How Changes Have Affected the Powerball Lottery in the USA.
What does the history of the Powerball tell us?
I analyzed the data for the Powerball lottery in the USA since it has started on April 22, 1992, up to recent results dated May 30, 2020. Since there was not one data set that fit the criteria I was looking for, I had to combine multiple data sets to get the information I needed. You can find how and where I got my data at the bottom of this post under resources.
The main objective of this project is to find out if my findings of the actual results relate to the odds that are given for each change. I also will look at other aspects that have or may have changed as a result of each revision.
There have been many changes to the Powerball lottery over the past 28 years since it started. After doing some research I was surprised to see there have already been 8 changes since the start. I found a chart on Wikipedia’s website that shows all the changes and what they were. I recreated that table here.
There have been only two changes that did not have an effect on the probability of winning. One was when the Power Play option became available on Mar 7, 2001. The other one was when the Power Play was removed on Jan 15, 2012, then reinstated on Jan 19, 2014. The reason the probability did not change is because there was no change to the number of white or red balls.
When looking at the probability (odds) of getting a specific combination there is some complicated math involved. This is not a post about math equations so I will spare you the mathematical explanation. Long story, short… The probability of winning is calculated based on the winning combination divided by the number of possible combinations.
The percentage of winners vs odds of winning.
It really is no surprise to see the probability of winning since the latest change is the lowest of them all. Since the change in 2015, the data shows the lowest percentage of winning (only 35 winners) compared to the number of games (486 games) that were played. Based on the information from Wikipedia, that revision also has the lowest odds (1 out of 292,201,338) of winning.
One thing that did surprise me though is that the change in 1997 (12.64%) and 2001 (11.45%), are not the same percentages of winning. They have a difference of 1.19%, yet the statistical probability (1 out of 80,089,127) of winning, for those two revisions, is the same. Though 1.19% does not seem like a big difference, consider this; During the 1997 revision, there were 348 games played and 44 jackpot winners, while during the 2001 revision there were only 166 games played and 19 winners.
There are a few other things that caught my attention as well. One is the revision in 2002, it actually had a percentage (14.24%) of winning and that is closer to the percentage (16.78%) of when the Powerball first started than it is to the change after it in 2005 (11.71%). Yet there is a big difference in the probability being 1992 was 1 out of 54,979,154 and 2002 was 1 out of 120,526,769. The number of games played before the first revision was 578 with 97 winners, the largest numbers out of all the changes. While the number of games during the 2002 change was 302 with 43 winners and the games played during the 2005 change was 350 with 41 winners.
Another thing that caught my attention is the 2012 (16.67%)and 2014 (13.48%) change. They both have the same probability of winning, yet there is a large difference in the percentage of actual winnings. The games played during the 2012 revision was 210 with 35 winners, while the 2014 change only had 178 games and 24 winners.
Also the 2005 (11.71%) and 2009 (13.61%) change. During the 2009 revision, there was a lower probability (1 out of 195,249,054) of winning versus the 2005 revision with a 1 out of 146,107,961 probability, yet there was a higher percentage of winners during the 2009 revision.
What does this data mean?
In my opinion, based on the data I examined, the odds of winning the Powerball lottery can not accurately be predicted. The statistical probability of winning the lottery can only be based on the number of possible winning combinations, however, that can not accurately determine the number of winners that will actually win the jackpot. I conclude the number of actual winners compared to the number of games played does not directly relate to the statistical probability of winning.
How has the size of the Jackpot won changed?
This bar chart race shows information about how things have changed over the life of the Powerball. As it goes through the animation you will also see facts about that time period on the bottom left.
The first thing to take away from the above graph is the outlier. This is the largest jackpot ever won in the history of Powerball and it is also the largest won since the latest revision in 2015. Most of the revisions create a tight clustering with the biggest exception being the 2015 revision. What do you think could cause this? I wanted to dig into the data further to find out why.
Before we dig deeper though, I want you to think about why the different revisions cluster together in a rather tight group? Could it be that this was planned out this way by the people who run the lottery? Could it be just a coincidence(if you believe in that sort of thing)? Or could it be because there were more winning jackpots and fewer rollovers? The numbers don’t lie, so lets now dig a little deeper into the data…
As you can see in the table above, most of the changes yielded approximately 83% — 88% for the number of games where there were no jackpot winners per revision. Then we look at the most recent change made in 2015 and you can see the percentage of games where the jackpot was not won, jumps into the low 90th percentile. This shows us that most likely the main reason for that one outlier (the largest jackpot) was based on the number of times that game had to roll over before there was a winner. I verified this by looking at the data for that time period.
For the jackpot of $1.586 Billion that was won on Jan 13, 2016, there were 19 rollovers before there was a jackpot winner. This is the largest number of times that the winning combination did not yield a winner.
What can we take away from this information?
The biggest change in the amount of the jackpot won was in 2015. The most probable reason for this is the increase in the number of possible winning combinations due to the increase in the number of white balls. That in turn increased the length of time the game went with no winners.
Now time to look at the top winning numbers!
Looking at the above graph you can see there is a large clustering of the amount of times the numbers were called between approximately 0–50 times. Then when you get into the higher occurrences it is more spread out. Those higher occurrences also happened during the same revision time period, which was the start of the Powerball.
Another thing that jumps out at me is the largest clustering is from approximately 0–40 for the winning numbers. The reason could be simply because during the earlier years of Powerball the total numbers only ranged from 45–49. Then in 2002–2014 the total numbers started to go up into the 50’s, starting at 53 up to 59. Then there was a dramatic jump during the 2015 revision where the total numbers went from 59 to 69.
How did the number of balls change winning?
Comparing the data, it is plain to see that by increasing the number of possible combinations, the odds of winning increases and the frequency of the numbers being drawn decreases.
Can you really predict what numbers will be drawn together? The short answer is no, but you could look at the top numbers and use those to give you a very small better chance at winning. Just keep in mind, no matter what, lottery games are gambling, totally random, and there is no sure-fire way to predict the winning combinations.
What about the participating states?
Another change that has taken effect over the years were the states that participate in the Powerball. Based on information from Wikipedia, this is a list of the states that participate in the Powerball and when they started:
You will notice that there are several states where the date they started participating in the Powerball is actually before the official start date. This is correct and not a misprint. The reason the dates are prior to the official start is that the Powerball lottery actually started under another name. It was originally called Lotto America and started in Feb 1988. Lotto America was the first game launched by the Multi-State Lottery Association, which was formed in Dec 1987. Lotto America became Powerball in Apr 1992 and that is when they had their first drawing under the new name on Apr 22, 1992.
This map shows the winners per state for the complete timeframe of the Powerball. Indiana is the state with the most winners. Then the next one is Missouri and then Minnesota. It really is no surprise that these are the top three winning states since they were some of the original states that participated when the Powerball started. So let’s take a look at some of the other states that joined the Powerball family later, within different changes.
Above you can see that the top three winning states were not the same with each change. Every revision yielded only one state and they were different during each change. Then you look at the 2nd and 3rd top states and there are several revisions that had multiple states that tied for that position.
Let’s now compare the top winning state for each revision to when they joined the Powerball family:
- Indiana, Missouri, and Kentucky were each one of the original states.
Indiana was the first one to be the top winning state. Then Missouri became the top state for the next revision in 1997. Kentucky then follows by being the top winning state in the following revision in 2001. - Pennsylvania joined on Jun 29, 2002. So they joined over 3 months before the revision when they became the top state in Oct 2002.
- Louisiana joined on Mar 5, 1995. It was just over 10 years before the change when they became the top state in Aug 2005.
- Florida joined on Jan 4, 2009. Just 3 days before the revision when they became the top state on Jan 7, 2009. I find this one rather ironic. Aside from Indiana taking the top before the very first revision, this is the closest that a state came to their join date.
- New Jersey joined on Jan 31, 2010, with 9 other states. That was just under 2 years before the revision when they became the top state in Jan 2012.
- California joined on Apr 8, 2013. That is approximately 9 months before the change when they became the top state in Jan 2014.
- New York joined on Jan 31, 2010, along with 9 other states. Over 5 years before the revision when they became the top state in Oct 2015, which is also the latest revision that Powerball has had.
What does this information tell us?
One thing that I wondered about was if there was any relationship between when a state joined the Powerball family and when they became the top winning state. Based on the information I analyzed, I do not see that there is any correlation between the two. Here again, there is no way to predict if a state will have more jackpot winners based on when they started participating. However, I do find this information rather interesting and something that I would like to further explore at another time.
Have you ever wondered if a winning number combination was ever repeated?
This is actually a little off topic but I was curious about this myself. So I used the data I have gathered already to look at this out of pure curiosity. I was very surprised to find that YES, only one winning number combination has been repeated in the entire history of the Powerball.
In Conclusion…
Yes, there have been quite a few changes to the Powerball over the past 28 years. Do the revisions have any sort of relationship to the data we have looked at here? Mostly no. However, there are a couple that does show some sort of correlation. One would be the Jackpot amounts won compared to each change. The other would be the top winning numbers drawn per revision.
With that being said though, I would not use any of this information to try to predict what will happen next. If you look at all the previous changes, yes you see some relation but once you look at the most recent revision in 2015, all of that sort of goes out the window, so to speak.
The moral of this story…
Don’t quit your day job anytime soon. I know I will not be.
The Powerball lottery, as with other lotteries, is purely randomized. There is not a sure-fire way of being able to precisely predict what the winning combinations will be. In researching for this project there were a few posts and websites out there that tried to figure out a way to predict the lottery but I was not able to find even one that made any sort of logical sense to me. So this tells me that if you are meant to win you will.
There is no mathematic equation or machine around “yet” that will predict the winning numbers for you or everyone would be doing it and then it would no longer be considered gambling.
Resources:
- The majority of the information I found on this topic, that was not in the data sets I used, came from Wikipedia.
- Data set 1: Scraped from Old Powerball Number Results: Starting in 1992
Ranges from Apr 22, 1992 — Dec 31, 2008, formatted to make it usable. - Data set 2: Powerball Winning Numbers — Kaggle
This one ranges from Jan. 3, 2009 — Jan. 30, 2010 after reduction. - Data set 3: Lottery Powerball Winning Numbers: Beginning 2010
- I also needed to add some information to these data sets as they were not complete with all the information I needed for my research. I searched the web to find where each of the jackpots were won.
- You can also view my projects on my portfolio website: Joanne Middour
- If you would like to see all of my data and work, you can take a look at my Google colab notebook. I also have a copy up on Github.
