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Predicting the outcome of sports events is a hard task. We quantify this di culty with a coe cient that measures the distance between the observed nal results of sports leagues and idealized perfectly balanced competitions in terms of skill. This indicates the relative presence of luck and skill. We collected and analyzed all games from 198 sports leagues comprising 1503 seasons from 84 countries of 4 di erent sports: basketball, soccer, volleyball and handball. We measured the competitiveness by countries and sports. We also identify in each season which teams, if removed from its league, result in a completely random tournament. Surprisingly, not many of them are needed. As another contribution of this paper, we propose a probabilistic graphical model to learn about the teams' skills and to decompose the relative weights of luck and skill in each game. We break down the skill component into factors associated with the teams' characteristics. The model also allows to estimate as 0.36 the probability that an underdog team wins in the NBA league, with a home advantage adding 0.09 to this probability. As shown in the rst part of the paper, luck is substantially present even in the most competitive championships, which partially explains why sophisticated and complex feature-based models hardly beat simple models in the task of forecasting sports' outcomes. CCS CONCEPTS•Computing methodologies → Model development and analysis; Uncertainty quanti cation;

Many methods have been proposed to estimate treatment effects with observational data. Often, the choice of the method considers the application's characteristics, such as type of treatment and outcome, confounding effect, and the complexity of the data. These methods implicitly assume that the sample size is large enough to train such models, especially the neural network-based estimators. What if this is not the case? In this work, we propose Causal-Batle, a methodology to estimate treatment effects in small high-dimensional datasets in the presence of another highdimensional dataset in the same feature space. We adopt an approach that brings transfer learning techniques into causal inference. Our experiments show that such an approach helps to bring stability to neural network-based methods and improve the treatment effect estimates in small high-dimensional datasets. The code for our method and all our experiments is available at github.com/causal-batle.

Causal Inference methods based on observational data are an alternative for applications where collecting the counterfactual data or realizing a more standard experiment is not possible. In this work, our goal is to combine several observational causal inference methods to learn new causes in applications where some causes are well known. We validate the proposed method on The Cancer Genome Atlas (TCGA) dataset to identify genes that potentially cause metastasis.

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