The cost of bad advice

In the last week, I kept being prompted by the recommendation engines to read the article in Slate titled "Don’t Just Look at the Odds: The Math Says You Should Buy a Mega Millions Ticket." It's obviously false but eventually I succumbed and clicked on the link.

I wanted to stop reading after I encountered this sentence, about half way through the article: "One assumption in this model is that you’ll take the annual payment option and receive the full $1.6 billion."

The pertinent assumption that they made isn't whether the winner should take the lump sum or annual payment options. The blockbuster is to assume that there would only be a single winner.

Earlier in the article, they stated a true but irrelevant point: that the odds of a winning ticket and the price of each ticket are still th same no matter how many tickets are sold.

I persisted in reading the entire article for the sake of writing this post. I wanted to know whether they will acknowledge the biggest factor here, which is that the more tickets are purchased, the more likely there will be more than one winners. Even having two winners can be devastating. The $1.6 billion suddenly turned into $0.8 billion. With three winners, it's $0.53 billion. If the ticket is purchased as part of an office pool with, say 10, participants, then $1.6 billion becomes $160 million. Not a bad payday but much, much worse than projected.

 

PS. They updated the post because too many people are pointing out the obvious about multiple winners. They continue to deny its importance.

Their math is wrong. Here is a good webpage that explains the math from a previous situation 10 years ago. The number of winners follows what is called a Poisson distribution. In the example given, there is a 60% chance of a single winner, but 30% chance of double winners and 10% chance of more than two winners. How can this be called "incredibly low odds"?

Another issue is that there are certain sets of numbers that attract much more tickets than usual. If one of those sets is the winner, you're going to have lots of winners.

They continue to completely miss the point.

 

 

 

 

Comments

[Jamie Briggs]

I'll never understand either side of the arguments about whether a person *should* buy a ticket.

Is there a compelling argument that at some point the odds are actually good? of course not.

Is there a compelling argument that the chance of winning a huge amount of money is never worth the $2 ticket cost? That's a personal decision for which the statistics are, frankly, immaterial.

What's the cost of this bad advice?

Still $2 :D

(unless, of course, such an article convinces someone to drop their electric bill check and buy as many tickets as they can with it... :( )

[Kaiser]

JB: Of course, data and math provide only a tool to aid decision making. The two interesting points to me about that Slate column are (a) from the perspective of the underlying mathematical analysis, there is good and bad math out there, especially so if we also consider bad assumptions leading to bad analysis; and (b) the cost I'm talking about is from the viewpoint of the columnist dishing out this advice to millions of readers. I recall writing a blog post, imagining that a company like Walmart just adds random 50 cents over-charge to a small proportion of transactions. One can say it doesn't hurt anyone materially but it does generate, in aggregate, a substantial chunk of money to Walmart's bottom line. What do you think of that?