Stochastic optimization algorithms have been successfully applied in several domains to find optimal solutions. Because of the ever-growing complexity of the integrated systems, novel stochastic algorithms are being proposed, which makes the task of the performance analysis of the algorithms extremely important. In this paper, we provide a novel ranking scheme to rank the algorithms over multiple single-objective optimization problems. The results of the algorithms are compared using a robust bootstrapping-based hypothesis testing procedure that is based on the principles of severity. Analogous to the football league scoring scheme, we propose pairwise comparison of algorithms as in league competition. Each algorithm accumulates points and a performance metric of how good or bad it performed against other algorithms analogous to goal differences metric in football league scoring system. The goal differences performance metric can not only be used as a tie-breaker but also be used to obtain a quantitative performance of each algorithm. The key novelty of the proposed ranking scheme is that it takes into account the performance of each algorithm considering the magnitude of the achieved performance improvement along with its practical relevance and does not have any distributional assumptions. The proposed ranking scheme is compared to classical hypothesis testing and the analysis of the results shows that the results are comparable and our proposed ranking showcases many additional benefits.

Machine learning models have become increasingly popular for predicting the results of soccer matches, however, the lack of publicly-available benchmark datasets has made model evaluation challenging. The 2023 Soccer Prediction Challenge required the prediction of match results first in terms of the exact goals scored by each team, and second, in terms of the probabilities for a win, draw, and loss. The original training set of matches and features, which was provided for the competition, was augmented with additional matches that were played between 4 April and 13 April 2023, representing the period after which the training set ended, but prior to the first matches that were to be predicted (upon which the performance was evaluated). A CatBoost model was employed using pi-ratings as the features, which were initially identified as the optimal choice for calculating the win/draw/loss probabilities. Notably, deep learning models have frequently been disregarded in this particular task. Therefore, in this study, we aimed to assess the performance of a deep learning model and determine the optimal feature set for a gradient-boosted tree model. The model was trained using the most recent five years of data, and three training and validation sets were used in a hyperparameter grid search. The results from the validation sets show that our model had strong performance and stability compared to previously published models from the 2017 Soccer Prediction Challenge for win/draw/loss prediction.

Artificial Intelligence has been used to help human complete difficult tasks in complicated environments by providing optimized strategies for decision-making or replacing the manual labour. In environments including multiple agents, such as football, the most common methods to train agents are Imitation Learning and Multi-Agent Reinforcement Learning (MARL). However, the agents trained by Imitation Learning cannot outperform the expert demonstrator, which makes humans hardly get new insights from the learnt policy. Besides, MARL is prone to the credit assignment problem. In environments with sparse reward signal, this method can be inefficient. The objective of our research is to create a novel reward shaping method by embedding contextual information in reward function to solve the aforementioned challenges. We demonstrate this in the Google Research Football (GRF) environment. We quantify the contextual information extracted from game state observation and use this quantification together with original sparse reward to create the shaped reward. The experiment results in the GRF environment prove that our reward shaping method is a useful addition to state-of-the-art MARL algorithms for training agents in environments with sparse reward signal.

Deep reinforcement learning (DRL) has achieved super-human performance on complex video games (e.g., StarCraft II and Dota II). However, current DRL systems still suffer from challenges of multi-agent coordination, sparse rewards, stochastic environments, etc. In seeking to address these challenges, we employ a football video game, e.g., Google Research Football (GRF), as our testbed and develop an end-to-end learning-based AI system (denoted as TiKick) to complete this challenging task. In this work, we first generated a large replay dataset from the self-playing of single-agent experts, which are obtained from league training. We then developed a distributed learning system and new offline algorithms to learn a powerful multi-agent AI from the fixed single-agent dataset. To the best of our knowledge, Tikick is the first learning-based AI system that can take over the multi-agent Google Research Football full game, while previous work could either control a single agent or experiment on toy academic scenarios. Extensive experiments further show that our pre-trained model can accelerate the training process of the modern multi-agent algorithm and our method achieves state-of-the-art performances on various academic scenarios.

Capturing the playing style of professional soccer coaches is a complex, and yet barely explored, task in sports analytics. Nowadays, the availability of digital data describing every relevant spatio-temporal aspect of soccer matches, allows for capturing and analyzing the playing style of players, teams, and coaches in an automatic way. In this paper, we present coach2vec, a workflow to capture the playing style of professional coaches using match event streams and artificial intelligence. Coach2vec extracts ball possessions from each match, clusters them based on their similarity, and reconstructs the typical ball possessions of coaches. Then, it uses an autoencoder, a type of artificial neural network, to obtain a concise representation (encoding) of the playing style of each coach. Our experiments, conducted on soccer-logs describing the last four seasons of the Italian first division, reveal interesting similarities between prominent coaches, paving the road to the simulation of playing styles and the quantitative comparison of professional coaches.

We use European football performance data to select teams to form the proposed European football Super League, using only unsupervised techniques. We first used random forest regression to select important variables predicting goal difference, which we used to calculate the Euclidian distances between teams. Creating a Laplacian eigenmap, we bisected the Fielder vector to identify the five major European football leagues' natural clusters. Our results showed how an unsupervised approach could successfully identify four clusters based on five basic performance metrics: shots, shots on target, shots conceded, possession, and pass success. The top two clusters identify those teams who dominate their respective leagues and are the best candidates to create the most competitive elite super league. Keywords: OR in sports; Selection; Unsupervised; Spectral clustering; Laplacian Eigenmap; Machine Learning 1. Introduction Operational research (OR) has a long history of using sport to explore operational insights and methodologies (see Wright, 2009 for a review).

A concentrate of passion, hope and romanticism. Every year thousands and thousands of teams compete in their leagues with different purposes. Some of them are built to win the title. Others just want to not be relegated. But the answer to their hopes always relies on the same thing: numbers.

Despite the massive popularity of the Asian Handicap (AH) football betting market, it has not been adequately studied by the relevant literature. This paper combines rating systems with hybrid Bayesian networks and presents the first published model specifically developed for prediction and assessment of the AH betting market. The results are based on 13 English Premier League seasons and are compared to the traditional 1X2 market. Different betting situations have been examined including a) both average and maximum (best available) market odds, b) all possible betting decision thresholds between predicted and published odds, c) optimisations for both return-on-investment and profit, and d) simple stake adjustments to investigate how the variance of returns changes when targeting equivalent profit in both 1X2 and AH markets. While the AH market is found to share the inefficiencies of the traditional 1X2 market, the findings reveal both interesting differences as well as similarities between the two.

We study the emergence of cooperative behaviors in reinforcement learning agents by introducing a challenging competitive multi-agent soccer environment with continuous simulated physics. We demonstrate that decentralized, population-based training with co-play can lead to a progression in agents' behaviors: from random, to simple ball chasing, and finally showing evidence of cooperation. Our study highlights several of the challenges encountered in large scale multi-agent training in continuous control. In particular, we demonstrate that the automatic optimization of simple shaping rewards, not themselves conducive to co-operative behavior, can lead to long-horizon team behavior. We further apply an evaluation scheme, grounded by game theoretic principals, that can assess agent performance in the absence of pre-defined evaluation tasks or human baselines.

In modern applications, we frequently encounter complex object-type data, such as functions (Ramsay and Silverman, 2006), trees (Wang and Marron, 2007), shapes (Srivastava et al., 2011), and networks (Durante et al., 2017). In many instances, such data are collected repeatedly under different conditions, with an additional response variable of interest available for each replicate. This has motivated an increasingly rich literature on generalizing regression on vector predictors to settings involving more elaborate object-type predictors with special characteristics, such as functions (James, 2002), manifolds (Nilsson et al., 2007), tensors (Zhou et al., 2013), and undirected networks (Guha and Rodriguez, 2018). Complex objects are often built recursively from simpler parts. In this article, we introduce a new class of object data, denoted composite objects (CO), which are structured data composed of primitive objects (POs). Many common data types can be seen as instances of the CO family, such as a collection of time-stamped events, connections between regions of the brain, or basketball shots on the court. The component POs in COtype data can be enormous and mostly distinctive from one another across replicates, presenting new challenges for data exploration, analysis, and visualization. We are interested in identifying the association between the patterns of coordinated interactions among individual units in a group and the performance of the group. In this article, we focus on analyzing the FIFA World Cup 2018 data collected by StatsBomb.