A lottery for limited affordable housing, part two

A story about a lottery for 95 affordable housing units in San Francisco discusses the technique of using a lottery to award limited goods and how the lottery happens:

Lotteries that allocate scarce resources are not set up to distinguish the neediest from the merely needy. Rather, they reward random chance, which is a distinctly different notion of what’s “fair.”…

For years, San Francisco conducted public lotteries in a bingo drum. But the raffle tickets were always getting stuck in the drum’s crevices. The city also tried a big box. People couldn’t see what was happening inside, however, and tickets got stuck under the lid.

This exercise — rolling the drum, shaking the box, inspecting for trapped tickets and repeating — lasted hours on a building the size of Natalie Gubb Commons. Ms. Torres would bus around town, picking up applications, dropping off applications. Lines would wrap around some developers’ offices on deadline day….

Last year, San Francisco moved the whole process online. Renters can now more easily apply, which means that more do, and the odds have grown longer. But the system is more humane. The parts of the process where it has been most awkwardly apparent that people in need are competing are now less visible. The city still holds public lotteries, but they are primarily pep talks.

Three things jumped out at me about the lottery process and how it is presented:

  1. On one hand, a lottery can seem fair in this situation. How else would would limited public goods be fairly split up? We know that in regular life, having more resources and better connections tends to lead to more opportunities. For people with fewer resources and fewer connections to powerful people, isn’t a lottery fair?
  2. On the other hand, having to go through a lottery for something as basic as an affordable place to live seems crazy. The documentary Waiting for “Superman” used the lottery for a good school very effectively in its plot. By starting and end with the image of honest American families simply trying to get a good education for their kids through a lottery, it all looks absurd. The lottery itself is an excellent argument for why more affordable housing is needed.
  3. The actual mechanics of lottery are intriguing. A public drawing has a lot of potential for drama, both with images of excitement and disappointment. (Again, Waiting for “Superman” played this up.) But, actually having a fair system of drawing names is more difficult than it looks. And how can the applicants be reassured that it is an effective process? The shift to online makes some sense and yet I could imagine the process now looks even less transparent. How do we know the online system isn’t rigged? Is it truly random? What if the algorithm is biased?

I know waiting lists are commonly used for housing spots – and this has the advantage that Americans often like that people should at least have to put effort into getting on the list – but a lottery has both strengths and weaknesses.

Fun with statistics: people flock to stores that sold winning lottery tickets in the past

Ahead of the recent large Powerball jackpot, stores that sold winning tickets in the past experienced an increase in business:

When word got out that a southeast Pennsylvania 7-Eleven sold a $1 million Powerball ticket on Saturday, customers hoping to experience some luck of their own flocked to the store…

At a Casey’s General Store in Bondurant, Iowa, everyone knows it’s the place where a $202.1 million Powerball jackpot ticket was sold to a local woman in September. Asked what types of questions the store gets when the jackpots get huge, assistant manager Debra Fetters said: “Does lightning strike twice here?”…

“When you get those stores where they’ve actually seen someone win, they’re very enthusiastic about it. They know about the game, they have regular customers. A lot of it really does come down to great retailers that support the lottery, understand that there are winners on both sides.”

Linda Hamlin, also of the New Mexico Lottery, noted the story of “Millionaire Mary” Torres of Albuquerque. After she sold a $1 million winning Powerball ticket to an Albuquerque man in May 2011, she became known as a good luck charm. Her customers followed her to another store a few miles away.

And the article ends with this quote:

“Humans tend to be superstitious about things,” said Strutt of the Multi-State Lottery Association. “We all have our ways to ensure our best luck. But every ticket has the exact same chance of winning.”

What would happen if this argument, that their odds of winning do not increase, was presented to these purchasers who go back to the place of past winners? Would they say the numbers aren’t right or say it doesn’t matter? Perhaps this is a sort of Pascal’s Wager for Powerball: it doesn’t increase my odds of winning to shop at this particular location, but it can’t hurt!

This could be chalked up to superstition but it is also the result of humans looking for patterns where there aren’t any. Two things make where the winning person bought the ticket stand out: (1) there are few big winners and (2) the big prizes are noteworthy. Put these two together and all of the sudden people start seeing trends even though there is little data to work with. But, then you have news coverage a few years ago about a woman in Texas who won the lottery four times – four data points make a much better pattern than a one-time winner!

Reading between the lines of an ABC News story on the bad odds of winning the $500 million Powerball lottery

Check out this ABC News video about the odds of winning the $500 million Powerball lottery.

Several things are striking about the content of the video beyond the bad odds of winning: 1 in 175 million chance.

1. A journalist admits he doesn’t know much about math or statistics. It is not uncommon for reporters to go to experts like statisticians in times like these (appealing to the expert boosts the credentials of the story) but it is more unusual for journalists to admit they are doing so because they don’t know the information. I’ve argued before we need more journalists who understand statistics and science.

2. The reporter mentions some interesting odds that are more favorable than winning the Powerball. One of these is the idea that you are more likely to be possessed by the devil today than win the lottery. Who exactly keeps track of these figures and how accurate are they?

3. The story includes some talk about being more likely to win in particular states than others. Really? This sounds more like statistical noise or something related to the population of the states with multiple Powerball winners (like Illinois and New Jersey).

4. Interesting closing: the math expert himself hasn’t bought a lottery ticket before. So the moral of the story is that people shouldn’t buy any tickets?

More $1 million lottery winners each year than NBA players since 1990 that have career earnings over $1 million

I’ve written before about using the average vs. the median salary in the NBA lockout discussions and here is some more fuel to add to the fire: there are more $1 million lottery winners each year than NBA players who since 1990 have had career earnings of more than $1 million.

I want to call foul on the mainstream media. As I mentioned, a majority of the players in the league make less than $2 million, and yet people like Stephen A. Smith throw around that $5 million figure as gospel. We keep hearing the NBA lockout being described as “millionaires versus billionaires”. But most NBA players won’t become big earners like Kobe and LeBron. Here’s a fun breakdown:

Since the 1990-1991 season 1461 players have entered the NBA and of those:

  • 490 — or 33% — never earned $1 million in career earnings*
  • and that means… 971 have earned at least $1 million in career earnings*
  • 752 have averaged a salary of at least $1 million per year*
  • 643 have earned at least $5 million in career earnings*
  • 165 averaged a salary of at least $5 million per year*

As we can see, less than half of all NBA players in the last 20 years — the period of time where NBA salaries have been at their highest — have hit that $5 million mark over their entire careers. Just over one third — 33% — of all NBA players in the last 20 years have not even hit the $1 million mark in career earnings. And these numbers have been adjusted for inflation!

Here’s a fun comparison: on average, 1600 people win a lottery of at least $1 million every year! That’s right; the lottery has produced almost twice as many millionaires in the last year as the NBA has in the last twenty years!  The popular perception is that once a player enters the NBA they will earn millions and millions of dollars. The truth is that many players don’t hit that high mark.

Both events, winning the big lottery jackpot and becoming a NBA player, are statistically unlikely. However, I suspect that most Americans would say that winning the lottery is much more unlikely. But this blog post points out that even when players do make it to the NBA, a third don’t rake in the big career earnings associated with professional athletes (measured here as $1 million).

This would make for an interesting discussion starter for any professional athlete’s union: should the union be more concerned with allowing a smaller percentage of the athletes maximize their salaries or be more interested in guaranteeing a baseline for the majority of the league that are not stars?

The lottery figures themselves are interesting:

According to the TLC television show, “The Lottery Changed My Life,” more than 1600 new lottery millionaires are created each year. That doesn’t include people that have won jackpots of, say, $100,000 because than the number would be much higher. Still, 1600 is quite a high number.

If 1600 win at least a million in the lotto every year, it means that there are more than 130 each month, more than 30 each week, and more than 4 each day. That’s a lot of winners.

It would be interesting to see more documentation on this.

Would having a math PhD really help you win the lottery?

A journalist suggests that one woman who won four multi-million dollar lottery payouts was able to do so because she had a mathematics PhD:

First, [Joan Ginther] won $5.4 million, then a decade later, she won $2 million, then two years later $3 million and finally, in the spring of 2008, she hit a $10 million jackpot.

The odds of this has been calculated at one in eighteen septillion and luck like this could only come once every quadrillion years.

Harper’s reporter Nathanial Rich recently wrote an article about Ms Ginther, which questioned the validity of this ‘luck’ with which she attributes her multiple lottery wins to.

First, he points out, Ms Ginther is a former math professor with a PhD from Stanford University specialising in statistics.

A professor at the Institute for the Study of Gambling & Commercial Gaming at the University of Nevada, Reno, told Mr Rich: ‘When something this unlikely happens in a casino, you arrest ‘em first and ask questions later.’…

Three of her wins, all in two-year intervals, were by scratch-off tickets bought at the same mini mart in the town of Bishop.

Mr Rich proceeds to detail the myriad ways in which Ms Ginther could have gamed the system – including the fact that she may have figured out the algorithm that determines where a winner is placed in each run of scratch-off tickets.

He believes that after Ms Ginther figured out the algorithm, it wouldn’t be too difficult to then determine where the tickets would be shipped, as the shipping schedule is apparently fixed, and there were a few sources she could have found it out from.

At first glance, the story does seem unlikely: four wins and three from scratch-off tickets from the same retail location. But here are three reasons to doubt the claim that this woman beat the system:

1. If lottery algorithms could be figured out by the public, wouldn’t other people have figured this out as well? A math PhD sounds problematic but other smart people could figure this out if it could be figured out. Additionally, couldn’t this woman win more than 4 times if she had it all figured out?

2. Just because someone won the lottery four times does not mean that something underhanded happened. Just because some events are “random,” like winning the lottery or being struck by lightning, does not mean that people can’t win multiple times. Aren’t there plenty of other multiple lottery winners?

3. The quote from the professor is interesting: be suspicious first and then figure out what is happening. This is the view from the business end. If someone is gambling and consistently winning your money, you might respond. For example, this book about card-counting MIT students is fascinating (much better than the movie based on the book) not only for how the students figured out how to count cards but also because of the response of the casinos. (My favorite part – and I think I am remembering this correctly: the students leave Las Vegas because they are raising suspicions with their winnings. But they eventually find that their names and photos have been sent to casinos around the country. It gets to the point where they are escorted out of a casino just moments after entering.) But it sounds like the Texas Lottery Commission doesn’t think anything is wrong. Shouldn’t they be the ones who care the most?

If you read the original story, Ginther’s buying habits do sound strange. But I still think this reporter needs to find some more evidence before Ginther could be accused with certainty.

Nobody’s a hero here

The thrill is gone:  today we find out that there will not be another Guitar Hero release anytime in the foreseeable future:

Activision Blizzard will close its music-game business division, laying off hundreds of employees, and cancel the Guitar Hero game that was in development for 2011, the publisher said in a conference call Wednesday.

The drastic move comes after significant industrywide declines in the music game business. In 2007, Activision sold 1.5 million copies of Guitar Hero III in its first month of sales. Last year, Activision only sold 86,000 copies of the latest game in the series, Guitar Hero: Warriors of Rock. Slowing sales of chief competitor Rock Band led Viacom to sell maker Harmonix and close the MTV Games publishing division.

Activision said that the decline of the genre, plus the high cost of licensing music and producing the games, led it to close the business. [emphasis added]

Arguably, Guitar Hero and Rock Band were fads (at least, at their white-hot sales peaks) whose time had passed.  Nevertheless, these games were probably some of the cheapest console games (from a technical/development standpoint) made in the last few years.  The real cost driver here had to be the music licensing fees.  At the right (i.e., low enough) price, these games probably could have been made indefinitely, but it appears that monopoly-imposed costs have outstripped demand and the dreaded deadweight loss triangle has destroyed the market.

Which begs the question:  why does the music industry continually insist on killing geese that lay it golden eggs? In my view, there’s a difference between profiting from risk taking (i.e., capitalism generally) and expecting other people to pay you an ever-increasing cut of the revenue stream based on the risks they took in finding and exploiting a new market which literally did not exist before.  As for the music industry’s attempt to parlay other people’s risk taking into ever bigger royalty streams for themselves, they can’t really complain when the market softens and no one can afford to pay their exorbitant fees.

(On a final, parenthetical note:  no-doubt-soon-to-be-former music industry execs should perhaps consider a career move into lottery management.  In addition to being the ultimate something-for-nothing industry, the lottery is bigger than porn, movies, and music combined. It’s also a regressive tax on the poor, a perfect money-laundering machine for organized crime, and easily rigged.)