Consider this.
Do your odds of being struck by lightning increase if you stand outside during a thunderstorm holding a golf club?
Do your odds of winning the Mega Millions Lotto get any better when you buy more tickets? With the latest lottery promising to top $1.5 billion it makes you wonder.
Often, we hear the comparison of winning the lottery to your chances of being struck by lightning and it must be because of the relevance of lightning. Rain, thunderstorms and lightning is something tangible – we have all experienced a downpour and seen a few heavy storms. Its rain and lightning often follows, we get it.
Look at the Money (not the data?)
Given an uncommon event like the lottery a reference point gives the chances of winning credibility. It appears to be possible. And how could we not when we look at marketing surrounding lotteries. Colorado’s “Welcome to Winning” and New Jersey’s “Extreme Winning” showing $100 bills falling from the sky just might be another way to relate the ease of winning. Other advertising is more subtle. Power Ball ads simply say “Believe” (my personal favorite) and the Illinois lottery adds “Anything’s Possible”, implying maybe its not and, well, they do not want to over promise. However, most lottery advertising shows the ‘upside’ of betting a few dollars with their images of luxury. They provide the possibility of being a rich person and rarely (except for the fine print) tell the story of the numbers, and that is what we call a Data Dupe.
Really Look at the Data
Behind all those glamourous images you will likely find how each lottery works and the spectacularly small odds of winning. The odds of picking the correct numbers are determined by how many numbers you need to choose and the range of those numbers. Pick one number from 1 to 50 and your probability is simply 1/50 or 2%. To pick a second number correctly (without replacement) is one out of the remaining 49 numbers (1/49) multiplied by the probability of the first number (1/50 x 1/49) or 0.0004. To put this in terms of odds, take the inverse or 1 in 2450. Not too bad, however with the addition of each number the odds quickly decrease. The odds of correctly choosing a five number sequence are 1 in 2.1 million. Increase the range of numbers from 50 to 70 and add a sixth ‘multiplier’ number similar to Mega Millions and odds are more than 1 in 300 million. Which brings us back to golf.
The numbers are not as thrilling as the magical images of owning a sports car with solid gold wheels or lounging in a tub of expensive wine (both real lottery ads). But it reminds us that the excitement of winning often prompts people to buy more than one ticket. Does a 2 in 300 million chance of winning really make a difference? Are two chances of winning something so nearly impossible any better? Not really. Just like your golf game. The more you play the better you get, and the more you play in the rain, well surprisingly doesn’t significantly change your risk. Simply being outside is the risky part with more lightning victims running, sitting at the beach, or on a soccer field, than holding a golf club. Golfers are about 2% of lightning fatalities. According to the National Weather Service your odds of being struck by lightning in any given year are 1 in 1.2 million which is a lot better than winning the lottery. Despite what most people say the two things just are not comparable.
A Sampling of Lottery Advertising
Data Duped 