Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final 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 different 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 first 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.