## 1 Introduction
The different marketing stakeholders have documentation where they focus on defining the \(FC\)[7; 8; 9] as well as documentation focus on how to implement in each of their platforms [10; 11; 12; 13]. However, unfortunately, there is still very little research, both in academia and industry, on how to decide the optimal value that maximizes performance and do not annoy the user. One of the paper's co-authors has been working in the digital marketing sector for six years, and he can confirm that, to the best of his knowledge, there are no systematic data-driven methodologies implemented in the industry to define \(FC\) values for ad campaigns. Our work aims to build a robust and reliable methodology to define the number of ads that should be delivered to different users (i.e., \(FC\)) to optimize marketing budgets, maximize the ROAS, and reduce the possibility that users get annoyed with the brand behind the ads. In addition, the proposed methodology will be validated both using simulations and using large-scale datasets obtained from real ad campaigns data from 5 different companies. Most of the works in the literature, which directly or indirectly address the optimization of the \(FC\), are validated only using simulations but not using data from real ad campaigns. In [14], the authors study the problem from the ad server point of view running simulations that include strong assumptions regarding the number of advertisers, the demand, the supply, and the \(FC\). In particular, this work analyses how the ad server should allocate ad impressions from advertisers when it does not know what will be the future ad impressions to users to maximize its revenue. In [15], the authors analyze the problem from the point of view of a website (publisher). They develop an algorithm that assumes an accurate prediction of the behaviour of the website users to define an optimal plan for delivering ad impressions to users. In [16; 17], the authors define a two-stage optimization model for the \(FC\) problem. They rely on a computational process approach to validate the proposed model. This model proposes an optimal \(FC\) value that adapts to reducing click-through rate as the number of impressions grows. Finally, the authors of [18] address the problem from a data privacy perspective. They propose a linear programming model that relies on the current page users are browsing to avoid cross-site cookies. The proposed model is tested in a simulation. We could only find two works--one academic paper [19] and one industrial report from Microsoft [20], where the proposed solution relies on actual advertising datasets. The first work uses Facebook ad data and shows that using large \(FC\) values is a bad strategy as the probability of gathering a user click quickly decreases with the number of ad impressions delivered to that user. More related to our work, the Microsoft report studies the impact of the \(FC\) on conversion rates for different companies. They conclude that the conversion rate on the first impression usually was the highest, and the first three impressions all had at least 100% conversion rate lift on average. Then, the most efficient frequency (best conversion rate) is not the most profitable (better cost per conversion). Finally, they found that it is difficult to apply a standard \(FC\) across advertisers, but defining an optimal \(FC\) requires analyzing each advertiser's data and campaign strategies. Our research differs from most of the previously described works because we validate our model using real datasets from ad campaigns beyond using simulations. In addition, our work focuses on improving the efficiency of \(FC\) to benefit the customers (advertisers) and product (users) of the AdTech ecosystem, rather than focusing on publishers or Ad Exchanges. Finally, the work of Microsoft is the most related one to our article. However, they do not provide any theoretical framework to optimize the \(FC\) but simply conclude that you require a specific analysis per advertiser, which is precisely what our framework offers.