A traditional average is easy to understand. If you take a group of people, add their heights together and divide by the number of people in the group, you know the average height. A simple average is a relatively easy way to create a prediction for future behavior – in many cases, you can reasonably assume a new person entering the room would be at or near the average height.
More often than not, though, a simple average is inapplicable to the real world. Your distribution is too varied (your room consists of small children and professional basketball players) or some other occurrence makes the simple average useless in analytical prediction. In these cases, we can weight our numbers to yield a more useful weighted average.
A weighted average is centered, typically, around zero. Numbers with a lower rating will be forced closer to this central point while numbers with a higher rating will remain fairly close to their original value. It’s a relatively easy way to identify which results you care about most and want included in your analysis and which you consider extraneous data. The “extra” information will carry a far less weight and will have a much smaller influence on your overall results.
Unfortunately, when it comes to rating content or quality based on demographic segmentation, a weighted average is less than idea. The only information you have at your disposal is the number of individuals in a market segment. Surely we don’t want to say that the smaller market segments have less valuable an opinion than the larger ones!
A Bayesian average, on the other hand, does help us in this instance. Unlike a weighted average that moves values closer to zero, a Bayesian average uses knowledge of the entire group to moves values closer to the simple average of the group. So a small market segment would carry at least the average content or quality rating given by everyone, but it will either be increased or decreased by the actual opinions of the smaller group.
First you multiply the total number of ratings for your products by the average rating for all products. This is a constant. Next, multiply the number of ratings for a particular product by its calculated rating (so if product C is rated at 4.3 stars by a total of 15,000 people, you’d multiply these two numbers). Add these two numbers to get the top half of the equation.
To get the bottom, you add the total number of ratings for all of your products to the number of ratings for the particular product you’re looking at. Divide the top by the bottom and you’ll have the Bayesian average rating for that product.
If your product is rated by a lot of people, its Bayesian average rating will be somewhat closer to its original calculated rating. If, on the other hand, this is a relatively new product with few ratings, its Bayesian average rating will be very close to the average rating for all of your products.
The advantage of this system is the fact that your product ratings will be comparable to one another independent of the sample size that rated them. So now you can really know how your most popular, long-standing product compares to your newest one in the eyes of the market.