of surviving, or so. :confused:

hhEb09'1
2005-Dec-16, 10:02 PM
That's only a mistake if you pay less then .5$ to play.
If you pay more, the mistake is in playing.:)Typically, you pay $1. I mean, "they" pay $1

Gillianren
2005-Dec-18, 12:00 AM
Actually, if you think about it, the odds of the same 3 numbers coming up two days in a row are 50%. Either they do or they don't, right? Simple math.



(Just kidding, btw)

You kid. I had a coworker once who believed it.

swansont
2005-Dec-18, 03:24 PM
Don't forget the 50-50-90 rule. Given a 50-50 chance, you will choose the wrong answer 90% of the time.

ZaphodBeeblebrox
2005-Dec-19, 11:41 AM
Don't forget the 50-50-90 rule. Given a 50-50 chance, you will choose the wrong answer 90% of the time.
Well, That's Just 'Cause, People are Stupid ...

Oh Darn, This Isn't The Betelgeusuian Interweb, Is It ...

Please Disregard!

:lol:

Certassar
2005-Dec-19, 05:03 PM
Given a 50-50 chance, you will choose the wrong answer 90% of the time.

Only if the question is loaded.

hhEb09'1
2005-Dec-19, 05:08 PM
Only if the question is loaded.Or one of you is

Certassar
2005-Dec-19, 05:15 PM
Or one of you is

I'll drink to that! (Though, I can say, with a 90% certainty, that I'm not sure if my glass is 50% full or 50% empty)

Dr Nigel
2005-Dec-20, 06:45 PM
It's probably a superposition of both states. Or does that not fit in with the Copenhagen interpretation?

Sorry, I couldn't resist.

Certassar
2005-Dec-20, 11:26 PM
It's probably a superposition of both states. Or does that not fit in with the Copenhagen interpretation?

Fits perfectly. But the police officer who took my drivers license the other day didn't agree. I told him that I might or might not have been drinking, but it was his fault if I were drunk. It wasn't until he actually measured for alcohol in my breath that I collapsed, and thus knew I were drunk.

Oh, man. This could go on forever....

Taks
2005-Dec-22, 09:04 PM
I'll drink to that! (Though, I can say, with a 90% certainty, that I'm not sure if my glass is 50% full or 50% empty)it's twice as large as it should be... :)

taks

ZaphodBeeblebrox
2005-Dec-22, 10:42 PM
it's twice as large as it should be... :)

taks
Or, As Phil, Would Say ...

Unless, It's Filled With Neutronium ...

It's Mostly, EMPTY Space!

Alasdhair
2005-Dec-23, 08:10 PM
Fits perfectly. But the police officer who took my drivers license the other day didn't agree. I told him that I might or might not have been drinking, but it was his fault if I were drunk. It wasn't until he actually measured for alcohol in my breath that I collapsed, and thus knew I were drunk.

Oh, man. This could go on forever....

"I have no idea how fast I was going, but I know precisely where I am"

SeanF
2005-Dec-23, 09:23 PM
On the subject of bad math in the media, check out the contradiction between the first two sentences in this article (http://go.reuters.com/newsArticle.jhtml?type=politicsNews&storyID=10617012&src=rss/ElectionCoverage):


President George W. Bush ranks as the least popular and most bellicose of the last ten U.S. presidents, according to a new survey.

Only nine percent of the 662 people polled picked Bush as their favorite among the last 10 presidents. John F. Kennedy topped that part of the survey, with 26 percent, closely followed by Bill Clinton (25 percent) and Ronald Reagan (23 percent).
(NOTE: I realize the article itself is political - it's the math I'm talking about, here!)

montebianco
2005-Dec-24, 10:10 AM
On the subject of bad math in the media, check out the contradiction between the first two sentences in this article (http://go.reuters.com/newsArticle.jhtml?type=politicsNews&storyID=10617012&src=rss/ElectionCoverage):


(NOTE: I realize the article itself is political - it's the math I'm talking about, here!)

Well, perhaps the remaining 17% voted for a six-way tie between Messers. Eisenhower, Johnson, Nixon, Ford, Carter, and Bush (George H).

Vilim
2005-Dec-26, 05:36 PM
The funny thing is, it is still wrong. The article now reads


University of Central Oklahoma mathematician Larry Lucas says that on any given day, the odds of choosing the correct three numbers in the order drawn is one in 1,000.

They imply contradictory quantities. When they say one in 1000 they imply probability which is (desirable outcome)/(undesirable outcome). This isn't the same as odds though which is a ratio of probabilities.

Given an event with probability p, the odds in favour of that event are o=p/(1-p) or the division of the probability of that event by the probability of all other events (p ranges between 0 and 1 so 1-p is essentially the probability of p not happening)

In this case the odds would be (1/1000)/(999/1000)=1/999. Not really a significant correction but still ...

01101001
2005-Dec-30, 08:57 PM
Meanwhile, the Kansas pick-3 lottery just did the actual one-in-a-million thing, the same 3 numbers three days in a row.

Kansas Lottery Picks Same Numbers Three Nights in a Row (http://abcnews.go.com/US/story?id=1425383)


Normally, the odds of winning the lottery are one in 1,000. The probability that the numbers will be the same three nights in a row are a staggering one in a billion.
What are the odds of a reporter writing: "The probability that the numbers will be the same as some particular pick three nights in a row are a staggering one in a billion."

HenrikOlsen
2005-Dec-31, 12:59 PM
one in a googolplex

SeanF
2006-Jan-16, 03:22 PM
Okay, did anybody else watch the season premiere of 24 last night? (Side note: Wow. Just wow.)

I've got to check my tape, but I'm pretty sure I heard a reference to a political candidate winning election "with a plurality of 60%." :doh:

NEOWatcher
2006-Jan-16, 03:46 PM
I've got to check my tape, but I'm pretty sure I heard a reference to a political candidate winning election "with a plurality of 60%." :doh:
I don't understand what your problem with that is. According to this, a winner of an election will naturally fit the definition.

the largest share of something, which may or may not be a majority (http://en.wikipedia.org/wiki/Plurality)

phunk
2006-Jan-16, 03:55 PM
That is a really good deal for the government. Not only do they get the money that does not go into the payout, but the actual value of the money they have to pay the winner shrinks thanks to inflation as the 20 years progresses and the government gets to keep all the interest they earn off the money that they don't pay out immediately.

Actually, almost all of the money that doesn't go to prizes goes to public education. In NJ 36% of the lotto money is given to public schools. 5% goes to the store for selling the ticket, a few percent goes to operational costs, and the rest goes to the prizes. The lotto isn't a scam to get extra taxes from dumb people, it's a fund raiser for public education in most states.

SeanF
2006-Jan-16, 04:10 PM
I don't understand what your problem with that is. According to this, a winner of an election will naturally fit the definition.

the largest share of something, which may or may not be a majority (http://en.wikipedia.org/wiki/Plurality)
Well, I suppose that technically the fifth definition (http://dictionary.reference.com/search?q=plurality) of "plurality" allows it to be also a majority, but the 1st and 2nd definitions don't even require it to be the largest part. Actually, now that I look at it, the 5th definition doesn't even require it to be the largest part.

The 4th definition, which regards elections, explicitly says, "if this number is not more than one half of the total votes cast."

At any rate, if he actually got 60% of the vote, nobody's going to refer to that as a "plurality."

But how exactly does definition 4b work? If A gets 40% and B gets 30% (and C gets 30%), did A win by a plurality of 10% (40-30), or a plurality of 25% (10/40), or a plurality of 33% (10/30), or even a plurality of 14% (10/70)? If we assume the 3rd, then a 48-30-22 breakdown could be described as a plurality of 60% (18/30), but I don't believe I've ever heard an election result described like that.


The lotto isn't a scam to get extra taxes from dumb people, it's a fund raiser for public education in most states.
I'm not sure why you think those two concepts are mutually exclusive. :)

Grey
2006-Jan-16, 04:53 PM
The lotto isn't a scam to get extra taxes from dumb people, it's a fund raiser for public education in most states.
I'm not sure why you think those two concepts are mutually exclusive. :)Hmm, if we assume that both are in fact true, we can imagine a sort of stable situation developing. If the lottery starts bringing in a larger amount of money, presumably public education will improve from the increased funding, people will be better educated and realise that the lottery isn't a very good investment. So funding for education will decrease, people won't be educated as well, and as a result, they'll be more likely to play the lottery. Eventually, we'd reach an equilibrium.


Disclaimer: This post was entirely tongue-in-cheek. Those who take this post seriously do so at their own risk. ;)

Certassar
2006-Jan-16, 05:50 PM
Hmm, if we assume that both are in fact true, we can imagine a sort of stable situation developing. If the lottery starts bringing in a larger amount of money, presumably public education will improve from the increased funding, people will be better educated and realise that the lottery isn't a very good investment. So funding for education will decrease, people won't be educated as well, and as a result, they'll be more likely to play the lottery. Eventually, we'd reach an equilibrium.

Or an eternal cycle. However, I suspect you are right, since They (i.e. the alien puppet masters) would want to regulate the percentage for education, so we live in a constant state of stupidity while the majority of the lottery money goes directly into Their pockets (or the alien equivalent of pockets). ;)

Ilya
2006-Jan-16, 10:34 PM
Actually, if you think about it, the odds of the same 3 numbers coming up two days in a row are 50%. Either they do or they don't, right? Simple math.

(Just kidding, btw)

You kid. I had a coworker once who believed it.
Oh gods. Once when I was an undergrad, I tried to explain the concept of probability to another student. I asked "If I throw a die, what are the chances a 6 comes up?" Her response: "Well, it will either happen, or won't, so it's 50-50"

I pointed out that when you throw a die there are six possible outcomes, so a 6 will come out 1/6 of the time. She was not convinced.

Perhaps I should have asked whether, in her opinion, ANYTHING in the world has chances other than 50-50. But maybe giving up was the right thing to do.

Gillianren
2006-Jan-17, 08:18 PM
Oh gods. Once when I was an undergrad, I tried to explain the concept of probability to another student. I asked "If I throw a die, what are the chances a 6 comes up?" Her response: "Well, it will either happen, or won't, so it's 50-50"

I pointed out that when you throw a die there are six possible outcomes, so a 6 will come out 1/6 of the time. She was not convinced.

Perhaps I should have asked whether, in her opinion, ANYTHING in the world has chances other than 50-50. But maybe giving up was the right thing to do.

Based on the literally hours we spent trying to fit the information into this guy's head, giving up was definitely the right thing to do. He never did believe us.

01101001
2006-Jan-17, 08:45 PM
Perhaps I should have asked whether, in her opinion, ANYTHING in the world has chances other than 50-50. But maybe giving up was the right thing to do.

That's when you say, "All right. I'm generous. I'm a sucker. Let's roll a die 10 times and whenever 6 comes up I'll give you $15 and whenever 6 doesn't come up, you give me just $10."

mike alexander
2006-Jan-18, 12:29 AM
My dad always said that if you want to make money gambling, open a casino.

James_Digriz
2006-Jan-18, 02:48 AM
Typical example of bad statistics.
Good catch.

Why waste time learning when ignorance is instantaneous?

HenrikOlsen
2006-Jan-18, 09:19 AM
At any rate, if he actually got 60% of the vote, nobody's going to refer to that as a "plurality."

But how exactly does definition 4b work? If A gets 40% and B gets 30% (and C gets 30%), did A win by a plurality of 10% (40-30), or a plurality of 25% (10/40), or a plurality of 33% (10/30), or even a plurality of 14% (10/70)? If we assume the 3rd, then a 48-30-22 breakdown could be described as a plurality of 60% (18/30), but I don't believe I've ever heard an election result described like that.

In the 40-30-30 case, I'd say the winner won by a 40% plurality, as he had the plurality of the votes cast, the % listed is also of those votes.

montebianco
2006-Jan-18, 09:55 AM
But how exactly does definition 4b work? If A gets 40% and B gets 30% (and C gets 30%), did A win by a plurality of 10% (40-30), or a plurality of 25% (10/40), or a plurality of 33% (10/30), or even a plurality of 14% (10/70)? If we assume the 3rd, then a 48-30-22 breakdown could be described as a plurality of 60% (18/30), but I don't believe I've ever heard an election result described like that.

Common usage in many areas seems to avoid percentages of percentages. For example, if the interest rate is 6%, and someone says "The interest rate rose by 0.2% today," I would usually assume this person meant the interest rate is now 6.2%, not 6.012%. This is, of course, completely arbitrary...

Tog
2006-Jan-18, 10:22 AM
Common usage in many areas seems to avoid percentages of percentages. For example, if the interest rate is 6%, and someone says "The interest rate rose by 0.2% today," I would usually assume this person meant the interest rate is now 6.2%, not 6.012%. This is, of course, completely arbitrary...

As an example of the other way this can go:
There is a computer game called City of Heores that I play. In this game, a player can have a power (such as resistance) that has a base value of (for example) 20%. This means that incoming damage is reduced 20% 100 becomes 80, 5 becomes 4. The player can enhance this value by adding 'enhancements' that will improve the value by 20%. The catch is, they mean 20% of the base. One 20% enhancement to the 20% base is 24%, not 40. Very few people seem to grasp this in the game. They see that their power is improved by 95% so thay assume that they have nearly maxed out the power, when in fact, that power's base is 3.5%, for a total of not quite 7%.