|
on Sports and Economics |
| By: | Gergely Cs\'aji; L\'aszl\'o Csat\'o |
| Abstract: | The Herfindahl--Hirschman Index (HHI), a standard measure of market concentration, is widely used to quantify competitive balance in sports tournaments. To enable comparisons over time or across leagues, both its minimum and maximum should be known. The minimum is usually trivial. Our paper provides results on the maximum HHI in incomplete round-robin tournaments, where the set of matches is represented by a regular but not complete undirected graph. We prove that the lower bound of maximum HHI is reached when the tournament consists of independent round-robin groups, while the upper bound of maximum HHI is reached when the set of matches is represented by a bipartite graph. Maximising HHI is computationally difficult even for highly structured graph types corresponding to real-world tournaments, where the teams are partitioned into pots and play the same number of matches against opponents from every pot. The complexity of the problem does not depend on the scoring system or the number of opponents from a pot. |
| Date: | 2026–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2611.01750 |
| By: | L\'aszl\'o Csat\'o; Di\'ana Ivett F\H{u}r\'esz; Zsolt Havran |
| 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. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.21296 |
| By: | Atkins, Matt; Dikgang, Johane |
| Abstract: | This study re-examines whether the performance of Major League Baseball batters changes in contract years. Using a panel of 3, 654 player-season observations covering 1, 003 players from 2015 to 2025, we estimate two-way fixed effects models with expected weighted on-base average (xwOBA) as the primary measure of performance. Pooled across all players, the contract-year coefficient is statistically indistinguishable from zero and is equivalent to zero within economically meaningful bounds. Disaggregating by career stage, however, reveals substantial heterogeneity: players with five or more years of major league service post xwOBA approximately six points higher in contract years, whereas players further from eligibility show no response (.. = .004 for the difference). Among veterans, the response is localized to the contract year rather than adjacent seasons, survives survivorship and selection diagnostics, and is most precisely estimated in freeagency years. These findings reconcile a literature in which veteran-restricted samples detected contract-year effects and broader samples did not. |
| Keywords: | contract year, personnel economics, incentives, career concerns, performance, Major League Baseball |
| JEL: | J33 J41 D82 Z22 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:glodps:1835 |
| By: | Jakobsson, Niklas; Moore, Kristjan; Barbarioli, Bruno; Brodeur, Abel |
| Abstract: | (2025a). The authors' response argues that the principal concerns are concentrated in the controls' first testing session. We examine an earlier dataset recovered from the public history of their repository. It contains 28 columns absent from the current BrazilianSample.xlsx. All twelve player D-KEFS columns were already public in a separate file, including the three columns labelled "Overall" in the recovered file. The recovered file adds control-group D-KEFS observations that closely reproduce the response's Table 1 and permits linkage across participant-level measures. Within individual teams, measures from different instruments and match statistics show near-perfect rank associations; team 5 contains 24 variable pairs with absolute Spearman correlations of at least 0.90. The Brazilian Design Fluency and Trail Making composites correspond less closely to their scaled subtest sums than in the Swedish comparison sample, with the player Trail Making correlation approximately zero. There are also 14 instances of successful events exceeding their corresponding totals, which is inconsistent if both refer to the same events and exposure. The article and response describe different testing sequences and intervals. These findings extend earlier concerns and require access to the exact analysis dataset, scoring and processing code, and documentation linking observations to source records. |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:i4rdps:335 |
| By: | Lens, Josh |
| Abstract: | College athletics and its finances are in flux due to several recent incidents. Many athletics departments claimed to lose millions of dollars due to the COVID-19 pandemic. The NCAA v. Alston Supreme Court decision will result in universities and athletics departments providing their student-athletes with additional education-related benefits. Due to the NCAA’s rule change permitting student-athletes to monetize their names, images, and likenesses, companies will likely divert sponsorship resources from athletics departments and toward student-athletes directly. Thus, it is increasingly important for athletics departments to be prudent with resources. One area where university athletics departments have historically wasted millions of dollars is head coach severance payments. Some have paid head coaches millions of dollars in severance upon terminating their employment. More specifically, universities, through their employment contracts with head coaches, put themselves in a no-win situation when they must make an employment decision regarding a head coach if the NCAA accuses that coach of committing a significant NCAA rules violation. Under the current standard head coach contract, universities often have two options. A university may terminate the coach’s employment without cause and pay the coach a large severance payment. Alternatively, if the university wants to terminate the coach’s employment with cause and avoid the severance payment, it must continue to employ and pay the coach while awaiting adjudication of the violation allegation, which can take years and result in litigation. This Article examines this no-win scenario for universities by first exploring a head coach’s job responsibilities and the relevant employment contract provisions under which they perform them. Next, the Article analyzes instances where prominent head coaches violated NCAA rules and how their employment contracts shaped their universities’ handling of the resulting employment decisions. Finally, the Article proposes contract language that would provide universities flexibility and potential cost savings when faced with an employment decision for a rule-breaking head coach. |
| Date: | 2026–10–15 |
| URL: | https://d.repec.org/n?u=RePEc:osf:lawarc:pyv47_v1 |
| By: | Hattori, Keisuke; Yamada, Mai |
| Abstract: | Helping colleagues builds up workplace relationships which have both productive and private benefits, at the cost of time that could otherwise be spent on one's own work. We model this trade-off to examine how the private value of workplace relationships affects reward design, team size, and leadership. Under individual rewards, helping is insufficient when the private value of relationships is low and excessive when it is high. More productive relationships can lead members to spend too much time helping, reducing team output even under an optimal reward scheme. When individual and team rewards are combined, the optimal weight on team performance is lower in teams whose members place greater private value on relationships, and higher in teams with greater common ability. Under individual rewards, expanding a team can curb excessive helping by weakening its mutual reinforcement, but also reduces the productive benefits of relationships. The optimal team size balances these effects and is larger when members place a higher private value on relationships. By committing to an effort allocation first, the leader induces more helping from the follower and strengthens social ties. This form of leadership can improve output when relationships are insufficiently developed, but lowers output when relationship formation is already at or beyond the output-maximizing level. Both members nevertheless gain in utility. |
| Keywords: | Social relationships, Helping, Team production, Incentive design, Effort allocation, Strategic complementarity |
| JEL: | D23 M52 M54 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:344455 |