Alex Krumer

• Krumer, Alex & Musau, Andrew (2026). Religion, football, and reconciliation: evidence from Israel. Empirical Economics. ISSN 0377-7332. 71(5). doi: 10.1007/s00181-026-02994-3. Full text in Research Archive Show summary

  This study examines the substitution between religious observance and secular leisure through the case of Israeli football games held on Shabbat, a holy day in Judaism. Although Jewish religion prohibits work on Shabbat, many top-tier games occur on Shabbat, generating tension between observant and secular camps. Using data from 1629 games and accounting for selection bias, we find that Shabbat games attract roughly 10% fewer spectators. The results suggest that losses from observant fans outweigh gains from secular ones. The findings highlight how religious norms can constrain participation in secular social activities, with implications beyond sports.

• Csató, László & Krumer, Alex (2026). Swiss-system chess tournaments and unfairness. Annals of Operations Research. ISSN 0254-5330. doi: 10.1007/s10479-026-07412-6. Full text in Research Archive Show summary

  Abstract The Swiss system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess tournaments if an odd number of rounds is played. To analyse this issue, our paper compares the number of points scored in the tournament between players who played one game more with the white pieces and players who played one game fewer with the white pieces. Using data from 28 highly prestigious competitions, we find that players with an extra white game score significantly more points. In particular, the advantage exceeds the value of a draw in the four Grand Swiss tournaments. A potential solution to this unfairness could be organising Swiss-system chess tournaments with an even number of rounds, and guaranteeing a balanced colour assignment for all players using a recently proposed pairing mechanism.

• Mattia, Alessandro Di & Krumer, Alex (2025). The effect of reducing the number of matches in round-robin tournaments with four teams: evidence from beach volleyball. Annals of Operations Research. ISSN 0254-5330. 360(2026)(2-3), p. 951–977. doi: 10.1007/s10479-025-06933-w. Full text in Research Archive Show summary

  Abstract In recent years, many sports tournaments have increased the number of participating teams, which resulted in larger number of matches. These expansions have raised many calls to reduce the number of matches because of significant logistical and physiological concerns. This paper examines the effects of reducing the number of matches in a widely used round-robin tournament format featuring four teams. We leverage a 2017 structural change in professional beach volleyball, where the number of matches per team in the round-robin (pool) stage was reduced from three to two. Utilising data from 6976 matches, our multivariate regression analyses reveal that this reduction does not impact the probability of a favourite team winning a single match nor the overall tournament's efficacy, measured by the final standings' alignment with teams' initial strengths. These findings hold across different strength definitions and genders. Our study offers insights for sports seeking to expand the number of teams while preserving a four-team round-robin structure.

• Adler, Lucas & Krumer, Alex (2025). Mapping the determinants of stadium attendance in Norwegian women’s Toppserien soccer league. Scandinavian Sport Studies Forum. 16, p. 47–74. doi: 10.24834/sssf.16.47. Full text in Research Archive Show summary

  Research question: This study is motivated by the scarcity of research on attendance demand in women’s soccer. We aimed to investigate the determinants that shape stadium attendance in Norwegian Toppserien women’s league. Research methods: Data was used from 12 seasons between 2010 and 2023. We employed a multiple OLS regression with more than 30 independent variables to investigate their relationship with attendance. Results and findings: From relatively low numbers, attendance has increased significantly over the examined period. Toppserien fans appear to respond positively to the level of game quality and the team’s performance. Surprisingly, the size of the municipality negatively correlates with attendance, and spillover effects from successful men’s teams play only a minor role. Finally, the first round of the season attracts larger crowds. Implications: The results suggest that the fans of women’s and men’s Norwegian soccer teams have rather distinct consumer profiles, highlighting the need for tailored marketing strategies for women’s teams. To maximize attendance, it also seems advisable to avoid scheduling collisions with mega events and to schedule more games on public holidays. Finally, home games of the first round could be more evenly allocated between the teams.

• Krumer, Alex; Shapir, Offer Moshe & Zou, Yifei (2024). The size of the crowd and home advantage in football : evidence from Chinese Super League. Asian Journal of Sport and Exercise Psychology (AJSEP). 4(3), p. 82–87. doi: 10.1016/j.ajsep.2024.10.009. Full text in Research Archive Show summary

  Home advantage is a well-established phenomenon in professional football. However, the literature on the effect of the size of the crowd on home advantage has produced mixed results. The present study utilized data from all the games in the Chinese Super League between the 2011 and 2019 seasons. Using multivariate regressions, where we control for teams’ abilities, different schedule related variables and referees’ unobserved characteristics, we find that the size of attendance has a positive effect on home advantage in terms of yellow cards, scored goals and points per game. Our finding emphasizes the important role of crowd on home advantage, not only for the dichotomous comparison between games with and without crowd, but also for the continuous case with varying levels of crowd.

• Krumer, Alex (2024). On the cost of wearing white shorts in women's sport. Journal of Behavioral and Experimental Economics. ISSN 2214-8043. 110. doi: 10.1016/j.socec.2024.102214. Full text in Research Archive Show summary

  The menstrual cycle and associated issues are still considered taboo in many societies, causing a lack of understanding and sub-optimal decision making. Sport can effectively promote awareness of social issues in general, including those concerning the menstrual cycle. One such issue is the anxiety arising from wearing white shorts. Despite increased awareness, still over half the teams participating in the recent 2023 FIFA Women's World Cup played in white shorts. In this study, I investigated women's and men's football games from the World Cups and the European Championships between 2002 and 2023. Using regression analysis, and after controlling for teams’ abilities and other factors, I found that women's teams wearing white shorts achieved between 0.32 and 0.37 fewer points per game. No such effect was observed among men. This result illustrates that a lack of understanding of period anxiety has an immediate cost that is very easy to avoid by simply not playing in white shorts. Most importantly, given that sport is an important vehicle of gender equality, increased awareness of period anxiety could result in higher participation of women in sports and, ultimately, in narrowing other gender gaps.

• Blum, Alexandra; Korlath, Alexander & Krumer, Alex (2024). Targeted investment in elite sports: an empirical lesson from professional fencing. Managing Sport and Leisure. ISSN 2375-0472. 31(2026)(5), p. 823–837. doi: 10.1080/23750472.2024.2424831. Full text in Research Archive Show summary

  Purpose/Rationale: Targeted investment is an important principle in allocating budgets between different sports. This paper analyzes whether the probability of a higher-ranked fencer winning a match differs between epee, sabre, and foil, the three weapons used in professional fencing. Design/Methodology/Approach: We used data on 6743 men’s and women’s fencing matches from the 120 most prestigious fencing tournaments from the 2014–2015 to 2018–2019 seasons. For that, we used multiple logistic regressions. Findings: Among men, epee competitions were the most balanced in the sense that higher-ranked fencers had the lowest probability of winning among the three weapons. Among women, epee competitions were significantly more balanced than sabre competitions, but not significantly more balanced than foil competitions. Practical implications: If a weaker fencing country wishes to enter the sport of fencing, it should prioritize epee competitions to increase the probability of sporting success. Research contribution: While targeted investment is a well-known theoretical tool, there are not many empirical studies that confirm its practicality. Our methodology may be used in other sports to achieve a more efficient targeted investment. Originality/Value: This study is an example of the intersection between theory and empirics in a sport that is not often being investigated.

• Guajardo, Mario & Krumer, Alexander (2024). Tournament design for a FIFA World Cup with 12 four-team groups : every win matters. In Breuer, Markus & Forrest, David (Ed.), The Palgrave handbook on the economics of manipulation in sport. Palgrave Macmillan. ISSN 9783031635809. p. 207–230. doi: 10.1007/978-3-031-63581-6_11. Full text in Research Archive Show summary

  After the expansion of the FIFA World Cup from 32 to 48 teams starting in the 2026 edition, the initial proposal was to split the 48 national teams into 16 groups of three. Among other drawbacks, this proposal provides potential for collusion. Recently, after widespread criticism, FIFA officials decided to revisit that proposal, instead approving a tournament with 12 groups of four teams. However, the approved format does not eliminate the possibility of collusion. In this chapter, we propose tournament formats for a World Cup with 12 groups of four teams, considering several criteria, such as non-collusion, symmetry in rest days, and no dead rubbers. At the same time, our proposals attempt to adhere to the traditional format, with some nuances in either the group or elimination stage.

• Krumer, Alex & Moreno-Ternero, Juan D (2023). The allocation of additional slots for the FIFA World Cup. Journal of Sports Economics. ISSN 1527-0025. 24(7), p. 831–850. doi: 10.1177/15270025231160757. Full text in Research Archive Show summary

  How to select participants for a sports tournament when they are divided into different sets, and one should find a fair number of slots for each set? We propose to address this question by resorting to standard tools from the fair allocation literature. To frame our discussion, we focus on the increase in the number of participating teams in the FIFA World Cup. We explore the allocation of additional slots among continental confederations. We consider 10 different allocations. Based on our analysis, we can argue that the European soccer confederation (UEFA) has a solid basis to claim for additional slots.

• Krumer, Alex; Megidish, Reut & Sela, Aner (2023). Strategic manipulations in round-robin tournaments. Mathematical Social Sciences. ISSN 0165-4896. 122(March), p. 50–57. doi: 10.1016/j.mathsocsci.2023.02.002. Full text in Research Archive Show summary

  We study round-robin tournaments with four symmetric players and two identical prizes where players compete against each other in games modeled as an all-pay contest. We demonstrate that in this common structure players may have an incentive to manipulate the results, namely, depending on the outcomes of the first round, a player may have an incentive to lose in the second round in order to maximize his expected payoff in the tournament. Keywords: multi-stage contests, all-pay auctions, round-robin tournaments

• Mattia, Alessandro Di & Krumer, Alex (2023). Fewer teams, more games, larger attendance? : evidence from the structural change in basketball's EuroLeague. European Journal of Operational Research. ISSN 0377-2217. 309(1), p. 359–370. doi: 10.1016/j.ejor.2023.01.002. Full text in Research Archive Show summary

  This study investigated whether an increased number of games between a reduced number of high-quality teams has a positive effect on stadium attendance. We did this by taking advantage of a recent structural change that occurred in basketball's EuroLeague tournament. Starting from the 2016/17 season, the two short round-robin tournaments (regular season and Top 16) among 24 teams merged into a longer round-robin tournament among 16 teams. In the new structure, the number of each team's games per season increased by more than 25 percent, which increased the aggregate attendance. In our empirical analyses, we investigated attendance per game by using data from the three seasons before and after the change. Comparing the attendance of the same teams that played before and after the change, our fixed effects estimation reveals a significant decrease of close to nine percent in attendance per game after the change compared to the Top 16 stage. We also found no significant difference in attendance after the change compared to the regular season before the change. Finally, we found that the main decrease in attendance after the change appears in the first half of the season, when the games are likely to be perceived as less decisive than in the second half of the season. Keywords: OR in sports, round-robin, attendance demand, basketball, time allocation

• Krumer, Alexander & Musau, Andrew (2023). Golden Tears : a cross-country study of crying in the Olympics. Emotion. ISSN 1528-3542. 24(2024)(1), p. 27–38. doi: 10.1037/emo0001247. Full text in Research Archive Show summary

  This article studies tears of joy by exploring data on the behavior of gold medalists of all 450 individual events at the 2012 and 2016 Summer Olympic Games at the end of the medalists’ respective competitions and during the medal ceremonies. We find that women cry more than men, older athletes cry more than younger athletes, athletes from the host country cry more at the end of the competition, and athletes cry more when they receive information on their victory immediately after completing their task. When looking at the socioeconomic characteristics of athletes’ countries, we find that men from countries with larger female labor force participation rates cry more than men from countries with lower female labor force participation, and athletes from countries with higher religious fractionalization cry less than those from countries with lower fractionalization. Finally, we find no relationship between the wealth of a country and the propensity of its athletes of any gender to cry. We discuss possible mechanisms that drive our results and suggest future directions for observational studies on emotions. (PsycInfo Database Record (c) 2023 APA, all rights reserved)

• Bühren, Christoph; Gschwend, Martin & Krumer, Alex (2023). Expectations, gender, and choking under pressure: Evidence from alpine skiing. Journal of Economic Psychology. ISSN 0167-4870. 100(2024). doi: 10.1016/j.joep.2023.102692. Full text in Research Archive Show summary

  In alpine skiing competitions, one of the coaches of the participating countries sets the course. This may provide an advantage, but it may also exert higher pressure on the racers. We analyze 45,467 men’s and 41,221 women’s performances from all competitions in alpine skiing’s Slalom, Giant Slalom, and Super Giant disciplines that took place in the World Cups, World Championships, and Olympic Games between the 2001/2002 and 2019/2020 seasons. We compare the performance of racers when competing on a course that was set by their compatriot to the performance of the same racers in the same season when the course was set by a coach from another country. Having a compatriot course setter only has an effect in the second (and decisive) run of the most technical discipline Slalom. We find that men fail significantly more often to complete their run when their compatriots set the course, whereas women fail significantly less in the same situation. The most likely drivers of our results relate to gender differences in response to expectations and choking under pressure in skill-based tasks.

• Faltings, Richard; Krumer, Alex & Lechner, Michael (2023). Rot-Jaune-Verde : on linguistic bias of referees in Swiss soccer. Kyklos (Basel). ISSN 0023-5962. 76(3), p. 380–406. doi: 10.1111/kykl.12332. Full text in Research Archive Show summary

  We utilize data from 5,010 soccer games in the top two Swiss divisions between the 2005/06 and 2018/19 seasons. In these games, a referee can share the same linguistic area with one of the teams. Using referee-per-season fixed effects, we find that referees issue significantly more penalties, in the form of yellow cards, to teams that are not from the referee's linguistic area. We also find some evidence, in the highest level league only, that referees issue more red cards to teams that are not from their linguistic area and that away teams achieve fewer points when home teams share the same linguistic area with the referee. Our analyses suggest that referees' bias is likely to be subconscious and reflexive rather than being a deliberate act of discrimination.

• Ermakov, Stepan & Krumer, Alex (2022). Saturday in the stadium : on higher attendance on Saturdays in Norwegian Eliteserien soccer league. European Sport Management Quarterly. ISSN 1618-4742. 23(6), p. 1800–1818. doi: 10.1080/16184742.2022.2067208. Full text in Research Archive Show summary

  Research question: This paper is motivated by the relatively late kick-off time of Sunday games (18:00), which is the main day in the Norwegian Eliteserien men’s soccer league. The paper investigates whether Saturday games attract a larger audience. Research methods: We used data from 11 seasons between 2009 and 2019. In our multivariate regression analyzes, we controlled for more than 30 confounding factors. Results and findings: We find that Saturday games attract close to 5% larger stadium attendance than Sunday games. Implications: Our results indicate that moving a large share of games from Sunday to Saturday would increase the gate revenues of teams that have had a negative trend for several years. These findings have implications for the stakeholders of the leagues, calendar committees, and local businesses. Keywords: schedule effects, soccer, attendance demand, Eliteserien

• Krumer, Alex & Smith, Vetle André Opland (2022). The Effect of COVID-19 on Home Advantage in Women’s Soccer: Evidence From Swedish Damallsvenskan. American Behavioral Scientist. ISSN 0002-7642. 67(2023)(10), p. 1168–1178. doi: 10.1177/00027642221118259. Full text in Research Archive Show summary

  Most studies of the effect of COVID-19 restrictions on home advantage have been conducted on men’s soccer, with the women’s game lacking scientific attention. The present study fills this gap by investigating games in Swedish Damallsvenskan women’s soccer league. Comparing games in the 2019 and 2020 seasons, we find a slight, but not statistically significant reduction in home advantage in games without crowds in terms of goals scored and points achieved. However, unlike in most studies on men’s soccer, we find that away teams received significantly more yellow cards in games without crowds compared to games with crowds. We discuss our results in the context of the findings in men’s soccer. Keywords: COVID-19, home advantage, referee bias, women’s soccer, gender differences

• Krumer, Alex (2021). Competing against the same team : does the length of time between the games matter? : evidence from the UEFA Champions League. In Koning, Ruud H. & Kesenne, Stefan (Ed.), A modern guide to sports economics. Edward Elgar Publishing. ISSN 9781789906530. p. 317–334. doi: 10.4337/9781789906530.00025. Full text in Research Archive Show summary

  There are many examples in professional sports in which two teams compete several times against each other over a short period of time. This structure raises many questions, including: Does the winner of the first match have a higher win probability in the second match? Does the length of time between these matches have an effect on win probabilities? Does it matter whether the winner of the first match was the underdog or the favorite? These questions are mostly asked by sports fans, journalists and coaches. However, repeated games may be of much broader interest among economists, psychologists and others. This is because repeated interactions occur very often in many areas of life, such as politics, the labor market, tenders, etc. Therefore, insights obtained from sports competitions may also be useful in other domains. In this study, I take advantage of real-life contests between professionals with large monetary rewards, where each pair of contestants competes against each other twice. However, some pairs compete twice in a row in two consecutive matches, whereas other pairs compete against each other for the second time after a longer period of time. Moreover, the allocation of pairs into treatment groups (playing the return match after a short period of time) and control groups (playing the return match after a long period of time) was determined via explicit randomization, which simplifies credible causal inference (Manski, 1995).

• Krumer, Alex (2021). Does psychological momentum differ for home and away teams? : evidence from penalty shoot-outs in European cups. In Altman, Hannah Josepha Rachel; Altman, Morris & Torgler, Benno (Ed.), Behavioural sports economics : a research companion. Routledge. ISSN 9780367531843. p. 159–171. doi: 10.4324/9781003080824-10. Full text in Research Archive
• Haugen, Kjetil K. & Krumer, Alex (2021). On the importance of tournament design in sports management : evidence from the UEFA Euro 2020 qualification. In Ratten, Vanessa (Eds.), Innovation and entrepreneurship in sport management. Edward Elgar Publishing. ISSN 9781783473946. p. 22–35. Full text in Research Archive
• Gschwend, Martin & Krumer, Alex (2021). On the importance of fixed effects over a short period of time when using sports data: a lesson from home advantage in alpine skiing. European Sport Management Quarterly. ISSN 1618-4742. 23(2023)(5), p. 1291–1303. doi: 10.1080/16184742.2021.1993297. Full text in Research Archive Show summary

  Research question The aim of this paper is to compare the effect of competing in a home country between a racer fixed effects model, which assumes a constant ability over the span of a racer’s career, and a racer per season fixed effects model, which has a more plausible assumption that ability may vary between the seasons. Research methods We use data on all 50,046 performances among men and 44,311 performances among women from all the top competitions in alpine skiing that took place in the seasons from 2001–2002 to 2017–2018. We use fixed effects estimations in which we compare the performance of racers when they compete in their home country to performance of the same racers when they compete abroad. Results and findings When using the racer fixed effects model, we find no relationship between competing at home and the likelihood of failing to finish the first run for both genders. However, when using the racer per season fixed effects model, we find that racers have a significantly higher probability of failing to complete the first run when competing abroad. In addition, we find that competing at home has a positive effect on racers’ performance in terms of World Cup points. Implications Given the widespread use of fixed effects models in sports-related studies, as well as in other fields, this paper illustrates the sensitivity of results to the length of the fixed effects. This should help practitioners and scholars to better understand the underlying assumptions that relate to athletes’ abilities over time. Keywords: Alpine skiing, fixed effects, home advantage

• Krumer, Alex (2021). Discouragement effect and alternative formats to increase suspense in professional biathlon. European Sport Management Quarterly. ISSN 1618-4742. 23(2), p. 391–410. doi: 10.1080/16184742.2020.1868547. Full text in Research Archive Show summary

  Research Question: The paper analyzes mass start competitions in professional biathlon, where 30 biathletes start simultaneously. This structure allows us to test the existence of discouragement effect, according to which biathletes reduce their efforts when lagging far behind the leaders. Research Methods: We use data on all 180 mass start competitions, for both genders, in World Cups, World Championships, and Olympic Games between the 2001/02 and 2019/20 seasons, and compare the gap times between the two consecutive ranks. For the same period, we execute the same analyses for all sprint and individual competitions that use interval starts. Results and Findings: We find that, in mass starts, the 95% confidence intervals of the gap times between the two consecutive ranks overlap in the range of rankings between 3 and 25 among men and between 5 and 24 among women, with mean gaps of 6.6 and 7.7 seconds among men and women, respectively. However, that gap increases sharply for the four bottom ranks (that is, ranks 27–30), which have mean gaps of 29.8 and 31.2 sec among men and women, respectively. However, in sprint and individual races, the lag time between two consecutive ranks does not exceed 4 (sprint) and 10 (individual) seconds in the range of rankings between 10 and 60. Implications: The results suggest that bottom-ranked biathletes in mass starts strategically reduce their efforts when there is nothing at stake. Such a strategy increases the duration of TV broadcasts and does not help maximize suspense, which is one of the main drivers of TV demands in professional sports. We offer an alternative format, according to which a certain number of the bottom-ranked biathletes will be eliminated after each bout of shooting. Such a format should dramatically increase the suspense-to-time ratio. Keywords: biathlon, tournament design, total effort, TV demand, suspense

• Krumer, Alex; Otto, Felix & Pawlowski, Tim (2021). Nationalistic bias among internationalexperts : evidence from professional skijumping. The Scandinavian Journal of Economics. ISSN 0347-0520. 24(1), p. 278–300. doi: 10.1111/sjoe.12451. Full text in Research Archive Show summary

  Ski jumping competitions involve subjective evaluations by judges from different countries. This may lead to nationalistic bias, according to which judges assign higher scores to their compatriots. To test this claim empirically, we exploit within-performance variation of scores from all World Cup, World Championship, and Olympic Games competitions between the 2010/11 and 2016/17 seasons. Our findings confirm that judges assign significantly higher scores to their compatriots. The magnitude of this nationalistic bias is significantly higher in more corrupt countries. We do not find that judges assign significantly different scores to jumpers whose compatriots are present on the judging panel.

• Bar-Eli, Michael; Krumer, Alex & Morgulev, Elia (2020). Ask not what economics can do for sports - ask what sports can do for economics. Journal of Behavioral and Experimental Economics. ISSN 2214-8043. 89(December), p. 1–5. doi: 10.1016/j.socec.2020.101597. Full text in Research Archive Show summary

  In this article we list the advantages of using sports data for economic research. We also provide a rich overview of economic literature that used sports data to test different fundamental economic theories as well as articles that presented divergences of economic decision making from neo-classical theories. Finally we present articles that were published in this special issue on behavioral economics and decision making in sports, all of which try to answer more general questions by means of sports data.

• Goller, Daniel & Krumer, Alex (2020). Let's meet as usual : Do games played on non-frequent days differ? : Evidence from top European soccer leagues. European Journal of Operational Research. ISSN 0377-2217. 286(2), p. 740–754. doi: 10.1016/j.ejor.2020.03.062. Full text in Research Archive Show summary

  Balancing the allocation of games in sports competitions is an important organizational task that can have serious financial consequences. In this paper, we examine data from 10,142 soccer games played in the top German, Spanish, French, and English soccer leagues between 2007/2008 and 2016/2017. Using a machine learning technique for variable selection and applying a semi-parametric analysis of radius matching on the propensity score, we find that all four leagues have a lower attendance in games that take place on four non-frequently played days than those on three frequently played days. We also find that, in all leagues, there is a significantly lower home advantage for the underdog teams on non-frequent days. Our findings suggest that the current schedule favors underdog teams with fewer home games on non-frequent days. Therefore, to increase the fairness of the competitions, it is necessary to adjust the allocation of the home games on non-frequent days in a way that eliminates any advantage driven by the schedule. These findings have implications for the stakeholders of the leagues, referees’ and calendar committees as well as for coaches and players. Keywords: performance, schedule effects, soccer

• Krumer, Alex (2020). Pressure versus ability : evidence from penalty shoot-outs between teams from different divisions. Journal of Behavioral and Experimental Economics. ISSN 2214-8043. 89(December), p. 1–6. doi: 10.1016/j.socec.2020.101578. Full text in Research Archive Show summary

  This study utilizes data from 586 shoot-outs between teams from different divisions in national cups of the top five European soccer countries. We find that a difference in one league between the teams increases the gap between probabilities of winning by 8 percentage points in favor of a team from a higher division. This result contradicts the widespread belief that penalty shoot-outs are a game of chance, highlighting the importance of ability even in a simple mechanical task that takes place in high-pressure situations.

• Joustra, Sanne J.; Koning, Ruud H. & Krumer, Alex (2020). Order effects in elite gymnastics. De Economist. ISSN 0013-063X. 169, p. 21–35. doi: 10.1007/s10645-020-09371-0. Full text in Research Archive Show summary

  We study the effect of order of performances on the final execution score in artistic gymnastics. We use data from all the finals for both genders at the main gymnastics tournaments in the period between 2009 and 2017 where the order of performances was fully randomised. We find that female gymnasts who perform later receive on average a significantly higher execution score for their routine, however, we find no effect of the order of performances in men’s competitions. The existence of subjective evaluation only in female competitions considering artistry, could be one of the possible explanations for gender differences. We also find no relationship between the score of an athlete and his or her immediate predecessor.

• Krumer, Alex; Megidish, Reut & Sela, Aner (2019). The optimal design of round-robin tournaments with three players. Journal of Scheduling. ISSN 1094-6136. 23(3), p. 379–396. doi: 10.1007/s10951-019-00624-8. Full text in Research Archive Show summary

  We study the optimal design of round-robin tournaments with three symmetric players. We characterize the subgame-perfect equilibrium in these tournaments with either one or two prizes. Our results show that the players who wish to maximize their expected payoffs or their probabilities of winning have different preferences about the order of games under tournaments with one or two prizes. We analyze the optimal allocations of players for a designer who wishes to maximize the players’ expected total effort in the tournaments with one and two prizes, and by comparing between them, it is demonstrated that in order to maximize the players’ expected total effort the designer should allocate only one prize. Keywords: Multi-stage contests, all-pay auctions, first-mover advantage, second-mover advantage, round-robin tournaments

• Iqbal, Hamzah & Krumer, Alex (2019). Discouragement effect and intermediate prizes in multi-stage contests : evidence from Davis Cup. European Economic Review. ISSN 0014-2921. 118(September), p. 364–381. doi: 10.1016/j.euroecorev.2019.06.001. Full text in Research Archive Show summary

  The discouragement effect of being the lagging player in multi-stage contests is a well-documented phenomenon. In this study, we utilize data from 2,447 Davis Cup matches in team tennis tournaments to test the effect of being behind or ahead on individuals’ performance with and without intermediate prizes. Using several different strategies to disentangle the effect of being ahead in the interim score from the effect of selection, we find the usual discouragement effect. However, the discouragement effect disappears after the introduction of intermediate prizes in the form of ranking points. The lagging favorite had close to a 20-percentage point greater probability of winning compared to matches without such a prize. We show that this result is not driven by the selection of better players into tournaments with intermediate prizes. As predicted by previous theoretical studies, our empirical findings suggest that intermediate prizes may mitigate or even eliminate the ahead-behind effects that arise in multi-stage contests. Keywords: collective decision-making, multi-stage contests, discouragement, tennis

• Harb-Wu, Ken & Krumer, Alex (2019). Choking under pressure in front of a supportive audience : evidence from professional biathlon. Journal of Economic Behavior and Organization. ISSN 0167-2681. 166, p. 246–262. doi: 10.1016/j.jebo.2019.09.001. Full text in Research Archive Show summary

  Performing in front of a supportive audience increases motivation. However, it also creates psychological pressure, which may impair performance, especially in precision tasks. In this paper, we exploit a unique setting in which professionals compete in a real-life contest with large monetary rewards in order to assess how they perform in front of a supportive audience. Using the task of shooting in the sprint competitions of professional biathlon events over a period of 16 years, we find that for both genders, biathletes from the top quartile of the ability distribution miss significantly more shots when competing in their home country compared to competing abroad. Our results are in line with the hypothesis that high expectations to perform well in front of a friendly audience prompt individuals to choke when performing skill-based tasks.

• Krumer, Alex (2019). Testing the effect of kick-off time in the UEFA Europa League. European Sport Management Quarterly. ISSN 1618-4742. 20(2), p. 225–238. doi: 10.1080/16184742.2019.1598456. Full text in Research Archive Show summary

  Research Question: The paper analyzes whether different kick-off times have an effect on attendance and performance of teams in the group stage of the UEFA Europa League. Research Methods: I use data on all of the games from the group stage of the UEFA Europa League between the 2009/10 and 2015/16 seasons that took place in time zones CET and CET + 1. I estimate the average treatment effect of the kick-off time by using the distance-weighted radius matching approach with bias adjustment. Results and Findings: There is less attendance as a share of the capacity of the stadiums in games that kick off at 21:05 CET compared to games that start at 19:00 CET. In addition, in games that begin later (21:05) a team with a lower UEFA ranking has a significantly lower home advantage compared to games that begin earlier (19:00). Implications: The results of this study suggest that a lower ranked team that competes three times at home at 21:05 CET loses on average about 270,000 Euros from lower revenue from tickets and UEFA prizes. Additionally, a lower number of points reduces the chances of qualifying for the next round of competition, which is a much larger loss of at least 800,000 Euros, not counting all other revenue from tickets and advertising in more advanced stages of competition. Hence, it seems to be an important organizational task to adjust kick-off times in a way that eliminates any advantage driven by the schedule. Keywords: European soccer, schedule, fairness, home advantage

• Krumer, Alex & Lechner, Michael (2018). Midweek effect on soccer performance : evidence from the German bundesliga. Economic Inquiry. ISSN 0095-2583. 56(1), p. 193–207. doi: 10.1111/ecin.12465. Full text in Research Archive Show summary

  The home advantage phenomenon is a well‐established feature in sports competitions. In this study, we examine data from 2,013 soccer matches played in the German Bundesliga during the seasons from 2007–2008 to 2016–2017. Using a very rich data set, our econometric analysis that is based on matching methods reveals that the usual home advantage disappears when the game is in the middle of the week instead of being on the weekend. Our results indicate that, as the midweek matches are unevenly allocated among teams, the actual schedules of the Bundesliga favor teams with fewer home games in midweek. The study also shows that these soccer‐specific findings may have some implications for the design of contests in general. (JEL D00, L00, D20, Z20)

• Cohen-Zada, Danny; Krumer, Alex & Shapir, Offer Moshe (2018). Testing the effect of serve order in tennis tiebreak. Journal of Economic Behavior and Organization. ISSN 0167-2681. 146(February), p. 106–115. doi: 10.1016/j.jebo.2017.12.012. Full text in Research Archive Show summary

  The order of actions in contests may generate different psychological effects which, in turn, may influence contestants’ probabilities to win. The Prouhet-Thue-Morse sequence in which the first ‘n’ moves is the exact mirror image of the next ‘n’ moves should theoretically terminate any advantage to any of the contestants in a sequential pair-wise contest. The tennis tiebreak sequence of serves is the closest to the Prouhet-Thue-Morse sequence that one can find in real tournament settings. In a tiebreak between two players, A and B, the order of the first two serves (AB) is a mirror image of the next two serves (BA), such that the sequence of the first four serves is ABBA. Then, this sequence is repeated until one player wins the tiebreak. This sequence has been used not only in tennis, but also recently in the US TV presidential debates. In this study we analyse 1701 men’s and 920 women’s tiebreak games from top-tier tournaments between the years 2012 to 2015. Using several different strategies to disentangle the effect of serving first from the effect of selection, we find that, for both genders, serving first does not have any significant effect on the winning probabilities of the two players. Thus, it might be useful for other sports, and contests in general, to consider adopting the ABBA sequence.

• Elaad, Guy; Krumer, Alex & Kantor, Jeffrey (2018). Corruption and sensitive soccer games : cross-country evidence. Journal of Law, Economics & Organization. ISSN 8756-6222. 34(3), p. 364–394. doi: 10.1093/jleo/ewy013. Full text in Research Archive Show summary

  We utilize data from sensitive soccer games in 75 countries between the years 2001 and 2013. In these games one team was in immediate danger of relegation to a lower division (Team A) and another team was not affected by the result (Team B). Using within-country variation, our difference-in-difference analysis reveals that the more corrupt the country, according to Corruption Perceptions Index, the higher is the probability that Team A would achieve the desired result in the sensitive games relative to achieving this result in other, non-sensitive games against the same team. We also find that in the later stages of the following year, the probability that Team A would lose against Team B compared to losing against a similar team (usually better than Team B) is significantly higher in more corrupt countries than in less corrupt countries. This result serves as evidence of quid pro quo behavior. (JEL A12, D73, C93, Z20)

• Cohen-Zada, Danny; Krumer, Alex; Rosenboim, Mosi & Shapir, Offer Moshe (2017). Choking under pressure and gender : evidence from professional tennis. Journal of Economic Psychology. ISSN 0167-4870. 61(August), p. 176–190. doi: 10.1016/j.joep.2017.04.005. Full text in Research Archive Show summary

  We exploit a unique setting in which two professionals compete in a real-life tennis contest with high monetary rewards in order to assess how men and women respond to competitive pressure. Comparing their performance in low-stakes versus high-stakes situations, we find that men consistently choke under competitive pressure, but with regard to women the results are mixed. Furthermore, even if women show a drop in performance in the more crucial stages of the match, it is in any event about 50% smaller than that of men. These findings are robust to different specifications and estimation strategies.

• Cohen-Zada, Danny; Krumer, Alex & Shtudiner, Ze'ev (2017). Psychological momentum and gender. Journal of Economic Behavior and Organization. ISSN 0167-2681. 135(March), p. 66–81. doi: 10.1016/j.jebo.2017.01.009. Full text in Research Archive Show summary

  We exploit a natural experiment in which two professionals compete in a one-stage contest without strategic motives and where one contestant has a clear exogenous psychological momentum advantage over the other in order to estimate the causal effect of psychological momentum on performance. This unique setting commonly occurs in bronze medal fights in professional judo. Based on data on all major international tournaments during the period between 2009 and 2013 we find that men's performance is significantly affected by psychological momentum, while women's is not. This result is robust to different specifications and estimation strategies. Our results are in line with evidence in the biological literature that testosterone, which is known to enhance performance of both men and women, commonly increases following victory and decreases following loss only among men.

• Krumer, Alex (2017). On winning probabilities, weight categories, and home advantage in professional judo. Journal of Sports Economics. ISSN 1527-0025. 18(1), p. 77–96. doi: 10.1177/1527002514560576. Full text in Research Archive Show summary

  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.

• Krumer, Alex; Megidish, Reut & Sela, Aner (2017). First-mover advantage in round-robin tournaments. Social Choice and Welfare. ISSN 0176-1714. 48(3), p. 633–658. doi: 10.1007/s00355-017-1027-y. Full text in Research Archive Show summary

  We study round-robin tournaments with either three or four symmetric players whose values of winning are common knowledge. With three players there are three rounds, each of which includes one pair-wise game such that each player competes in two rounds only. The player who wins two games wins the tournament. We characterize the subgame perfect equilibrium and show that each player’s expected payoff and probability of winning is maximized when he competes in the first and the last rounds. With four players there are three rounds, each of which includes two sequential pair-wise games where each player plays against a different opponent in every round. We again characterize the subgame perfect equilibrium and show that a player who plays in the first game of each of the first two rounds has a first-mover advantage as reflected by a significantly higher winning probability as well as by a significantly higher expected payoff than his opponents.

• Krumer, Alex & Lechner, Michael (2017). First in first win : evidence on schedule effects in round-robin tournaments in mega-events. European Economic Review. ISSN 0014-2921. 100(November), p. 412–427. doi: 10.1016/j.euroecorev.2017.09.006. Full text in Research Archive Show summary

  The order of actions in contests may have a significant effect on performance. In this study, we examine the role of the schedule in round-robin tournaments with sequential games between three and four contestants. Our empirical analysis, based on soccer FIFA World Cups and UEFA European Championships, and on two Olympic wrestling events, reveals that there is a substantial advantage to the contestant who competes in the first and third matches. Our findings are in line with the hypothesis that winning probabilities in multi-stage contests with sequential games are endogenously depending on the schedule of contests as predicted by game-theoretical models. We also discuss possible ways to reduce the effect of the schedule.

• Krumer, Alex; Megidish, Reut & Sela, Aner (2017). Round‐robin tournaments with a dominant player. The Scandinavian Journal of Economics. ISSN 0347-0520. 119(4), p. 1167–1200. doi: 10.1111/sjoe.12204. Full text in Research Archive Show summary

  We analyze the subgame perfect equilibrium of the round‐robin tournament with one strong (dominant) and two weak players, and we compare this tournament and the one‐stage contest with respect to the players' expected payoffs, expected total effort, and their probabilities of winning. We find that if the contest designer's goal is to maximize the players' expected total effort, then – if the asymmetry between the players is relatively low – the one‐stage contest should be used. However, if the asymmetry is relatively high, then the round‐robin tournament should be used.

• Krumer, Alex; Rosenboim, Mosi & Shapir, Offer Moshe (2016). Gender, competitiveness, and physical characteristics : evidence from professional tennis. Journal of Sports Economics. ISSN 1527-0025. 17(3), p. 234–259. doi: 10.1177/1527002514528516. Full text in Research Archive Show summary

  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. Keywords: gender differences, performance under pressure, contests, tennis

• Krumer, Alex (2015). The order of games in a best-of-three contest. Journal of Sports Economics. ISSN 1527-0025. 16(2), p. 185–200. doi: 10.1177/1527002512471537. Full text in Research Archive Show summary

  We study a best-of-three all-pay contest with two players in which the first player to win two games wins the contest. Each player has a value of winning the contest as well as a value of winning a single game. It is assumed that a player’s value of winning a game in his home field is higher than his value of winning a game away from home. The stronger player (the player with the higher value of winning the contest) plays twice at his home field and once away from it. We analyze the order of games that both players agree to, according to which no one has an incentive to switch to a different order, since switching would not yield a higher expected payoff. In this order, the weaker player plays at his home field in the first stage and then plays two games at the stronger player’s field. Keywords: winner-take-all contests, all-pay auctions, best-of-three contests

• Krumer, Alex (2013). Best-of-two contests with psychological effects. Theory and Decision. ISSN 0040-5833. 75(1), p. 85–100. doi: 10.1007/s11238-012-9313-8. Full text in Research Archive Show summary

  We study a best-of-two contest with two homogeneous players (teams). The winner is the player who wins in both stages. In the case of one victory for each team, a draw determines the identity of the winner. Each team has a value of winning the contest as well as a value of winning a single game. A team’s value of winning a game at its home field is higher than its value of winning a game away from home. We show that if winning in the first stage provides a psychological advantage in the second stage, each team would prefer to play the second stage at its home field. Keywords: winner-take-all contests, all-pay contests, best-of-two contests

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• Krumer, Alex & Haugen, Kjetil K. (2026). En billett til fotball-VM er ingen menneskerett. doi: https:/www.forskersonen.no/debattinnlegg-fotball-meninger/en-billett-til-fotball-vm-er-ingen-menneskerett/2682178. Full text in Research Archive
• Haugen, Kjetil K. & Krumer, Alex (2025). Norge skal til VM, men kan vi vinne? doi: https:/www.forskersonen.no/fotball-kronikk-meninger/norge-skal-til-vm-men-kan-vi-vinne/2589413. Full text in Research Archive Show summary

  Den voldsomme euforien etter landslagets uovertrufne VM-kvalifisering har muligens lagt seg noe. Noen besinnede tanker om lagets faktiske sjanser i VM kan kanskje være på sin plass.

• Krumer, Alex & Szymanski, Stefan (2025). Review for the beautiful dataset. Sports Economics Review (SER). 11(September). doi: 10.1016/j.serev.2025.100057. Full text in Research Archive
• Krumer, Alex (2025). Why wearing white shorts in women’s aoccer is a bad idea. Full text in Research Archive
• Krumer, Alex (2025). Yama Wolasmals ensidige narrativ : en skam for journalistikken. Dagen : kristelig dagblad. ISSN 0805-4738. Full text in Research Archive
• Krumer, Alex (2025). Når alle skal ha en mening om ting de ikke kan nok om. Klassekampen. ISSN 0805-3839. Full text in Research Archive
• Krumer, Alex (2024). What sports can teach us about discrimination. www.psychologytoday.com. Full text in Research Archive
• Haugen, Kjetil K. & Krumer, Alex (2024). A well-written, sensation seeking book marred by fundamental analytical flaws. Idrottsforum.org - Nordic Sport Studies Forum. Full text in Research Archive
• Krumer, Alex (2024). Akademisk boikott av Israel er lite gjennomtenkt. Subjekt.no. Full text in Research Archive
• Krumer, Alex (2024). Støtt vitenskapen – ikke boikott Israel! Forskerforum.no. Full text in Research Archive
• Krumer, Alex (2024). On the cost of wearing white shorts in women’s sport. Full text in Research Archive
• Krumer, Alex (2024). [On the pitfalls of the tournament design with 24 teams in the Euro 2024]. sports.walla.co.il. Full text in Research Archive
• Krumer, Alex (2023). Several milestones in innovation in football. In Ratten, Vanessa (Eds.), Football entrepreneurship. Routledge. ISSN 9780367235185. Full text in Research Archive
• Krumer, Alex & Jørgensen, Andreas (2023). Professorer i uenighet om straffesparkanalyser: – Det er bare tull. [Journal]. VG Pluss. Full text in Research Archive
• Krumer, Alex (2023). [On transfer market values and final rankings]. sports.walla.co.il. Full text in Research Archive
• Krumer, Alex (2023). [On previous experience of coaches]. sports.walla.co.il. Full text in Research Archive
• Krumer, Alex & Szymanski, Stefan (2023). Sports economics: Time for a new journal. Sports Economics Review (SER). 1(March), p. 1–2. doi: 10.1016/j.serev.2023.100008. Full text in Research Archive
• Guajardo, Mario & Krumer, Alex (2023). Tournament designs and schedules for a FIFA World Cup with 12 groups of 4 teams. Full text in Research Archive
• Krumer, Alex; Engen, Ingrid Syrstad; Maanum, Frida & Stensrud, Anna (2023). Fargen på shortsen til kvinnelige fotballspillere har betydning for kampresultatet : det viser en studie fra Høgskolen i Molde. [TV]. tv.nrk.no. Full text in Research Archive
• Krumer, Alex; Maanum, Frida; Engen, Ingrid Syrstad; Støre, Heidi; Mjelde, Maren & Svarstad, Anne [Show all 8 contributors for this article] (2023). Ny forsking: Kvinnelag tek langt færre poeng når dei spelar med kvite shortsar. [Internet]. nrk.no/sport. Full text in Research Archive
• Krumer, Alex & Szymanski, Stefan (2023). A short summary of the first year. Sports Economics Review (SER). 4. doi: 10.1016/j.serev.2023.100023. Full text in Research Archive
• Guajardo, Mario & Krumer, Alex (2023). Are 104 games the way forward for the 2026 FIFA World Cup? Insideworldfootball. Full text in Research Archive
• Krumer, Alex (2022). Is soccer a matter of life and death? : wins and losses in soccer may be related to health, financial markets, and more. Full text in Research Archive
• Krumer, Alex (2022). Who cries more in the Olympics? Psychologytoday.com. Full text in Research Archive
• Krumer, Alex (2022). Why do top athletes choke under pressure? : the psychological mechanisms behind the stress and pressure of peak performance. Psychologytoday.com. Full text in Research Archive
• Krumer, Alex (2022). Who cries most at the Olympics? : a new study on the emotional tears of Olympic champions. Psychologytoday.com. Full text in Research Archive
• Krumer, Alex & Gammelsæter, Hallgeir (2022). De fattige subsidierer de rike. Dagens næringsliv. ISSN 0803-9372. p. 78–79. Full text in Research Archive
• Krumer, Alex (2021). Saturday games attract a significantly higher attendance at football matches. sciencenorway.no. Full text in Research Archive
• Krumer, Alex (2021). Голландский судья на игре сборной Бельгии? Hе лучший выбор. Full text in Research Archive
• Krumer, Alex (2021). Бельгия – фаворит с вероятностью в 76% НЕ выиграть Евро-2020: наш блогер составил прогноз вместе с профессором и доктором экономики. Full text in Research Archive
• Krumer, Alex (2021). ?מחסום שפה: מה קורה כששופט חולק שפת אם עם קבוצה אחת בלבד. Full text in Research Archive
• Krumer, Alex (2021). אסור היה לחדש את המשחק בדנמרק: לרצון לנצח יש גם צד שלילי. Full text in Research Archive
• Krumer, Alex (2021). Решать, доигрывать ли матч Дании и Финляндии, должны были не игроки. Мнение профессора. Full text in Research Archive
• Krumer, Alex (2021). למה לי פוליטיקה עכשיו: המנהיגים שניצלו לרעה אירועי ספורט גדולים. Full text in Research Archive
• Krumer, Alex & Gammelsæter, Hallgeir (2021). Gir flere kamper mellom de beste lagene større publikumsinteresse? Nettavisen. Full text in Research Archive
• Krumer, Alex & Gammelsæter, Hallgeir (2021). Skihopp-dommere gir bedre poeng til utøvere fra egne land. Forskersonen.no. Full text in Research Archive
• Krumer, Alex (2021). Hva gir flest tilskuere - lørdagskamper eller søndagskamper? Forskersonen.no. Full text in Research Archive
• Krumer, Alex & Gammelsæter, Hallgeir (2021). Gir flere kamper mellom de beste lagene større publikums­interesse? Forskersonen.no. Full text in Research Archive
• Krumer, Alex (2021). Реальна ли угроза бана топ-клубов и топ-игроков? Подключаем теорию игр! Full text in Research Archive
• Krumer, Alex (2020). Idrettsforskning avslører skjult nasjonalisme. Full text in Research Archive
• Krumer, Alex (2019). Choking under pressure in front of a supportive audience : evidence from professional biathlon. Full text in Research Archive
• Krumer, Alex & Harb-Wu, Ken (2018). Choking under pressure in front of a supportive audience : evidence from professional biathlon. Full text in Research Archive
• Krumer, Alex (2018). Corruption and sensitive soccer games : cross-country evidence. Full text in Research Archive
• Krumer, Alex (2017). First in first win : evidence on unfairness of round-robin tournaments in mega-event. Full text in Research Archive
• Krumer, Alex & Lechner, Michael (2017). First in first win : evidence on unfairness of round-robin tournaments in mega-events. Full text in Research Archive Show summary

  In this study, we test a game theoretical prediction on the first mover advantage in round-robin tournaments with sequential games between three and four contestants. Our empirical analysis, based on FIFA World Cups, UEFA European Championships, and on Olympic wrestling events, reveals a substantial advantage to the contestant who competes in the first and third matches.

• Bread, Alison & Krumer, Alex (2017). Women respond better than men to competitive pressure. [Journal]. Harvard Business Review. Full text in Research Archive
• Krumer, Alex (2017). Memory and Confidence. Full text in Research Archive
• Krumer, Alex & Lechner, Michael (2016). First in first win : evidence of the first mover advantage in round-robin tournaments. Full text in Research Archive
• Krumer, Alex & Lechner, Michael (2016). Midweek effect on performance : evidence from the German Soccer Bundesliga. Full text in Research Archive
• Krumer, Alex & Lechner, Michael (2016). First in first win : evidence of the first mover advantage in round-robin tournaments. Full text in Research Archive
• Krumer, Alex (2016). Corruption and contests : cross-country evidence from sensitive soccer matches. Full text in Research Archive
• Klitgaard, Steffen Thomas Hyldgaard & Krumer, Alex (2025). The effect of structural change on attendance demand in the Danish Superliga. Høgskolen i Molde - Vitenskapelig høgskole i logistikk. Full text in Research Archive
• Guajardo, Mario & Krumer, Alex (2023). Format and schedule proposals for a FIFA World Cup with 12 four-team groups. Norges Handelshøyskole. Full text in Research Archive Show summary

  After the expansion of the FIFA World Cup from 32 to 48 teams starting from the 2026 edition, the initial proposal was to split the 48 national teams into 16 groups of three. Among other drawbacks, this proposal provides potential for collusion. Recently, after widespread criticism, FIFA officials signaled the possibility to re-discuss that proposal, pointing to a tournament with 12 groups of four teams. If this new proposal prevails, relevant questions arise about tournament design and schedule. In this paper, we propose tournament formats for a World Cup with 12 groups of four teams, considering a number of criteria, such as non-collusion, symmetry in rest days, no dead rubbers, and a tournament length of about one month. At the same time, our proposals attempt to adhere to the traditional format, with some nuances either in the group stage or in the knockout stage.

• Krumer, Alex (2021). Life, death and sports [YouTube]. [Ukjent]. Full text in Research Archive Show summary

  This video provides examples, which illustrate that sports in general and football in particular are indeed matters of life and death. And sometimes even more than this. It provides examples of a cynical use of sports by governments and criminals. Finally, it describes situations of an increased and decreased likelihood of having a heart attack.

• Krumer, Alex (2021). From judo to financial crisis via gender and psychology [YouTube]. [Ukjent]. Full text in Research Archive Show summary

  This video shows how data from judo competitions can help investigating the effects of psychological momentum. It also discusses the relationship between testosterone levels and financial decision making, emphasising the lack of women in financial markets.

• Krumer, Alex (2021). On corruption, UN, and soccer [YouTube]. [Ukjent]. Full text in Research Archive Show summary

  This video describes the relationship between the Corruption Perceptions Index of a country and the probability to achieve a desired result to avoid relegation in a country's soccer league.

• Krumer, Alex (2021). Sports for economics like apples for physics [YouTube]. [Ukjent]. Full text in Research Archive Show summary

  This video provides several examples that illustrate the usefulness of sports data in economic research.

• Krumer, Alex; Megidish, Reut & Sela, Aner (2017). The optimal design of round-robin tournaments with three players. University of St. Gallen. Full text in Research Archive Show summary

  We study the optimal design of round-robin tournaments with three symmetric players. We characterize the subgame perfect equilibrium in these tournaments with either one or two prizes. Our results show that the players who wish to maximize their expected payoffs or their probabilities of winning have different preferences about the order of games under tournaments with one or two prizes. We analyze the optimal allocations of players for a designer who wishes to maximize the players' expected total effort in the tournaments with one and two prizes, and by comparing between them, it is demonstrated that in order to maximize the players' expected total effort the designer should allocate only one prize. Keywords: Multi-stage contests, all-pay auctions, first-mover advantage, second-mover advantage, round-robin tournaments.

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