In February 2020, an Australian rugby fan produced a study, claiming to show how South African rugby referees were exhibiting favorable bias towards South African home teams. The study did not consider how other countries’ referees treat South African home teams, an important comparison that needs to made before any conclusion can be drawn. Yet, the unvetted study was reported by sports journalists from all over the Southern Hemisphere, leading to calls for official inquiries. The study’s conclusions are shown to be unfounded. Yes, this is about 6 months late; we’ve all been a little preoccupied.

2020年2月，一名澳大利亚橄榄球迷进行了一项研究，声称要展示南非橄榄球裁判员如何表现出对南非主队的偏见。 这项研究没有考虑其他国家的裁判员如何对待南非主队，这是在得出任何结论之前需要进行的重要比较。 然而，这项未经审查的研究是南半球各地体育记者的报道，导致要求进行正式调查。 研究的结论被证明是没有根据的。 是的，这大约晚了6个月； 我们全神贯注。

Earlier in the year, an Australian rugby fan, Rebels3, produced a study that presumes to show how South African referees favored South African teams playing at home in the Southern Hemisphere’s Super Rugby tournament. While it is a solid preliminary study and certainly deserving of a deeper look, the conclusions drawn from it are premature. Yet, sports reporters from across the Southern Hemisphere were only too keen to publish the fan’s data, as shown in these examples:

今年早些时候， 澳大利亚橄榄球迷Rebels3进行了一项研究 ，推测该研究表明南非裁判员如何偏爱南非人在南半球的超级橄榄球锦标赛中主场比赛。 虽然这是一项扎实的初步研究，并且当然值得更深入的了解，但从中得出的结论还为时过早。 但是，南半球各地的体育记者都热衷于发布球迷的数据，如以下示例所示：

• Study shows huge bias by ‘home’ refs towards South African teams in Super Rugby

  研究显示，“主场”裁判对超级橄榄球中的南非球队有极大的偏见

• Super Rugby boss denies referee bias despite alarming statistics

  超级橄榄球老板否认裁判偏见尽管统计数据令人震惊

• Super Rugby: SA teams favoured by home referees — study

  超级橄榄球：SA球队受到主裁判的青睐-研究

At least one brazenly worded open-letter was sent to the CEO of SANZAAR, the body that oversees Super Rugby. The hype around the unfounded conclusions prompted Australia’s rugby franchise executives to call for an official inquiry.

至少有一个措辞大胆的公开信被发送给监督超级橄榄球的机构SANZAAR的首席执行官。 对毫无根据的结论的炒作促使澳大利亚的橄榄球特许经营主管要求进行正式调查 。

All of this for a fan’s unvetted spreadsheet.

所有这些都是粉丝未经审查的电子表格。

For context, Super Rugby (at least until the coronavirus pandemic) is a tournament between up to five teams each from Australia, New Zealand, and South Africa. Recently one team each from Argentina and Japan joined the tournament. Each team’s schedule is split more-or-less evenly between home and away matches. The tournament’s professional referees are are not required to be neutral, a matter at the heart of the alleged problem. The term “neutral” is being used to describe a referee officiating a match in which neither the home nor away teams are from the same country as the ref.

就背景而言， 超级橄榄球赛(至少在冠状病毒大流行之前)是多达五支来自澳大利亚，新西兰和南非的球队之间的比赛 。 最近，来自阿根廷和日本的一支队伍参加了比赛。 每个队的日程安排在主场和客场比赛之间大致相同。 比赛的专业裁判不需要中立，这是所谓问题的核心。 “中立”一词用于描述主持比赛的裁判，在比赛中，主队和客队都不与裁判员来自同一国家/地区。

原创粉丝研究 (Original Fan-study)

The table below shows how the fan-study sampled different groups of matches.

下表显示了粉丝研究如何采样不同的比赛组。

The below bar-chart shows each group’s average penalty difference, the metric used in the fan-study. The penalty difference is simply the difference between the penalties awarded against the home and away teams.

下面的条形图显示了每个组的平均惩罚差异，即球迷研究中使用的度量。 罚金的区别就是对主队和客队的罚款之间的区别。

The chart shows an Australian home team with an Australian referee, on average, was penalized 0.5 fewer times than their foreign opposition between 2017 to 2019. A New Zealand home team with a compatriot referee received 0.1 fewer penalties. These two figures are in stark contrast to the fact that South African home teams refereed by a South African were penalized 3.5 fewer times than their overseas rivals. This large difference is what drives the the idea that South African referees have a demonstrable bias toward South African teams.

图表显示，在2017年至2019年之间，有澳大利亚裁判的澳大利亚主队平均受到的处罚比他们的外国对手少0.5倍。有同胞裁判的新西兰主队受到的处罚少0.1％。 这两个数字与南非主队推荐的南非主队被罚比海外对手少3.5倍的事实形成鲜明对比。 这种巨大的差异驱使人们认为南非裁判对南非队有明显的偏见。

The fan study only considered the years 2017 to 2019, but if we expand the range to 2009 to 2019 (there is no Super Rugby penalty count data before 2009) we see a similar picture:

粉丝研究仅考虑了2017年至2019年，但如果将范围扩展到2009年至2019年(2009年之前没有超级橄榄球罚球数数据)，我们会看到类似的图片：

Again, this is a sound preliminary study, or maybe the first step of a preliminary study, and Rebels3 is clearly onto something. But, to know what that something is, one needs to dig deeper.

再次，这是一个完善的初步研究，或者一个初步研究的第一步，Rebels3显然是到一些东西 。 但是，要知道这是什么，就需要深入研究。

球迷研究忽略其他裁判员如何对待南非队 (Fan-study Ignores How Other Referees Treat South African Teams)

This is where the misunderstanding happened. People saw the dissimilarity in average penalty differences and immediately jumped to the conclusion that South African referees unfairly favor South African teams.

这就是误会发生的地方。 人们看到了平均罚款差异的差异，并立即得出一个结论，即南非裁判不公平地偏爱南非队。

However, the study only makes comparisons between Australian home matches officiated by Australians, New Zealand home matches officiated by New Zealanders, and South African home matches officiated by South Africans. What it doesn’t do, is compare South African home matches officiated by different groups of referees, for example. This is a huge oversight. Obviously, we cannot say South African referees favor South African home teams if we haven’t even looked at how other referees treat South African home teams. It’s completely possible that referees from other countries favor South African home teams to a similar or even greater extent (foreshadowing).

但是，该研究仅对澳大利亚人主持的澳大利亚主场比赛，新西兰人主持的新西兰主场比赛和南非人主持的南非主场比赛进行了比较 。 例如，它没有做的是比较由不同裁判组主持的南非主场比赛。 这是一个巨大的疏忽。 显然， 如果我们甚至不看其他裁判如何看待南非主队 ， 就不能说南非裁判更喜欢南非主队 。 来自其他国家/地区的裁判员完全有可能以相似甚至更大的程度偏爱南非主队(前锋)。

The problem can be more formally expressed in terms of the study’s variables.

可以根据研究变量更正式地表达问题。

In each of Rebels3’s groupings, not one variable is kept constant. With such distinct groups and uncontrolled variables, it would be incredible if the fan-study didn’t show a difference between the groups. How can one conclude that referee nationality, and not any of the other variables, is responsible for the dissimilarity in penalty difference? Such a conclusion would indeed be highly premature and unfounded, given the limited information we have so far.

在Rebels3的每个分组中，没有一个变量保持恒定。 拥有如此独特的群体和不受控制的变量，如果粉丝研究没有显示出群体之间的差异，那将是不可思议的。 如何得出一个结论，认为裁判员的国籍而不是其他任何变量是造成罚金差异的原因？ 鉴于我们到目前为止所掌握的信息有限，这样的结论确实是非常不成熟和毫无根据的。

In any experiment or study, to test any single variable, we need to keep the others as constant as possible, a sentiment voiced in the forum where this study first appeared. So, to test if a referee’s nationality really is a factor, we need to break our referees into different nationality groups, much like Rebels3 did. But, we need to control the variables we aren’t testing, as in the below table. The setup in the table below isn’t in conflict with or even an alternative to Rebels3’s study, but rather its natural next step.

在任何实验或研究中，要测试任何单个变量，我们都需要使其他变量尽可能保持不变 ，这是本研究首次出现的论坛中表达的一种观点 。 因此，要检验裁判员的国籍是否确实是一个因素，我们需要像Rebels3一样将裁判员分为不同的国籍组。 但是，我们需要控制未测试的变量，如下表所示。 下表中的设置与Rebels3的研究没有冲突，甚至没有替代方案，而是下一步的工作。

In controlling the variables we aren’t testing, we are able to say with more surety that the independent variable, referee nationality, is or is not a significant factor in the dissimilarity between each groups’ penalty difference.

在控制我们未测试的变量时，我们可以更有把握地说，独立变量(裁判国籍)是或不是影响各组处罚差异之间差异的重要因素。

In other words, as previously said, before we can know if South African referees are treating South African home teams differently, we need to see how other groups of referees treat South African home teams.

换句话说，如前所述，在我们知道南非裁判员对南非主队的待遇不同之前，我们需要了解其他裁判员如何对待南非主队。

进一步分析 (Further Analysis)

Let’s do just that. Let us keep the home team South African and the away team not South African, while breaking the referees into five clearly defined groups:

让我们开始吧。 让我们保留主队南非人和客队而不是南非人，同时将裁判员分为五个明确定义的组：

• neutral Australian
  中立的澳大利亚人
• neutral New Zealand
  中性新西兰
• non-neutral Australian
  非中性澳大利亚人
• non-neutral New Zealand
  非中性新西兰
• non-neutral South African
  非中性南非

Since the home team is always South African in this case, there can be no neutral South African referees.

由于在这种情况下主队始终是南非人，所以不能有中立的南非裁判。

Looking at the chart below, we see that all groups of referees favor the South African home team, albeit marginally in the case of non-neutral New Zealand referees. However, there is one group that favors South African home teams more than any other. And it’s not the South African referees.

从下面的图表可以看出，所有裁判组都偏爱南非主队，尽管对于非中立的新西兰裁判来说，这是微不足道的。 但是，有一个团体比其他任何人都更喜欢南非主队。 不是南非的裁判。

On average from 2009 to 2019, South African referees penalized South African home teams 3.1 times fewer then the non-South African away teams (2017-2019: 3.5). However, the non-neutral Australian referees’ penalty difference was 4.1 in favor of the South African home team (2017-2019: 6). It’s simply impossible to conclude that the South African referees' penalty difference is proof or even evidence of unfair bias when the Australian referees penalty difference favors South African teams even more.

从2009年到2019年，南非裁判员平均对南非主队的处罚是非南非客队的3.1倍(2017-2019年：3.5)。 但是，非中立的澳大利亚裁判员的罚分差为4.1 ，这对南非主队是有好处的(2017-2019： 6 )。 当澳大利亚裁判员的罚款差异更偏爱南非队时，不可能得出南非裁判的罚款差异是不公平偏见的证据甚至证据。

Taking that a step further, using the groups from the above chart, the South African referees’ average penalty difference was closest to that of the neutral referees (see bar charts above and below). So, not only is it unfounded to claim that South African referees favor South African teams, but there is evidence that South African referees may be the least biased when officiating non-neutral matches in South Africa.

再往上走一步，使用上表中的组，南非裁判的平均罚分差最接近中立裁判的罚分(请参见上方和下方的条形图)。 因此，不仅声称南非裁判员偏爱南非队是没有根据的，而且有证据表明，在主持南非的非中立比赛时，南非裁判员的偏见最少 。

结论 (Conclusion)

Blaming the ref is as old as sports officiating itself. As is usual in such cases, there simply is no evidence to justify the claim that South African Referees are biased towards South African teams.

责怪裁判与体育裁判一样古老。 在这种情况下，像往常一样，没有证据证明南非裁判员偏向南非队。

To reiterate, there is no problem with the original stats presented by Rebels3, if taken for what they are: part of a preliminary study, drawing attention to a potential issue. The real problem with this scenario is how the story was blown out of proportion without being properly examined. Andy Marinos, the CEO of SANZAAR, showing calm leadership, said it best in his response to the outcry,

重申一下，Rebels3提出的原始统计数据按其原样是没有问题的： 初步研究的一部分，引起人们对潜在问题的关注。 这种情况的真正问题在于，如何在不进行适当检查的情况下将故事夸大。 SANZAAR的首席执行官Andy Marinos表现出镇定的领导力，他最好的回应是对抗议的回应 ，

“We need to validate those numbers and we need to put a proper picture in place, which is something we will do and respond in due course. It’s very interesting that the whole neutrality thing comes up when we’ve been a merit based system for 10 or 12 years. You’ve got to take a lens as to where it’s coming from. In terms of statistics, people are always producing statistics. At the right time we will communicate our view in terms of where we are from a competition perspective and the performances of our referees.”

“我们需要验证这些数字，并且需要适当摆放图片，这是我们会做的并在适当时候做出回应。 有趣的是，当我们已经成为基于绩效的系统10或12年时，整个中立事物就会浮现。 您必须了解镜头的来源。 在统计方面，人们总是在编制统计数据。 在适当的时候，我们将从竞争的角度和裁判的表现来传达我们的观点。”

• An edited version of this article was published on SARugbyMag.co.za

  本文的编辑版本已发布在SARugbyMag.co.za上

• The dataset used to recreate both Rebels3’s study and perform the further analysis, was pulled from super.rugby’s archives using a short Python script using the BeautifulSoup library and a Selenium webdriver. Any missing data was filled in manually from Wikipedia and Rugby.com.au.

  用来重建Rebels3的研究并进行进一步分析的数据集是 通过 使用 BeautifulSoup 库和 Selenium网络驱动 程序 的简短 Python脚本 从 super.rugby的档案中 提取的 。 任何丢失的数据都可以从 Wikipedia 和 Rugby.com.au 手动 填写 。

• In 2010 there was a 19 match period where no penalty counts could be found. These matches have been left out of the study.

  在2010年的19场比赛期间，没有发现点球计数。 这些比赛已被排除在研究范围之外。

• The analysis was performed in a Jupyter notebook.

  该分析是在 Jupyter笔记本中进行的 。

• All project files can be found in this Github repository.

  所有项目文件都可以在此Github存储库中找到。