Maybe hosting the Olympics just shuffles income around a country, rather than increasing it

There is a large, and still growing, literature on the economic impact of large sporting events (see this post, and the links at the end of it, for some examples). My conclusion from that body of research is that large sporting events are expected to generate large economic impacts (based on studies conducted before the event), but generally the actual economic effects are small or non-existent (when measured after the event). However, the studies are typically based on a single event, or a small number of events. Are the typical null results driven by a small sample size and if so, would a larger and more diverse sample demonstrate different results?

That is the question essentially underlying this 2021 article by Matthias Firgo (Austrian Institute of Economic Research), published in the journal Regional Science and Urban Economics (ungated earlier version here). Firgo looks at the effect of the Olympic Games (both summer and winter) on regional GDP per capita in the host region (not GDP per capita in the whole host country, or only in the host city), using data from the 1992 Winter Olympics in Albertville to the 2020 Summer Olympics in Tokyo. Importantly, Firgo uses a control group made up of regions with cities that had been shortlisted by the International Olympic Committee (IOC) to host in the same year, but were unsuccessful (more on that a bit later).

Because of data limitations, Firgo focuses on GDP per capita as a percentage of national GDP per capita - essentially a relative measure of wellbeing at the regional level. Using this measure, he finds that for the Summer Olympics:

...regional per capita GDP significantly increases by 3.6 %-points (3.3 %-points) relative to national per capita GDP in the year of the event (the year before the event).

In other words, the host region’s GDP per capita rises by around 3 to 4 percentage points relative to national GDP per capita in the lead-up to the event. In contrast, there is only very weak evidence of any persistent effect of the event on regional GDP per capita, and the Winter Olympics (which are a smaller event, and typically held in smaller cities) had no significant effects. The positive effect of the Summer Olympics on regional GDP per capita in the years immediately before the event is consistent with increasing spending on infrastructure (including sporting, transport, hospitality, and cultural infrastructure) in the lead-up to a substantial event. That there is no persistent effect is fairly consistent with the other research on the economic impact of large events.

However, there are two other things to take away from this research. First, if anything these results might overstate the impact of successfully bidding for the Olympics. Whether a potential host city's bid is successful or not is not a random event. Cities that are more likely to be successful hosts should, at least in theory, be more likely to be selected as hosts. So, the control group is an imperfect comparator for the treatment cities in a way that is likely to bias the results. If successful hosts were cities that the IOC believed were already on an upward trajectory at the time of the Olympics, then that would bias upwards the estimated impact of the event. Of course, such foresight from the IOC would have to be executed seven years before the event (which is when the hosts are typically selected), but nevertheless there is potential for upward bias. That said, shortlisted cities are still likely to be a better comparison group than all non-host cities, since they had already demonstrated some capacity and willingness to host.

Second, these results tell us more about relative effects within the host country, rather than absolute economic impacts. They show that the GDP per capita increases in the host region relative to the rest of the country. Given that the overall economic impact is small to negligible, as are population changes arising around the event (both of which many other studies have shown), a large part of the relative increase in GDP per capita in the host region must arise from a combination of increased GDP per capita in the host region, and decreased GDP per capita in other regions in the same country. Effectively then, hosting the Summer Olympic Games simply shuffles income around a country in the lead-up to the games, with the host region benefitting while other regions are negatively impacted. Then after the event, there is a return to the normal inter-regional distribution of incomes.

The Olympic Games is a large spectacle - an opportunity for national celebration as we watch sporting heroes compete to win medals. The evidence still suggests that the Games are not a source of sustained economic growth, and that any short-run gains may be highly localised rather than national, and some of those gains come at the expense of other regions.

Read more:

• Tim Hazeldine on economic impact studies
• Beware economists bearing impact studies of the America's Cup
• Even less reason to believe in the economic impact of the America's Cup
• The overstated impact of the Super Bowl
• The economic impact of the 2010 World Cup in South Africa
• The economic impact of the 2000 Sydney Olympics

The impact of Taylor Swift on the Kansas City Chiefs' TV ratings

In 2023, Taylor Swift began a relationship with Kansas City Chiefs tight end Travis Kelce. After that, Kansas City Chiefs broadcasts seemed increasingly eager to cut to shots of Taylor Swift in the corporate boxes, rather than fans in the stands. The NFL was clearly trying to appeal to Swift's fans, but did it work? In a new article published in the Journal of Sports Economics (sorry, I don't see an ungated version online), Kerianne Rubenstein (Syracuse University) and Frank Stephenson (Berry College) show that it did.

Rubenstein and Stephenson collated data on 247 NFL games played in the 2022 and 2023 seasons, noting that the first Chiefs game that Taylor Swift attended was in the third week of the 2023 season. They apply a difference-in-differences analysis, comparing the difference in TV ratings between before and after Week 3 of 2023 for the Chiefs, with before and after Week 3 of 2023 for other teams, while controlling for other variables expected to affect TV ratings. In other words, Rubenstein and Stephenson check whether the Chiefs' TV ratings increased by more than the average before-and-after change that other teams experienced. They find that:

...Chiefs’ games after Taylor Swift started attending see an increase of 2.15 ratings points, which is an approximately 32% increase relative to the mean Nielsen rating... total viewership increased by about 4.8 million after Taylor Swift started attending Chiefs’ games.

So, it appears that Taylor Swift did increase TV ratings for the Kansas City Chiefs. Good news for the Chiefs (and for other NFL teams, who share in the broadcast revenue). Interestingly, and to be expected given Swift's young fan base, the effect was even larger on TV viewership among those aged 18-34 years, with a 40.1 percent increase in TV rating.

An important question, though, is whether Swift attracted new fans, and whether they stuck around. In terms of the former, Rubenstein and Stephenson find some evidence that games played at the same time as Chiefs games suffered a decrease in TV ratings (although that analysis is based on a sample of only ten games, which limits how much we can take from it). However, they also find an increase in TV ratings when the Chiefs game was the only game in its timeslot. So, while there was some substitution between NFL games, new fans were also attracted to watch. And, they did stick around - Rubenstein and Stephenson find limited evidence that the effect declined over time, with Chiefs games later in 2023 having a similar TV rating as those earlier in the season (it is worth noting that the Chiefs had a particularly good 2023 season though, finishing the regular season 11-6, winning their division, and ultimately winning Super Bowl LVIII).

Celebrities are a common feature of sports games. Rubenstein and Stephenson note the example of the Atlanta Hawks, who make courtside seats available to celebrities with large social media followings in the hopes of increasing game attendance and TV ratings. Not every celebrity has the profile of Taylor Swift. However, the results in this study suggest that the Hawks' strategy might be a sensible strategy for increasing the profile of games. The NFL should take notice. Certainly, this would make much more sense than, as some conspiracy theorists would have you believe, biasing the officiating in favour of particular teams (like the Chiefs). So, leaving conspiracies aside, what we learn from this paper is that celebrity appearances at games can increase demand. That seems to be exactly what happened here, with Taylor Swift’s presence helping to increase the audience for Kansas City Chiefs games.

What the COVID public health mandates taught us about home advantage in the NFL

The final weekend of the NFL regular season is upon us, and my favourite Carolina Panthers will play for the NFC South division title against the Tampa Bay Buccaneers tomorrow. The winner wins the division and goes to the playoffs. The loser goes home disappointed [*]. The game is being played in Tampa, which conveys some home advantage to the Bucs. How much home advantage, and why?

Those are essentially the questions answered by this new article by Adam Cook (State University of New York at Fredonia), published in the Journal of Sports Economics (sorry, I don't see an ungated version online). There have been lots of studies of home advantage across many sports, including the NFL. The problem is that, while it is obvious that there is home advantage (home teams do win more often), it isn't clear why home advantage exists. Cook notes that:

Various mechanisms have been proposed to explain the persistent advantage enjoyed by the home team: direct crowd effects, home crowd influence upon referee decisions, travel hardships for the visiting athletes, unexpected temperature, wind and precipitation shocks may all explain portions of the persistent difference in success between home and visiting competitors.

Cook focuses his attention on the home crowd. However, untangling the effect of attendance on home advantage is difficult, because:

...better home team performance will positively affect demand for stadium attendance, but greater stadium attendance may positively affect home team success at the same time; the two quantities are likely simultaneously determined...

To overcome this problem, Cook leverages the COVID public health mandates, which limited some stadiums to 31,700 fans, while others had zero fans, during the 2020 NFL season [**]. The good thing about this approach is that COVID mandates created sharp constraints on attendance that weren’t driven by team quality or local demand. However, COVID mandates were not the only disruption in 2020, and if any of those other disruptions affected game outcomes directly, the instrument could partly pick those up as well. That said, it’s an plausible instrument and one that that others have used (although in less comprehensive analyses than Cook's).

Cook uses data from the 2009 to 2022 seasons, and uses a binary variable for the 2020 season as an instrument for stadium attendance (and, in separate analyses, as an instrument for how full the stadium was, in terms of percentage of capacity). Cook looks at the impact on a number of variables, including the probability of a home win, home advantage (measured in points differential), total points scored (by the home team, the away team, and both combined), and various measures of penalties (to pick up differences in referee decisions). To deal with travel hardships, Cook includes travel distance (and number of time zones crossed) in the model, while to deal with the weather variables, he initially includes temperature, weather, and precipitation as variables in the model, then estimates models separately for games played indoors (where weather cannot be a factor) and outdoors (where it can).

Cook finds initially that:

The stadium attendance effect on home winning percentage, home field advantage, total points scored and visiting team points scored are significant at the 5% level...

...for every 10000 fans who attend an NFL game, the probability of a home team victory rises by 1.10% and the home field advantage grows by 0.3323 points. When evaluated at the average NFL stadium attendance, 63407 fans, home attendance accounts for 2.11 points (or 97%) of the mean 2.17 point home field advantage observed in the full sample.

The total number of points scored falls by 0.6542 per 10000 fans, but the reduction in aggregate scoring is not shared between home and away teams– instead it is the visiting team who suffers more, scoring 0.4933 fewer points per 10000 fans.

Summing up, home advantage is related to crowd size, and operates primarily through the away team scoring fewer points. Turning to the effect on penalties (and thereby, influence on refereeing crews), Cook finds that:

For every additional 10000 fans in attendance, the total number of penalties rises by 0.2499 total penalties per game. This increase in total penalties is shared equally between the home and visiting teams, however, with home teams receiving 0.1077 extra accepted penalties and visitors an extra 0.1052 extra accepted penalties per 10000 fans in attendance. The effect of attendance on penalty yardage is also comparable, with home teams receiving 0.7461 extra penalty yards and visitors receiving 0.7754 extra yards per 10000 fans in attendance.

There is no home advantage in terms of penalties, so NFL refereeing crews do not appear to be biased towards the home team. At least, not through a mechanism of crowd influence on penalties.

What about travel effects? In an earlier OLS regression, Cook finds that the correlation between the distance the visiting team travelled and game outcomes, and the correlation between the number of west-to-east time zone changes the visiting team experienced and game outcomes, are both small and statistically insignificant.

Turning to weather, Cook's separate analyses between games played indoors, and those played outdoors, reveal that:

When compared to the full sample results, rising attendance in outdoor games no longer has any measurable effect on the probability of the home team winning, nor on home team points scored and the effects on home field point advantage, total points scored and visiting team points scored are all diminished compared to the full sample estimates...

...playing indoors is associated with a larger home field advantage– a much larger advantage. For every 10000 fans in attendance at an indoor game, the probability of a home team win rises by 3.15% and home advantage rises by 0.6227 points– almost double the effect found using the full sample and 243% larger than the attendance effect on home advantage at outdoor games. Evaluated at the mean indoor attendance, 64678 fans, the average home field advantage rises to 4.03 points, or 186% of the average home field advantage observed in the full data sample.

Total points scored falls by 1.412 points, and this decrease is accounted for by a 0.3947 point decrease in home team scoring, but a 1.017 point decrease in away team scoring per 10000 in attendance, suggesting that greater indoor crowd size negatively affects both teams’ scoring output compared to the full sample and outdoor sample results, but affects the visiting side to a much greater degree.

Penalties were similar between indoor and outdoor games. What we learn from these results is that the home advantage is not driven by the weather, because it is bigger when weather is not a factor (in indoor stadiums). So, going back to the list of explanations for home advantage that Cook begins with, he has eliminated home crowd influence upon referee decisions (no differences between home and away teams), travel hardships for the visiting athletes (not statistically significant), unexpected temperature, wind and precipitation shocks (the home advantage is bigger when games are played indoors). That only leaves direct crowd effects, unless we are missing something. Cook concludes that:

In the absence of any detectable NFL referee bias, these results suggest that it is the NFL home stadium crowd itself that is directly affecting the on-field performance of the home and visiting athletes. Despite a lack of data tracking in-match noise intensity, given the acoustic differences between indoor and outdoor stadiums, this effect is likely related to crowd noise levels.

That conclusion will certainly please many fans attending NFL games, who really believe that they have a direct impact on team performance. The 12th Man is real!

Should my Panthers be worried? Based on these results, they should be somewhat worried about the crowd, but not as much as for some other opponents. Raymond James Stadium is outdoors, and although Cook found no significant effect on the probability of the home team winning, there was still an (albeit smaller) effect on home advantage measured in points. The betting odds have the Panthers as 2.5-point underdogs. With a 70,000-capacity stadium, Cook's results for outdoor games imply that 1.8 points [***] of that spread comes from the home advantage.

Let's go Panthers! Keep pounding!

*****

[*] Although, if the Bucs beat the Panthers and then the Atlanta Falcons beat the New Orleans Saints the next day, the Bucs, Panthers, and Falcons will all finish with a record of 8-9. Due to round-robin results between those three teams, the Panthers win the division. Hopefully, a Falcons win won't be necessary!

[**] It was eerie to watch that season, with 'simulated' crowd noise for the stadiums that had no fans present.

[***] The coefficient of 0.2563 points differential is for each 10,000-person increase in attendance. The difference between 0 and 70,000 attendance is 7 times the coefficient, or 1.7941.

Ask not what economics can do for sports; ask what sports can do for economics

Regular readers of this blog will know that I enjoy blogging about research that uses a sports setting to illustrate economic concepts (except when the research is terrible). Sport makes for an interesting setting for testing economic theories. The rules are known. The incentives are usually clear. The outcomes are usually unambiguous. Other real-world settings don't provide the same clarity. This matters because sports can tell us something about real-world behaviour that lab experiments can’t. And essentially, that is one of the points that Ignacio Palacios-Huerta (London School of Economics) makes in this new review of the literature, published in the Journal of Economic Literature (ungated earlier version here).

As a researcher, Palacios-Huerta has frequently exploited sports data (and has a book using data from football, Beautiful Game Theory, which makes some of the same points as this review, but with a narrower focus on football, or soccer). In this review, Palacios-Huerta argues that:

...many sports settings are in fact natural experiments that “happen to occur” and provide evidence that is as direct and convincing as controlled experiments... And yet other settings offer such a clean environment for identification that they seem designed as a perfect vacuum for measuring theoretical postulates. The precise knowledge of participants’ goals and rules and the clear observability of strategies, incentives, actions, and consequences in these settings is indeed rare in other field settings.

Mainstream economics mostly ignores sports as a source of data and a test of theories. Palacios-Huerta notes that this is limiting scientific progress in economics:

A reluctance to view sports settings from this perspective may reflect a deep misunderstanding of the virtues of sports data. And this reluctance has discouraged the study of these settings and slowed down the production of knowledge in economics and other social sciences.

The review then provides a wide review of specific examples where sports data has informed tests of economic theories. The range of theories is too broad to note in full here, but encompasses things like game theory, risk and uncertainty, behavioural economics, market design, labour economics, discrimination, technological change, and lots of examples of the roles of incentives. The variety of sports that provide the data is also vast, including football (of all kinds), golf, chess, basketball, baseball, motor racing, and even biathlon and gymnastics. Surprisingly, there is no mention of cycling, athletics, or swimming. My only disappointment is that Palacios-Huerta doesn't draw on e-sports (although they do make an appearance in the appendix to the paper). He could also have given a nod to game shows, which provide similar benefits to sports (and are also a favourite topic for me to blog about).

If you're looking for data to test a particular theory, sports might help. But sports can offer more than just data: they can generate new insights into theory itself. As Palacios-Huerta notes in the conclusion to the review:

...sports settings offer more than unparalleled opportunities for measurement, verification, and falsification; they are unique from the perspective of a key component of science that is largely ignored: discovery... Ironically, one of the main benefits of the excessive highbrowism that sports have endured is that they remain an important and largely unexplored setting for discovering new phenomena and hypotheses.

The opportunities that sports offers for economists are broad, and sports data are underutilised. And, economics research that uses sports as a setting can have broader appeal as well. Hopefully, economists are listening.

Read more:

• The increasing role of economics in sports, and teaching sports economics

This Kansas City Chiefs conspiracy theory article is a mess

I have to admit to experiencing a non-trivial amount of schadenfreude this year, as the Kansas City Chiefs find themselves with a losing record in December for the first time in a decade. My mild animosity towards the Chiefs is based entirely on their supreme performance over that decade. After they've had a few losing seasons, I won't care anymore (which is how I feel about the Patriots right about now). However, there are plenty of people who have griped about the Chiefs, and claimed that the Chiefs receive favourable referee calls.

I'd label that a conspiracy theory, but it has apparently caught the attention of researchers. This recent article by Spencer Barnes (University of Texas at El Paso), Ted Dischman (an independent researcher), and Brandon Mendez (University of South Carolina), published in the journal Financial Review (sorry, I don't see an ungated version online), explicitly tests whether the Kansas City Chiefs receive favourable referee calls. Specifically, Barnes et al.:

...compare penalty calls benefiting the Mahomes-era Kansas City Chiefs (from 2018 to 2023) and the Brady-era New England Patriots (2015–2019) across the regular and postseason...

Barnes et al. argue that:

...financial pressures, particularly those related to TV revenue (the primary source of revenue for the NFL), serve as the underlying mechanism.

In other words, Barnes et al. claim that the NFL has a strong financial incentive to bias officiating in favour of the 2018-2023 Kansas City Chiefs, to a greater extent than any bias in favour of the 2015-2019 New England Patriots. As we’ll see, the empirical strategy is poorly chosen, parts of the results are misinterpreted, and the proposed TV-revenue mechanism is implausible. All up, you shouldn't believe this paper's results.

What did they do? Barnes et al. use play-by-play data covering the 2015 to 2023 seasons. They restrict their attention to defensive penalties only, which gives them a sample of 13,136 penalties across 2435 games. They apply a fairly simple linear regression model to the data:

Here we find the first problem with their analysis. If you want to show that the Mahomes-era Kansas City Chiefs benefited from more defensive penalties than other teams, you should be running a difference-in-differences analysis. Essentially, you compare the difference between the Chiefs and other teams, between the period before and the period after Patrick Mahomes started playing. In other words, you should test whether the Chiefs’ advantage in penalties grows after Mahomes started playing, compared with their earlier advantage and with other teams over the same period. Barnes et al. simply test for a level difference between the Chiefs and other teams during that time (using the 'Dynasty' variable), but fail to account for whether the Chiefs might already benefit from more defensive penalties before Mahomes became the starting quarterback (in 2018). Indeed, Figure 1 in the paper shows that the Chiefs did benefit from more defensive penalties per game before 2018:

That difference prior to 2018 should be controlled for. Having said that, the difference from the rest of the NFL teams looks bigger from 2018 onwards (but mostly concentrated in 2018-19, and in 2023), so if they had used the more correct difference-in-differences model (or, when comparing regular and post-season, a triple-differences model), they might still have found a statistically significant effect.

There is a further, albeit more minor, issue with the analysis. Barnes et al. control for 'defensive team fixed effects', which they argue controls "for differences in how opposing teams play defense and how frequently they are penalized". However, teams change the way they play defence, particularly when the defensive coordinator changes. So really, they should have used defensive-team-by-season fixed effects there, which would allow the way a team plays (and gets penalised) to vary from season to season, and control for that.

Barnes et al. look at the effect on several outcome variables:

Our primary dependent variables capture different dimensions of officiating decisions. The first is Penalty Yards, which measures the total yards gained or lost due to penalty calls. If the NFL or its officials favor a particular team, we expect them to benefit from potentially more penalty yards assessed against their opponents. The second variable, First Down, is a binary indicator that takes a value of 1 if a penalty call results in an automatic first down. Because first downs have a direct impact on a team’s ability to sustain drives and score points, this measure captures whether penalties disproportionately help a team advance the ball. The third variable, Subjective, is a binary indicator equal to 1 if the defensive penalty falls into a category requiring referee discretion...

The 'Subjective' variable is described in the appendix to the paper, and appears to be far too inclusive since it includes penalties like 'Face Mask' and 'Horse Collar Tackle' that seem to me not to be particularly subjective (and those two categories alone made up 6 percent of all penalties, and a much higher proportion of the 'subjective' penalties).

Putting aside the issues with the analysis for a moment, Barnes et al. find that:

...penalties against Kansas City during the regular season result in 2.02 fewer yards (𝑝 < 0.01), are 8 percentage points less likely to have a penalty call that results in a first down (𝑝 < 0.01), and are 7 percentage points less likely to have subjective penalties (𝑝 < 0.05) compared to the rest of the NFL. This pattern is decisively reversed in postseason contests, where penalties against the Chiefs offense yield 2.36 more yards (𝑝 < 0.05), are 23 percentage points more likely to have a penalty call that results in a first down (𝑝 < 0.01), and are 28 percentage points more likely to have subjective calls (𝑝 < 0.01) compared to the rest of the NFL in the playoffs.

Barnes et al. have explained this incorrectly. Notice their wording suggests the penalties are called on Kansas City (i.e. hurting the Chiefs). Their analysis actually shows that penalties against Kansas City Chiefs' opponents result in 2.02 fewer yards during the regular season, and penalties against Kansas City Chiefs' opponents (not the Chiefs offense) yield 2.36 more yards in the postseason. At least, that is according to the notes to their Table 3, which says:

The dependent variable in Columns (1) and (4) is the realized yardage for the offensive team resulting from a penalty on the defensive team... The independent variable of interest, Kansas City Chiefs, is a binary indicator variable that equals 1 if the offensive team is the Kansas City Chiefs and 0 otherwise.

So, the correct way of interpreting those results is penalties against the opposing defence, not penalties against Kansas City. Barnes et al. then turn to applying the same analysis to the 2015-2019 New England Patriots, and find effects that are mostly statistically insignificant (and small). For other teams that might arguably be called a 'dynasty' (for a sufficiently low bar for what constitutes a dynasty, Barnes et al. find no evidence of differences in defensive penalty calls. That sample includes the Philadelphia Eagles (2017-2023), the Los Angeles Rams (2018-2023), and the San Francisco 49ers (2019-2023).

At this point, the problem with the mechanism starts to become clear. Barnes et al. start to look at TV viewership, and argue that:

If certain teams, particularly those associated with high-profile players, systematically attract larger audiences, then maintaining the success or visibility of those teams may align with the league’s broader financial interests.

If the NFL wanted to attract a larger audience, and aimed to do so by biasing officiating in favour of a particular team, why on earth would they choose a small market team like Kansas City? Surely they would want to boost a large-market team? According to this ranking, Kansas City is only the 35th-largest sports media market in the US. Now, Patrick Mahomes is a star quarterback (he was the 10th overall pick in the 2016 NFL draft), so maybe it's the combination of star quarterback and media market that matters. However, Tom Brady was also a star quarterback, and Boston is the 10th-largest sports media market. So, why weren't the Patriots getting favourable calls in 2015-2019? If, as Barnes et al. seem to argue, the NFL was going through some particular challenges in 2016, then Kansas City is still not the obvious choice for biased officiating. They should have favoured the LA Rams (in the second-largest sports media market, with star quarterback Jared Goff, the first overall pick in the 2016 NFL draft).

Barnes' et al.'s argument falls apart. Their TV viewership analysis does show that:

...the Chiefs’ emergence as a marquee team coincided with a material increase in viewership interest, consistent with the broader financial incentives we hypothesize.

However, that analysis also has issues, because they don't control for the win/loss record of the teams in each game (and winning teams likely attract more TV viewers). And, all it really tells you is that Patrick Mahomes attracts a big TV audience. He is a good player. That's what they do. Higher ratings for teams with star players is not evidence that referees are biased. As noted above, if the NFL thought that way, they should have preferred biasing the officiating towards the LA Rams instead, and Barnes et al.'s analysis shows that didn't happen.

As a final point, there is a real risk that the analysis in this paper gets causality backwards. Did the Chiefs get favourable referee calls because they are a dynasty, or did they become a dynasty because they received favourable referee calls at key moments? Barnes et al. never consider the possibility of reverse causality. Overall, the paper does much more to flatter an existing conspiracy theory than to seriously test it. Even if we take their estimates at face value, nothing in the paper convincingly links referee calls to incentives to increase NFL TV viewership.

[HT: Marginal Revolution]

The lifespan benefit of being elected to the MLB Hall of Fame

There is a clear difference in life expectancy between the rich and the poor (see this post, for example). However, disentangling how much of the life expectancy differential is a causal effect of socioeconomic status on mortality is difficult, because there are so many things that affect both socioeconomic status and mortality. This recent article by Chengyuan Hua and Brad Humphreys (both West Virginia University), published in the journal Economics Letters (sorry, I don't see an ungated version online), takes an interesting approach to answering the question.

Hua and Humphreys look at lifespan of professional baseball players, comparing those that have been elected to the MLB Hall of Fame with those who narrowly missed out on election. The idea is that election to the Hall of Fame increases socioeconomic status, and so comparing those who were elected and those who were not but are otherwise similar, means that the difference attributable just to the change in socioeconomic status can be identified.

In relation to election to the Hall of Fame, Hua and Humphreys note that:

Baseball players elected to the HoF must appear on 75% of the annual ballots cast, get removed from the ballot after appearing on fewer than 5% of ballots, and can only appear on a limited number of consecutive ballots...

The exogenous 75% election threshold permits a fuzzy regression discontinuity design (RDD) to identify the causal effect of HoF election on longevity.

Their dataset:

...includes the universe of candidates eligible for HoF induction from 1936 to 2024. We divide the sample into two groups: a treatment group of 131 players voted into the HoF while alive and a control group of 1067 players nominated by the BBWAA but not inducted.

Comparing the two groups, Hua and Humphreys find that:

...HoF members live 1.97 years longer than HoF nominees.

Hua and Humphreys go on to look at possible mechanisms that might explain the lifespan benefit of Hall of Fame election. They find that:

...HoFers are 5.8 p.p. more likely to become an MLB manager... MLB managers lived 2.86 years longer than their counterparts. We interpret this as evidence that HoFers are more likely to become MLB managers, a high-paying occupation.

In other words, Hua and Humphreys argue that the mechanism is that higher socioeconomic status leads to a better paying occupation, which in turn leads to longer lifespan. Of course, it could be more likely that healthier players are more likely to become managers, so the RDD approach isn't as clean in terms of identifying the mechanism. Nevertheless, it is plausible.

Now, what these results tell us more broadly about socioeconomic status and lifespan is unclear. Baseball players are very different from the general population. The sample here is both unusually affluent and unusually healthy, before we even consider the effect of raising their socioeconomic status. At best, these results tell us something about groups at a similar prior level of affluence and health.

Nevertheless, the implications for professional baseball players are clear. It's Hall of Fame or bust (two years earlier)!

Don't expect to see a Danish Grand Prix any time soon

Big events are fun, and draw in large crowds. But by itself, that doesn't mean that big events are worth the cost. Someone, often but not always taxpayers, has to be willing to pay the cost of hosting. A rational decision-maker would only be willing to host the event if the benefits outweigh the costs. This is a point that I'll be teaching in my ECONS102 class next week, so I was interested to read this recent article by Christian Gjersing Nielsen (Danish Institute for Sports Studies), Søren Bøye Olsen (University of Southern Denmark), and Arne Feddersen (University of Copenhagen), published in the Journal of Sports Economics (sorry, I don't see an ungated version online).

Nielsen et al. focus on the case of a return of the Danish Formula One Grand Prix (which was last held in 1962, although a Danish Grand Prix for Formula Three cars was last run in 1995). They focus on this because:

In 2017, a Danish consortium of private investors presented a plan to host a Formula 1 (F1) Grand Prix... in Copenhagen in 2020, 2021, and 2022.

Ultimately, the plan fell through because it required government funding, and while the national government seemed supportive, but only if the Copenhagen City Council contributed financially. The Council ultimately withdrew its support for the event, and the idea never progressed. Nielsen et al. ask whether the Copenhagen public would actually have been willing to fund the costs of the event, which are significant:

...hosting an F1 Grand Prix in Copenhagen would cost approximately €58 million (adjusted to 2023 prices) annually, including salaries (€15.5 million) and temporary stands (€14 million)... plus an additional annual fee of between €14 million and €50 million for hosting to the rights owners, Liberty Media Corporation...

Nielsen et al. undertook a survey of Copenhagen residents, asking a hypothetical question about their willingness to pay (WTP) for a Grand Prix to be hosted in Copenhagen. Specifically:

Respondents were then asked to imagine that Liberty Media had approved Copenhagen hosting F1 in 2026, 2027, and 2028 and that the private and government funding was already in place. To make hosting conditioned on their response, they were also told that Copenhagen would only accept hosting the race if enough taxpayers would support a temporary municipal tax increase at the household level... Following this, respondents were randomly assigned to two groups. The first group was told that the tax amount that they would have to pay if Copenhagen ended up hosting F1 would depend on their household income... Respondents assigned to the second group did not receive this information and were instead asked to state their household income in the latter part of the survey...

This is an application of the contingent valuation method (which is quite a polarising method, with many debates that I have written about, most recently here). Their sample is about 2000 people, once they exclude 'protest' responses, and just 1452 in their preferred 'weak knife-edge' sample - those who were responsive to a difference in the cost of hosting the event. Based on their range of samples, Nielsen et al. find that:

...mean annual WTP (in the 3 years that Copenhagen hosts F1) estimates between €22.95 and €36.94, while the weighted models result in mean WTP estimates between €24.34 and €43.07, with €30.24... as our central estimate due to the theoretical considerations about consequentiality... Extrapolating our mean WTP estimates to the 320,825 households in Copenhagen Municipality, the aggregated annual WTP (in each of the 3 years that Copenhagen hosts F1) is between €7.36 million and €13.82 million, with €9.70 million (n=1,452, weighted) being our central estimate.

This compares unfavourably with the costs. Specifically:

...the public costs—ignoring indirect or intangible costs—would amount to between €14.4 and €21.6 million annually. Based on our central mean estimate of €9.70 million, the benefits for the households in Copenhagen make up between 44.9% and 67.4% of the public costs, which does not justify hosting F1.

The Copenhagen public are not willing to pay enough to cover the costs of hosting a Grand Prix. So, don't expect to see a Danish Grand Prix any time soon.

Penalty shootouts and first-mover advantage

I enjoyed watching the UEFA Nations League final on Monday. Spain and Portugal put on a good show, and the scores were tied at 2-2 at the end of extra time. The game went to a penalty shootout. Portugal had the first penalty shot, and eventually ended up winning the shootout 5-3, after Portuguese goalkeeper Diogo Costa saved a weak shot by Alvaro Morata.

Would the result have been different if Spain had taken the first penalty shot? There certainly is conventional wisdom that says that going first in a penalty shootout conveys an advantage (a first-mover advantage in game theory terminology). The argument is that, because the team going second is often trying to come from behind, that team faces more pressure than the team going first.

However, the evidence in favour of that conventional wisdom has been challenged, most recently and most thoroughly in this new article by David Pipke (Kiel Institute for the World Economy), published in the Journal of Economic Psychology (open access). Pipke looks at the outcomes of 7116 penalty shootouts from 1970 to 2024, across top leagues and international competitions. He then tests whether the outcome deviates from a random outcome (in which the team kicking first wins 50 percent of the time). He finds that:

In soccer, the first-kicking team wins 50.2 % of the time (p =0.785) across 7,116 matches in the Flashscore data.

So, there is no statistical evidence for a first-mover advantage in penalty shootouts in football (soccer). Pipke then turns to ice hockey, which also features shootouts but where the probability of a successful shot in a shootout is much lower. Using data from 4407 shootouts in North American ice hockey leagues over the period from 2010 to 2024, Pipke finds that:

In ice hockey, the first team wins 48.9 % of shootouts (p =0.148)...

It's closer to statistical significance, but not quite. There is no evidence for a first-mover advantage in ice hockey shootouts either. Pipke then notes that his statistical tests can:

...reject the hypothesis that the first-mover’s winning probability deviates by more than 1.6 percentage points in soccer... and 2.9 percentage points in hockey from a 50:50 split, at a 1 % significance level.

Pipke then looks at some subsets of the football data, and finds that:

In 342 women’s soccer competitions, the first-moving team wins 172 times (50.3 %, p = 0.957). In youth soccer shootouts, the first-kicking team prevails in 130 out of 277 cases (46.9 %, p = 0.336).

Second, between 2017 and 2019, an alternative format, where teams alternate in an A,B,B,A pattern, was tested in various competitions to address concerns about an inherent advantage of kicking first. In 44 shootouts following this sequence, the first-kicking team won 56.8 % of the time (25 shootouts), with no statistically significant deviation from a 50:50 split (p = 0.451).

So, overall, there is no evidence of a first-mover advantage in a penalty shootout (in football or ice hockey). The result may have been different if Spain had gone first in the UEFA Nations League final penalty shootout, but going first wouldn't have given Spain a statistical advantage.

Read more:

• Game theory and the penalty shootout
• More on game theory and the penalty shootout
• How not to strategise for penalty kicks

The economic impact of the 2000 Sydney Olympics

Economic impact studies are typically used to justify large sporting events. However, those studies typically apply a set of overly positive assumptions, leading to large overestimates of economic impact. Andrew Zimbalist even wrote a book about this problem, Circus Maximus (which I reviewed here).

Now, it is rare for the authors of an economic impact study to go back and revise their estimates. So, it was refreshing to read this 2011 article by James Giesecke and John Madden (both Monash University), published in the journal Economic Papers (sorry, I don't see an ungated version online). Madden was one of the authors of the official (1999) economic impact study for the 2000 Sydney Olympic Games (when he was at the Centre for Regional Economic Analysis at the University of Tasmania), which is available here. That report presents a central estimate of an increase in household real consumption of $3.125 billion for NSW and $3.7 billion for Australia as a whole (and in a 'resource-constrained' scenario, the corresponding figures are $2.4 billion for NSW and $2.1 billion for Australia). In this new article with Giesecke, Madden revisits the analysis.

First, using data on actual tourism flows from 1997/09 to 2005/06, they find that:

...our historical modelling results do not provide any indication of an induced tourism effect associated with the 2000 Olympics.

In other words, there was no long-lasting impact of the Olympics on tourism, so any impact from tourist spending was only during the period of the Olympics. Then, they impact the earlier analysis based on actual spending on construction, and actual tourist numbers and spending, and advertising and sponsorship rights. Interestingly (and unsurprisingly), in terms of tourist spending:

In our study, the total of direct expenditures related to the Games is $5.5 billion... This is $2.9 billion less than the CREA⁄ Arthur Andersen (1999) report. The difference is mainly induced visitor spending. The CREA⁄ Arthur Andersen (1999) report contains $2.7 billion of such spending.

So, tourist spending at the time of the event was 'only' about $200 million less than originally projected in the 1999 report. The outcome of the analysis is that:

...the Sydney Olympics generated a loss in Australian real private and public consumption in present value terms of $2.1 billion. This suggests that the Olympics did not bring the economic stimulus that has been claimed by ex ante analysis.

In other words, Australian (and especially NSW) consumers were made worse off (in terms of consumption) by Sydney hosting the Olympics. I wish there were more studies like this, that revisited the economic impact analyses of large events, using actual data after the fact. Then, perhaps, we would start to see more realistic assumptions being employed in the ex ante analyses (sadly, I feel like you could make a Tui billboard with that sentiment).

Of course, the negative impact of the Sydney Olympics isn't the end of the story. You can think of the loss of private and public consumption as being the net cost of hosting they Olympics, which could be offset if there were sufficient un-measured (perhaps intangible) benefits of hosting. Giesecke and Madden note that:

This does not necessarily mean that Australia should not have hosted the Games. An Olympic Games is a great international sporting event that brings much enjoyment to a large number of people around the globe. For the population of the host nation increased utility can arise from factors such as national-pride effects, consumer surplus on local ticket sales, the advantages of the Games being held in one’s own time zone (an advantage shared by countries with a similar longitude) and so on...

These benefits, like enjoyment and increase utility for Australians, are not quantified. The Olympics is a party. It makes people happy (especially if they're winning, which is something that host countries are more likely to do). Happiness and good vibes are not easily measured in dollars, so at that point you can't conduct a strict cost-benefit analysis. However, you can try to evaluate whether the extra good vibes are worth the cost, just like you might for any party, even a giant national party. It was an expensive party though!

[HT: This article in The Conversation by John Madden, back in 2023]

Read more:

• Tim Hazeldine on economic impact studies
• Beware economists bearing impact studies of the America's Cup
• Even less reason to believe in the economic impact of the America's Cup
• The overstated impact of the Super Bowl
• The economic impact of the 2010 World Cup in South Africa

The deadweight loss of free beer

My excellent (and sports-mad) colleague Shaen Corbet shared with me a story about the Nebraska-Northwestern college football game played in Ireland last year. As reported in the Irish Mirror:

But what couldn't be predicted was the events in the Aviva Stadium on Saturday night as technical glitches saw thousands upon thousands take advantage of free food, drink and alcohol.

There was always going to be a party atmosphere for the first Aer Lingus College Football Classic since 2019, a momentous occasion to remind us just how lucky we are to have these events back.

But the Aviva Stadium was rocking like a Harry Styles gig from just a few weeks prior as queues went a dozen deep as match attendees fleeced the concession stand and bar in a one time only offer of everything being free.

A Twitter (ok, X, but it was Twitter then) user posted this video of the queues for beer, where you can see that the entire foyer area in front of the bar is jam-packed with spectators looking for free beer. Usually, if the price is reduced to zero, we would expect to see a shortage. That's because the sellers would want to sell less (because it is less profitable) at the same time that the buyers are wanting to buy more.

However, in this case, the government chose to subsidise the beer (Shaen tells me it was to reduce the chance of unruly fans getting out of control). We can see the effect of this subsidy, reducing the price to zero, using a supply and demand model as shown below. If the beer market was operating in equilibrium, the price would have been P0, and the quantity of beer traded Q0. Instead, the government paid a subsidy to the beer sellers. We demonstrate this on the diagram with a new curve, S-subsidy, which is below the supply curve S by the amount of the subsidy (which was exactly enough to lower the price from P0 to zero). The effective price for the beer sellers increases to PP, which is the zero price they receive from the spectators, plus the per-unit amount of the subsidy. The quantity of beer demanded increases to Q1, and so does the quantity of beer supplied. There is no shortage of beer.

It is worth considering the impacts on economic welfare of this subsidy though. Consumer surplus is the difference between the amount that consumers are willing to pay (shown by the demand curve), and the amount they actually pay (the price). In the diagram, at the equilibrium price and quantity, consumer surplus is the triangle AEP0. Producer surplus is the difference between the amount the sellers receive (the price), and their costs (shown by the supply curve). In the diagram, at the equilibrium price and quantity, producer surplus is the triangle P0EB. Total welfare is the sum of the two areas (consumer surplus and producer surplus), and is equal to the triangle AEB.

Once the subsidy is introduced, the consumer surplus increases to AQ1O, while the producer surplus increases to the area BCQ1O. The government loses the area of subsidy, which is the rectangle PPCQ1O (this rectangle is the per-unit amount of the subsidy, multiplied by the quantity of subsidised beer). Total welfare is the sum of consumer surplus and producer surplus, minus the subsidy (the subsidy is subtracted because it has an opportunity cost of lower government spending in other areas), and is equal to the area AEB-ECQ1 [*]. In other words, total welfare is lower by ECQ1 as a result of the subsidy. This is the deadweight loss of the subsidy.

To add insult to injury, even though the price of beer may have been zero, the cost of beer was not free. That's because you have to factor in the cost of the time spent waiting to be served (which will be much higher when the queues are longer), as well as the loss of enjoyment of missing part of the game while waiting for beer. Plus, there are external costs of over-drinking imposed on other fans. Shaen, who was at the game, tells me that there were spectators who vomited all over other spectators after over-indulging in 'free' beer. So, free beer wasn't necessarily a good deal for everyone, least of all for Irish taxpayers and for those who needed a dry-cleaner (and possibly a counselling session) after the game.

[HT: Shaen Corbet]

*****

[*] The overlapping areas of consumer surplus, producer surplus, and subsidy make this tricky to see. However, there is a shortcut. The area of total welfare is the area that is in-between marginal social benefit (MSB) and marginal social cost (MSC) out to the quantity that is traded (in this case, Q1). When MSB is greater than MSC, this represents positive welfare (the area AEB). But when MSB is less than MSC, this represents negative welfare (the area BCQ1).

The Tour de France, public goods, and the chicken game

I finally finished watching this year's Tour de France on Sunday. Yes, I was a week behind. That's because I was overseas when it started, and it took me that long to catch up (with big thanks to Sky On Demand!). Jonas Vingegaard well deserved his win. The individual time trial he rode on Stage 16 was amazing to watch (even if his team Jumbo Visma says so themselves).

Anyway, this is a blog about economics. Sports provide lots of great examples of economics in action, because economics is ultimately about choices, and so are sports. One striking example of economics in action in cycling road races occurs when there is a breakaway, and it is getting close to the finish line. The riders in the breakaway face a difficult choice. They can ride hard at the front of the breakaway, ensuring that the breakaway won't be caught by the peloton, and one of the breakaway riders will surely win the race. Or they can hold back, riding in the slipstream of the rider who is riding at the front, which lets them conserve energy for a sprint finish, but at the risk that the peloton catches them.

This exact scenario played out in Stage 18 of the Tour de France this year, with three riders approaching the finish. Victor Campenaerts rode hard towards the finish, ensuring the breakaway would succeed. However, it was Kasper Asgreen who won the stage, having conserved his energy for the final sprint among the breakaway riders.

Let's think about the incentives for a breakaway rider. Riding hard is a public good. It is non-rival (one cyclist benefiting from a rider riding hard at the front of the breakaway doesn't reduce the amount of the benefit available for the other riders in the breakaway) and non-excludable (if a rider is riding hard at the front of the breakaway, they can't easily prevent the other breakaway riders from sitting in their slipstream and conserving their energy).

Public goods, like riding hard at the front of the breakaway group, suffer from a free rider problem (pun intended!). Other riders can benefit from the front rider's hard work, without paying any of the cost themselves. It is difficult for a rider to justify riding hard at the front if other riders are unwilling to contribute, since they face all of the cost of riding hard, but the benefit (in terms of a better chance of winning the race) goes to the other riders (the free riders).

Ordinarily, the provision of public goods breaks down. They cannot be privately provided, because of the free rider problem. In this case though, cycling has developed norms that ensure some cooperation within the breakaway group. The riders tend to take turns at the front of the breakaway group, helping to increase the chances of success. However, the closer the race gets to the finish, the greater the incentives to free ride become. Regular cycling fans will no doubt remember many instances where a breakaway group has been caught, within sight of the finish line, because they failed to work together.

Another way of thinking about the incentives within a breakaway group is to use game theory. To make the problem simpler, let's say that the breakaway group only consists of two riders, and there are two strategies: (1) to ride hard; or (2) to hold back. We'll assume each rider makes their decision just once, and they make their decisions at the same time (a simultaneous game).  The payoffs for this scenario are shown in the table below. If both riders ride hard, they have a 50% chance of winning the race (since they will both be equally tired). If one rider rides hard and the other holds back, the rider that holds back wins the race for sure. If both riders hold back, then they are caught by the peloton, and neither of them wins (and they don't even finish in the top two in the race). What will happen?

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If Rider B chooses to ride hard, Rider A's best response is to hold back (since winning for sure is better than a 50/50 chance of winning) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Rider B chooses to hold back, Rider A's best response is to ride hard (since losing and finishing in the top two is better being caught by the peloton and finishing much lower in the order);
3. If Rider A chooses to ride hard, Rider B's best response is to hold back (since winning for sure is better than a 50/50 chance of winning); and
4. If Rider A chooses to hold back, Rider B's best response is to ride hard (since losing and finishing in the top two is better being caught by the peloton and finishing much lower in the order).

In this scenario, there are no dominant strategies. Neither rider has a strategy that is always better for them, no matter what the other rider chooses to do. However, there are two Nash equilibriums (outcomes where both players are playing their best response), which occur when one rider rides hard, and the other holds back. Neither rider will want to be the rider that rides hard, so both may be holding out hoping that the other rider will ride hard. This is the free rider problem described earlier. This game is an example of the chicken game (which I have discussed here). If both riders hold back, hoping that the other rider will ride hard, both riders will be caught by the peloton.

The chicken game is an example of a coordination game. To end up at one of the equilibriums (or another), the players need to coordinate their actions. However, in this case neither rider really wants to coordinate on the other rider's preferred equilibrium. Both really want to hold back, especially closer to the finish line, which is why the breakaway can often be caught.

Riders are motivated by the chance to win the race. That is why breakaway groups form in the first place. However, the incentives outlined above work against the breakaway succeeding. And riders are aware of these issues. One thing that often happens is that, towards the end of a race, one rider will ride especially hard, breaking away from the breakaway group. There is no free rider problem when a rider is riding by themselves. Sadly, solo breakaways are seldom successful (except on mountain stages), because the effort required to remain clear from a group of breakaway riders who suddenly become more motivated to work together and catch the solo breakaway rider is very high. The solo breakaway rider is often caught, after which the chicken game and free riding begins again.

One thing that can increase the success of a breakaway is to have multiple teammates in the breakaway group. Teammates are more likely (but not certain) to be able to coordinate their strategies, and work together, reducing the free riding problem. That's why riders in the peloton are more vigilant and energetic in chasing down an early breakaway group that has multiple riders from the same team. Most of the time, a breakaway group will only go clear if every rider in the group is from a different team. Riders in the peloton don't want the breakaway to succeed, and having all breakaway riders from different teams decreases the chance that a rider from the breakaway wins the race.

There is a lot of strategy in sports, and cycling is no exception. There are also a lot of choices for athletes to make, and choices involves trade-offs. That, along with the transparent rules and the obvious goals of the athletes involved (they want to win), is why sports can provide a lot of useful illustrations of economic concepts.

The effect of banning indoor mass gatherings on the spread of COVID-19

One of the first responses that many governments enacted during the coronavirus pandemic was limiting or banning mass gatherings like sporting events, concerts, conferences, and weddings. But how effective were those measures in reducing the number of coronavirus infections and subsequent mortality? In a recent article by Alexander Ahammer, Martin Halla, and Mario Lackner (all Johannes Kepler University), published in the journal Contemporary Economic Policy (open access), we get an answer. Ahammer et al. make use of a cool natural experiment:

We quantify how NBA and NHL games have contributed to the early spread of COVID‐19 in the United States... We analyze how much games held between March 1 and March 11 have contributed to the community spread of COVID‐19 in counties surrounding NBA and NHL venues. Since the game schedules were determined long before the first COVID‐19 case became public, their spatial and temporal distribution should be unrelated to the initial spread of COVID‐19 in the US...

Specifically, Ahammer et al. look at how the number of NBA and NHL games (combined) between 1-11 March 2020 relate to the cumulative number of coronavirus cases and deaths as of 30 April 2020 (6-8 weeks later) in the county that hosted the games, or neighbouring counties. They find that:

...that each additional mass gathering between March 1 and 11 increased cases by 269 per million and deaths by approximately 15 per million population. These are substantial effects. Compared to the average case and death rates across the counties in the data, our estimates correspond to increases of 9.2% and 10.3% per game, respectively. Both estimates are statistically significant at the 1% level.

When they run separate models for cumulative cases (and deaths) as at each day from 13 March to the end of April, where:

...we expect effects to be strongest around 3 weeks after the shutdown. This is precisely what we find. The effect of games starts to pick up around March 19 and increases at a decreasing rate since then. This is true for both cases and deaths. Furthermore, we see that cases respond sooner than deaths, which makes sense given the natural lag between diagnosis and death. In terms of magnitudes, estimates for COVID‐19 deaths (cases) range between 0.002 (0.367) on March 13 and 15.195 (269.131) on April 30.

And, in case you're wondering:

If we split our treatment variable and count NBA and NHL games separately, we find that games in both leagues positively affect COVID‐19 spread...

Finally, when they stratify their analysis, they find that:

These effects are larger in densely populated areas and in colder regions.

No surprises there. The obvious conclusion overall is that limiting or banning mass gatherings was an effective strategy in arresting the spread of coronavirus. Ahammer et al. conclude that:

...banning indoor mass gatherings has an enormous potential to save lives. This is especially important given that such measures are relatively easy and cheap to implement.

Their results don't necessarily extend to outdoor gatherings, but at least we have some surety now of the effectiveness of one of the early tools that governments employed during the pandemic.

How not to strategise for penalty kicks

In game theory, a pure strategy is an unconditional choice of strategy for a player. In other words, the player chooses that strategy for sure. That distinguishes it from mixed strategy, where the player randomises their actions, choosing each of the possible strategies with some probability (which might be zero). There are lots of examples of mixed strategies. One that I use in my ECONS101 class is the choice for a tennis player over whether to serve down the middle, into the body, or out wide. If they chose one strategy for sure, they would reduce their chances of winning. Instead, they should randomise - sometimes choosing the first strategy, sometimes the second, and sometimes the third.

Another example from sports is the penalty kick in football (or soccer, if you prefer). The penalty taker must choose which side to kick towards, and the goalkeeper must choose which way to defend. I've discussed this game and the mixed strategy equilibrium before (see here and here).

The key problem with mixed strategy is that it genuinely involves randomisation. You cannot reason a pure strategy solution to a mixed strategy game. If you do, you end up with something like this:

I'm not sure where the video comes from (TV or movies, or something else), but it is very similar to a story related in the book Soccernomics, by Simon Kuper and Stefan Szymanski (as Robbie Butler notes here). The solution to mixed strategy games is not to try and solve them with pure strategy, but to randomise.

[HT: Jadrian Wooten at Critical Commons, via the Economics Media Library]

Read more:

• Game theory and the penalty shootout
• More on game theory and the penalty shootout

Home crowds and home advantage

It is well known that, in most if not all sports, there is a sizeable advantage to playing at home. However, it isn't clear exactly what mechanism causes this home advantage to arise. Is it because when a team (or individual sportsperson) is playing at home, they don't have to travel as far, and are refreshed and comfortable at game time? Or, is it because the team (or individual sportsperson) is more familiar with the home venue than their competitors are? Or, is it because of home fan support?

Previous research has found it very difficult to disentangle these different mechanisms as being the underlying cause of home advantage. Cue the coronavirus pandemic, which created an excellent natural experiment that allows us to test a range of hypotheses, including about home advantage in sports. Since fans were excluded from stadiums in many sports, if home advantage was no longer apparent, we can at least rule out home fan support as being a contributor to home advantage.

And that is essentially what the research reported in this new article by Jeffrey Cross (Hamilton College) and Richard Uhrig (University of California, Santa Barbara), published in the Journal of Sports Economics (open access), tries to do. Specifically, they look at four of the top five European football leagues (Bundesliga, La Liga, Premier League, and Serie A), all of which faced a disrupted 2019-20 season, and after the disruption resumed play with restrictions that prevented fan attendance at games. Essentially, they compare home team performance before and after the introduction of the no-fans policy. Their preferred outcome variable is 'expected goals' rather than actual goals scored. Cross and Uhrig justify the choice as:

Due to randomness, human error, and occasional moments of athletic brilliance, the realized score of a match is a noisy signal for which team actually played better over the course of 90 minutes. In order to mitigate this noise, we focus on expected goals, or xG, which measure the quantity and quality of each team’s chances to score; they have been shown to better predict future performance and more closely track team actual performance than realized goals... Expected goals are calculated by summing the ex ante probabilities that each shot, based on its specific characteristics and historical data, is converted into a goal... For example, if a team has four shots in a game, each with a scoring probability of 0.25, then their expected goals for the match would sum to 1. However, their realized goals could take any integer value from 0 to 4...

Their data goes back to the 2009-10 season, and includes some 15,906 games in total. However, they only have data on expected goals from the 2017-18 season onwards, which includes 4,336 games. Because the games with no fans were played later than usual, the temperature was higher (as the season was extending closer to summer), so they make sure to control for weather, as well as for the number of coronavirus cases.

Looking at realised goals, Cross and Uhrig find that:

...raw home field advantage decreased by 0.213 goals per game from a baseline of a 0.387 goals per game advantage for the home team... This represents a decrease of 55%.

But, as they argue, this is quite a noisy measure of home advantage. So, they turn to their measure of expected goals, and find that:

...raw home field advantage, as measured by expected goals instead of realized goals, decreased by 64% from a 0.307 expected goal advantage for the home team to just 0.110 expected goals. Although the magnitude of the decrease is smaller than realized goals in absolute terms (0.197 xG as opposed to 0.213 G), it represents a larger fraction of the initial home field advantage (64% as opposed to 55%) because the initial home field advantage is smaller as measured by expected goals than realized goals.

Finally, looking at game outcomes, they find that:

...the lack of fans led to fewer home wins and more home losses, but the probability of a draw is unaffected, suggesting that fans are symmetrically pivotal: fans are approximately as likely to shift a result from a draw to a home win as they are from a home loss to a draw... Approximately 5.4 percentage points are shifted from the probability of winning to the probability of losing.

So, coming back to the question we started with, at least some of the home advantage that football teams experience is due to home crowd support. Given that home advantage decreased by somewhere between 55 percent and 64 percent, the share of home advantage that home crowd support is responsible for is sizeable. Of course, this doesn't necessarily extend to all sports. But it does show that home crowd support is important.

NFL owners' rational response to the anthem protests

One of the most memorable aspects of the 2016 NFL season was the national anthem protests. Starting with Colin Kaepernick in a preseason game for the 49ers, players chose to remain seated, to kneel, to raise their fists, or to stay in the locker room, during the playing of the national anthem, in order to protest racial inequality. The anthem protests sent President Trump into something of an apoplectic frenzy. However, ultimately Kaepernick paid a high price for his protests, as he wasn't offered a contract by any other team after opting out of his 49ers contract at the end of the season. But did teams also pay a price for the protest actions of their players?

That is the question addressed in this recent article by Noah Sperling and Donald Vandegrift (both College of New Jersey), published in the Journal of Sports Economics (sorry, I don't see an ungated version online). Specifically, Sperling and Vandegrift look at the effect of protests on TV viewership, for the following game. The reason for looking at TV viewership, rather than game attendance, is:

Though attendance captures actions rather than attitudes, attendance as an outcome measure is still flawed. Stadium capacities impose an inherent upper bound on attendance and tickets are often purchased months in advance. Thus, attendance is unable to track short-term, weekly changes in demand.

They focus on the following game to overcome two timing issues with the TV viewership data:

Given that Nielsen ratings are calculated based on average ratings over an entire game, it is difficult to determine if the observed rating is capturing the full effect of the protest behavior. It is possible that this averaging could be capturing disgruntled viewers who were unable to change the channel in time following a protest and thus they are counted as a viewer for purposes of the rating. Other situations could include an anti-protest viewer who failed to notice the protest during the game and only became aware of the action from media reporting following the game’s conclusion. The same concerns apply to the viewership-in-millions measure which is also averaged across the span of the entire game.

Sperling and Vandegrift also distinguish between two 'levels' of protests:

Unambiguous protests include any protests in which a player kneels or sits during the national anthem, stays in the locker room during the national anthem, or raises a fist during the national anthem. By contrast, ambiguous protests include all other player protests (e.g., locking arms with teammates during the national anthem)...

They find that:

...(1) the unambiguous protests reduce viewership in the week following the protests by about 15% while ambiguous protests do not generally produce statistically significant reductions in viewership; (2) the negative effect of unambiguous protests on viewership is particularly strong in metro locations that voted more heavily for Donald Trump in 2016; and (3) following Donald Trump’s statements in week 3 of the 2017 season, both ambiguous and unambiguous protests increased and the increase in ambiguous protests was particularly large.

That put the profit-maximising NFL team owners in a difficult position. The protests negatively affected TV viewership, which (if the protests continued) would be sure to negatively impact future revenues that the NFL (and team owners) would receive from TV broadcast contracts. Sperling and Vandegrift note in the conclusion that the increase in protests following President Trump's statements in 2017:

...taken together with: (1) subsequent negotiations between players and owners over the anthem protests; (2) the willingness of some owners to join players in less objectionable forms of protest; and (3) the May 2018 agreement to “stand and show respect for the flag and the anthem” (Haislop, 2020), suggests that the owners advanced or supported the ambiguous protests to rebut arguments that they sought to suppress the players’ expressive rights while they pursued actions to curtail unambiguous protests that threatened their income derived from TV broadcasts.

The owners responded in a very carefully constructed way that would ensure that their profits were maintained. They supported ambiguous protests, which ensured that the protests had virtually no effect on TV viewership (and future team revenue). However, letting the players continue to protest (albeit in an ambiguous way) kept the players happy and willing to continue to play for the team. Such rational owners!

The endowment effect in the trading of professional sports draft picks

If we believe that decision-makers are loss averse (and until recently, that seemed reasonably clear), then one consequence of loss aversion is the endowment effect. The explanation is fairly simple. When people are loss averse, they value losses much greater than otherwise equivalent gains. Giving something up therefore makes people very unhappy, and so people prefer to hold onto the things that they have. That means that, when a person owns something, they have to be given much more to compensate them for giving it up than what they would have been willing to pay to get it in the first place.

With the NFL regular season starting later this week, I was interested to read this new article by Jeff Hobbs (Appalachian State University) and Vivek Singh (University of Michigan), published in the journal Economic Inquiry (open access), because it looked at the endowment effect in professional sports. Specifically, Hobbs and Singh investigate whether draft picks in the NBA, NFL, and NHL over the period from 1988 to 2017 demonstrate an endowment effect. Their data set includes nearly 17,000 draft picks. For a little more context for those unfamiliar with professional sports drafts, Hobbs and Singh explain that:

Every year, each of the major professional sports leagues in the United States holds what is known as its “entry draft.” During the entry draft the teams select, in inverse order of success from the previous season such that the worst teams get the first picks, amateur players with a view toward signing them to professional contracts. In most of these leagues, teams can trade draft picks (before they are used to select players) at least as freely as they can trade players who are already under contract.

So, teams are initially endowed with a certain number of draft picks. They can choose to keep those picks (which they can use to select young players who are eligible to be drafted), or they can trade picks to other teams (and those teams can use the picks instead). Teams trade picks for a variety of reasons, often trading picks for players. Teams can also trade picks that they themselves acquired in some other trade. However, the nature of the trade doesn't matter for Hobbs and Singh's analysis. They are only interested in whether teams are more or less likely to trade draft picks that they originally endowed with, than other draft picks.

To do this, they look at what happens after a pick is first traded. If there is an endowment effect, then the team that originally had the pick should be less willing to trade than a team that acquired the pick in a trade. They do this by comparing the proportion of times that a traded pick is 're-traded', compared with the pick just before or just after that pick in the draft order. They find that:

After we control for the frequency of selling, we find that non‐endowed picks for all three leagues combined were 12%-15% more likely to trade again than were their adjacent, endowed counterparts from the same point in time afterward. These results are statistically significant, but we notice some differences when we look at each league individually. Regardless of whether we attempt first to match the once‐traded pick with the pick directly below it or above it, the results for the NFL become insignificant. However, the results for the other two leagues remain significant in both a statistical and economic sense. In the NBA, the average once‐traded and non‐endowed pick is between 24.5% and 29.2% more likely to trade afterward than is its match. In the NHL, the once‐traded, non‐endowed pick is between 14.8% and 23.6% more likely to trade.

In other words, there is a substantial endowment effect for draft picks in the NBA and NHL, but it appears not for the NFL. However, Hobbs and Singh aren't willing to let the NFL off completely, noting in their conclusion that:

The relative rationality of the NFL documented here pertains only to the endowment effect with respect to the trading of draft picks; other studies have found examples of other irrationalities in professional football.

Fair enough, but it seems like a bit of a cheap shot. I'm sure there's a lot of other irrationalities in basketball and hockey as well. As one example, the endowment effect probably doesn't just play out in the draft. It is likely to be present when considering free agent players as well (as I noted in this 2017 post). The sabermetrics revolution may have increased the use of analytics in sports, but it doesn't appear to have eliminated quasi-rationality entirely.

Read more:

• Free agents, the draft, and the winner's curse

Online elite chess and cognitive performance during the pandemic

Does remote working increase productivity, or decrease productivity? The pandemic forced a lot of workers into remote working, so perhaps this natural experiment can give us some idea of the impacts of remote working. Do we gain more from avoiding commuting time, greater flexibility over work time and workspace, and fewer interruptions from colleagues, than we lose from reduced interaction, supervision and structure (in addition to whatever other effects might happen in either direction)? Despite the hype, the results so far are far from clear, especially in terms of what types of jobs or work improve in a remote setting.

An interesting new article by Steffen Künn, Christian Seel (both Maastricht University), and Dainis Zegners (Rotterdam School of Management), published in The Economic Journal (open access) provides a contribution towards answering those questions. Künn et al. look at the impact of the shift to online of elite chess tournaments. Specifically:

Our data consist of games from the World Rapid Chess Championships 2018–2019, played offline in Saint Petersburg and Moscow, and from the Magnus Carlsen Chess Tour and its sequel, the Champions Chess Tour, both played online from April to November 2020 on the internet chess platform chess24.com... the majority of players (20 out of 28) in the online tournaments also competed in at least one of the World Rapid Chess Championships in the years 2018–2019, enabling us to make within-player comparisons of performance for each of these 20 players.

Künn et al. measure the performance of each chess player for every move in every one of those tournaments (with a few exceptions, and excluding the first fifteen moves for each player in each game), relative to one of the top chess engines. As they explain:

To estimate the effect of playing online on chess players’ performance, we evaluate each move in each game in our sample using the chess engine Stockfish 11... 

For a given position in game g before individual move mig, the chess engine computes an evaluation of the position in terms of the pawn metric Pigm... The numerical value of the pawn metric indicates the size of the advantage from the perspective of player i, with one unit indicating an advantage that is comparable to being one pawn up...

Künn et al. use this evaluation to generate a measure of 'raw error', being the difference in the pawn metric between the player's choice of move, and the 'optimal' move as determined by Stockfish. They then compare this raw error between play in online tournaments and play in face-to-face tournaments, for the same players. They find that:

...playing online leads to a reduction in the quality of moves. The error variable... is, on average, 1.7 units larger when playing online than when playing identical moves in an offline setting. This corresponds to a 1.7% increase of the measure... or an approximately 7.5% increase in the RawError... The effect is statistically significant at the 5% level.

The effect is quite sizeable:

Playing online increases the error variable, on average, by 1.7 units, which corresponds to a loss of 130 points of Elo rating.

In reading the paper, my first thought was that the results would be contaminated by the psychological effects of the pandemic. Fear or anxiety could easily lead to suboptimal performance, and cause the observed increase in error, rather than reduced performance in the online format per se. However, Künn et al. anticipate this in their robustness checks, noting that:

...to mitigate concerns that results are related to the pandemic, we add a control variable to the regression model to capture the severity of regulations implemented in a player’s home country during the tournament times... Although the aggregate online dummy reduces in size and significance (p-value of 0.172), presumably because lockdowns occurred only during the online tournaments, the effect pattern on the separate tournament dummies remains almost identical relative to the main results...

That doesn't quite allay my concerns, for two reasons. First, it assumes that all players react similarly to the local pandemic context, since it assumes all experience the average effect on their performance. That average effect is statistically insignificant. Second, including the pandemic variable renders the impact of online play statistically insignificant. Part of the problem is that the pandemic is happening at the same time as the switch to online play (for obvious reasons). Clearly, the natural experiment is not sufficient to disentangle the effects of online play from the effects of the pandemic. That really limits what we can learn from this study.

Finally, and interestingly, the negative effects (if we accept that there are some) decrease over time. As Künn et al. note:

...the negative effect of playing online on the quality of moves is strongest for the first (and second) online tournament. Thus, the adverse effect of playing online on the quality of moves decreases over time, possibly because players adapt to the remote online setting...

Perhaps the players have adapted to the online setting, or perhaps they have adapted to the pandemic, or perhaps the pandemic is becoming less severe over time. Given that we can't disentangle the effects of pandemic or online setting, we can't really tell.

I'm not trying to pick on this study, which uses an interesting setting to try and estimate the impact of remote work, in a case where performance can be measured reasonably accurately and consistently. In theory, that should provide as clean a measure of impact as we can find. However, once you recognise the problem in this study, it is easy to see why it would be even more difficult to use the pandemic natural experiment where the data on performance are not as clear.