With the most professional leagues, professional players, and national competitions, soccer is perhaps the most popular sport in the world. One of the reasons why soccer is so popular is because it is simple: two teams trying to score in each other’s goal only using their feets and heads. However, when we go deeper inside, there are numerous factors that can subtly or significantly impact the entire result of the game. The factor that this paper focuses on is the ball distribution between each player. It is common sense that teams with equal contribution from every player indicate better teamwork, and thus they are more likely to be stronger than teams that rely on one or two key players. In order to qualify this idea and devise useful strategies accordingly, we employed Markov chain and Principal Component Analysis (PCA). Through the Markov chain, we modeled a soccer game into a system (team) of eleven sections (players) continuously transitioning (giving passes) to other sections until they score a goal. Through PCA, we compared the patterns we found from the Markov chain modeling to other soccer statistics to evaluate how related the pattern we found is to the victory of the soccer team compared to other well-known soccer statistics. The evaluation of our approach shows promising results in analyzing soccer and constructing the most ideal player formation to win the game.

From hair implants to plastic surgeries that reduce wrinkles, there is numerous evidence that reflect the full-grown adult’s interest in appearances. The most classic, but also the most difficult to answer, question in this field is "what makes a face attractive?" Indeed, there are certain facial features that are commonly seen in attractive faces, but it is hard to generalize them since the beauty standard differs from person to person and sometimes, it is not one or two features, but the harmony of every feature that makes the face look more appealing. In order to find a more objective and reliable way to assess attractiveness of different faces, we employed a face mesh technique based on a lightweight statistical analysis method called Procrustes Analysis and Principal Component Analysis (PCA). As a result, we constructed an algorithm that predicts the appearance rating of a random face. This system can be exploited in fields like dating apps, plastic surgery counseling, or cosmetic developments.