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，一名澳大利亞橄欖球迷進行了一項研究，聲稱要展示南非橄欖球裁判員如何表現出對南非主隊的偏見。 這項研究沒有考慮其他國家的裁判員如何對待南非主隊，這是在得出任何結論之前需要進行的重要比較。 然而，這項未經審查的研究是南半球各地體育記者的報道，導致要求進行正式調查。 研究的結論被證明是沒有根據的。 是的，這大約晚了6個月； 我們全神貫注。

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:

今年早些時候， 澳大利亞橄欖球迷Rebels3進行了一項研究 ，推測該研究表明南非裁判員如何偏愛南非人在南半球的超級橄欖球錦標賽中主場比賽。 雖然這是一項扎實的初步研究，并且當然值得更深入的了解，但從中得出的結論還為時過早。 但是，南半球各地的體育記者都熱衷于發布球迷的數據，如以下示例所示：

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

  研究顯示，“主場”裁判對超級橄欖球中的南非球隊有極大的偏見

• Super Rugby boss denies referee bias despite alarming statistics

  超級橄欖球老板否認裁判偏見盡管統計數據令人震驚

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

  超級橄欖球：SA球隊受到主裁判的青睞-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.

至少有一個措辭大膽的公開信被發送給監督超級橄欖球的機構SANZAAR的首席執行官。 對毫無根據的結論的炒作促使澳大利亞的橄欖球特許經營主管要求進行正式調查 。

All of this for a fan’s unvetted spreadsheet.

所有這些都是粉絲未經審查的電子表格。

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， 超級橄欖球賽(至少在冠狀病毒大流行之前)是多達五支來自澳大利亞，新西蘭和南非的球隊之間的比賽 。 最近，來自阿根廷和日本的一支隊伍參加了比賽。 每個隊的日程安排在主場和客場比賽之間大致相同。 比賽的專業裁判不需要中立，這是所謂問題的核心。 “中立”一詞用于描述主持比賽的裁判，在比賽中，主隊和客隊都不與裁判員來自同一國家/地區。

原創粉絲研究 (Original Fan-study)

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

下表顯示了粉絲研究如何采樣不同的比賽組。

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.

下面的條形圖顯示了每個組的平均懲罰差異，即球迷研究中使用的度量。 罰金的區別就是對主隊和客隊的罰款之間的區別。

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.

圖表顯示，在2017年至2019年之間，有澳大利亞裁判的澳大利亞主隊平均受到的處罰比他們的外國對手少0.5倍。有同胞裁判的新西蘭主隊受到的處罰少0.1％。 這兩個數字與南非主隊推薦的南非主隊被罰比海外對手少3.5倍的事實形成鮮明對比。 這種巨大的差異驅使人們認為南非裁判對南非隊有明顯的偏見。

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:

粉絲研究僅考慮了2017年至2019年，但如果將范圍擴展到2009年至2019年(2009年之前沒有超級橄欖球罰球數數據)，我們會看到類似的圖片：

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，這是一個完善的初步研究，或者一個初步研究的第一步，Rebels3顯然是到一些東西 。 但是，要知道這是什么，就需要深入研究。

球迷研究忽略其他裁判員如何對待南非隊 (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.

這就是誤會發生的地方。 人們看到了平均罰款差異的差異，并立即得出一個結論，即南非裁判不公平地偏愛南非隊。

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，該研究僅對澳大利亞人主持的澳大利亞主場比賽，新西蘭人主持的新西蘭主場比賽和南非人主持的南非主場比賽進行了比較 。 例如，它沒有做的是比較由不同裁判組主持的南非主場比賽。 這是一個巨大的疏忽。 顯然， 如果我們甚至不看其他裁判如何看待南非主隊 ， 就不能說南非裁判更喜歡南非主隊 。 來自其他國家/地區的裁判員完全有可能以相似甚至更大的程度偏愛南非主隊(前鋒)。

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

可以根據研究變量更正式地表達問題。

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的每個分組中，沒有一個變量保持恒定。 擁有如此獨特的群體和不受控制的變量，如果粉絲研究沒有顯示出群體之間的差異，那將是不可思議的。 如何得出一個結論，認為裁判員的國籍而不是其他任何變量是造成罰金差異的原因？ 鑒于我們到目前為止所掌握的信息有限，這樣的結論確實是非常不成熟和毫無根據的。

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.

在任何實驗或研究中，要測試任何單個變量，我們都需要使其他變量盡可能保持不變 ，這是本研究首次出現的論壇中表達的一種觀點 。 因此，要檢驗裁判員的國籍是否確實是一個因素，我們需要像Rebels3一樣將裁判員分為不同的國籍組。 但是，我們需要控制未測試的變量，如下表所示。 下表中的設置與Rebels3的研究沒有沖突，甚至沒有替代方案，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.

在控制我們未測試的變量時，我們可以更有把握地說，獨立變量(裁判國籍)是或不是影響各組處罰差異之間差異的重要因素。

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.

換句話說，如前所述，在我們知道南非裁判員對南非主隊的待遇不同之前，我們需要了解其他裁判員如何對待南非主隊。

進一步分析 (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:

讓我們開始吧。 讓我們保留主隊南非人和客隊而不是南非人，同時將裁判員分為五個明確定義的組：

• neutral Australian
  中立的澳大利亞人
• neutral New Zealand
  中性新西蘭
• non-neutral Australian
  非中性澳大利亞人
• non-neutral New Zealand
  非中性新西蘭
• 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.

由于在這種情況下主隊始終是南非人，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.

從下面的圖表可以看出，所有裁判組都偏愛南非主隊，盡管對于非中立的新西蘭裁判來說，這是微不足道的。 但是，有一個團體比其他任何人都更喜歡南非主隊。 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.

從2009年到2019年，南非裁判員平均對南非主隊的處罰是非南非客隊的3.1倍(2017-2019年：3.5)。 但是，非中立的澳大利亞裁判員的罰分差為4.1 ，這對南非主隊是有好處的(2017-2019： 6 )。 當澳大利亞裁判員的罰款差異更偏愛南非隊時，不可能得出南非裁判的罰款差異是不公平偏見的證據甚至證據。

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，使用上表中的組，南非裁判的平均罰分差最接近中立裁判的罰分(請參見上方和下方的條形圖)。 因此，不僅聲稱南非裁判員偏愛南非隊是沒有根據的，而且有證據表明，在主持南非的非中立比賽時，南非裁判員的偏見最少 。

結論 (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.

責怪裁判與體育裁判一樣古老。 在這種情況下，像往常一樣，沒有證據證明南非裁判員偏向南非隊。

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提出的原始統計數據按其原樣是沒有問題的： 初步研究的一部分，引起人們對潛在問題的關注。 這種情況的真正問題在于，如何在不進行適當檢查的情況下將故事夸大。 SANZAAR的首席執行官Andy Marinos表現出鎮定的領導力，他最好的回應是對抗議的回應 ，

“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.”

“我們需要驗證這些數字，并且需要適當擺放圖片，這是我們會做的并在適當時候做出回應。 有趣的是，當我們已經成為基于績效的系統10或12年時，整個中立事物就會浮現。 您必須了解鏡頭的來源。 在統計方面，人們總是在編制統計數據。 在適當的時候，我們將從競爭的角度和裁判的表現來傳達我們的觀點。”

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

  本文的編輯版本已發布在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.

  用來重建Rebels3的研究并進行進一步分析的數據集是 通過 使用 BeautifulSoup 庫和 Selenium網絡驅動 程序 的簡短 Python腳本 從 super.rugby的檔案中 提取的 。 任何丟失的數據都可以從 Wikipedia 和 Rugby.com.au 手動 填寫 。

• 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場比賽期間，沒有發現點球計數。 這些比賽已被排除在研究范圍之外。

• The analysis was performed in a Jupyter notebook.

  該分析是在 Jupyter筆記本中進行的 。

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

  所有項目文件都可以在此Github存儲庫中找到。