The purpose of this study was to evaluate the physical demands of English Football Association (FA) Premier League soccer of three different positional classifications (defender, midfielder and striker). Computerised time-motion video-analysis using the Bloomfield Movement Classification was undertaken on the purposeful movement (PM) performed by 55 players. Recognition of PM had a good inter-tester reliability strength of agreement (κ= 0.7277). Players spent 40.6 ± 10.0% of the match performing PM. Position had a significant influence on %PM time spent sprinting, running, shuffling, skipping and standing still (p < 0.05). However, position had no significant influence on the %PM time spent performing movement at low, medium, high or very high intensities (p > 0.05). Players spent 48.7 ± 9.2% of PM time moving in a directly forward direction, 20.6 ± 6.8% not moving in any direction and the remainder of PM time moving backward, lateral, diagonal and arced directions. The players performed the equivalent of 726 ± 203 turns during the match; 609 ± 193 of these being of 0° to 90° to the left or right. Players were involved in the equivalent of 111 ± 77 on the ball movement activities per match with no significant differences between the positions for total involvement in on the ball activity (p > 0.05). This study has provided an indication of the different physical demands of different playing positions in FA Premier League match-play through assessment of movements performed by players. Key pointsPlayers spent ~40% of the match performing Pur-poseful Movement (PM).Position had a significant influence on %PM time spent performing each motion class except walking and jogging. Players performed >700 turns in PM, most of these being of 0°-90°.Strikers performed most high to very high intensity activity and most contact situations.Defenders also spent a significantly greater %PM time moving backwards than the other two posi-tions.Different positions could benefit from more specific conditioning programs.
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This project report presents a hybrid AI-assisted workflow for extracting and reintegrating archival metadata from League of Nations index cards. The project is situated in the broader context of the Total Digital Access to the League of Nations Archives project (LONTAD). Rather than attempting full OCR of the underlying archival collections, the workflow targets the index cards themselves as documentary access points to files, series, archival descriptions, and digital objects. The project evolved from a layout-aware pipeline combining YOLO, TrOCR, and local LLM post-correction to a hybrid architecture using a fine-tuned vision-language model for broad extraction while retaining specialized OCR for file and series identifiers.
Fantasy Premier League engages the football community in selecting the Premier League players who will perform best from gameweek to gameweek. Access to accurate performance forecasts gives participants an edge over competitors by guiding expectations about player outcomes and reducing uncertainty in squad selection. However, high-accuracy forecasts are currently limited to commercial services whose inner workings are undisclosed and that rely on proprietary data. This paper aims to democratize access to highly accurate forecasts of player performance by presenting OpenFPL, an open-source Fantasy Premier League forecasting method developed exclusively from public data. Comprising position-specific ensemble models optimized on Fantasy Premier League and Understat data from four previous seasons (2020-21 to 2023-24), OpenFPL achieves accuracy comparable to a leading commercial service when tested prospectively on data from the 2024-25 season. OpenFPL also surpasses the commercial benchmark for high-return players ($>$ 2 points), which are most influential for rank gains. These findings hold across one-, two-, and three-gameweek forecast horizons, supporting long-term planning of t
Starting in the 2024/25 season, the Union of European Football Associations (UEFA) has fundamentally changed the format of its club competitions: the group stage has been replaced by a league phase played by 36 teams in an incomplete round robin format. This makes ranking the teams based on their results challenging because teams play against different sets of opponents, whose strengths vary. In this research note, we apply several well-known ranking methods for incomplete round robin tournaments to the 2024/25 UEFA Champions League league phase in order to check the robustness of the official ranking, as well as to call the attention of organizers to the non-trivial issue of ranking in these competitions. Our results show that it is doubtful whether the currently used point-based system provides the best ranking of the teams.
The RoboCup Logistics League is a RoboCup competition in a smart factory scenario that has focused on task planning, job scheduling, and multi-agent coordination. The focus on production logistics allowed teams to develop highly competitive strategies, but also meant that some recent developments in the context of smart manufacturing are not reflected in the competition, weakening its relevance over the years. In this paper, we describe the vision for the RoboCup Smart Manufacturing League, a new competition designed as a larger smart manufacturing scenario, reflecting all the major aspects of a modern factory. It will consist of several tracks that are initially independent but gradually combined into one smart manufacturing scenario. The new tracks will cover industrial robotics challenges such as assembly, human-robot collaboration, and humanoid robotics, but also retain a focus on production logistics. We expect the reenvisioned competition to be more attractive to newcomers and well-tried teams, while also shifting the focus to current and future challenges of industrial robotics.
When $n$ teams play in a football league with home and away matches against every opponent there are $M = n \cdot (n-1)$ matches. There are 3 possible match results: a victory is awarded 3 points, a draw 1 point and 0 points for a defeat. Hence we have $3^M$ possible outcomes. In this paper the number of ways is determined that a football league can complete with all teams having the same number of points. An algorithm that works until $n=8$ is presented.
The group draw of major sports tournaments implies some uncertainty, with lucky teams often enjoying a substantial unfair advantage. First in the literature, we propose a technique to quantify this draw uncertainty, which, arguably, has an optimal level of zero. Our simulation-based approach requires generating a representative set of random draws to compute the variance of qualifying probabilities for each team. The method is applied to compare draw uncertainty in the former group stage and the current incomplete round-robin league phase of the UEFA Champions League, under both accurate and inaccurate seedings. We also break down the impact of the 2024/25 reform into various components. The new format is found to decrease draw uncertainty, but the reduction is mainly attributable to the inaccurate seeding system used by UEFA. Consequently, the primary benefit of an incomplete round-robin tournament compared to the standard group stage lies in the robustness of its draw uncertainty to the seeding of the teams.
I present a simple and transparent standard for career greatness in baseball: any major league player with H > 2500 or HR > 350 or K > 2800 or W > 240 makes my Hall of Fame Cut. Rate statistics are avoided due to small sample issues and to ensure the standard is permanent once achieved. Hits and home runs were chosen to represent the two extremes of batting styles. Strikeouts are chosen as the most fundamental unit of pitching performance whereas wins are included in deference to their historical importance as a benchmark. Most major league batters and pitchers in the elected Hall of Fame also make my Hall of Fame Cut but my quantitative standard shifts attention to several under-appreciated players, such as Johnny Damon and Bartolo Colon, and allows us to celebrate recent and active players without the waiting period (5 years post-retirement) needed for Hall of Fame election. My Hall of Fame Cut is also agnostic to performance enhancement or off-field issues and strongly favors longevity over peak performance.
We undertake extensive analysis of English Premier League data over the period 2009/10 to 2017/18 to identify and rank key factors affecting the economic and footballing performances of the teams. Alternative end-of-season league tables are generated by re-ranking the teams based on five different descriptors - total expenditure, total funds spent on players, total funds spent on foreign players, the ratio of foreign to British players and the overall profit. The unequal distribution of resources and expenditure between the clubs is analyzed through Lorenz curves. A comparative analysis of the differences between the alternative tables and the conventional end-of-season league table establishes the most likely factors to influence the performances of the teams that we also rank using Principal Component Analysis. We find that the top teams in the league are also those that tend to have the highest expenditure overall, for all players, including foreign players; they also have the highest ratios of foreign to British players. Our statistical and machine learning study also indicates that successful performance on the field may not guarantee healthy profits at the end of the season.
Fantasy football is a billion-dollar industry with millions of participants. Under a fixed budget, managers select squads to maximize future Fantasy Premier League (FPL) points. This study formulates lineup selection as data-driven optimization and develops deterministic and robust mixed-integer linear programs that choose the starting eleven, bench, and captain under budget, formation, and club-quota constraints (maximum three players per club). The objective is parameterized by a hybrid scoring metric that combines realized FPL points with predictions from a linear regression model trained on match-performance features identified using exploratory data analysis techniques. The study benchmarks alternative objectives and cost estimators, including simple and recency-weighted averages, exponential smoothing, autoregressive integrated moving average (ARIMA), and Monte Carlo simulation. Experiments on the 2023/24 Premier League season show that ARIMA with a constrained budget and a rolling window yields the most consistent out-of-sample performance; weighted averages and Monte Carlo are also competitive. Robust variants and hybrid scoring metrics improve some objectives but are not u
One of the most popular club football tournaments, the UEFA Champions League, will see a fundamental reform from the 2024/25 season: the traditional group stage will be replaced by one league where each of the 36 teams plays eight matches. To guarantee that the opponents of the clubs are of the same strength in the new design, it is crucial to forecast the performance of the teams before the tournament as well as possible. This paper investigates whether the currently used rating of the teams, the UEFA club coefficient, can be improved by taking the games played in the national leagues into account. According to our logistic regression models, a variant of the Elo method provides a higher accuracy in terms of explanatory power in the Champions League matches. The Union of European Football Associations (UEFA) is encouraged to follow the example of the FIFA World Ranking and reform the calculation of the club coefficients in order to avoid unbalanced schedules in the novel tournament format of the Champions League.
Recently, UEFA changed the group stage of its international soccer competitions to an incomplete round robin tournament. Previously, teams were divided into groups, each playing a double round robin tournament with a resulting ranking table. In contrast, the new format has all teams competing in one league, producing a single ranking. We investigate the effect of the new format on the number of competitive matches in the UEFA Champions League. A match is non-competitive if the prize for at least one opponent does not depend on the match outcome, or if there exists an opportunity for both opponents to collude; otherwise, we call a match competitive. Using Monte Carlo simulations, we show that the new format results in more competitive matches than the old format.
Plate discipline is an important feature of a hitter's success. Hitter who are able to recognize good pitches to swing at and balls to take are generally recognized as disciplined hitters. Although there are some metrics that can provide insight into the patience of a hitter, most do not capture the ability of a batter to take balls. In this research, we introduce two new metrics, Discipline Score (DS) and Adjusted Discipline Score (ADS), which evaluate batters' discipline when the pitch is a ball compared with the predicted tendencies of all batters in the league.
Although large language models (LLMs) have shown exceptional capabilities across a wide range of tasks, reliable evaluation remains a critical challenge due to data contamination, opaque operation, and subjective preferences. To address these issues, we propose League of LLMs (LOL), a novel benchmark-free evaluation paradigm that organizes multiple LLMs into a self-governed league for multi-round mutual evaluation. LOL integrates four core criteria (dynamic, transparent, objective, and professional) to mitigate key limitations of existing paradigms. Experiments on eight mainstream LLMs in mathematics and programming demonstrate that LOL can effectively distinguish LLM capabilities while maintaining high internal ranking stability (Top-$k$ consistency $= 70.7\%$). Beyond ranking, LOL reveals empirical findings that are difficult for traditional paradigms to capture. For instance, ``memorization-based answering'' behaviors are observed in some models, and higher in-family scores are found in the OpenAI model family ($Δ= 9$, $p < 0.05$). Finally, we make our framework and code publicly available as a valuable complement to the current LLM evaluation ecosystem.
League of Legends (LoL) has been a dominant esport for a decade, yet the inherent complexity of the game has stymied the creation of analytical measures of player skill and performance. Current industry standards are limited to easy-to-procure individual player statistics that are incomplete and lacking context as they do not take into account teamplay or game state. We present a unified performance model for League of Legends which blends together measures of a player's contribution within the context of their team, insights from traditional sports metrics such as the Plus-Minus model, and the intricacies of LoL as a complex team invasion sport. Using hierarchical Bayesian models, we outline the use of gold and damage dealt as a measure of skill, detailing players' impact on their own-, their allies'- and their enemies' statistics throughout the course of the game. Our results showcase the model's increased efficacy in separating professional players when compared to a Plus-Minus model and to current esports industry standards, while metric quality is rigorously assessed for discrimination, independence, and stability. Readers might also find additional qualitative analytics which
One of the key problems in the field of soccer analytics is predicting how a player performance changes when transitioning from one league to another. One potential solution to address this issue lies in the evaluation of the respective league strength. This article endeavors to compute club ratings of the first and second European and South American leagues. In order to calculate these ratings, the authors have designed the Glicko-2 rating system-based approach, which overcomes some Glicko-2 limitations. Particularly, the authors took into consideration the probability of the draw, the home-field advantage, and the property of teams to become stronger or weaker following their league transitions. Furthermore, authors have constructed a predictive model for forecasting match results based on the number of goals scored in previous matches. The metrics utilized in the analysis reveal that the Glicko-2 based approach exhibits a marginally superior level of accuracy when compared to the commonly used Poisson regression-based approach. In addition, Glicko-2 based ratings offer greater interpretability and can find application in various analytics tasks, such as predicting soccer player
From 2020 to 2023, Major League Baseball changed rules affecting team composition, player positioning, and game time. Understanding the effects of these rules is crucial for leagues, teams, players, and other relevant parties to assess their impact and to advocate either for further changes or undoing previous ones. Panel data and quasi-experimental methods provide useful tools for causal inference in these settings. I demonstrate this potential by analyzing the effect of the 2023 shift ban at both the league-wide and player-specific levels. Using difference-in-differences analysis, I show that the policy increased batting average on balls in play and on-base percentage for left-handed batters by a modest amount (nine points). For individual players, synthetic control analyses identify several players whose offensive performance (on-base percentage, on-base plus slugging percentage, and weighted on-base average) improved substantially (over 70 points in several cases) because of the rule change, and other players with previously high shift rates for whom it had little effect. This article both estimates the impact of this specific rule change and demonstrates how these methods for
Large-scale heterogeneous multiagent systems feature various realistic factors in the real world, such as agents with diverse abilities and overall system cost. In comparison to homogeneous systems, heterogeneous systems offer significant practical advantages. Nonetheless, they also present challenges for multiagent reinforcement learning, including addressing the non-stationary problem and managing an imbalanced number of agents with different types. We propose a Prioritized Heterogeneous League Reinforcement Learning (PHLRL) method to address large-scale heterogeneous cooperation problems. PHLRL maintains a record of various policies that agents have explored during their training and establishes a heterogeneous league consisting of diverse policies to aid in future policy optimization. Furthermore, we design a prioritized policy gradient approach to compensate for the gap caused by differences in the number of different types of agents. Next, we use Unreal Engine to design a large-scale heterogeneous cooperation benchmark named Large-Scale Multiagent Operation (LSMO), which is a complex two-team competition scenario that requires collaboration from both ground and airborne agent
Competitive balance, which refers to the level of control teams have over a sports competition, is a crucial indicator for tournament organisers. According to previous studies, competitive balance has significantly declined in the UEFA Champions League group stage over the recent decades. Our paper introduces alternative indices to investigate this issue. Two ex ante measures are based on Elo ratings, and four dynamic concentration indicators compare the final group ranking to reasonable benchmarks. Using these indices, we find no evidence of any long-run trend in the competitive balance of the UEFA Champions League group stage between the 2003/04 and 2023/24 seasons.