arxiv.org - Hiroaki Hanyu, Shunsuke Ishii, Suguru Otani, Kazuhiro Teramoto
Abstract:Most betting market models employ static frameworks that condition decisions on final odds. Using a unique dataset of interim odds from Japanese horse racing, this study examines the validity of such static analyses by asking whether there is a systematic relationship between expected returns and the trajectory of odds. We find that returns are negatively related to last-minute changes in odds, and that these late movements attenuate the favorite-longshot bias by weakening the correlation between final odds and returns. These patterns suggest that informed bettors place wagers at the final stage based on private signals, leaving surprises in final odds.
substack.com - Louis
Why a defensive team (1.5 xG/ 0.5 xGA) might outperform an attacking one (2.5 xG/ 1.5 xGA)
expectinggoals.com - Michael Caley
Playersâ positions and touch profiles move gradually away from goal as they age. This raises the question, to what degree have the statistical age-curve effects reflected the real tendencies of player skills to change over time, and to what degree do they reflect changes in tactical use? Obviously these two effects are overlapping, as players whose ability to get separation against a defender declines while their creative passing improves will be moved deeper on the pitch simply as a recognition of those skills.
byu.edu - Matthew Jewell, Garritt L. Page, C. Shane Reese
Assessing end-of-season performance as a function of average minutes played for NBA players
soccer-net.org
The SoccerNet Challenges return for their 6th edition, with brand-new tasks and upgraded classics that push the frontier of sports AI. The competition runs until April 24, 2026, giving you time to craft breakthrough solutions and climb the leaderboard.Stay engaged with updates, standings, and discussions on Discord, and dive into our YouTube tutorials and highlights for inspiration.Whether youâre tackling a new task or refining last yearâs work, join us in shaping the future of sports AI. SoccerNet Challenges 2026 awaitâare you in?
substack.com - Alex Marin Felices
A Spatio-Temporal Approach to Analyzing Match Events and Possession Utilization.
degruyterbrill.com - Ryan S. Brill, Ronald Yurko, Abraham J. Wyner
Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state variables. To illustrate just how difficult it is to accurately fit such a model from noisy and highly correlated observational data, in this paper we conduct a simulation study. We create a simplified random walk version of football in which true win probability at each game-state is known, and we see how well a model recovers it. We find that the dependence structure of observational play-by-play data substantially inflates the bias and variance of estimators and lowers the effective sample size. Further, to achieve approximately valid marginal coverage, win probability confidence intervals need to be substantially wide. Concisely, these are high variance estimators subject to substantial uncertainty. Our findings are not unique to the particular application of estimating win probability; they are broadly applicable across sports analytics, as myriad other sports datasets are clustered into groups of observations that share the same outcome.
degruyterbrill.com - Ali Baouan, Sébastien Coustou, Mathieu Lacome, Sergio Pulido, Mathieu Rosenbaum
We introduce an innovative methodology to identify football players at the origin of threatening actions in a team. In our framework, a threat is defined as entering the opposing teamâs danger area. We investigate the timing of threat events and ball touches of players, and capture their correlation using Hawkes processes. Our model-based approach allows us to evaluate a playerâs ability to create danger both directly and through interactions with teammates. We define a new index, called Generation of Threat (GoT), that measures in an unbiased way the contribution of a player to threat generation. For illustration, we present a detailed analysis of Chelseaâs 2016â2017 season, with a standout performance from Eden Hazard. We are able to credit each player for his involvement in danger creation and determine the main circuits leading to threat. In the same spirit, we investigate the danger generation process of Stade Rennais in the 2021â2022 season. Furthermore, we establish a comprehensive ranking of Ligue 1 players based on their generated threat in the 2021â2022 season. Our analysis reveals surprising results, with players such as Jason Berthomier, Moses Simon and Frederic Guilbert among the top performers in the GoT rankings.
degruyterbrill.com - Michael A. Lapré, Julia G. Amato
Prior research found significant competitive imbalance in FIFA World Cup tournaments because FIFA does not allocate World Cup slots to continental confederations in proportion to the distribution of the best teams in the world. Since the UEFA Euro only consists of teams from Europe, it should be much easier for UEFA to create competitive balance. We empirically investigate competitive imbalance between groups at the UEFA Euro tournaments from 1980 through 2024. We find that competitive imbalance at the Euro is just as bad as it is in the World Cup. We also find that the impact of competitive imbalance on the probability of reaching the quarterfinals is the same across the World Cup and the Euro. UEFA creates competitive imbalance by sometimes protecting multiple low-ranked hosts and, most importantly, using inadequate methods to rank teams. We recommend that UEFA adopt an Elo rating system to rank teams.
degruyterbrill.com - Nicholas Kiriazis, Christian Genest, Alexandre Leblanc
In basketball, traditional methods of assessing individual rebounding ability are problematic because they depend on all players present on the court rather than just on the player of interest. Although there exist modeling approaches to correct for this dependence, they are generally unsuitable for events with binary outcomes. In this paper, a Bayesian two-stage model is proposed to predict both individual and team rebound allocation. This approach makes it possible to identify players who help their team win the fight for rebounds, regardless of their individual rebounding totals. Although similar in flavor to the popular Adjusted Plus-Minus (APM) framework, the proposed strategy is different in that it does not assume that individual contributions are linearly additive on the response scale. Furthermore, the regularization approach is improved through rebounding-specific heuristics. A simulation study is performed to show the effectiveness of the proposed model, and the parameters are estimated using data from the 2020â21 NBA season. Predictions are then made for rebounding in the 2021â22 season. This study confirms that relying exclusively on individual rebounding rates could lead to the mis-evaluation of playersâ rebounding abilities.
arxiv.org - Andrey Skripnikov, Ahmet Cemek, David Gillman
Abstract:In soccer, game context can result in skewing offensive statistics in ways that might misrepresent how well a team has played. For instance, in England's 1-2 loss to France in the 2022 FIFA World Cup quarterfinal, England attempted considerably more shots (16 to France's 8) and more corners (5 to 2), potentially suggesting they played better despite the loss. However, these statistics were largely accumulated when France was ahead and more willing to concede offensive initiative to England. To explore how game context influences offensive performance, we analyze minute-by-minute event-sequenced match data from 15 seasons across five major European leagues. Using count-response Generalized Additive Modeling, we consider features such as score and red card differential, home/away status, pre-match win probabilities, and game minute. Moreover, we leverage interaction terms to test several intuitive hypotheses about how these features might cooperate in explaining offensive production. The selected model is then applied to project offensive statistics onto a standardized "common denominator" scenario: a tied home game with even men on both sides. The adjusted numbers - in contrast to regular game totals that disregard game context - offer a more contextualized comparison, reducing the likelihood of misrepresenting the relative quality of play.
arxiv.org - Ali Baouan, Mathieu Rosenbaum, Sergio Pulido
Abstract:This study presents a quantitative framework to compare teams in collective sports with respect to their style of play. The style of play is characterized by the team's spatial distribution over a collection of frames. As a first step, we introduce an optimal transport-based embedding to map frames into Euclidean space, allowing for the efficient computation of a distance. Then, building on this frame-level analysis, we leverage quantization to establish a similarity metric between teams based on a collection of frames from their games. For illustration, we present an analysis of a collection of games from the 2021-2022 Ligue 1 season. We are able to retrieve relevant clusters of game situations and calculate the similarity matrix between teams in terms of style of play. Additionally, we demonstrate the strength of the embedding as a preprocessing tool for relevant prediction tasks. Likewise, we apply our framework to analyze the dynamics in the first half of the NBA season in 2015-2016.
arxiv.org - Robert Bajons, Jan-Ole Koslik, Rouven Michels, Marius Ătting
Abstract:Traditional assessments of tackling in American Football often only consider the number of tackles made, without adequately accounting for their context and importance for the game. Aiming for improvement, we develop a metric that quantifies the value of a tackle in terms of the prevented expected points (PEP). Specifically, we compare the real end-of-play yard line of tackles with the predicted yard line given the hypothetical situation that the tackle had been missed. For this, we use high-resolution tracking data, that capture the position and velocity of players, and a random forest to account for uncertainty and multi-modality in yard-line prediction. Moreover, we acknowledge the difference in the importance of tackles by assigning an expected points value to each individual tree prediction of the random forest. Finally, to relate the value of tackles to a player's ability to tackle, we fit a suitable mixed-effect model to the PEP values. Our approach contributes to a deeper understanding of defensive performances in American football and offers valuable insights for coaches and analysts.
arxiv.org - Nathaniel Josephs, Elizabeth Upton
Abstract:In team sports, traditional ranking statistics do not allow for the simultaneous evaluation of both individuals and combinations of players. Metrics for individual player rankings often fail to include the interaction effects between groups of players, while methods for assessing full lineups cannot be used to identify the value of lower-order combinations of players (pairs, trios, etc.). Given that player and lineup rankings are inherently dependent on each other, these limitations may affect the accuracy of performance evaluations. To address this, we propose a novel adjusted plus-minus (APM) approach that allows for the simultaneous ranking of individual players, lower-order combinations of players, and full lineups within a team. The method adjusts for the complete dependency structure and is motivated by the connection between APM and the hypergraph representation of a team. We discuss the similarities of our approach to other advanced metrics, demonstrate it using NBA data from 2012-2022, and suggest potential directions for future work.
arxiv.org - David Winkelmann, Rouven Michels, Christian Deutscher
Abstract:For the 2024/25 season, the Union of European Football Associations (UEFA) introduced an incomplete round-robin format in the Champions League, Europa League, and Conference League, replacing the traditional group stage with a single league table of all 36 teams. Under this structure, the top eight teams advance directly to the round of 16, while those ranked 9th-24th compete in a play-off round. Simulation-based analyses, such as those by commercial data analyst Opta, provide indicative point thresholds for qualification but reveal deviations when compared with actual outcomes in the first season. To overcome these discrepancies, we employ a bivariate Dixon-Coles model that accounts for the lower frequency of draws observed in the 2024/25 UCL season, with team strengths proxied by Elo ratings. This framework enables the simulation of match outcomes and the estimation of qualification thresholds for both direct advancement and play-off participation. Our results provide scientific guidance for clubs and managers, supporting strategic decision-making under uncertainty regarding their progression prospects in the new UEFA club competition formats.
arxiv.org - Robert Bajons, Lucas Kook
Abstract:A popular quantitative approach to evaluating player performance in sports involves comparing an observed outcome to the expected outcome ignoring player involvement, which is estimated using statistical or machine learning methods. In soccer, for instance, goals above expectation (GAX) of a player measure how often shots of this player led to a goal compared to the model-derived expected outcome of the shots. Typically, sports data analysts rely on flexible machine learning models, which are capable of handling complex nonlinear effects and feature interactions, but fail to provide valid statistical inference due to finite-sample bias and slow convergence rates. In this paper, we close this gap by presenting a framework for player evaluation with metrics derived from differences in actual and expected outcomes using flexible machine learning algorithms, which nonetheless allows for valid frequentist inference. We first show that the commonly used metrics are directly related to Rao's score test in parametric regression models for the expected outcome. Motivated by this finding and recent developments in double machine learning, we then propose the use of residualized versions of the original metrics. For GAX, the residualization step corresponds to an additional regression predicting whether a given player would take the shot under the circumstances described by the features. We further relate metrics in the proposed framework to player-specific effect estimates in interpretable semiparametric regression models, allowing us to infer directional effects, e.g., to determine players that have a positive impact on the outcome. Our primary use case are GAX in soccer. We further apply our framework to evaluate goal-stopping ability of goalkeepers, shooting skill in basketball, quarterback passing skill in American football, and injury-proneness of soccer players.
arxiv.org - Joris Bekkers
Abstract:Understanding team formations and player positioning is crucial for tactical analysis in football (soccer). This paper presents a flexible method for formation recognition and player position assignment in football using predefined static formation templates and cost minimization from spatiotemporal tracking data, called EFPI. Our approach employs linear sum assignment to optimally match players to positions within a set of template formations by minimizing the total distance between actual player locations and template positions, subsequently selecting the formation with the lowest assignment cost. To improve accuracy, we scale actual player positions to match the dimensions of these formation templates in both width and length. While the method functions effectively on individual frames, it extends naturally to larger game segments such as complete periods, possession sequences or specific intervals (e.g. 10 second intervals, 5 minute intervals etc.). Additionally, we incorporate an optional stability parameter that prevents unnecessary formation changes when assignment costs differ only marginally between time segments. EFPI is available as open-source code through the unravelsports Python package.
arxiv.org - Quang Nguyen, Ronald Yurko
Abstract:Change of direction is a key element of player movement in American football, yet there remains a lack of objective approaches for in-game performance evaluation of this athletic trait. Using tracking data, we propose a Bayesian mixed-effects model with heterogeneous variances for assessing a player's ability to make variable directional adjustments while moving on the field. We model the turn angle (i.e., angle between successive displacement vectors) for NFL ball carriers on both passing and rushing plays, focusing on receivers after the catch and running backs after the handoff. In particular, we consider a von Mises distribution for the frame-level turn angle and explicitly model both the mean and concentration parameters with relevant spatiotemporal and contextual covariates. Of primary interest, we include player random effects that allow the turn angle concentration to vary by ball carrier nested within position groups. This offers practical insight into player evaluation, as it reveals the shiftiest ball carriers with great variability in turning behavior. We illustrate our approach with results from the first nine weeks of the 2022 NFL regular season and explore player-specific and positional differences in turn angle variability.
arxiv.org - Vito Chan, Lennart Ebert, Paul-Julius Hillmann, Christoffer Rubensson, Stephan A. Fahrenkrog-Petersen, Jan Mendling
Abstract:Object-centric event logs expand the conventional single-case notion event log by considering multiple objects, allowing for the analysis of more complex and realistic process behavior. However, the number of real-world object-centric event logs remains limited, and further studies are needed to test their usefulness. The increasing availability of data from team sports can facilitate object-centric process mining, leveraging both real-world data and suitable use cases. In this paper, we present a framework for transforming football (soccer) data into an object-centric event log, further enhanced with a spatial dimension. We demonstrate the effectiveness of our framework by generating object-centric event logs based on real-world football data and discuss the results for varying process representations. With our paper, we provide the first example for object-centric event logs in football analytics. Future work should consider variant analysis and filtering techniques to better handle variability
arxiv.org - Kenjiro Ide, Taiga Someya, Kohei Kawaguchi, Keisuke Fujii
Abstract:Understanding football tactics is crucial for managers and analysts. Previous research has proposed models based on spatial and kinematic equations, but these are computationally expensive. Also, Reinforcement learning approaches use player positions and velocities but lack interpretability and require large datasets. Rule-based models align with expert knowledge but have not fully considered all players' states. This study explores whether low-dimensional, rule-based models using spatiotemporal data can effectively capture football tactics. Our approach defines interpretable state variables for both the ball-holder and potential pass receivers, based on criteria that explore options like passing. Through discussions with a manager, we identified key variables representing the game state. We then used StatsBomb event data and SkillCorner tracking data from the 2023/24 LaLiga season to train an XGBoost model to predict pass success. The analysis revealed that the distance between the player and the ball, as well as the player's space score, were key factors in determining successful passes. Our interpretable low-dimensional modeling facilitates tactical analysis through the use of intuitive variables and provides practical value as a tool to support decision-making in football.
arxiv.org - Silvio Giancola, Anthony Cioppa, Marc Gutiérrez-Pérez, Jan Held, Carlos Hinojosa, Victor Joos, Arnaud Leduc et al.
Abstract:The SoccerNet 2025 Challenges mark the fifth annual edition of the SoccerNet open benchmarking effort, dedicated to advancing computer vision research in football video understanding. This year's challenges span four vision-based tasks: (1) Team Ball Action Spotting, focused on detecting ball-related actions in football broadcasts and assigning actions to teams; (2) Monocular Depth Estimation, targeting the recovery of scene geometry from single-camera broadcast clips through relative depth estimation for each pixel; (3) Multi-View Foul Recognition, requiring the analysis of multiple synchronized camera views to classify fouls and their severity; and (4) Game State Reconstruction, aimed at localizing and identifying all players from a broadcast video to reconstruct the game state on a 2D top-view of the field. Across all tasks, participants were provided with large-scale annotated datasets, unified evaluation protocols, and strong baselines as starting points. This report presents the results of each challenge, highlights the top-performing solutions, and provides insights into the progress made by the community. The SoccerNet Challenges continue to serve as a driving force for reproducible, open research at the intersection of computer vision, artificial intelligence, and sports. Detailed information about the tasks, challenges, and leaderboards can be found at this https URL, with baselines and development kits available at this https URL.
arxiv.org - Charlton Teo
Abstract:The use of Large Language Models (LLMs) in recent years has also given rise to the development of Multimodal LLMs (MLLMs). These new MLLMs allow us to process images, videos and even audio alongside textual inputs. In this project, we aim to assess the effectiveness of MLLMs in analysing sports videos, focusing mainly on tennis videos. Despite research done on tennis analysis, there remains a gap in models that are able to understand and identify the sequence of events in a tennis rally, which would be useful in other fields of sports analytics. As such, we will mainly assess the MLLMs on their ability to fill this gap - to classify tennis actions, as well as their ability to identify these actions in a sequence of tennis actions in a rally. We further looked into ways we can improve the MLLMs' performance, including different training methods and even using them together with other traditional models.
harbourfronts.com
A key challenge in system development is that trading performance often deteriorates after going live. In this post, we look at why this happens by examining the post-publication decay of stock anomalies, and we address a practical question faced by every trader: when a system is losing money, is it simply in a drawdown or has it stopped working altogether?
ssrn.com - Marcos Lopez de Prado, Alexander Lipton, Vincent Zoonekynd
The Sharpe ratio is the most widely used measure of investment efficiency, yet its statistical inference is often conducted incorrectly. This paper reviews the pitfalls of naive Sharpe ratio analysis and provides a comprehensive framework for its proper use. We identify five main pitfalls: (a) the Normality assumption; (b) neglect of statistical significance and minimum sample length assessment; (c) insufficient test power; (d) confusion between classical p-values and the probability of the null hypothesis given the data; and (e) failure to correct for multiple testing. To address these issues, we survey and extend a set of methods, including the Probabilistic Sharpe Ratio (PSR), Minimum Track Record Length (MinTRL), the Sharpe ratioâs Observed Bayesian Tail-Area False Discovery Rate (oFDR), and the Deflated Sharpe Ratio (DSR). Monte Carlo experiments confirm that these corrections yield more reliable inference than traditional t-statistics and general-purpose multiple-testing adjustments. We further distinguish between familywise error rate (FWER), false discovery rate (FDR), and hybrid FWER-FDR frameworks, showing their respective suitability for academic versus industrial applications. The central conclusion is that the Sharpe ratio remains a valuable metric only when properly corrected; without these adjustments, it risks misleading researchers and practitioners alike.
su.domains - Amir Dembo (revised by Kevin Ross)
These are the lecture notes for a one quarter graduate course in Stochastic Processes that I taught at Stanford University in 2002 and 2003. This course is intended
for incoming master students in Stanfordâs Financial Mathematics program, for advanced undergraduates majoring in mathematics and for graduate students from
Engineering, Economics, Statistics or the Business school. One purpose of this text is to prepare students to a rigorous study of Stochastic Differential Equations. More
broadly, its goal is to help the reader understand the basic concepts of measure theory that are relevant to the mathematical theory of probability and how they apply
to the rigorous construction of the most fundamental classes of stochastic processes.
cambridge.org - Zihao Zhang and Stefan Zohren
This Element provides a comprehensive guide to deep learning in quantitative trading, merging foundational theory with hands-on applications. It is organized into two parts. The first part introduces the fundamentals of financial time-series and supervised learning, exploring various network architectures, from feedforward to state-of-the-art. To ensure robustness and mitigate overfitting on complex real-world data, a complete workflow is presented, from initial data analysis to cross-validation techniques tailored to financial data. Building on this, the second part applies deep learning methods to a range of financial tasks. The authors demonstrate how deep learning models can enhance both time-series and cross-sectional momentum trading strategies, generate predictive signals, and be formulated as an end-to-end framework for portfolio optimization. Applications include a mixture of data from daily data to high-frequency microstructure data for a variety of asset classes. Throughout, they include illustrative code examples and provide a dedicated GitHub repository with detailed implementations.