On the fairness of single round-robin tournaments: Evidence from European football

László Csató; Diána Ivett Fűrész; Zsolt Havran

Home/Archive/arXiv

arXiv · 2610.21296

On the fairness of single round-robin tournaments: Evidence from European football

László Csató·Diána Ivett Fűrész·Zsolt Havran

View original source ↗Read source document ↗Export metadata ↓

Abstract

Single round-robin tournaments are widely regarded as unfair because of their home-away imbalance: some competitors play more home games than the others. Therefore, most sports leagues are played in a double round-robin format. However, some European football leagues contain a single round-robin (sub)tournament. To test whether empirical data can validate their unfairness, we construct a unique database and develop a strength of schedule metric based on Elo ratings with favourable theoretical properties. In contrast to the robust impact of relative team strength, the strength of schedule is found to have no significant effect on the number of points scored under the assumption of a league-specific home advantage. Consequently, the theoretical unfairness is not a serious issue in practice, or the standard approach of modelling home advantage in Elo ratings might need to be reconsidered.

Explore related subjects

econ.EM physics.soc-ph stat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

László Csató, Diána Ivett Fűrész, Zsolt Havran. 2026-10-15. On the fairness of single round-robin tournaments: Evidence from European football. https://arxiv.org/abs/2610.21296

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Estimating treatment-effect heterogeneity across sites, in multi-site randomized experiments with few units per site

Multi-site randomized experiments, which are common in economics and medicine, can reveal how treatment effects vary across settings. However, differences between site-specific estimates reflect both treatment-effect heterogeneity and estimation noise. We build on established measurement-error corrections and develop new ones to study this heterogeneity in experiments with many sites and few units per site. In particular, our results can be used to estimate the variance and centered third moment of treatment effects across sites, relate site effects to untreated outcomes, conduct mediation analyses, assess the roles of provider effectiveness and site responsiveness, and study heterogeneity in local average treatment effects (LATEs) under imperfect compliance. We apply our methods to counseling programs delivered by public and private providers in about 200 French employment offices. Average employment gains of about 2 percentage points conceal cross-site standard deviations of intention-to-treat effects of 8 to 9 percentage points. We also find substantial LATE heterogeneity.Effects are negatively associated with untreated employment rates. The two programs also tend to be more effective in the same sites, consistent with a role for heterogeneous site responsiveness.

econ.EM↗

arXiv2026

Efficient GMM and Weighting Matrix under Misspecification

This paper develops efficient GMM estimation under misspecified moment conditions. The influence function of the standard GMM estimator under misspecification depends on both the moment conditions and their Jacobian, motivating a new class of estimators based on augmented, recentered moment conditions. Standard GMM is a special case and generally suboptimal. By optimally weighting the augmented system, we obtain a misspecification-efficient (ME) estimator with the smallest asymptotic variance for the same GMM estimand. In linear models, its asymptotic variance takes the textbook form $(G'W^{*}G)^{-1}$, where $W^{*}$ is the inverse variance of the residualized moments after projection on the Jacobian $G$. We propose a feasible bootstrap estimator, which is a misspecification-robust and efficient version of the Hall and Horowitz (1996) bootstrap GMM estimator. Finally, we establish uniform local asymptotic minimax bounds over a class of weighting matrices. We illustrate the proposed methods in simulation and two empirical examples.

econ.EM↗

arXiv2026

Identification and Inference for Algorithmic Frontiers with Selective Labels

This paper provides identification results to characterize a fairness-accuracy (FA) frontier, and statistical inference tools to test hypotheses and build a confidence set for the FA-frontier, when outcomes are observed only for selected individuals. When the selection process is unrestricted but loss is measured in specific ways, we provide a characterization of the sharp identification region of the FA-frontier. When the observed distribution rules out frontier membership for a binary status quo algorithm, we construct a single alternative algorithm that improves both groups' accuracy without worsening fairness, uniformly over all admissible distributions of missing labels. For any loss functions, under selection on observables and strict overlap assumptions, we obtain point identification and propose a debiased machine learning estimator, derive its asymptotic distribution, and show how this can be used to carry out inference for the FA-frontier.

econ.EM↗