England’s Chelsea lost the 2008 Champions League final to Manchester United on penalties when taking the shots second. Did United deserve to win? Were they just lucky? Or is the penalty shootout system bluntly unfair? FIFA’s European soccer governing body UEFA is suspecting the unfair hypothesis   . UEFA conjectures the teams taking the first penalty have a biased advantage, as they win 60 percent of shootouts. This possibly happens because the player taking the second kick is under greater mental pressure   . On purely theoretical grounds, it can be demonstrated that the current mechanism of the soccer penalty shootout is not sequentially fair  -  .
In the current penalty shootout system, teams take turns in a shootout, with the choice of who goes first decided by a coin toss. Team A goes first, then team B, then team A again. This is an ABAB pattern, where one side has allegedly the pressure of going second. FIFA thinks a change is needed to stop the team going second from having to play catch-up. One possible solution is to adopt the tennis tiebreak format, which follows an ABBA pattern. Team A is followed by team B, before team B goes again. Team A would then get two successive penalties, and so on until there is a winner. A coin would still be tossed to decide who goes first.
This work takes data from the penalty shootout of soccer and explicitly contrasts them with data from the tiebreak of tennis. Although FIFA claims a 60 percent advantage for the team going first, it does not show that the tiebreak of tennis is unbiased. Here, we show FIFA is right regarding soccer, and the tiebreak data do show one cannot say that the tennis system favors who goes first.
Section 2 presents the data used in the study and shows the results found, and Section 3 concludes the report.
2. Data and Results
We diligently collected data from the 2017 Grand Slam tennis tournaments as one of the matches progressed in order to spot 345 tiebreak situations (Table 1). We examined both men’s and women’s singles matches. Data from Table 1 were used to test whether a tiebreak winner is biased to the player who serves first. We expected that would not occur because of the ABBA pattern.
In contrast, we expected the first player in a soccer penalty shootout to have an advantage because of the ABAB pattern. To test this, we meticulously gathered data from the internet to find 232 penalty kick situations in several soccer matches from 1970 to the present day (Table 2).
As for the tiebreak, 163 players ended up as winners after serving first. This equates to 47.25 percent. However, before one can jump to the conclusion that it is better not to serve first, it can be said this result was not statistically significant. Based on a chi-square test, as a winning probability of 0.5 could not be rejected ( , p-value = 0.306), we could not conclude there was an advantage by serving first in our data sample. This result matches those in the previous literature   .
As for the penalty shootout, 138 teams ended up as winners after having the first penalty kick. This equates to 59.48 percent and, considering again the chi-square test, a winning probability of 0.5 was rejected ( , p-value = 0.004). This allowed us to conclude that it was significantly greater than 0.5. If one considers r to be the quantity of goals scored by a team starting the penalty shootout, and s the scores of the other team, then one has 232 bivariate observations (r, s) drawn from a conjoint distribution function , where R and S denote the corresponding random variables (Table 3). The null hypothesis of interest is that R and S are exchangeable, which translates into no effect by going first. This hypothesis of exchangeability can be written as , for all (r, s). In addition, one can
Table 1. Selected situations of tiebreaks for the 2017 grand slam tennis tournaments.
Table 2. Selected situations of soccer penalty kicks.
Table 3. Observed quantity of goals scored by a team starting the penalty shoutout, r, and the scores of the other team s.
consider the null hypothesis, , for every difference d. Considering Hollander’s test of bivariate symmetry  for , the RFPW test of symmetry  for , and Wilcoxon’s signed rank test for , we found a statistically significant piece of evidence against such null hypotheses with p-values 0.0001, 0.0013, and 0.00000003, respectively. Thus, it pays to start a penalty shootout.
In sum, it does not matter who begins in tennis tiebreak, but it does matter in soccer penalty shootout.
In a sample of 345 tennis tiebreak situations and 232 soccer penalty kick situations, we found the current ABAB system of soccer to be biased in that the team going first has a 59.48 percent advantage to end up as the winner. This figure is close to the 60 percent reported by FIFA. The tennis ABBA system does not exhibit the bias in our sample, as in the previous literature. This means FIFA is not wrong in suggesting the penalty shootout should adopt the tennis tiebreak format.
“Football (soccer) is a simple game,” former English player Gary Lineker once said. “Twenty-two men chase a ball for 90 minutes and, at the end, the Germans always win,” he added. As for penalty shootouts, the Germans are famed for their penalty-spot prowess after winning five shootouts at major finals (have another look at Table 2 and at Ref.  ). By adopting the tennis tiebreak system, FIFA would then give no grounds for a cold war in football.
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