Hacking Growth: How Today's Fastest-Growing Companies Drive Breakout Success

by Sean Ellis

While the formula looks a bit intimidating, in reality it is straightforward. What the equation says is that the similarity between two items, A and B, is equal to the size of the intersection of A and B divided by the union of A and B. Let’s use our grocery app to walk through a quick example of how it works. Let’s say they want to test the hypothesis that recommending products that are typically purchased together in the app will increase the average order size of each shopping trip. In order to make these recommendations effective, they need to calculate the likelihood that people who purchase one product, such as peanut butter, will also purchase the recommended one, such as jelly, is greater than that likelihood for other product combinations. The team will want to recommend items that are most often purchased together to increase the likelihood that shoppers accept a recommendation and add that additional product to their shopping cart. The intersection size in the Jaccard index is how many people buy both peanut butter and jelly together, while the union is how many people bought either peanut butter and jelly independently. For example, if you find that 30 people have purchased both peanut butter and jelly together, while 100 people have purchased either peanut butter or jelly independently, you’ll get a Jaccard similarity score of 0.3, which is actually quite high as these scores go. In contrast, the score for peanut butter and, for example, laundry detergent will...

jaccard index