US Open

Home Advantage in Individual Sports

Undoubtedly, playing away from home always adds an extra difficulty in team sports. The home advantage is commonly accepted across fans and athletes. Terms for expressing the importance of the home crowd in an exhibition, such as the 12th man (Football) or the 6th man (Basketball), are widely known. But can the same be anticipated for individual sports, too? Do the home fans hold a major role in the performance of an athlete?

Abstract

In various studies, statistical analyses support the popular belief in the advantage of playing at home, even though this advantage has only been demonstrated for team sports. The current research investigates whether performance in individual sports is affected by the presence of home crowds. The home advantage in such sports is evaluated via three segments (tennis, weightlifting and free throw shooting). Data analytic tools were also employed to quantify the extent of the home advantage in such sports.

Introduction

Regarding team sports, there is a general agreement that the home team has an advantage as the supporters encourage their own players and at the same time prevent the opposition players from performing at their maximum potential. However, the extent of the home advantage varies, starting from relatively low proportions in baseball (54%) and reaching up to 62% in basketball and football.

Generalizations about individual sports are much less common and literature is rather scarce. Therefore, the goal of this report is to investigate whether there is an actual home advantage in individual sports as well as quantify its extent.

The two individual sports examined throughout this report are weightlifting and tennis. Both of them are widely known and appealing to the audience, which is a criteria that has to be met as we are discussing the effect of this particular crowd on the performance of the athletes; sports with a small audience may inhibit the so called home advantage.

The third part concerns the free throw percentage and is defined as an embedded effort. An embedded effort is considered as an individual performance where the player’s teammates cannot help him. In basketball, for example, a player must take his free throws all by himself. All of the factors that might affect the team can also play a role in individual efforts embedded in them: the same home crowd, the same officials, the same fatigue or family disruption, even the same players.

Data Collection & Methodology

Three different approaches for the three sports mentioned above were used in order to examine the dependence of wins on participating in a set of home matches competition.

Regarding weightlifting, only the final phase of the Olympic Games was taken into consideration, with the main assumption that all 8 athletes participating in the final possess of equal skills. In other words, their past atomic records and previous performances in the qualifying stages were not considered to have a significant effect on the final stage. The categories examined were 85 kg, 69 kg and 62 kg for men and 53 kg, 63 kg and 75 kg for women. Data was collected from the Sydney Olympics (2000) until Rio Olympics (2016).

For tennis, the Grand Slam of 2017 was selected to study the effect of home crowd on the success of the athletes. The Grand Slam tournaments, also called majors, are the four most important annual tennis events. Majors consist of the Australian Open in mid January, the French Open in May and June, Wimbledon in July, and the US Open in August and September.

All major team sports have a balanced home and away schedule. On the other hand, individual sports rarely are characterized by this balance. As a consequence, it is essential and necessary to take individual player ability into account when assessing home advantage over this type of sports. The Wimbledon Championship was not examined at this report as the mean ranking of the British players was very low and no reliable results could be derived.

Success in the Grand Slams was evaluated by how far a player progressed in it. The tournament winner was ranked 1, the losing finalist 2, the losing semifinalists 3.5, which is derived from the average position of the losing participants [i.e. (3+4)/2], the losing quarterfinalists 6.5 [(5+6+7+8)/4], etc. For technical reasons, log tournament ranking was regressed on log world ranking; and the regression was done separately for home and away players. Home advantage was indicated if the curve for the home players lay numerically below that for the away players, that is, more toward the more advanced rounds of the competition.This approach had been used by Alan Nevill during his experimental research in 1996, and is followed at the current report as well.

When it comes to basketball, data was collected from 3 NBA Regular seasons (2015, 2016 and 2017). To reduce the extent of the research, only 7 teams out of 30 were accounted for free throw rates in regular season games between 2015 and 2017, but they were equally distributed (final ranking of teams chosen  was 1st,2nd, 14th,15th,16th,29th, 30th respectively) to minimize individual potential effect.

Results & Discussion

I. Weightlifting Analysis

Adopting Carron’s approach, a win percentage in a competition over than 50% is considered to indicate the existence of the home advantage, even in the analysis of individual sports. Below, the mean rankings of all the athletes participated on the final stage of the Olympic weightlifting are displayed. Note that in 2012 in London, no British athlete managed to book a place at the final stage, and for that reason a zero ranking was granted. On the other hand, all Chinese athletes from the formerly mentioned 6 categories had managed to get the gold medal in the Beijing Olympics.

 

It can be observed that the mean ranking for home competitors in this 5 Olympic Games period is close to 4.1 out of 8 contenders. In other words, their winning ratio is approximately 49%, indicating that no explicit boost in the performance occurs. The former statement could be attributed to the high level of the participating athletes, who possess abilities that could actually minimize the home advantage effect.

 

II. Tennis Analysis

As stated earlier, regression analysis can be used to detect any home advantage associated with competitors representing the host country compared to their visiting counterparts (away competitors). Having log-transformed both the result rankings and the world rankings, the recommended procedure is the saturated model, which actually produces two regression lines (home and away) and tests their homogeneity.

Regarding the US Open championship, the graph illustrates that no home advantage is visible and therefore should not be accounted for in this particular occasion. The regression line has values for b0 and b1 0.56351 and 0.67341 for all away competitors, while for the home performance the values are 3.8515 and -0.1741, respectively. The curve of the away athletes lies numerically lower than the home one, meaning that visitors often perform better than home competitors. However, it has to be mentioned that the trend of these curves indicate a home advantage but for very low-ranked athletes, that would possibly never attend this kind of event.

To continue, the Australian Open again has no indication of the existence of the home advantage. The regression line has values for b0 and b1 0.4376 and 0.3975 for all away competitors, while for the home performance the values are 1.537 and 0.10537, respectively. The home curve lies above the away curve and, like the US Open, home competitors are not expected to thrive based only to the crowd support they get, but probably due to their own skills and abilities.

Moreover, the French Open follows the same trend with the US open but with a major difference; the home curve lies below the away one when athletes are medium ranked (position ranking above 16th). The regression line has values for b0 and b1 0.5926 and 0.7564 for all away competitors, while for the home performance the values are 3.431 and -1.4081, respectively. The former observation reveals a correlation in performance of French athletes when playing at their country as long as these athletes are not ranked in the top 15.

III. Free Throws Analysis

When a visiting player in the NBA steps to the foul line to attempt a free throw, the hometown crowd behind the backboard frequently erupts in sound and distracting motions; his opponent in the same situation playing at home is allowed to shoot in comparative peace. It seems inevitable that the player at home would convert a higher proportion of his attempts than the visiting player would of his. The facts, however, do not indicate this assumption.

T-test could provide a question to whether home actually plays a role when it comes to accuracy of free throws. The null hypothesis is that shooting in home does not differ from shooting away from it. For a significance level of 5%, the p-value is calculated around 0.32. This number supports the null hypothesis; there is no statistical relationship between home and away performance regarding free throws. Again, this absence of home advantage in NBA free throw shooting could be explained by the high level of skill of NBA players. It is derived that NBA athletes have learned to ignore any crowd attempt to disrupt their in-game concentration.

Conclusion

To sum up, the home advantage in individual sports was investigated in this research via 3 sports: tennis, weightlifting and free throws. The results had shown that, as opposed to team sports, home supporters do not have a significant influence in any of the former mentioned activities. However,  in the case of the French Open home advantage seems to have an effect on athletes’ performance, but only for those who are ranked below the 15th position of ATP World rankings.

 


Biblography

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As an engineer I have learned that it is not only about deriving the result but also explaining it. In Statathlon I found the unique opportunity to combine mathematics with my other passion, football, and strive to describe the phenomena that rule it.

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