Elo Rating Research Articles

Psychophysiological and Performance Effects of Biofeedback and Neurofeedback Interventions in a Top 100 Female Chess Player

(1) Background: Previous studies showed that neurofeedback and biofeedback could improve stress levels, enhance self-control over physiological factors, improve behavioral efficiency, and increase reaction speed to stimuli. Specifically, the sensorimotor rhythm stimulation (12–15 Hz) can enhance cognitive functions such as selective attention and working memory. However, there is no study that analyzes the effect of these interventions in chess players. (2) Methods: A Chess Woman Grandmaster and Chess International Master, with an ELO ranking higher than 2350 points, was selected to participate in this case study. The participant conducted a total of 14 sessions of biofeedback and neurofeedback, training in breathing, sensorimotor rhythm stimulation in Cz, skin conductance, temperature, and heart rate variability combined with chess work. Specific and non-specific tasks were designed to evaluate the intervention. (3) Results: The chess player enhanced the heart rate variability during specific and non-specific chess tasks: chess problems, 15 + 10 games, and puzzle rush games. In addition, the sensorimotor rhythm power decreased during the chess problem and increased during the 15 + 10 game and puzzle rush. Also, chess performance and anxiety levels improved after the intervention. (4) Conclusions: Neurofeedback and biofeedback training combined with chess training could improve the performance of chess players.

Evaluating aerial duel ability of football players using height-adjusted Elo rating model

ABSTRACT Football players’ aerial duel ability has been typically evaluated based on the “aerial duel success rate (success/attempt)”. However, sole reliance on this indicator implies excluding other factors like the opponent’s aerial duel ability and height. This makes the evaluation of a player’s true ability difficult. The Elo rating system is an alternative method that addresses such exclusion. This study analysed a player’s aerial duel ability more accurately using an Elo model adjusted by height. All players from all matches in the K League 1 over the 3 seasons were analysed. The player rankings for aerial duel ability calculated using the Elo rating system showed significant differences compared to the rankings based on aerial duel success rates used in previous studies e.g. the player ranked 1st in Elo was 3rd in aerial duel success rate, the 2nd and the 3rd players remained 21st and 54th. These results serve as valuable information for analysing players’ abilities and understanding team tactics in the applied field. These will also be crucial for player evaluation while scouting.

Breaking the board: the rise of female Go players in Korea

In the historically male-dominated world of Go—a game with a rich history and a current global player base of 46 million—recent years have marked a significant shift in gender dynamics, highlighted by Choi Jeong’s historic achievement as the first female to reach the open major world tournament finals. This study investigates the rise of female Go players in Korea through multiple lenses: descriptive analyses cover demographic data, Elo ratings, and competition statistics, while social representation analyses employ in-depth interviews and core-periphery analysis. A core finding is the profound transformation within the Korean Go community, where female players are not just witnessing increased representation but also significant enhancements in performance, opportunities, and financial rewards. Narratives from the players unravel the intricate web of performance disparities, community engagement, and evolving infrastructures. Economic incentives, societal and cultural shifts, and institutional support are identified as key contributors to their success. Beyond its application to professional Go, this research underscores a paradigmatic shift, illuminating strategies for fostering gender inclusivity in fields traditionally overshadowed by male dominance.

An Improved Point System for Cricket’s World Test Championship

With the advent of formats of limited overs in cricket like the One Day and Twenty-20 Internationals, test cricket, the longest-running version of the game, has witnessed a significant decline in popularity. The World Test Championship (WTC) was launched in 2019 by the International Cricket Council to reignite interest in test cricket. However, the initial point distribution system devised for the inaugural WTC had several shortcomings, which include allocating points based on the outcome of the entire series rather than the number of test matches played, the absence of rewards for teams winning matches away from home, failing to take into consideration the margin of victory (MOV) and not accounting for the relative strength of competing teams. Considering these shortcomings, this article proposes a new point system, thus providing an alternative to the existing one. The point system uses the Elo rating system, including factors such as home-field advantage, impact of the toss and MOV. Statistical analyses were conducted to validate the home-field advantage and toss impact. Subsequently, the proposed model developed was named the points won per match system. The team rankings in the WTC are established based on this proposed model and compared with the actual one.

Can Proficiency in Chess Predict Situation Awareness in a Novel Task?

This study explored the correlation between situation awareness (SA) and proficiency in chess. Eighteen participants were tested, performing a letter factory (LF) task and providing their ELO scores. Each participant received $10 for 30 min of participation. The results showed a negative correlation between the number of games played and the SA score, suggesting that increased gameplay was associated with lower SA in the letter factory task. Additionally, the ELO score was negatively correlated with the number of double attempts to place a designated letter in the loading boxes, indicating that more skilled players made fewer errors.

Stochastic Extensions of the Elo Rating System

This work studies how the Elo rating system can be applied to score-based sports, where it is gaining popularity, and in particular for predicting the result at any point of a game, extending its statistical basis to stochastic processes. We derive some new theoretical results for this model and use them to implement Elo ratings for basketball and soccer leagues, where the assumptions of our model are tested and found to be mostly accurate. We showcase several metrics for comparing the performance of different rating systems and determine whether adding a feature has a statistically significant impact. Finally, we propose an Elo model based on a discrete process for the score that allows us to obtain draw probabilities for soccer matches and has a performance competitive with alternatives like SPI ratings.

A spectral approach for the dynamic Bradley–Terry model

SummaryThe dynamic ranking, due to its increasing importance in many applications, is becoming crucial, especially with the collection of voluminous time‐dependent data. One such application is sports statistics, where dynamic ranking aids in forecasting the performance of competitive teams, drawing on historical and current data. Despite its usefulness, predicting and inferring rankings pose challenges in environments necessitating time‐dependent modelling. This paper introduces a spectral ranker called Kernel Rank Centrality, designed to rank items based on pairwise comparisons over time. The ranker operates via kernel smoothing in the Bradley–Terry model, utilising a Markov chain model. Unlike the maximum likelihood approach, the spectral ranker is nonparametric, demands fewer model assumptions and computations and allows for real‐time ranking. We establish the asymptotic distribution of the ranker by applying an innovative group inverse technique, resulting in a uniform and precise entrywise expansion. This result allows us to devise a new inferential method for predictive inference, previously unavailable in existing approaches. Our numerical examples showcase the ranker's utility in predictive accuracy and constructing an uncertainty measure for prediction, leveraging data from the National Basketball Association (NBA). The results underscore our method's potential compared with the gold standard in sports, the Arpad Elo rating system.

The Role of Emotionality, Self-efficacy, Rational- and Intuitive- Thinking Styles in Advanced Chess Expertise

"Literature is scarce regarding the psychological predictors of chess expertise and A-level chess performance. Methods: A cross-sectional study was designed and conducted on a total number of 90 Hungarian and Romanian competitive chess players. More than half were males, the average age was 32.07 (SD=12.99). The study aimed to explore the predictive influence of age, gender, number of hours spent practicing, preferences for rational and intuitive thinking styles, self-efficacy, and emotionality on the likelihood of obtaining a publicly accessible ELO rating within the range of 1800-2500 (indicating at least A-level expertise or higher). Binary logistic regression was applied to examine the weight of each predictor. Results: The data evinced the statistically significant role of gender, and rational thinking style on A-level chess expertise and from all the conclusive predictors the most determinant was the rational thinking style which raised the chance of high expertise more than 60 times. Conclusions: Practice contributes positively to the development of A-level competence. However, the most crucial factor in predicting high chess expertise and performance is the preference for rational thinking style. Keywords: chess expertise, ELO rating, A-level, emotionality, self-efficacy, rational thinking, intuitive thinking, practice, adults"

Impact of socioeconomic status on healthy immune responses in humans.

Individuals with low socioeconomic status (SES) are at greater risk of contracting and developing severe disease compared with people with higher SES. Age, sex, host genetics, smoking and cytomegalovirus (CMV) serostatus are known to have a major impact on human immune responses and thus susceptibility to infection. However, the impact of SES on immune variability is not well understood or explored. Here, we used data from the Milieu Intérieur project, a study of 1000 healthy volunteers with extensive demographic and biological data, to examine the effect of SES on immune variability. We developed an Elo-rating system using socioeconomic features such as education, income and home ownership status to objectively rank SES in the 1000 donors. We observed sex-specific SES associations, such as females with a low SES having a significantly higher frequency of CMV seropositivity compared with females with high SES, and males with a low SES having a significantly higher frequency of active smoking compared with males with a high SES. Using random forest models, we identified specific immune genes which were significantly associated with SES in both baseline and immune challenge conditions. Interestingly, many of the SES associations were sex stimuli specific, highlighting the complexity of these interactions. Our study provides a new way of computing SES in human populations that can help identify novel SES associations and reinforces biological evidence for SES-dependent susceptibility to infection. This should serve as a basis for further understanding the molecular mechanisms behind SES effects on immune responses and ultimately disease.

Redefining dominance calculation: Increased competition flattens the dominance hierarchy in dairy cows

Dominance hierarchies are known for mitigating conflicts and guiding priority of access to limited resources in gregarious animals. The dominance hierarchy of dairy cows is typically investigated using agonistic interactions, often monitored at the feed bunk right after fresh feed delivery when competition is high resulting in frequent interactions. Yet, the outcome of agonistic interactions during times of high competition may be more influenced by cows' high valuation of fresh feed than their intrinsic attributes, such that the dominance hierarchy constructed using agonistic interactions under high versus low competition times might differ. We tested how the structure of the dominance hierarchy changes in relation to different levels of competition in a dynamic group of 48 lactating dairy cows over 10 mo, with 6 cows exchanged every 16 d for a total of 159 cows. Using a validated algorithm we continuously detected the actor and reactor of replacement behaviors in 30 feed bins as cows competed for feed. We also calculated the percentage of occupied feed bins to characterize competition at the moment of each replacement. These data were combined to create hierarchies using Elo ratings, separately for 25 occupancy levels ranging from 13% to 100%. For each 1% rise in feeder occupancy, hierarchy steepness fell by 2.41 × 10-3 ± 9.71 × 10-5 (SE), and the percentage of dyads where both cows replaced each other rose by 0.13% ± 0.01%. At the highest feeder occupancy level in comparison to the lowest one, we observed 7.57% more dyads in which the dominant individual (those won more interactions at the lowest feeder occupancy) started to lose proportionally more. The magnitude of decrease in the winning rate of the dominant individual in those dyads also got amplified by 1.06 × 10-3% ± 1.37 × 10-4% (SE) for each 1% increase in feeder occupancy. These findings illustrate how inferred hierarchies vary with competition, with high competition flattening the hierarchy due to increased success of subordinate animals. We suggest that during heightened competition, increased valuation of resources can affect competitive success more than the individual's intrinsic dominance attributes. We recommend against calculating dominance hierarchies based on agonistic interactions during periods of high competition alone, and more generally urge researchers to differentiate agonistic interactions based on context when constructing dominance hierarchies.

Competitive Balance in the Post-2024 Champions League and the European Super League: A Simulation Study

The proposal of the European Super League and the 2024/25 reform of the UEFA Champions League are both major events in European club football. This study compares the competitive balance (CB) of these new tournament formats with the previous Champions League format. Short-, mid- and long-term CB are quantified by measuring the average uncertainty of match outcomes, the ratio of stakeless matches, and the recurrence ratio of teams in knockout rounds. A simulation method is applied using the teams, their seeding, and Elo ratings in the 2020/21 and 2021/22 Champions League seasons. Results suggest that the 2024/25 reform improves CB, especially in match uncertainty and the occurrence of stakeless matches. In comparison, the Star League of the European Super League concept of December 2023 is superior concerning average match uncertainty. However, it has a worse CB regarding stakeless matches and dynamic CB. Reasons and suggestions for improvement are also discussed.

Modeling and prediction of tennis matches at Grand Slam tournaments

In this manuscript, different approaches for modeling and prediction of tennis matches in Grand Slam tournaments are proposed. The data used here contain information on 5,013 matches in men’s Grand Slam tournaments from the years 2011–2022. All regarded approaches are based on regression models, modeling the probability of the first-named player winning. Several potential covariates are considered including the players’ age, the ATP ranking and points, odds, elo rating as well as two additional age variables, which take into account that the optimal age of a tennis player is between 28 and 32 years. We compare the different regression model approaches with respect to three performance measures, namely classification rate, predictive Bernoulli likelihood, and Brier score in a 43-fold cross-validation-type approach for the matches of the years 2011 to 2021. The top five optimal models with highest average ranks are then selected. In order to predict and compare the results of the tournaments in 2022 with the actual results, a comparison over a continuously updating data set via a “rolling window” strategy is used. Also, again the previously mentioned performance measures are calculated. Additionally, we examine whether the assumption of non-linear effects or additional court- and player-specific abilities is reasonable.

Using simulations to compare the current Davis Cup ranking system to Elo.

The Davis Cup is the premier men's team event in tennis, run by the International Tennis Federation and in which over 130 nations compete. It uses a merit-based ranking system that allows nations to gain a pre-determined number of points when they win. The rankings are integral to the competition structure and used in the draws of every round. Therefore, it is essential that the ranking method performs well with respect to required performance criteria of the International Tennis Federation. The Elo rating method is a commonly used method of rating and ranking participants in a competitive exercise and is used by FIFA for the ranking of male and female national teams. The performance of the current Davis Cup ranking method and Elo rating were compared using a simulation of the Davis Cup competition structure. Four criteria were used for the comparison: Finishing Order Correlation, Skill Level Correlation, Responsiveness, and Protection. Such a comparison has not previously been published. The two methods were comparable across three of the criteria, with the Davis cup easily outperforming Elo in responsiveness. Indeed, the Elo method had such poor responsiveness that improved performance may not be fully recognised within a player's career. An alternative method of optimising the Elo K-factor parameter was developed and this improved the performance of Elo to match the current Davis Cup method. In conclusion, the current Davis Cup ranking method is performing at a standard that cannot be matched by typically optimised Elo but can be matched when an alternative optimisation method is used. Therefore, no evidence was found to suggest that the current Davis Cup ranking method could be improved upon by using Elo. However, alternative K-factor optimisation methods should be considered when applying Elo to a competition.

Composite rating method: Application to European basketball leagues

ABSTRACT This paper introduces the Composite Rating Method (CRM), a novel approach for the integrated evaluation of basketball player and team performances across multiple leagues. Utilizing data from Euroleague, EuroCup, and Basketball Champions League, the presented method provides comprehensive and accurate rankings, including accounting for actions not included in personal statistics. Drawing inspiration from established methodologies such as ELO, PER, Offensive and Defensive ratings, CRM offers a balanced assessment of player and team capabilities. The paper delineates the data collection and preprocessing procedures, details the algorithmic framework of CRM, and showcases its predictive capacity. By presenting a well-rounded approach to ranking, this paper aims to contribute to the advancement of performance evaluation methods in basketball and sports in general.

Optimal prize design in team contests with pairwise battles

This paper studies the effort-maximizing design of a team contest with an arbitrary number (odd or even) of pairwise battles. In a setting with full heterogeneity across players and battles, the organizer determines the prize allocation rule (or the winning rule of an indivisible prize) contingent on battle outcomes. We propose a measure of team's strength, which plays a crucial role in prize design. The optimal design is a majority-score rule with a headstart score granted to the weaker team: All battles are assigned team-invariant scores, the weaker team is given an initial headstart score which is the difference in strengths between teams, and the team collecting higher total scores from its winning battles wins the entire prize. The optimal rule resembles the widely-adopted Elo rating system.

A comparative evaluation of Elo ratings- and machine learning-based methods for tennis match result prediction

Elo ratings-based methods, including the recently proposed Weighted Elo method, have been found to perform well when forecasting tennis match results, however, whether they can outperform machine learning (ML) has not been established. In this study, a comparative evaluation of the two types of methods is conducted using the Sports Result Prediction CRISP-DM experimental framework. The first full year of mens ATP tennis data (2006), in a dataset containing matches from 2005 to 2020, was set to be the initial training set and 1 year of data was incrementally added to this set to predict 14 test years, from 2007 to 2020. Features were ranked based on their average rank across five feature selection techniques. It was found that, of the five ML models, Alternating Decision Trees (ADTrees) and Logistic Regression achieved higher accuracies than Elo ratings and similar accuracies to predictions derived from betting odds. Furthermore, ADTrees show potential in this domain, with solid performance achieved with an interpretable decision tree that allows for variation in the average betting odds difference threshold.

Rating players by Laplace’s approximation and dynamic modeling

The Elo rating system is a simple and widely used method for calculating players’ skills from paired comparison data. Many have extended it in various ways. Yet the question of updating players’ variances remains to be further explored. In this paper, we address the issue of variance update by using the Laplace approximation for posterior distributions, together with a random walk model for the dynamics of players’ strengths and a lower bound on player variance. The random walk model is motivated by the Glicko system, but here we assume nonidentically distributed increments to deal with player heterogeneity. Experiments on men’s professional matches showed that the prediction accuracy slightly improves when the variance update is performed. They also showed that new players’ strengths may be better captured with the variance update.

Crowdsourcing Subjective Annotations Using Pairwise Comparisons Reduces Bias and Error Compared to the Majority-vote Method

How to better reduce measurement variability and bias introduced by subjectivity in crowdsourced labelling remains an open question. We introduce a theoretical framework for understanding how random error and measurement bias enter into crowdsourced annotations of subjective constructs. We then propose a pipeline that combines pairwise comparison labelling with Elo scoring, and demonstrate that it outperforms the ubiquitous majority-voting method in reducing both types of measurement error. To assess the performance of the labelling approaches, we constructed an agent-based model of crowdsourced labelling that lets us introduce different types of subjectivity into the tasks. We find that under most conditions with task subjectivity, the comparison approach produced higher f1 scores. Further, the comparison approach is less susceptible to inflating bias, which majority voting tends to do. To facilitate applications, we show with simulated and real-world data that the number of required random comparisons for the same classification accuracy scales log-linearly O(N log N) with the number of labelled items. We also implemented the Elo system as an open-source Python package.

Occupation density of every chess piece by phases, levels of game, outcomes and phase-space according to their entropy differences

In this paper, we statistically analyze the density of each chess piece in four square concentric frames for different skill levels (according to the Elo ranking system), phases (opening, middlegame and endgame) and outcomes. The results indicate a tendency for pawns, knights and bishops to move towards the central areas, particularly during the opening phase. Additionally, we identified intrinsic entropy patterns for each piece throughout the entire game, independent of player skill level. We constructed a phase-space from entropy delay time series to provide probabilistic predictions for game outcomes.

RETRACTED ARTICLE: Research on Data Analysis of Efficient Innovation and Entrepreneurship Practice Teaching Based on LightGBM Classification Algorithm

The transformation of innovation and entrepreneurship practice teaching and education methods has put forward higher requirements for the intelligence and personalization of online education platforms. The aim of this study is to predict learning outcomes based on students' learning outcomes and habits, identify weak areas of knowledge, and provide targeted guidance and recommend the most suitable teaching resources. According to the concept of LightGBM model and the method of Feature selection, the research puts forward an integrated classification model ELO–LightGBM based on Elo Rating System (ELO) scoring system and Light Gradient Boosting Machine (LightGBM), trying to further mine the potential information of the practical teaching management data set. The model obtained a score of 0.7928 when using the dataset training, and a large number of comparative experiments were carried out between the ELO–LightGBM model and other classification models in different public datasets. The experimental results proved that the ELO–LightGBM model is more accurate than other classification models. In the comparative experiment on the practical teaching data set, the accuracy of the ELO–LightGBM model also surpassed the LightGBM model and the linear support vector machine model that performed well in small data sets, and the model was in the accuracy rate. The accuracy rate of winners in the comparison of micro-average is as high as 82.6%. It can be seen that the ELO–LightGBM model is of great significance to the intelligence and personalization of the online education platform.