The allocation of rewards in athletic contests

Similar to most top-tier matches in professional basketball, baseball and soccer, high-level competitions in individualistic sports, such as the tennis tournaments of Wimble-don and Flushing Meadows, the golf tournaments of Augusta and St. Andrews, as well as the marathons of New York and London attract not only thousands of spectators, but also a TV audience of millions of fans. Moreover, these (and other) individualistic sports have recently received increased attention also from economists trying to test a number of hypotheses that can be derived from "tournament theory" or - as a synonym - from "contest theory". The chapter is structured as follows: We first provide a brief description of the development of prize money levels and structures in the three different individual sports men-tioned in the previous paragraph (and, consequently, athletes' incomes over the last years (section 2). We then summarize the basic insights and the core predictions of tour-nament/contest theory (section 3) and review the available literature on the incentive effects of tournament pay systems in athletic contests (section 4). Finally, section 5 concludes and raises some of the questions that have not been answered yet and that should, therefore, be dealt with in future research.

A Computer Model of Drafting Effects on Collective Behavior in Elite 10,000 m Runners

Purpose Drafting in cycling influences collective behaviour of pelotons. Whilst evidence for collective behaviour in competitive running events exists, it is not clear if this results from energetic savings conferred by drafting. This study modelled the effects of drafting on behavior in elite 10,000 m runners. Methods Using performance data from a men’s elite 10,000 m track running event, computer simulations were constructed using Netlogo 5.1 to test the effects of three different drafting quantities on collective behaviour: no drafting, drafting to 3m behind with up to ~8% energy savings (a realistic running draft); and drafting up to 3m behind with up to 38% energy savings (a realistic cycling draft). Three measures of collective behaviour were analysed in each condition; mean speed, mean group stretch (distance between first and last placed runner), and Runner Convergence Ratio (RCR) which represents the degree of drafting benefit obtained by the follower in a pair of coupled runners. Results Mean speeds were 6.32±0.28m.s-1, 5.57±0.18 m.s-1, and 5.51±0.13 m.s-1 in the cycling draft, runner draft, and no draft conditions respectively (all P<0.001). RCR was lower in the cycling draft condition, but did not differ between the other two. Mean stretch did not differ between conditions. Conclusions Collective behaviours observed in running events cannot be fully explained through energetic savings conferred by realistic drafting benefits. They may therefore result from other, possibly psychological, processes. The benefits or otherwise of engaging in such behavior are, as yet, unclear

Skeletal Muscle PGC-1β Signaling is Sufficient to Drive an Endurance Exercise Phenotype and to Counteract Components of Detraining in Mice

Peroxisome proliferator-activated receptor-γ coactivator (PGC)-1α and -1β serve as master transcriptional regulators of muscle mitochondrial functional capacity and are capable of enhancing muscle endurance when overexpressed in mice. We sought to determine whether muscle-specific transgenic overexpression of PGC-1β affects the detraining response following endurance training. First, we established and validated a mouse exercise-training-detraining protocol. Second, using multiple physiological and gene expression end points, we found that PGC-1β overexpression in skeletal muscle of sedentary mice fully recapitulated the training response. Lastly, PGC-1β overexpression during the detraining period resulted in partial prevention of the detraining response. Specifically, an increase in the plateau at which O2 uptake (V̇o2) did not change from baseline with increasing treadmill speed [peak V̇o2 (ΔV̇o2max)] was maintained in trained mice with PGC-1β overexpression in muscle 6 wk after cessation of training. However, other detraining responses, including changes in running performance and in situ half relaxation time (a measure of contractility), were not affected by PGC-1β overexpression. We conclude that while activation of muscle PGC-1β is sufficient to drive the complete endurance phenotype in sedentary mice, it only partially prevents the detraining response following exercise training, suggesting that the process of endurance detraining involves mechanisms beyond the reversal of muscle autonomous mechanisms involved in endurance fitness. In addition, the protocol described here should be useful for assessing early-stage proof-of-concept interventions in preclinical models of muscle disuse atrophy

Pace and motor control optimization for a runner

Our aim is to present a new model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour is well approximated by a turnpike problem. We provide numerical simulations quite consistent with this approximation which leads to a simplified problem. We are also able to estimate the effect of slopes and ramps

Psychological States Underlying Excellent Performance in Sport: Toward an Integrated Model of Flow and Clutch States

This study investigated the psychological states underlying excellent performance in 26 athletes (Mage = 29 years, SD = 7.7) across a range of sports (team, net/wall, sprint, endurance, adventure) and standards (world class to recreational). Participants were primarily interviewed on average 4 days after excellent performances. The data were analyzed thematically. Distinct states of flow and clutch were reported, each of which occurred through separate contexts and processes, while athletes also transitioned between states during performance. These findings extend current knowledge of the psychology of excellent performance and are discussed in terms of implications for future research and applied practice

RUNNER\u27S LOG AND PREDICTIVE PERFORMANCE ANALYTICS

This report, prepared for the Worcester Polytechnic Institute, describes the development of a running log application and the development and analysis of a data-centric approach to running performance prediction. The java application incorporated common UI principles as well as a community aspect to facilitate and encourage its use. The data-centric predictive model was developed by analyzing individuals who have performed similarly to the input. As tested with 1148 male track performances and 1265 female track performances, the data-centric approach provided predictions with an average error of 3.05 percent for men and 3.63 percent for women. These errors are approximately 9 percent and 20 percent lower, respectively, than the leading Purdy Points model

The Relationship Between Tactical Positioning and the Race Outcome in 800-m Running at the 2016 Olympic Games and 2017 IAAF World Championship

The purpose of this analysis was to quantify the probability of achieving a top-3 finishing position during 800-m races at a global championship, based on dispersion of the runners during the first and second laps and the difference in split times between laps. Overall race times, intermediate and finishing positions and 400 m split times were obtained for 43 races over 800 m (21 men’s and 22 women’s) comprising 334 individual performances, 128 of which resulted in higher positions (top-3) and 206 the remaining positions. Intermediate and final positions along with times, the dispersion of the runners during the intermediate and final splits (SS1 and SS2), as well as differences between the two split times (Dsplits) were calculated. A logistic regression model was created to determine the influence of these factors in achieving a top-3 position. The final position was most strongly associated with SS2, but also with SS1 and Dsplits. The Global Significance Test showed that the model was significant (p < 0.001) with a predictive ability of 91.08% and an area under the curve coefficient of 0.9598. The values of sensitivity and specificity were 96.8% and 82.5%, respectively. The model demonstrated that SS1, SS2 and Dplits explained the finishing position in the 800-m event in global championships

More pace variation and pack formation in successful world-class 10,000-m runners than in less successful competitors

Purpose To determine different relationships between, and predictive ability of, performance variables at intermediate distances with finishing time in elite male 10,000 m runners. Methods Official electronic finishing and 100 m split times of the men’s 10,000 m finals at the 2008 and 2016 Olympic Games and IAAF World Championships in 2013 and 2017 were obtained (125 athlete performances in total). Correlations were calculated between finishing times and positions and performance variables relating to speed, position, time to the leader and time to the runner in front at 2000, 4000, 6000, 8000 and 9900 m. Stepwise linear regression analysis was conducted between finishing times and positions and these variables across the race. One-way ANOVA was performed to identify differences between intermediate distances. Results The standard deviation and kurtosis of mean time, skewness of mean time and position and time difference to the leader were either correlated with or significantly contributed to predictions of finishing time and position at one of the analysed distance at least (0.81 ≥ r ≥ 0.30 and 0.0001 ≤ P ≤ 0.03, respectively). These variables also displayed variation across the race (0.0001 ≤ P ≤ 0.05). Conclusions The ability to undertake a high degree of pace variability, mostly characterised by acceleration in the final stages, is strongly associated with the achievement of high finishing positions in championship 10000 m racing. Furthermore, the adoption and maintenance of positions close to the front of the race from the early stages is important to achieve a high finishing position