Shane Sanders

The extant literature on choice aggregation paradoxes focuses on strict instances given their empirical availability, despite the prevalence of ties in many settings. In this paper we consider the incidence of weak transitivity violations (cycles) in rank sum aggregation in a unique empirical setting, the IAAF Cross Country World Championships . In this setting, rank sum scoring is used to aggregate 4 team members per group into a group score. Unlike other prominent empirical cases of rank sum scoring, the even number of constituents per group means pairwise group ties, and therefore weak cycles, are possible and may be probable. We compute the empirical likelihood of 3-group weak cycles from pairwise rank sum scoring across 83 Championships. We also compute combinatorial likelihoods of said violations in this setting using a novel, large sample space enumerative algorithm for statistical comparison. Like the concept of a p-value , cycle incidence sheds light on the robustness of a given statistical result. We find regular occurrences of both weak and strict cycles, and that weak cycles occur more regularly than strict cycles in theory and our data. Both weak and strict cycles are under-represented in our empirical setting relative to the corresponding theoretical incidence—in which all rank-sum outcome sequences are equally likely—due to correlated within-group ability levels. While the degree of ambiguity for a weak cycle is less relative to a strict cycle, weak cycles are more prevalent in the data and may therefore introduce a greater aggregate level of ambiguity.

Title IX of the 1972 Educational Amendments stipulates equal benefits to females and males in federally funded educational programs. A large sport finance empirical literature tests for Title IX compliance in National Collegiate Athletic Association athletics programs and interprets compliance according to proportional representation of female athletes. Quoting the legislation, we demonstrate that Title IX reaches more broadly than proportionality to require educational program benefits equality across gender. We examine expense-based financial support to women’s and men’s National Collegiate Athletic Association Division I basketball programs from 2006 to 2019, after scholarship-count based compliance was largely achieved. The sample implicitly matches on sport of play. Conditional on lagged-generated revenues, lagged-allocated revenues, school, and year of observation, we find women’s programs receive significantly and substantially less expected revenue-conditional expense funding (slope effect) and expected revenue nonconditional expense funding (level effect), a two-part funding deficit. Resulting Oaxaca–Blinder–Kitagawa decomposition estimates a $383,000 ($2,076,000) expected women’s program funding deficit at mean women’s (men’s) annual program revenue.

Neoclassical economics holds that agents use resources to maximize objectives subject to constraints. Behavioral economics allows agents to engage in suboptimal decision making due to a host of cognitive biases. We test these theories in a prominent sport management setting. Many sports teams use management information systems to aid in multistream optimization tasks. We find that National Basketball Association team shot-selection tools—shot charts that do not account for shot-pursuant free-throw scoring—distort characterizations of optimal basketball shot selection (e.g., between two- and three-point attempts). Chart aggregations suggest a substantial, persistent three-point premium—continued gains from increases in three-point shooting volume. Through 2021–2022, teams have undertaken these increases, creating the National Basketball Association “Three-Point Revolution.” Using data science methods, we develop refined shot charts that consider shot-pursuant free-throw scoring. Accounting for this, the National Basketball Association has been in significant and widening three-point dispremium since 2018–2019.

Purpose: We introduce a novel type of basketball shot chart, a true shot chart, that incorporates total points, accounting for both field goals and free throws, corresponding to each shot taken. We then create a shot selection measure called shot selection efficiency that summarizes the efficiency of a team’s shot chart. Lastly, we validate the measure using fixed effects regression analysis and determine whether shot selection is priced efficiently in the NBA player labor market.Design/methodology/approach: We utilize fixed effects regression analysis to validate a measure and also to determine managerial payroll efficiency in the NBA.Findings: We find that shot selection efficiency is a source of wins not fully explained by team payroll. That is, it is not fully priced into the player labor market.Research limitations/implications: Teams are in need of the shot chart summary measure provided, as they are not efficiently pricing players in the player labor market with respect to shot selection.Originality/value: This research introduces a novel shot chart type for basketball as well as a novel shot chart summary measure. It also validates the measure and establishes an NBA player labor market inefficiency related to the measure.

From the “landmark” Alston v. NCAA antitrust decision, we examine whether the legally hypothesized fan wage-repugnance effect implies procompetitive benefits in NCAA sports output markets via increased output demand from student-athlete wage restriction. In Alston v. NCAA, the Courts took this benefit as given but failed to recognize the empirically-verified relationship between league talent and fan demand. We assume a legally-hypothesized wage-repugnance line exists and present a theoretical output-demand model functionally dependent upon allocations in a wage-constrained labor-input market. Even given fan repugnance, wage restrictions do not necessarily generate procompetitive benefits. For families of model parameterizations, wage restrictions impose anticompetitive harm.

This study establishes sufficient conditions for observing instances of Simpson's (data aggregation) Paradox under rank sum scoring (RSS), as used, e.g., in the Wilcoxon-Mann-Whitney (WMW) rank sum test. The WMW test is a primary nonparametric statistical test in FDA drug product evaluation and other prominent medical settings. Using computational nonparametric statistical methods, we also establish the relative frequency with which paradox-generating Simpson Reversals occur under RSS when an initial data sequence is pooled with its ordinal replicate. For each 2-sample, n-element per sample or 2 x n case of RSS considered, strict Reversals occurred for between 0% and 1.74% of data poolings across the whole sample space, roughly similar to that observed for 2 x 2 x 2 contingency tables and considerably less than that observed for path models. The Reversal rate conditional on observed initial sequence is highly variable. Despite a mode at 0%, this rate exceeds 20% for some initial sequences. Our empirical application identifies clusters of Simpson Reversal susceptibility for publicly-released mobile phone radiofrequency exposure data. Simpson Reversals under RSS are not simply a theoretical concern but can reverse nonparametric or parametric biostatistical results even in vitally important public health settings. Conceptually, Paradox incidence can be viewed as a robustness check on a given WMW statistical test result. When an instance of Paradox occurs, results constituting this instance are found to be data-scale dependent. Given that the rate of Reversal can vary substantially by initial sequence, the practice of calculating this rate conditional on observed initial sequence represents a potentially important robustness check upon a result.

Ostrom suggests that collective action problems may present an obstacle to the reduction in (external costs from) global greenhouse gas emissions and that a polycentric approach is necessary to find a solution. A market-based prong of such a polycentric solution—alongside, e.g., governance-based prongs such as transferable pollution permits—may lie in the nature of certain salient “environmentally friendly” goods (e.g., Toyota Prius, Tesla cars, home solar panels). The present study analyzes the social welfare consequences of positional conservation (i.e., consumption of salient environmentally friendly goods for the purpose of status signaling) within a choice theoretic model. For example, the Toyota Prius and Tesla have been shown to be such a type of good. In a two-good model of strategic consumer choice, in which consumers choose between a positional, “conservation good” and an externally costly, “non-conservation good”, we find that positional conservation improves social welfare if the unit external cost of the non-conservation good consumption is sufficiently large. In such a case, positionality serves to (partly or fully) correct an under-consumption of the positional good. Fershtman and Weiss find, within a one-good (action) model, that positionality can be corrective of distortions from positive externalities but not of distortions from negative externalities (e.g., pollution). Within a two-good model of consumer choice, we find that “social rewards” can help to correct distortions generated by negative externalities and improve social welfare. The results of the present study suggest that the Paretian objective may not be to curb positional spending but to shift positional spending toward conspicuous goods that are otherwise under-consumed (e.g., conservation goods or education).