How often are Powerball jackpots won?

For any lottery player, one hot topic is surely the frequency of winnings. How often do winners emerge? We are not referring to winners of small prizes (fifty dollars to a few thousand dollars). Some of the larger small prizes are interesting for sure (e.g. $50,000). But these small prizes, though nice to have, are far too small to give the feeling that the winner is “set for life”. So the question is: how many “million-dollar plus” winners are there? In fact, the most read post in this blog is on this question. The post is called How many lottery winners are there in a year?. For California lottery, the answer is about 10 prizes a year that pay out$1 million or more. This fact is based on the lottery winnings data from California Lottery from 1985 to 2010 (discussed here).

What about Powerball? How many jackpot winners are there? How often do people win Powerball jackpots? There’s plenty of winners winning small prizes. Powerball is surely the biggest lottery game in United States. The jackpot sizes are now in the hundreds of million dollars range (sometimes in the billion dollar range). Powerball definitely catches people’s imagination. The essential question is: how often do people win these jackpots that are in the hundreds of million dollars (or more)?

We answered this question in a blog post called Making Sense of Powerball Data. Go there to look at the graphics and analysis. Here’s the graphics used in that blog post.

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How often do people win the Powerball jackpot? The short answer is that there are fewer Powerball jackpot winners than there used to be. But the jackpot sizes are much larger than what it used to be. The average jackpot size in 2016 (the last full year of data) is about $490 million (almost half a billion dollars). The jackpot sizes prior to 2016 were in the one hundred million dollars range. So the average jackpot size is almost five times larger than what they used to be. Fewer winners but larger winnings. This is by design. A rule change in 2015 made it harder to win the jackpot. As a result, weeks and months go by without a jackpot winner. Once the jackpot accumulates to the hundreds of million dollars range, people are really excited. Excitement drive ticket sales. Some people call this a cynical ploy. Regardless of whether it should be labeled cynical, it is definitely a ploy. The ploy is working spectacularly. So buyers beware. Powerball is an exciting game. The prize of a ticket can allow the buyer to fantasize for a few days. The odds for the fantasy to become a reality are 1 in 292 million. There are not these many adults in the United States! If every adult in the United States buys a Powerball ticket, it is still possible that there be no jackpot winner! This is one part of the ploy that makes it hard to win the jackpot. With winning less frequent, the jackpot grows larger and larger. So the jackpot sizes in the hundreds of millions of dollars are indeed manufactured. It is OK to buy a ticket or two. But be sober minded. Just know that there is a larger force working against you than for you. The featured post gives further explanation on the Powerball data. It also has links to other posts on the business model of Powerball (the model is for the enrichment of Powerball and not for the players). It also talks about alternative money strategy for anyone who do not want to be manipulated by Powerball. $\text{ }$ $\text{ }$ $\text{ }$ $\copyright$ 2017 Dan Ma Advertisements How wealthy are the world’s eight wealthiest people? To find out the total wealth of the top 8 richest people in the world (Bill Gates, Warren Buffet and six other people), we can certainly look up publicly available information on the Internet or from other sources. According to one tabulation based on data from Credit Suisse Global Wealth Data book 2016, the total net worth of these 8 richest men (they are all men) in 2016 is$426.2 billion. Of course, this is a big number. What is a good way to put this number into a proper context? For further meaning of this number, a comparison will be helpful. It turns out that according to the same tabulation, the total wealth of the 3.6 billion people in the poorer half of the current world population is $409 billion. This is a stunning contrast and is a vivid demonstration of the wide gulf between the richest and poorest people in the world. There is no need to use chart and graph to enhance the demonstration. Just the fact 8 individuals own more wealth than the combined wealth of the people in the bottom half of the world’s economy is enough to convince anyone of the disparity between the have and the have not. I came across this report recently in an article from npr.org. It discussed a recent report released by Oxfam International on global wealth inequity. Here’s the press release by Oxfam on this report. Here’s the actual report by Oxfam. Oxfam International is a confederation of 19 organizations working together with partners and local communities in more than 90 countries to combat poverty. The top 8 richest people are, in the of net worth: 1. Bill Gates: America founder of Microsoft (net worth$75 billion).
2. Amancio Ortega: Spanish founder of Inditex which owns the Zara fashion chain (net worth $67 billion). 3. Warren Buffett: American CEO and largest shareholder in Berkshire Hathaway (net worth$60.8 billion).
4. Carlos Slim Helu: Mexican owner of Grupo Carso (net worth: $50 billion). 5. Jeff Bezos: American founder, chairman and chief executive of Amazon (net worth:$45.2 billion).
6. Mark Zuckerberg: American chairman, chief executive officer, and co-founder of Facebook (net worth $44.6 billion). 7. Larry Ellison: American co-founder and CEO of Oracle (net worth$43.6 billion).
8. Michael Bloomberg: American founder, owner and CEO of Bloomberg LP (net worth: $40 billion). The number of the richest people with total wealth equal to the poorer half of the world works like a metric to measure wealth inequality. So it is in some sense a measure of wealth gap. It is not clear if this measure of wealth gap is used by anyone other than Oxfam. But it sure is an effective metric. It gives a vivid demonstration of the wealth disparity between the richest and the poorest. In 2016, “the number of richest people = half of world” metric is 8 as discussed above. In past years, the number was higher. For example, in 2015, the number was 62. Going back further the number got progressively larger. $\displaystyle \begin{array}{rrr} \text{Year} & \text{ } & \text{Number of Richest People} \\ \text{ } & \text{ } & \text{ } \\ 2010 & \text{ } & 388 \\ 2011 & \text{ } & 177 \\ 2012 & \text{ } & 159 \\ 2013 & \text{ } & 92 \\ 2014 & \text{ } & 80 \\ 2015 & \text{ } & 62 \\ 2016 & \text{ } & 8 \end{array}$ The above table is found in the Oxfam press release in 2016 (for the 2015 data). Even in 2010, the contrast with 388 richest people equal half the world is already a clear and lopsided contrast. The trends exhibited in the table show that the wealth gap keeps getting wider. In addition to the 8 richest people equal half the world, the same report also shows that the 1,180 people in the 2016 Forbes list of the world’s richest people own as much wealth as a full 70% of the rest of the world. The average wealth of the 3.6 billion people in the poorer half is$113.6 (=409 / 3.6). On the other hand, the average wealth of the top 8 men is $53.275 billion (= 426.2 / 8). This is again a contrast as skewed as the one mentioned at the beginning (basically 50 billion dollars versus 100 hundred dollars). It will be interesting to know the median wealth of the 3.6 billion people in the poorer half of the world economy. It is likely that the wealth data in the poorer half is skewed as well, meaning that most people have very little (say subsisting on$2 a day) while the top part in the group have wealth in the hundreds or thousands.

Statistics is comparative. There are other comparisons that can be made. For example, how does the total wealth of $426 billion stack up against the GDPs of countries of the world. Of course, we cannot expect the total wealth of Bill Gates and Warren Buffet and 6 others men to equal the GDP of a large economy like the United States. The GDP of the United States is over$18 trillion, which is over 42 times the combined wealth of the 8 richest men. This is still a staggering amount of wealth. Take the combined wealth of the 8 men discussed here, multiply that by 42 and we are approaching the size of the US economy! According to this GDP ranking, $426 billion is about the same as the GDP of Iran, which is about$425 billion. Iran is in the 26th largest economy in the world (according to one of the three ranking in the Wikipedia link). Any way you cut it, these 8 individuals are very wealthy.

A Periodic Look at the California Lottery

What are the odds of winning the California Lottery? I am talking about the winning of $1 million or more (the kind of winning that is a game changer in one’s personal life). How often are these million-dollar tickets won? Ten months ago I estimated that the odds of winning$1 million or more in the California Lottery were one in 36 million (see Taking another look at the California Lottery). The data were based on data from California Lottery that I obtained in November 2010 (see Shining a light on the California Lottery). Nothing happened in the last ten months indicates that the odds of winning has fundamentally changed.

Just to confirm, I count the number of winning million-dollar winning tickets as of today (August 30, 2011). This is done at the website of the California Lottery. The data are not readily available. I have to search at this site. I count the tickets by searching one county at a time (there are 58 counties in the state). The result: since the inception of the California Lottery in 1985, there are only 257 tickets that paid out $1 million or more (an increase of 10 winning tickets over 10 months ago). So in its 26-year history, there are only about 260 winning tickets, about 10 per year. The increase of 10 tickets in the last 10 months also confirms the average of 10 winning tickets per year. With the increase of 10 more winning tickets, the odds are actually a little higher, about one in 36.7 million, but still not fundamentally different from 1 in 36 million. The mantra of many lotto players is that you have to buy a ticket in order to win. That is so true. You have to get in the game to have a chance to win, even though the chance of winning is infinitesimally small. On average it takes the purchase of about 36 million tickets to support one winning ticket. Still dreaming of winning big? Wrong Side of the Road, Wrong Side of the Law Jessica Lynn Shekell was a 21-year old and a sociology major at California State University at Fullerton in 2009. In the wee hours of October 26th of that year, she was driving in the wrong direction on a stretch of the 91 freeway in Anaheim. Shekell’s Toyota pick-up truck crashed head-on into a Chevy’s pick-up truck. The results: Sally Miguel and Patricia Miguel (two sisters in the front of the Chevy’s pickup truck) were dead and their two young nieces (Mary Miguel and Sara Miguel) suffered permanent internal injuries. The lessons? Avoid being on the wrong side of the road and being on the wrong side of the law. With drinking and driving, only do one of them. Some actions in life have grave consequences. Alcohol imparied driving is one of them. Approximately 45 minutes after the crash, Shekell’s blood alcohol content (BAC) was 0.26 percent, three times over the legal limit (0.08 percent in all 50 states). This meant that the BAC at the time of crash would be higher. According to the BAC calculator of the Police Department of the University of Oklahoma, for someone weighing 120 pounds, two hours after drinking eight 8-oz beers, the estimated BAC is only 0.21 percent (Shekell’s weight was 115 pounds at the time of the crash). The same calculator estimates that drinking eight margarita will result in a BAC of 0.24 percent. Shekell likely had many more drinks than eight. On the night of the DUI crash, Shekell and her friends were drinking at two bars in Placentia, California for several hours. Shekell was sentenced on Wednesday March 9 to six years for the DUI crash. The prosection asked for 13 years. The defense asked for probation (nice try). Orange County Superior Court Judge Robert Fitzgerald picked the middle point. Is the justice served? In my view, a stiffer sentence is called for. Interestingly, on the night of the crash, Shekell was not yet 21 years of age (less than two months away from her 21st birthday on December 12). So she was not of legal drinking. According to the prosecutor Susan Price, Shekell was also cited for underage drinking in 2009. Prior to sentencing, Judge Robert Fitzgerald sent Shekell to a 90-day diagnostic program operated by the state Department of Corrections and Rehabilitation, during which she denied being an alcoholic. When the program was over, officials recommended she be sent to prison. Was it that Shekell was not showing remorse to the the satisfaction of the officials in the diagnostic program? It seems clear that she denied she had an alcohol problem. Two lives were snuffed out by someone who denied having an alcohol problem. Six years do not seem fair to the victims’ family. Both nieces of the victims suffered permanent injuries in their bodies, having to deal with gaping physical and emotional wounds for the rest of their lives. Another lesson from this crash is that wearing seatbelt can save lives. The victims in this crash did not wear seatbelts. In my view, this does not lessen the gravity of the crime committed by Shekell. On the other hand, even with wearing seatbelts, the victims would still sustain serious and likely debilitating injuries. With or without seatbelts, it is a no win situation for the victims. If Shekell has any shred of decency in her bones, she will have to deal with the weight of this tragedy for the rest of her life. At least she will be out of prison before her 30th birthday. Sally and Patricia Miguel are gone forever. In comparison, Shekell’s prospect seems quite good. Justice aside, it is also not a good situation for Shekell. She was hospitalized for facial trauma and fractures to both arms. Any normal person will have to grapple with the enormous guilt from murdering two people. Though she got a light sentence, she still have to spend six years in a state prison, which could be put to other productive uses. She could finish school and start a career. Any plans she had before the crash will have to wait until she turns 30. Shekell surely had put her family through much anguish. Think of the legal costs her family had to shell out. For all those who drink and drive, think about this. If you do not care about the victims, you ought to at least care about your future and your family. I sure do hope that the drinking buddies of Shekell on the night of October 26, 2009 had learned this lesson too. It is really simple. If you get plastered, do not get behind the wheel. How many lottery winners are there in a year? I have been wanting to answer the questions in the title. I found that statistics on lottery winning is hard to come by. Even when the state lottery commissions are required by law to made the information public, they tend to bury the information and you have to do work to dig it up. I have strong indication that on an annual basis, winning tickets that pay out one million dollars or more only number in the hundreds. In contrast, there were 37,261 people killed in motor vehicle crashes in 2008 in the United States (see the report from the National Highway Traffic Satety Administration). So if you are passionate about winning various state lotteries, it makes sense to be passionate about not winning the negative lottery of fatality in a motor vehicle crash too. As of November 2010, there were only 247 winning tickets paying one million dollars or more (see the previous post with this discussion). To get this information, I had to look up the winning tickets in each of the 58 California counties in the official site of CalLottery. So about 10 people are made millionaires by CalLottery each year (since its inception 25 years ago). The state of Iowa is more forthcoming. The official site of the Iowa Lottery actually had a press release listing out the stats. The number of Iowa Lottery tickets that have won prizes of$1 million or more (through August 2010) is 110. Once again in the 25 years history of the Iowa Lottery, only 110 people were made millionaires, on average 4.4 per year. For the Iowa Lottery, the odds for winning $100,000 or more are better for sure (1089 winnings so far in 25 years) but the odds are still small. The state lotteries are in the business of selling dreams. I suspect that they do not want to provide a picture reflecting the true odds of winning big. With all the state lottery commisions across the United States combined, I cannot see how the number of winning tickets ($1 million or more in each one) in one year can be in the thousands. If someone is forking over hard earned cash each week to play the lottery in the hope of winning big, it also makes sense to pay attention to traffic safety in the hope of not winning the negative lottery of death in a car crash.

Update (12/20/2017). A recent blog post answer the same question for Powerball. The winning of the Powerball jackpot occurs much less frequently than used to be. This is a cynical ploy to drive ticket sales. You can read it here. The blog post gives the link to the blog post in a companion blog that gives the graphics and analysis.

Governor Brown wants to take your cell phone

No, this is not a government seizure of private cell phones. Jerry Brown wants your cell phone only if it was issued by the California state government. Even then, the chance of it having to turn it in is only 50%. The newly installed Governor Brown is only proposing to take away government paid cell phones from certain California state employees in an effort to save money. The potential saving is to the tune of $20 million. Trying to close a budget gap in the California state government that is expected to be about$28 billion, the governor needs to find money anywhere he can.

On the way to work this morning, I heard a report on the radio about the proposal from Governor Brown (here’s one link). The gist of the report is:

1. Governor Brown does not want all the cell phones back. He just wants half of them back. The total number of phones to be turned in by June 1: about 48,000.
2. The state government currently foots the cell phone bills for about 40% of its workforce. The total number of state employees with free cell phones: about 90,000.
3. The state government is currently paying on average $36 a month per cell phone. 4. Governor Brown’s proposed cell phone reduction order should save the state$20 million.
5. Even with the proposed saving, one fifth of the state workers will still use state-funded cell phones.

After I heard this report on the radio, I jotted down the nummbers and I found that these numbers are internally consistent and for the most part accurate. The numbers seem to hang together quite well. Definitely there is no glaring errors. In this one instance of budget cutting at least, Governor Brown and his staff got the numbers right.

Here’s how I looked at these numbers. I am going to discuss each of the points listed above.

1. Currently there are about 96,000 state-funded cell phones in the hands of California state givernment employees. Half of these phones are to be turned in by June 1. That leaves 48,000 cell phones still being in the hands of state employees.
2. About 90,000 state employees have government cell phones. The count of 90,000 is about 40% of the total state workforce. This means there are currently about 225,000 state employees (see note 1 below).
3. The average monthly bill per cell phone is $36, making the average annual bill per cell phone$432.
4. The total annual expense for the 48,000 cell phones being cut would be $20,736,000 (see note 2). This amount is slightly over$20 million and is thus in line with the \$20 million being reported.
5. Even with the proposed saving, one fifth of the state workers will still use state-funded cell phones. One fifth of 225,000 (from point 2) is 45,000. From point 1, about 48,000 government paid cells phones will still be used by state employees. Though the 45,000 is less than 48,000 by 3,000, the difference is not large.

The only external number that I had to find is the total number of state employees in California. The number I obtained from the California State Controller’s Office is 237,576 (as of October 2010). The estimate obtained from the radio report is 225,000 (point 2 above). Overall, the numbers hang together well.

The proposed cut makes sense. According to Governor Brown, some agency heads and managers need to be in touch with employees 24/7. But most state employees do not. However, not the entire amount of proposed saving will be realized this year since some of the cell phones may be under contract with cell carriers. I hope the savings will work out as planned.

Note 1
To find 40% of 225,000, we multiply 225,000 by 0.40.

$225000 \times 0.40=90000$

But in the radio report, the number 90,000 is given instead. To derive 225,000, we need to do the opposite, i.e. divide 90,000 by 0.40.

$\displaystyle \frac{90000}{0.40}=225,000$

Note 2

$432 \times 48000=20,736,000$.