The Law of Large Numbers

On today’s show we’re talking about the law of large numbers. The law of large numbers is a mathematical theorem in statistics thatdescribes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and will tend to become closer to the expected value as more trials are performed. But we’re not going to be talking about statistical theorems today.

We’re talking about the ability of the human mind to process large numbers when presented with these big numbers.

We have so many facts and figures that are so big that they become incomprehensible. If I said to you 100,000 or 1,000,000,000, the impact is almost the same.

I mean think about it.

The wildfires in California have burned 2.3 million acres so far this fire season. Most people can’t process what that means. Yes, I know it’s a lot. But how big is 2.3 million acres. It’s not a unit of area that most people can process, let alone multiply by a large number.

An acre is a unit of area that measures about 208 feet by 208 feet. In a dense urban setting you will often get between 6-8 houses per acre, and 12-15 townhouses per acre. An acre isn’t huge, but it’s not small either.

Maybe square feet are easier to understand. A square foot is a unit of area that measures 12 inches by 12 inches. Or if you prefer metric, it’s a unit of area that measures 30 cm x 30 cm. We’re talking wildfires that have burned 100 billion 188 million square feet. Somehow, I’m not finding it any easier to comprehend how much has been burned in California in this year’s wild fires. Perhaps it’s easier to talk in square miles. This year’s fires have burned about 3,600 square miles. Even that is hard to process. If I told you that this is an area equivalent to 12 times the size of New York City, it’s starting to get easier to understand. Or if I told you that it’s about 40% of the total area of the Dallas-Fort Worth metro area, you’re now starting to be able to comprehend it. In truth, I haven’t told you anything different in any of these examples. But when I give you a frame of reference, it’s starting to become easier to process.

So far this year, the Corona Virus pandemic has killed 196,000 people in the US over a six month period. Exactly how many people is that? Yes, that’s a lot of people. It’s a massive human tragedy. It’s three times more American soldiers than were killed in the Vietnam War. That doesn’t really help either.

Think about taking Fenway Park in Boston where the Boston Red Socks play. You would need 5.2 stadiums the size of Fenway park to hold that number of people. That’s a jarring visual image.

Numbers by themselves are abstract, even for mathematicians to comprehend the scale and proportion.

If I told you that the newest Amazon fulfillment center to be built in my home town was 1 million square feet, how many people could truly comprehend what that means? But if I told you that you could put 60 NHL hockey rinks in the same area, or you could fit 17 football fields, it is starting to get easier to understand.

So why am I telling you this?

As you communicate with your investors, with your stakeholders, with your business partners, or with you grandmother, don’t throw numbers at them. Make sure you create a frame of reference that is understandable when you communicate a number.

Have an awesome 86400 seconds.