# What’s the expected value of your Powerball ticket?

As the Powerball jackpot grows to over \$300 million, we start to wonder if maybe buying a ticket is “worth it.” While the lottery is “worth it” in that ticket sales goes to things like state education, buying tickets is typically not worth it for yo because the projected payoff is far less than the ticket price.

The concept of Expected Value is a central idea in probability and statistics and refers to a weighted average outcome. For our Powerball example, the expected value equals the probability of getting each combination of winning numbers, multiplied by the payoff of the combinations.

Thehas a table with the odds and the payouts of each winning combination of numbers, making our job relatively easy.

We can transcribe these into a spreadsheet:

There isn’t much logic to this one. First we convert the odds column into probability, by taking one over the odds plus one.

Then we multiply the probabilities with the respective payouts by using the Sumproduct() Function:

Since Powerball tickets cost \$2, it seems we’re still losing about 65 cents on each ticket even with the jackpot above \$300 million.

It looks even worse given the \$302 million is the simple sum of annuity payments, while the cash value is much less at \$187.3 million.

That takes us down to 96 cents.

Taking into account a 35% tax rate would then take us down to 62 cents. And then there’s the chance that there are multiple jackpot winners, resulting in a split (we won’t get into that one here, but . Finally, let’s use the Goalseek function in excel to see when it becomes worth it to buy a lottery ticket taking into account a 35% tax bracket.

Pull up Goalseek from the Data Tab –> What-If Analysis –> Goal Seek

Then we set the after tax expected value cell (D16) to \$2, by changing the jackpot cell (B5). Basically Goalseek is Excel’s functionality for “guessing and checking”, for those who are not as algebraically inclined…

The answer? \$806 million! And that isn’t accounting for potential splits which is pretty likely once the jackpot gets that high.

# Monte Carlo Simulation – Fantasy Football playoff predictor

How likely will you make the fantasy football playoffs? It’s week 11 of the Fantasy Football season, which means there’s only three more weeks until the Fantasy Football playoffs. All your hard work up to this point – drafting your team, closely following daily fantasy football podcasts and injury reports, and agonizing over who to play in your Flex spot – rests upon what happens in these next few weeks. Continue reading

# What are the chances a Little League baseball player gets to the Major Leagues someday?

It’s that time of the year when Little League World Series coverage heats up on ESPN, and viewers get to see a miniaturized version of baseball played at the highest level. This year has been especially impressive with a super-team from Las Vegas that rarely makes errors, the Chicago team that beat them, and of course the sensational female pitcher Mo’ne Davis, who throws as hard as some high school pitchers. Every Little Leaguer dreams of making it to the big leagues, someday making a career of playing the game they love.  But how hard is it to get there? This is a question that we will try to solve this week with the help of a spreadsheet.

# Averages Matter: Mean, Median, & Mode

Illustration by Amie

The average value is very desirable in the world of statistics! Known as the central tendency, averages provide a way to understand the characteristics of a broad set of data. What are the different measures of central tendency? How can we calculate them? Let’s explore this below!

# Hypothesis Testing with Spreadsheets – Part II

Is the “height success rate” for seeds grown in organic soil significantly higher than that for those grown in the non-organic soil? Let’s use a statistical test to find out! But before we delve in, let’s review the amazing Central Limit Theorem (CLT). Why so remarkable, you may ask? Continue reading

# Hypothesis Testing with Spreadsheets – Part I

Seedlings for Experiment. Photo: Amie

What is the impact of organic soil on a seedling’s height? Will an organically-grown seedling be taller than one grown in non-organic soil? Armed with data, we’ll now tackle these questions by performing a statistical test in a spreadsheet!

To see how we our experimental design and data collection method, please see:

# Design & Conduct Experiments with Spreadsheets

Seedlings for Experiment. Photo: Amie

Seeking science experiment ideas? Want to conduct an experiment? Curious about hypothesis testing? Understanding how to design and test an effective experiment is an essential skill. Let’s investigate this research question: What is the impact of organic soil on a seedling’s height?

Spreadsheets are a platform to test an experiment or conduct a research study. With spreadsheets, we can collect & organize data, compute summary statistics, and even test hypotheses!

So, let’s begin our experiment with spreadsheets, statistics, seeds, & soil! Continue reading

# Should schools adopt B.Y.O.T?

A new trend across schools has emerged:  B.Y.O.T for Bring Your Own Technology.   Recently, an article in the New York Times describes the debate of whether schools should adopt B.Y.O.T.   Are you a fan or a critic of B.Y.O.T?  Do the advantages of adopting this policy outweigh the drawbacks, or do they not?  How can we think about this?  Before you answer our poll, let’s first discover how we can use a spreadsheet to develop a logical framework to better inform our opinion!