Google Meridian | Adstock and Hill

— Hi, I'm Alex. The adstock and Hill functions are two transformations used in Meridian. Before we look at the code or the math in Meridian, we need to agree on how marketing actually works in the real world. It is rarely instantaneous and it is rarely linear. Imagine you see an ad for noise-canceling headphones. You probably won't buy them this afternoon. You might watch a few tech reviews, wait for a paycheck, and then place the order. This illustrates the concept of lagged effects. Meridian captures this using the adstock function. Now, imagine an advertiser decides to double their advertising budget. Will they get double the sales? Likely not. This is saturation, which Meridian captures using the Hill function. Now, let's break these down mathematically, starting with the adstock function. Adstock is a function of media execution at time t, one time period back, all the way to L time periods back. This is reflected in the summation, which starts at time t minus zero and goes all the way to time t minus L. Let's talk about this L term, which determines how far to look back. This L term is called max lag in Meridian and is set by the user. While media effects could theoretically last much longer, we truncate them at L. It's not always advised to set L to a very large value, say 100 weeks. If you look back too far, you increase noise without adding much signal. The adstock function represents a weighted average with weights for each time period. For example, here's a geometric decay curve. The weights for each value of S is determined by this curve, whose shape is controlled by the parameter alpha. Think of alpha as the retention rate. A high alpha means the weight stays high for longer. A low alpha means the memory drops off fast. For example, here's a geometric decay curve with a smaller alpha than the previous one. In this new geometric decay curve, the weights are very small sooner. Use geometric for when the media drives action quickly. Meridian also offers a binomial decay curve. Binomial decay is mathematically stretched to fit the window you define. Specifically, the curve is defined so that its x-intercept is always at L plus one. Use binomial decay when you believe a significant proportion of the media effect persists into the latter half of the time window. The Hill function reflects the reality that doubling your budget rarely doubles your revenue. It's controlled by two parameters, EC and slope. Here's an example of a Hill function. EC is the half-saturation point. It tells you exactly how much spend is required to get 50% of your maximum impact. For example, for this curve, EC is here. Meridian learns EC from your data to identify where your channel starts losing efficiency. Then we have the slope. This controls how steep the curve is. By default, Meridian fixes the slope to one to ensure a concave curve, which guarantees that the budget optimizer can reliably identify a global optimum for your budget allocation. Let's discuss this top equation. It illustrates that the Hill adstock function is a term in Meridian's regression model.

Notice the order of operations. We apply adstock first and then Hill. This assumes saturation is driven by the lagged history of media, not just a single week's media. This order can optionally be flipped in Meridian. You don't need to calculate the adstock or Hill transformations manually. You feed Meridian the raw execution data, your choice of decay curve, and max lag. The model estimates the remaining parameters for you and applies the transformations to Meridian's regression model. Check out the documentation to learn more. Thanks for watching.