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Testing Rosen's Sequential Elimination Tournament Model: Incentives and Player Performance in Professional Tennis
Abstract
The authors use an extensive and unique data set from the men's professional tennis circuit to test Rosen's sequential elimination style tournament model. Specifically, they investigate what effect an increase in prize money differentials between rounds has on the stronger player's probability of winning the match. This involves estimat- ing a standard probit model utilizing data from 2,632 individual matches over 68 tour- naments during the 2001 men's professional tennis circuit. The results of the study support predictions associated with Rosen's match play tournament model. Increases in prize money differentials have a positive, statistically significant effect on the stron- ger player's probability of winning the match.
... Some surveys in this research line are Kendall et al. (2010), (Wright, 2014), and Rabadi et al. (2015). Also, several papers have studied essential aspects of elimination (also named knockout) tournaments; for example, Rosen et al. (1986), Sunde (2003), Knyazev (2017), Gilsdorf and Sukhatme (2008), and Huang (2016) have studied prize and incentives structures. In fact, the paper by Rosen et al. (1986) is the first paper that provides economic arguments in the current prize structure. ...
... Knyazev showed that the optimal prize structure strongly depends on the output function and that only in a separable linear case coincides with Rosen's optimal structure. In Gilsdorf and Sukhatme (2008), they studied the effect of an increase in prize money differentials between rounds on the stronger player's probability of winning the match, following Rosen's sequential elimination-style tournament model. The results of the study support predictions associated with Rosen's model. ...
... Note that due to the constraints the results show that improved money prizes are assigned to the first rounds (third column) when compared to the prizes assigned in 2019 by the ATP (first round). As mentioned in the Literature Review section, Gilsdorf and Sukhatme (2008) suggested looking at the number of sets played as a measure of duration or effort. The effort function that we propose aims to assign different prizes to the losers in each round and to maintain the total budget available in the rounds. ...
The Association of Tennis Professionals (ATP) distributes a considerable amount of money in prizes each year. Studies have shown that only the top 100 ranked players can self-finance; hence, it is convenient to introduce changes to the prize distribution to promote a more sustainable system. A Linear Programming model to distribute the tournament’s budget under a new concept for the fair distribution of prize money is proposed. Additionally, to distribute the prizes, a function based on the effort of the players is designed. The model was applied to tournaments to demonstrate the impact on improving the player’s prizes distribution.
... The existence of a direct relationship between level of heterogeneity in relative quality (hereinafter, heterogeneity) and the winning probability of a stronger contestant in individual sports has been well documented in studies focusing on tennis (e.g., Gilsdorf & Sukhatme, 2007;Klaassen & Magnus, 2001;Koning, 2011;Sunde, 2009). 2 But unlike tennis or other individual noncombat sports, combat sports involve not only different genders but also different weight categories. As noted, in judo, there are seven different contestants ranked number one in the world within each gender, implying that we should consider each weight category as a completely different competition. ...
... Estimation (1) in Tables 3 and 4 shows the results for men's and women's fights as a function of level of heterogeneity. As predicted by contest theory (e.g., Rosen, 1986) and previously found for individual sports (e.g., Gilsdorf & Sukhatme, 2007;Klaassen & Magnus, 2001;Koning, 2011;Sunde, 2009), an increase in the Rank-Dif FU variable yields a greater probability that the higher ranked judoka will win and is statistically significant at any reasonable level of significance for both men and women. According to the estimation results based on estimation (1) in Tables 3 and 4, for example, the probability that a judoka ranked 8 will win against a judoka ranked 22 is equal to 1 1þe À0:509 Ã log 2 ð22ÞÀlog 2 ð8Þ ð Þ ¼ 0:677 in men's judo and 12 (5) 120 (10) 91 (23) 223 (12) 16 (9) 134 (16) 38 (10) (1) Note. ...
Judo is a combat sport with seven different weight categories. In this article, we examined data from 1,902 men’s and 1,400 women’s fights at the eight most prestigious judo tournaments during the period 2010-2013. Using a single fight as the unit of observation, we found that the probability for the favorite to win against the underdog in the men’s half-lightweight category is significantly lower than in most other categories. Moreover, in fights in which only European and/or Asian judokas participate, we found that the men’s half-lightweight category is significantly more balanced than all other men’s categories. For women, there is no consistent evidence that any one weight category is more balanced than any of the others. Our results indicate that in choosing the members of a national team, it is to some extent reasonable for national coaches to select a lower ranked judoka in the men’s half-lightweight category over a higher ranked judoka in several other weight categories. We also found that the home advantage increases the probability of winning a single fight for both genders. This result implies that it might be worthwhile for national judo associations to bid to host international tournaments in order to improve the world rankings of their domestic judokas.
... The existence of a direct relationship between level of heterogeneity in relative quality (hereinafter, heterogeneity) and the winning probability of a stronger contestant in individual sports has been well documented in studies focusing on tennis (e.g., Koning, 2011; Sunde, 2009; Gilsdorf and Sukhatme, 2007; Klaassen and Magnus, 2001). 2 But unlike tennis or other individual non-combat sports, combat sports involve not only different genders but also different weight categories. As noted, in judo there are seven different contestants ranked 1 This new rule was introduced after a previous change made in December 2009, when IJF decided that starting from 2010 two athletes per weight category were allowed to represent a nation. ...
... Estimation (1) in Tables 3 and 4 shows the results for men's and women's fights as a function of level of heterogeneity. As predicted by contest theory (e.g., Rosen, 1986) and previously found for individual sports (e.g., Koning, 2011; Sunde, 2009; Gilsdorf and Sukhatme, 2007; Klaassen and Magnus, 2001), an increase in the FU ...
Judo is a combat sport with seven different weight categories. In this paper, we examined data from 1,902 men’s and 1,400 women’s fights at the eight most prestigious judo tournaments during the period 2010-2013. Using a single fight as the unit of observation, we found that the probability for the favorite to win against the underdog in the men’s half-light weight category is significantly lower than in most other categories. Moreover, in fights in which only European and/or Asian judokas participate, we found that the men’s half-light weight category is significantly more balanced than all other men's categories. For women, there is no consistent evidence that any one weight category is more balanced than any of the others. Our results indicate that in choosing the members of a national team, it is to some extent reasonable for national coaches to select a lower ranked judoka in the men's half-light weight category over a higher ranked judoka in several other weight categories. We also found that the home advantage increases the probability of winning a single fight for both genders. This result implies that it might be worthwhile for national judo associations to bid to host international tournaments in order to improve the world rankings of their domestic judokas.
... As tests of equity theory have often found, individuals who were unfairly underpaid (i.e., performed better but received equal wages) reacted more negatively in terms of effort reduction than those who received proportionally more than expected given their inputs. Two final studies of pay dispersion and individual performance were conducted among samples of men (Gilsdorf & Sukhatme 2007) and women (Gilsdorf & Sukhatme 2008) competing in their respective professional tennis tours. In cross-level tests with match-level outcomes, the studies yielded virtually identical results: The higher the prize spread associated with winning a given match, the more likely that the player with the higher seed would win the match. ...
... Additional indirect evidence can be gleaned from the tournament theory tests among players on the professional tennis tours. Here, higher prize money spreads were associated with a greater likelihood of the stronger player (higher seed) winning a given match (Gilsdorf & Sukhatme 2007). Although he did not examine prize spread, Sunde (2009) also found that heterogeneity in terms of capabilities had significant motivational effects (in terms of games won) for underdogs and favorites in professional tennis. ...
This article describes and evaluates the substantial literature on the
performance-, turnover-, and attitude-related outcomes of pay dispersion.
In the past 15 years, compensation researchers have identified
and pursued the resolution of well-known theoretical dilemmas about
reward allocations and, as a result, have made much progress in terms
of understanding the consequences of pay structures. This review
explores the evolution of several contingencies of these relationships,
including the effects of explained versus unexplained variation in pay,
the role of work interdependence, and the nature of other pay-system
characteristics. The article concludes with a summary evaluation, the
proposal of several stylized facts about the consequences of pay dispersion,
and a research agenda to aid researchers in addressing unresolved
issues in the literature.
... 6 Much of the research (building on Lazear & Rosen, 1981) has assumed that homogeneous competitors in a rank-order tournament make simultaneous decisions about effort. The literature then expands this initial model to examine tournaments with heterogeneous competitors (Sunde, 2009), multiple stage tournaments (Gilsdorf & Sukhatme 2008a, 2008bRosen, 1986), and sequential tournaments (Brown & Minor, 2011;Jost & Kräkel, 2005). ...
... While this is not the primary question of this research, it still provides important insights into the determinants of an athlete's performance. The most widely known results on the empirical relationship between prize structure and performance are from individual sports, including golf (Ehrenberg & Bognanno, 1990a, 1990bOrszag, 1994), running (Frick & Prinz, 2007;Lynch & Zax, 2000;Maloney & McCormick, 2000), and tennis (Gilsdorf & Sukhatme 2008a, 2008b. Other important empirical findings are that effort is highest in tournaments with homogeneous competitors (Sunde, 2009) and that effort increases in multiple stage tournaments where prize differentials increase through stages. ...
Qualification in track and field events involves runners competing against individuals within their heat and runners in other heats. Given that the heats are run sequentially, runners in each heat have different information about their competitors. Using data on track and field events from 2001-2011, this article examines whether an individual’s placement in a specific heat and their peers affect their performance and qualification probability. Results indicate that runners’ times and qualification are correlated with the abilities of their peers as well as heat-specific fixed effects. In addition, these effects differ according to runner ability.
... Other examples of studies estimating factors impacting the probability of winning a football match include (but are not limited to) Koning (2000), Forrest, Goddard and Simmons (2005) and Chumacero (2009). This type of analysis is certainly not limited to football, with other researchers analyzing everything from tennis (Gilsdorf and Sukhatme (2008)) to cricket (Allsopp and Clarke (2004)). ...
... Our methodology is very similar to the method used in Gilsdorf and Sukhatme (2008) in their analysis of the probability of winning a tennis match, only they positioned players based on tournament seed. Much of the analyses of the determinants of winning football matches also use similar techniques, often positioning teams based on home vs. away team (see e.g., Carmichael and Thomas (2005), Forrest, Goddard and Simmons (2005) and Chumacero (2009)). ...
Within the last decade, mixed martial arts has become one of the most popular sports worldwide. The Ultimate Fighting Championship
(UFC) is the largest and most successful organization within the industry. In the USA, however, the sport is not sanctioned
in all states because some politicians view the sport as too violent. The sport consists of many fighting forms and, unlike
boxing, winning a decision requires judging in multiple facets including wrestling, boxing, kick boxing, and jiu-jitsu. In
this study, we estimate the likelihood of winning a decision in the UFC. Using data on individual fights, we estimate the
probability of winning based on fighter characteristics. We emphasize power strikes as it relates to aggression to determine
the likelihood of winning. Our results indicate that knockdowns and damage inflicted are all statistically significant determinants
of winning a fight and have the largest marginal effect of influencing judge’s decisions.
... Thus, it is expected that the lowest coefficient would belong to clay surface and the highest to grass surface. Likewise, the round dummies are expected to be lower when advancing round because Gilsdorf and Sukhatme (2007) found that the larger the del Corral / Competitive Balance and Match Uncertainty in Grand-Slam Tennis 575 difference in prizes between the winner and the loser, the less likely the upset, but upsets will be less likely on 1st rounds due to the seeding system because seeded player are going to face between them. Thus, it is unclear which effect will predominate. ...
... This suggests that younger players tend to perform better than older players, given the ranking and other covariates. Similar results were found by Gilsdorf and Sukhatme (2007), using data from men's matches. The coefficients of EXTOP10U are positive and EXTOP10F are negative, reflecting that players who were top 10 players several years before tend to make more upsets as underdog and to lose less matches as favorites than other players. ...
This article tests whether the increase in seeded players in tennis grand-slam tournaments from 16 to 32 in 2001 led to decreased competitive balance. In doing so, two alternative measures of competitive balance for single-elimination tournaments are proposed based on the performance of seeded players. Likewise, the differences in competitive balance due to gender and court surface are also analyzed. Additionally, using data from tennis grand-slam matches from 2005 to 2008, this
article analyzed the determinants of ex post match level uncertainty with probit models.
... Moreover, Cyrenne (2018) argues that the salary distribution on a team has a mixed effect. This controversial debate can be observed in different sports disciplines, such as baseball (Hill et al., 2017;Richards and Guell, 1998), tennis (Gilsdorf and Sukhatme, 2008), football (Gasparetto and Barajas, 2022), basketball (Katayama and Nuch, 2011). ...
Purpose
Previous studies focused predominantly on wage dispersion within men’ sports teams. This study aims to reveal how the relationship between wage dispersion and team performance applies for women’s sport.
Design/methodology/approach
The sample comprises 168 observations of four consecutive National Basketball Association (NBA) and Women’s National Basketball Association (WNBA) regular seasons (2018–2021). Eight econometric models are performed for comparing the leagues.
Findings
The findings indicate that the wage dispersion within the squads affects the women’s and men’s basketball teams differently. Cohesiveness theory is applicable for WNBA teams, while NBA teams follow the tournament theory.
Originality/value
To the best of the authors’ knowledge, this is the first paper which inspects the relationship between wage dispersion and team performance using data from women’s sports. Further research may examine whether the differences found in sports also apply in different labor markets.
... As with ROTs in general, non-experimental studies of gender responses to tournaments are most readily found in sports contexts. Sukhatme (2008a and2008b) find no difference in how men and women respond to incentives in elimination tennis tournaments. ...
Using data from the 1995-2006 LPGA Tour, we analyse players’ response to the presence of Annika Sorenstam, a dominant champion on the LPGA Tour at the time. We find that the measures of players’ responses are highly sensitive to specification. Employing course fixed effects (FEs) greatly reduces the impact Sorenstam had on other golfers. We also find that players do not respond positively to the size of the reward to winning the tournament, which contradicts experimental studies of rank-order tournaments (ROTs). Our findings lead us to question both experimental and non-experimental studies of ROTs and of gender differences in response to them.
... Some studies have found positive effects of rank-order tournaments on individual performance in sports such as golf, tennis, and car racing (e.g. Becker & Huselid, 1992;Ehrenberg & Bognanno, 1990;Gilsdorf & Sukhatme, 2008), although it was found in racing that safety was also diminished when the prize spread was very large. But of course, these are sports where individuals compete against each other. ...
People are certainly motivated to obtain money. Money helps them to take care of their families , but also attain social status and wealth. Nevertheless, it can create a lot of competition and can often lead to deception and fraud. It was hypothesized that large vertical pay gaps would motivate the best performers to aspire to top positions, but that's often not the case. Managers that stimulate internal competition cause a lot of harm too. Let's have a look. What is the rank-order tournaments theory and vertical pay dispersion about? Tournament Theory is inspired by the widespread belief that people are motivated by internal competition. This theory proposes taking things one step further than the piece-rate pay scheme where workers are paid a fixed amount per produced piece or the beat-the-standard pay scheme, which awards people for beating the standard. In rank-order payment schemes, the employee's relative position counts and so those people who produce most are paid an extra prize. You have winners and losers and the pie stays the same for all the 'contestants' together. Economists Lazear and Rosen (1981) developed tournament theory, basically contending that organizations should create rank-order tournaments, for example by paying high wages at the top of the organization. Thus, employees are viewed as competitors and are evaluated on the basis of relative performance rather than objective performance. Indeed, they wrote that if a vice-president rises to the rank of president (CEO), she or he could easily triple their salary even though this doesn't mean that her or his skills have tripled also overnight. Rather, it is the prize they get for winning the contest. In order to stimulate competition, they contended that firms should create wide pay gaps, even for small differences in actual contribution. In their opinion, this pay-gap would serve several purposes such as (1) avoiding shirking and (2) creating a sorting effect because 'prizes' would attract and retain the most talented workers, but also get rid of the 'losers' (it is predicted they will leave the organization). The central propositions of their theory were that: (1) pay-for-level-of-output is better than pay per hour because input-wage schemes without good effort monitoring often invite shirking; (2) 'competitive lotteries' are sometimes even better: the people in the game are uncertain about how much they will earn, as the payment scheme follows a rank-order: the best performers get paid more ('a prize'); (3) large salaries for executives will provide incentives for employees who are willing to work hard to reach the 'coveted top positions'-this is called the prize spread. It is predicted that each worker's effort level will increase with the spread between the 'winning and the losing' prize;
... Traditionally, the literature has prioritised talent (i.e., the quality of a team or a player) to be a major factor/motive underlying fans' consumption of sport (Funk, Filo, Beaton, & Pritchard, 2009;Hansen & Gauthier, 1989;Kunkel, Doyle, & Berlin, 2017;Shilbury, Westerbeek, Quick, Funk, & Karg, 2014). Consequently, the value of athletes has been occasionally equated to their performance on the court (e.g., Gilsdorf & Sukhatme, 2008;Radicchi, 2011) or their professional rankings. In tennis, player quality is frequently estimated by the player's world ATP rankings (Association of Tennis Professionals, 2019) or her/his Elo ratings (Elo, 1978). ...
Understanding the interest of sports fans in professional tennis has valuable operational and marketing implications for tournament organisers, marketeers, player sponsors and the media. In sports, professional tennis in particular, the player effect on social media user engagement is still elusive. Using data from the 2019 Australian Open grand slam period, the authors examine Adler’s (1985) theoretical construct in the context of sports and social media. A social listening tool is used to probe more than 2 million posts and comments mentioning elite male and female tennis players on four major social media channels: Twitter, Facebook, Instagram and YouTube, over the grand slam period. It is shown that the effect of professional tennis players on social media user engagement extends beyond their talent. A selection of players had a strong positive impact on prompting social media activity, even after accounting for factors related to their performance, the tournament rounds in which they were featured and the opponents against whom they played. Furthermore, the connection between social media research and sports economics is considered by examining the relationship between a player’s effects on social media engagement and her/his differential influence on demand for tickets at the Australian Tennis Open. The authors further discuss how the social media star influence can be used, in combination with other quantitative measures, to optimise tennis tournament scheduling, determine player appearance fees and lift participation in the sport.
... EXPL.Round: the round of the tournament (e.g., semi-final). Here, it is reasonable to assume that the incentives from substantially higher prize money in the later rounds -consisting of the stronger players -have an influence (see, for instance, Gilsdorf and Sukhatme (2008)). ...
... Further, prediction models could help assess fan engagement and determine who is the favourite player, by how much, and who is currently the best player. See, for example, Glickman (1999); Klaassen and Magnus (2003); Barnett and Clarke (2005); Newton and Keller (2005); Gilsdorf and Sukhatme (2008); Gomes et al. (2011);Smith (2013); Irons et al. (2014); Kovalchik (2016) and references therein. ...
In professional tennis, it is often acknowledged that the server has an initial advantage. Indeed, the majority of points are won by the server, making the serve one of the most important elements in this sport. In this paper, we focus on the role of the serve advantage in winning a point as a function of the rally length. We propose a Bayesian isotonic logistic regression model for the probability of winning a point on serve. In particular, we decompose the logit of the probability of winning via a linear combination of B-splines basis functions, with athlete-specific basis function coefficients. Further, we ensure the serve advantage decreases with rally length by imposing constraints on the spline coefficients. We also consider the rally ability of each player, and study how the different types of court may impact on the player's rally ability. We apply our methodology to a Grand Slam singles matches dataset.
... Given the very nature of individual (professional) sports events, where scheduling can be fluid, appearance fees are common and multiple pairings/matches are simultaneously played, the lack of scientific scrutiny is surprising. To this end, in individual sports like tennis, the value of players has only been evaluated, in depth, according to their performance on the court (e.g., Gilsdorf & Sukhatme, 2008;Radicchi, 2011) or their professional rankings. ...
Akin to other sports, professional tennis is urged to adopt a consumer-centred strategy and understand the influence of the star status of elite players on demand for its core product. Measuring the impact that tennis players have on demand for match attendance remains a key element towards achieving that goal. Using data from the Australian Open ticket sales, the authors demonstrate how individual players have influenced stadium attendance at the Grand Slam. Findings indicate that some players are associated with a strong positive impact on demand for tickets, above and beyond their performance ratings, reflecting their value to the Australian Open. The authors discuss how this star status can be used to inform business decisions related to tournament management, match scheduling, and determining player appearance fees, to ultimately drive better commercial outcomes and deliver a world-class sporting event. The findings have implications for tournament organisers, player managers and those that market player activities.
... Ehrenberg and Bognanno (1990) tested the theory by examining the impact of prize structure in golf tournaments on performance of golfers. Since that time, the predictions of tournament theory have been studied in a number of sporting contexts including auto racing (Becker and Huselid, 1992;Depken and Wilson, 2004), marathons (Frick et al., 2007), tennis (Gilsdorf and Sukhatme, 2008) and in the presence of superstars (Brown, 2011). ...
... Gleiches gilt für die Messung von Heterogenität der Leistungsfähigkeit von Akteuren. Diese lässt sich im Sport, unter der Annahme effizienter Märkte (Fama, 1970) (Ehrenberg & Bognanno, 1990;Orszag, 1994;Frick, 2003;Matthews et al., 2007;McFall et al., 2009;Brown, 2011), Amateurgolf (Franke, 2012), Motorsport (Becker & Huselid, 1992;von Allmen, 2001;Maloney & Terkun, 2002;Bothner et al., 2007;O'Roark et al., 2012), Laufsport (Frick & Klaeren, 1997;Maloney & McCormick, 2000;Lynch & Zax, 2000;Azmat & Möller, 2009), Tennis (Lallemand et al., 2008;Sunde, 2009;Gilsdorf & Sukhatme, 2008), Pferdesport (Higgins & Tollison, 1990), Triathlon (Sowell & Mounts, 2005) und professionelles Bowling (Abrevaya, 2002). ...
... In the context of tennis win predictions, according to Kovalchik (2016), three categories of statistical models can be identified: regression, point-based and paired comparison models. Regression models directly model the winner of the match; most are logit or probit models (del Corral and Prieto-Rodríguez, 2010;Gilsdorf and Sukhatme, 2008;Klaassen and Magnus, 2003;Boulier and Stekler, 2003). Point-based approaches model the win probability as the probability of winning a single point, often on serve Spanias and Knottenbelt, 2012;Barnett and Clarke, 2005). ...
We propose a logistic regression model to predict the win probability in a tennis match. The variables included in the model are ATP points and rankings, the players' ages, the home factor and the information derived from bookmaker odds. The model is estimated using data related to 2012 tournaments, and it is then used in an out-of-sample betting experiment where the odds implied by the model are used, following a specific procedure, for betting against bookmakers. The algorithm is applied to all matches of the four Grand Slam Championships 2013, and the whole procedure is evaluated with respect to the global return of the strategy. After 501 matches, the total cumulative return is 15.9%.
... Ehrenberg and Bognanno (1990) tested the theory by examining the impact of prize structure in golf tournaments on performance of golfers. Since that time, the predictions of tournament theory have been studied in a number of sporting contexts including auto racing (Becker and Huselid, 1992;Depken and Wilson, 2004), marathons (Frick et al., 2007), tennis (Gilsdorf and Sukhatme, 2008) and in the presence of superstars (Brown, 2011). ...
... The authors found a difference in the model coefficients for men's singles play at Wimbledon, so separate parameters for the seeding variables were obtained for Wimbledon. Gilsdorf and Sukhatme (2008) were interested in the explanatory role of monetary incentives for win probabilities. In their model (Prize Probit), the main predictor was the gap between the top prize money for the tournament and the earnings for a loss at the current stage of the match. ...
Sports forecasting models – beyond their interest to bettors – are important resources for sports analysts and coaches. Like the best athletes, the best forecasting models should be rigorously tested and judged by how well their performance holds up against top competitors. Although a number of models have been proposed for predicting match outcomes in professional tennis, their comparative performance is largely unknown. The present paper tests the predictive performance of 11 published forecasting models for predicting the outcomes of 2395 singles matches during the 2014 season of the Association of Tennis Professionals Tour. The evaluated models fall into three categories: regression-based, point-based, and paired comparison models. Bookmaker predictions were used as a performance benchmark. Using only 1 year of prior performance data, regression models based on player ranking and an Elo approach developed by FiveThirtyEight were the most accurate approaches. The FiveThirtyEight model predictions had an accuracy of 75% for matches of the most highly-ranked players, which was competitive with the bookmakers. The inclusion of career-to-date improved the FiveThirtyEight model predictions for lower-ranked players (from 59% to 64%) but did not change the performance for higher-ranked players. All models were 10–20 percentage points less accurate at predicting match outcomes among lower-ranked players than matches with the top players in the sport. The gap in performance according to player ranking and the simplicity of the information used in Elo ratings highlight directions for further model development that could improve the practical utility and generalizability of forecasting in tennis.
... Sunde's (2009) data on professional tennis matches support the assumption that unevenly matched tournaments between heterogeneous players lead to the exertion of less effort. Gilsdorf and Sukhatme (2007) found that increased monetary prize differentials between the winner and the loser of a match have a positive effect on the winning probability of the higher ranked player. Malueg and Yates' (2010) empirical results support the theoretical predictions that tennis players adjust their efforts strategically during a best-of-three sets contest. ...
Gender differences in tennis have sparked a great deal of heated debate. Using data from the 24 top men’s and 23 top women’s singles tournaments in 2010, we find a gender difference in the competitiveness (tightness) with regard to the final score of tennis sets. However, when using two physical variables (height and body mass index) that have not been investigated in this context before and controlling for the physical characteristics of the players, this gender difference completely disappears. Moreover, this result remains robust in propensity score analysis. To narrow this disparity between the number of games in men’s and women’s sets, it might be worthwhile for tennis authorities to consider making some changes in court conditions on a gender basis.
... Previous economic literature has used the outcomes from professional tennis tournaments to examine the incentive effects of prizes in tournaments (Gilsdorf and Sukhatme, 2008b;Lallemand et al., 2008). As well, professional tennis player data have been used to examine sequential elimination tournament effects (Gilsdorf and Sukhatme, 2008a). These other studies examined the most elite tennis players possible. ...
Recent studies have found that females are less competitive than men. These studies have all relied on a similar framework where individuals have little information about their
relative abilities compared to other potential competitors. It has also been found that performance feedback leads to more efficient choices for students and in experimental settings. Professional athletes competing in individual sports typically have access to performance feedback and good information about the quality of their potential competitors when choosing to enter competitive tournaments. In this paper, I use data from the International Tennis Federation (ITF) on tournament entry decisions by professional players to study gender differences in tournament entry and preferences in this competitive labor market.
I find that even among this highly competitive population, gender differences exist in
performance and tournament entry. In terms of performance I find that men exhibit a “hot
hand” effect that can last for multiple periods while females are affected by only their
performance in their last tournament. This effect is obvious in tournament entry where
both men and women are more likely to enter tournaments after doing well, but women
are affected by their last tournament while men’s previous performance can affect entry
beyond the next tournament. The gender difference from feedback is more striking when
taking into account whether individuals actually played in a tournament. In that case, higher
ability females respond positively to performance from their last tournament while males
do not. But both genders see similar effects from previous performance in the short-term
and the effects are larger for worse ranked individuals. Thus, in very competitive settings
of same-sex tournaments, females and males respond differently to performance feedback information suggesting that information has very different, gender-specific effects for competitions and may be largely dependent on the length of time that has elapsed from the competition that the feedback is coming from.
... Thus, it is expected that the lowest coefficient would belong to clay surface and the highest to grass surface. Likewise, the round dummies are expected to be lower when advancing round becauseGilsdorf and Sukhatme (2007)found that the larger the del Corral / Competitive Balance and Match Uncertainty in Grand-Slam Tennis 575 difference in prizes between the winner and the loser, the less likely the upset, but upsets will be less likely on 1st rounds due to the seeding system because seeded player are going to face between them. Thus, it is unclear which effect will predominate. ...
This article tests whether the increase in seeded players in tennis grand-slam tournaments from 16 to 32 in 2001 led to decreased competitive balance. In doing so, two alternative measures of competitive balance for single-elimination tournaments are proposed based on the performance of seeded players. Likewise, the differences in competitive balance due to gender and court surface are also analyzed. Additionally, using data from tennis grand-slam matches from 2005 to 2008, this article analyzed the determinants of ex post match level uncertainty with probit models.
... In addition, match round is entered into our model, to control its impact on match outcomes. This is because Gilsdorf and Sukhatme (2007) claimed that modelling is better at predicting outcomes in later-round matches. ...
Abstract This study examines factors that lead to winning matches in men's singles Grand Slam tennis, and proposes guidelines for coaches and professional tennis players both in training and preparation for Grand Slam competitions. Using longitudinal data between 1991 and 2008 retrieved from the official website of the Association of Tennis Professionals, we analysed player performance over 9,144 matches in men's singles Grand Slam tournaments. To predict match outcome, 16 variables were classified into one of three categories: player skills and performance, player characteristics and match characteristics. The three categories were entered sequentially into a logistic regression model to predict the dependent variable: the chance of winning a men's singles Grand Slam match. The final altered model explains 79.4% of the variance (Nagelkerke's pseudo R 2) in match outcomes and correctly predicted 90.6% of cases. The importance of serving, receiving, and break points is further confirmed. The positive effect of stature diminishes when players are taller than 186 cm. We recommend more training in returning skills; to avoid overestimation of the positive impact of stature, left hand and professional experience; and that a male player begins his professional tennis career by participating in the US Open or Wimbledon.
... The round dummies are expected to increase when advancing rounds. This expectation is based on the analysis of Gilsdorf and Sukhatme (2007), who found that the larger the difference in prizes between the winner and the loser, the less likely an upset was. ...
This paper tests whether the differences in rankings between individual players are good predictors for Grand Slam tennis outcomes. We estimate separate probit models for men and women using Grand Slam tennis match data from 2005 to 2008. The explanatory variables are divided into three groups: a player's past performance, a player's physical characteristics, and match characteristics. We estimate three alternative probit models. In the first model, all of the explanatory variables are included, whereas in the other two specifications, either the player's physical characteristics or the player's past performances are not considered. The accuracies of the different models are evaluated both in-sample and out-of-sample by computing Brier scores and comparing the predicted probabilities with the actual outcomes from the Grand Slam tennis matches from 2005 to 2008 and from the 2009 Australian Open. In addition, using bootstrapping techniques, we also evaluate the out-of-sample Brier scores for the 2005-2008 data.
Despite its popularity, outcome uncertainty in professional tennis did not receive much attention from academics in the recent past. This is astonishing because it should be of utmost importance in professional tennis in the following years with the approaching end of the era of the Big 3. This study investigates match-level uncertainty in professional women's and men's tennis between 2010 and 2019 using a logit model with a dataset consisting of 51,054 matches. In the different analyses, the variations in the ranking and quality differences between players are taken into account in addition to differences across surfaces, tournaments, and genders. In the investigated period, women's tennis has relatively higher outcome uncertainty when compared to men's. The results also illustrate that talent seems to be distributed more evenly in women's tennis, whereas men's tennis has high heterogeneity in terms of talent. Moreover, very specific subgroups of matches having the highest and lowest uncertainty in men's and women's tennis are identified. Managerial implications are also presented to show how organizers, policy makers and, eventually, fans can benefit from the insights presented in this study.
Abstract
The purpose of the research was to construct a model that could forecast the probability of winning in the case of Novak Djokovic in the men’s singles grand slam event of the Australian Open and to determine the relative relevance of the match data that contribute to victory. A total number of 147 matches were recorded for all nine years i.e., from 2013 to 2021, from the first round to the exit round over the years. One of the few assumptions in logistic regression is that the dependent variable must be binary in nature. Therefore, the dependent variable selected for this study was Match Outcome (Win/Loss). Ace, (DF) Double Fault, (FS) First Serve, (FSPW) first serve point win, (SSPW) second serve point win, (BPC) Breakpoint converted, and (TPW) Total point win were selected as the predictor variables. All the data were collected from ATP world tour.com. In order to accomplish the goals of the research, the only matches that Novak Djokovic competed in during the Grand Slam AO (Australian Open), were analyzed. The prediction of the likelihood of Mr. Novak Djokovic winning or losing in the men’s singles Australian open grand slam by fitting the logistic regression model. According to the statistical significance of the predictor variables, they were numerically weighted and can be used to predict the match outcome. Out of seven predictor variables, only the variable Breakpoint Converted was included in the prediction model with a coefficient of determination (R2) of.424 (Cox & Snell) and .588 (Nagelkerke). The case adds seven independent variables and one dependent binary logistic variable for all the Australian Open Grand slam matches played from 2013 to 2021. The given result of it verifies conclusive evidence that the prediction fits quite well as it classifies an 88.9% winning probability.
Keywords: Australian open, statistical model, prediction, binary logistic regression, win/loss, probability
The purpose of the research was to construct a model that could forecast the probability of winning in the case of Novak Djokovic in the men's singles grand slam event of the Australian Open and to determine the relative relevance of the match data that contribute to victory. A total number of 147 matches were recorded for all nine years i.e., from 2013 to 2021, from the first round to the exit round over the years. One of the few assumptions in logistic regression is that the dependent variable must be binary in nature. Therefore, the dependent variable selected for this study was Match Outcome (Win/Loss). Ace, (DF) Double Fault, (FS) First Serve, (FSPW) first serve point win, (SSPW) second serve point win, (BPC) Breakpoint converted, and (TPW) Total point win were selected as the predictor variables. All the data were collected from ATP world tour.com. In order to accomplish the goals of the research, the only matches that Novak Djokovic competed in during the Grand Slam AO (Australian Open), were analyzed. The prediction of the likelihood of Mr. Novak Djokovic winning or losing in the men's singles Australian open grand slam by fitting the logistic regression model. According to the statistical significance of the predictor variables, they were numerically weighted and can be used to predict the match outcome. Out of seven predictor variables, only the variable Breakpoint Converted was included in the prediction model with a coefficient of determination (R 2) of.424 (Cox & Snell) and .588 (Nagelkerke). The case adds seven independent variables and one dependent binary logistic variable for all the Australian Open Grand slam matches played from 2013 to 2021. The given result of it verifies conclusive evidence that the prediction fits quite well as it classifies an 88.9% winning probability.
This paper examines the incentive effects of increased prize differentials and productivity spillovers from substitute coworkers within the context of esports. A direct behavioral measure called “actions per minute (APM)” is utilized to gauge Dota 2 players’ on-field exertion of effort dedicated to winning the game. The results based on empirical analysis support the incentive effects of the convex prize structure of esports tournaments on eliciting effort. Further investigation indicates that the incentive effects of high-stakes esports tournaments are more a result of the size of total prize than the relative prize distribution. It is also found that players who serve subordinate roles are more likely to engage in shirking behavior in the presence of teammates with similar roles.
Kernproblem empirischer Forschung ist die Bestimmung von Kausalitäten aus Korrelationen. Experimente können das Problem lösen. Der folgende Beitrag stellt Labor-, Online-, Feld- und Quasi-Experimente vor und nennt jeweils bedeutende Beispiele aus der Sportökonomik. Aufgrund der hervorragenden Datenlage sind sportökonomische Quasi-Experimente über den Sport hinaus interessant für unterschiedlichste Fragestellungen aus der Wirtschaftspolitik, insbesondere der Wettbewerbspolitik, ferner für Verhaltensökonomik, Recht, Psychologie, Marketing, Management und Personalökonomik. Dieser Beitrag ist Teil der Sektion Sportökonomik, herausgegeben von den Teilherausgebern Eike Emrich und Christian Pierdzioch, innerhalb des Handbuchs Sport und Sportwissenschaft, herausgegeben von Arne Güllich und Michael Krüger.
Machine learning and its numerous variants have meanwhile become established tools in many areas of society. Several attempts have been made to apply machine learning to the prediction of the outcome of professional sports events and to exploit “inefficiencies” in the corresponding betting markets. On the example of tennis, this paper extends previous research by conducting one of the most extensive studies of its kind and applying a wide range of machine learning techniques to male and female professional singles matches. The paper shows that the average prediction accuracy cannot be increased to more than about 70%. Irrespective of the used model, most of the relevant information is embedded in the betting markets, and adding other match- and player-specific data does not lead to any significant improvement. Returns from applying predictions to the sports betting market are subject to high volatility and mainly negative over the longer term. This conclusion holds across most tested models, various money management strategies, and for backing the match favorites or outsiders. The use of model ensembles that combine the predictions from multiple approaches proves to be the most promising choice.
In the context of the current uncertain, complex, and interdependent work systems, teams have become organizations’ substantial working unit, which in turn challenges the traditional view of employee performance and ultimately results in the emergence of team member work role performance. Employee team-oriented work role behaviors with proficiency, adaptivity, and proactivity, which are integrated by the new construct, are so crucial to team effectiveness that many organizations keenly expect to achieve team member work role performance through implementing a dispersed pay-for-performance plan within a team. This study seeks to address the organizational practitioners’ main concern that whether pay dispersion among team members (i.e., horizontal pay dispersion, HPD) could actually help realize team member work role performance and further examines why and when an employee could respond to HPD within a team by engaging in team member work role behaviors from the perspective of the performance-shaping basis and team member’s workplace benign envy. Drawing on emotion-related theory, social comparison theory, legitimacy theory, expectation theory, and relative deprivation theory, it proposes that performance-based HPD could not only positively impact team member work role performance via workplace benign envy but also exert a direct-positive effect. Moreover, the activating effect of performance-based HPD on workplace benign envy and the mediating role are much stronger when a team member’s pay position is higher. The multi-source data including objective information and subjective perception among 362 ordinary employees within 66 Chinese organizational teams primarily supported the moderated mediation model. Yet, the direct-positive effect was not established.
In professional tennis, it is often acknowledged that the server has an initial advantage. Indeed, the majority of points are won by the server, making the serve one of the most important elements in this sport. In this paper, we focus on the role of the serve advantage in winning a point as a function of the rally length. We propose a Bayesian isotonic logistic regression model for the probability of winning a point on serve. In particular, we decompose the logit of the probability of winning via a linear combination of B-splines basis functions, with athlete-specific basis function coefficients. Further, we ensure the serve advantage decreases with rally length by imposing constraints on the spline coefficients. We also consider the rally ability of each player, and study how the different types of court may impact on the player’s rally ability. We apply our methodology to a Grand Slam singles matches dataset.
This paper examines how within-match variation in incentives affects the performance of darts players. The game of darts offers an attractive naturally occurring research setting, because performance can be observed at the individual level and without obscuring effects of risk considerations and behavior of others. We analyze four data sets covering a total of 29,381 darts matches of professional, amateur, and youth players. We find that amateur and youth players display a sizable performance decrease at decisive moments. Professional players appear less susceptible of such choking under pressure. Our results speak to a growing literature on the limits of increasing incentives as a recipe for better performance.
Understanding and predicting how individuals perform in high-pressure situations is of importance in designing and managing workplaces, but also in other areas of society such as disaster management or professional sports. For simple effort tasks, an increase in the pressure experienced by an individual, e.g. due to incentive schemes in a workplace, will increase the effort put into the task and hence in most cases also the performance. For the more complex and usually harder to capture case of skill tasks, there exists a substantial body of literature that fairly consistently reports a choking phenomenon under pressure. However, we argue that many of the corresponding studies have crucial limitations, such as neglected interaction effects or insufficient numbers of observations to allow within-individual analysis. Here, we investigate performance under pressure in professional darts as a near-ideal setting with no direct interaction between players and a high number of observations per subject. We analyze almost one year of tournament data covering 23,192 dart throws, hence a data set that is very much larger than those used in most previous studies. Contrary to what would be expected given the evidence in favor of a choking phenomenon, we find strong evidence for an overall improved performance under pressure, for nearly all 83 players in the sample. These results could have important consequences for our understanding of how highly skilled individuals deal with high-pressure situations.
I fit a Bayesian hierarchical model to tennis match outcomes. Players' skills change dynamically over time, and their serve, return and surface skills are estimated. It predicts match outcomes using the iid model of a tennis match and does this more accurately than previous published models.
This study investigates the factors that determine winning in men's professional tennis. Using 27,388 tennis matches played on the men's singles ATP World Tour between 2000 and 2009, we estimate probit models which explain how several tournament, match, and player characteristics influence the probability of the higher ranked player winning the match. The results are used to confirm or dispel ten performance hypotheses concerning match outcomes. The results of the study provide insights into what matters to winning in head-to-head competitions, and are used to evaluate various economic issues such as how labor compensation, specialization, and experience can influence performance.
Bill James’ discovery of a Pythagorean formula for win expectation in baseball has been a useful resource to analysts and coaches for over 30 years. Extensions of the Pythagorean model have been developed for all of the major professional team sports but none of the individual sports. The present paper attempts to address this gap by deriving a Pythagorean model for win production in tennis. Using performance data for the top 100 male singles players between 2004 and 2014, this study shows that, among the most commonly reported performance statistics, a model of break points won provides the closest approximation to the Pythagorean formula, explaining 85% of variation in season wins and having the lowest cross-validation prediction error among the models considered. The mid-season projections of the break point model had performance that was comparable to an expanded model that included eight other serve and return statistics as well as player ranking. A simple match prediction algorithm based on a break point model with the previous 9 months of match history had a prediction accuracy of 67% when applied to 2015 match outcomes, whether using the least-squares or Pythagorean power coefficient. By demonstrating the striking similarity between the Pythagorean formula for baseball wins and the break point model for match wins in tennis, this paper has identified a potentially simple yet powerful analytic tool with a wide range of potential uses for player performance evaluation and match forecasting.
Objective
We inquire whether the glass ceiling stems in part from the fact that women are more discouraged by setbacks than men are, as suggested by economic and psychological experiments. We use data from professional tennis to test this hypothesis.
Method
We apply ordered probit, ordinary least squares, and binomial probit to data from the 2012 ATP and WTA tennis tours.
Results
Women are not more likely than men to lose in straight sets or to lose the second two sets. Women who lose in straight sets win fewer games in the second set than men do. Women who lose the second set are more likely than men to withdraw from the third set.
Conclusion
Women are not more likely to lose because of setbacks, but those who do tend to lose by wider margins than men. This suggests that the glass ceiling is not the result of women being more easily discouraged than men.
Paired-comparison models have been previously used in the literature to assess the relative performance of tennis players over a given period of time. In this paper, I discuss how the rankings of tennis players can be modified to address variations in the importance of tennis tournaments, and concerns about under-participation over the tennis season. The methods are applied to the 2011 WTA season, where the WTA-ranked number one player Caroline Wozniacki was often criticized for not being the true top player. The alternative rankings proposed here indicate that Petra Kvitova was the top player in 2011, with Serena Williams a close second. These rankings do appear to perform better in predicting match probabilities in early 2012 than methods based on the official rankings.
Rank-order tournaments with heterogeneous competitors work best when the competitors are relatively equal in abilities. Using data from 2007-2012 on major track and field events, this paper examines whether the presence of a superstar, Usain Bolt, has an effect on competitors. Results indicate a positive superstar effect. For average runners, the presence of Bolt is associated with running faster times and a higher likelihood of setting a personal record, but these results vary across runner abilities and stage of tournament. In general, the positive superstar effect is smaller for relatively fast runners, and the positive effect diminishes as the tournament progresses.
Gender differences in outcomes are often explained by gender differences in competitiveness. Using evidence from the outdoor World Championships and Olympics 1,500 meter event, this paper investigates whether gender differences exist in the behavior of runners. Results indicate that there are some gender differences in the competition. Where the gender differences exist, the evidence indicates that there is a difference in the relationship between ability and performance and between peer effects and performance. These results are suggestive of males running more strategically.
We consider how past, current, and future competition within an elimination tournament affect the probability that the stronger player wins. We present a two-stage model that yields the following main results: (1) a shadow effect wherein the stronger the expected future competitor, the lower the probability that the stronger player wins in the current stage; and (2) an effort spillover effect wherein previous effort reduces the probability that the stronger player wins in the current stage. We test our theory predictions using data from high-stakes tournaments. Empirical results suggest that shadow and spillover effects influence match outcomes and have already been priced into betting markets.
This paper was accepted by Bruno Cassiman, business strategy.
Decisions on whether to retain recent hires are often limited by small sample size. We empirically assess whether uncertainty in employee retention decisions could be significantly reduced by increasing sample size. Using a unique data set from professional tennis matches to measure small sample outcomes, we find little difference in giving three chances, relative to five chances, in determining innate ability.
Sport is becoming an activity of increasing importance: over time more people participate in sport (active sport consumption), more time is spent watching sport (passive sport consumption). An important part of sport consumption is passive sport consumption where production and consumption are separate: (professional) athletes engage in a contest, and fans pay to watch the contest. An important characteristic of sport that generates this demand is relative competition: the competitiveness of a particular match or league. In this paper, we set out to measure competitive balance in three sports (soccer, tennis, and skating), and assess its development over time. As we separate variation in quality of teams or athletes from randomness of outcome, we can compare relative competition in these three sports.
Tournament models have developed into an important component of the theoretical literature on organizational reward systems. However, with one exception there have been no empirical tests of the incentive effects of tournament models in a field setting. Drawing on a panel data set from auto racing, we show that the tournament spread (prize differential) does have incentive effects on both individual performance and driver safety, that these effects peak at higher spreads, and that controlling for the dollar value of the tournament spread, the prize distribution has little influence on individual performance.
This article explicitly compares the incentive and sorting theories of tournament per formance in road races. Regressions omitting controls for runner ability suggest that runners record faster times the greater the loss they would suffer from finishing below their pre race ranking. However, the relationship between prize money at risk and finishing time weakens or vanishes with these controls. These results strongly suggest that races with large prizes record faster times because they attract faster runners, not because they encourage all runners to run faster.
The authors examine labor supply using 1,426 responses of individual runners to prizes in open invitational foot races. The data are used to decompose the overall market response of higher prizes into two components based on the basic tournament model. First, an entry effect exists in which higher wages attract more highly skilled runners to participate. Second, the spread between prizes incites runners individually to work harder. This second effect is detected across the entire sample and for individuals measured against their own average performance. The authors also examine the supply elasticities between the sexes. As a group, women respond more to higher wages than men in both the entry and individual effort dimensions. Also, the more concentrated the prize money in a race, the higher the revealed effort level by the runners. The authors find that the tournament nature of competition has important incentive effects.
We propose several Lagrange multiplier tests of logit and probit models, which may be inexpen- sively computed by means of artificial linear regressions. These maybe used to test for various forms of model inadequacy, including the omission of specified variables and heteroskedasticity of known form. We perform a number of sampling experiments, in which we compare the small-sam- ple properties of these tests and of likelihood ratio tests. One of the LM tests turns out to have better small-sample properties than any of the others. We then investigate the power of the tests against local alternatives, and conduct a further series of sampling experiments to compare the power of various tests.
Much attention has been devoted to studying models of tournaments or situations in which an individual's payment depends only on his or her output or rank relative to that of other competitors. Under certain sets of assumptions, tournaments have desirable normative properties because of the incentive structures they provide. Our paper uses nonexperimental data to test whether tournaments actually elicit effort responses. We focus on professional golf tournaments because information on the incentive structure (prize distribution) and measures of individual output (players' scores) are both available. We find string support for the proposition that the level and structure of prizes in PGA tournaments influence players performance. Copyright 1990 by University of Chicago Press.
This analysis of data from the 1987 European Men's Professional Golf Association (PGA) Tour strongly supports the hypothesis that the level and structure of prizes in PGA tournaments influence players' performance. Specifically, players' performance appears to vary positively with both the total money prizes awarded in a tournament and the marginal return to effort in the final round of play (a value that varies among players largely depending on how the prize money is allocated among finishers of different ranks). The authors suggest that these results, together with the similar results of their earlier study of the 1984 U.S. Men's PGA Tour, may have implications for the design of compensation systems for certain groups of workers, such as corporate executives, college professors, and salespeople. (Abstract courtesy JSTOR.)
This paper analyzes compensation schemes which pay according to an individual's ordinal rank in an organization rather than his output level. When workers are risk neutral, it is shown that wages based upon rank induce the same efficient allocation of resources as an incentive reward scheme based on individual output levels. Under some circumstances, risk-averse workers actually prefer to be paid on the basis of rank. In addition, if workers are heterogeneous inability, low-quality workers attempt to contaminate high-quality firms, resulting in adverse selection. However, if ability is known in advance, a competitive handicapping structure exists which allows all workers to compete efficiently in the same organization.
Evidence shows that real-effort investments can affect bilateral bargaining outcomes. This paper investigates whether similar investments can inhibit equilibrium convergence of experimental markets. In one treatment, sellers’ relative effort affects the allocation of production costs, but a random productivity shock ensures that the allocation is not necessarily equitable. In another treatment, sellers’ effort increases the buyers’ valuation of a good. We find that effort investments have a short-lived impact on trading behavior when sellers’ effort benefits buyers, but no effect when effort determines cost allocation. Efficiency rates are high and do not differ across treatments.
This paper examines performance in ladder tournaments, using data from professional bowling competitions. Although there is a distinct advantage to starting with a higher rank in a ladder tournament, the results indicate that “underdogs” win more often than expected. The findings are explained by regression-to-the-mean and hot-hand theories, both of which are consistent with the particular structure of the ladder tournament.
Sequential-elimination career games promote survival-of-the-fittest competitors. However, top prizes must be elevated to provide performance incentives in later stages of the game. The option value of achieving a high rank encourages performance effort in early rounds, but the continuation option plays out toward the finals. Concentrating an extra share of the purse on the top prize replaces the option value of early stage competition and ensures that contestants who have achieved high ranks do not rest of their laurels in attempting to climb higher. Copyright 1986 by American Economic Association.
We investigate the salary returns to the ability to play football with both feet. The majority of footballers are predominantly right footed. Using two data sets, a cross-section of footballers in the five main European leagues and a panel of players in the German Bundesliga, we find robust evidence of a substantial salary premium for two-footed ability, even after controlling for available player performance measures. We assess how this premium varies across the salary distribution and by player position.
ATP 2001 official rulebook
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An empirical test of tournament theory. Unpublished doctoral dissertation
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Bognanno, M. (1990). An empirical test of tournament theory. Unpublished doctoral dissertation,
Cornell University.
Pay and performance in professional road running. Paper presented at the Western Economic Association Conference
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Frick, B., & Prinz, J. (2002, June). Pay and performance in professional road running. Paper presented at
the Western Economic Association Conference, Seattle, WA.
Sukhatme is an Edward J. Noble Professor of Economics at Macalester College
- A Vasant
Vasant A. Sukhatme is an Edward J. Noble Professor of Economics at Macalester College, St. Paul,
Minnesota.
Gilsdorf is an associate professor of economics at Augsburg College
- F Keith
Keith F. Gilsdorf is an associate professor of economics at Augsburg College, Minneapolis, Minnesota.