image source: gulfcup.sa
It was February 29, 2012. Leap Day. Phil Dunphy’s absolute favorite. It was the final day of the 3rd round of AFC World Cup Qualification. Group E featured Iran, Qatar, Bahrain and Indonesia. The top 2 teams would advance to the final round of qualifying. Entering the day, Iran had already advanced and Indonesia had been eliminated. The final spot would be between Qatar and Bahrain.
Qatar had a 3 point lead over Bahrain, meaning for Bahrain to have any chance, they’d have to win and Qatar would have to lose. But that would merely put the two teams level on points. Qatar had a +5 goal differential, and Bahrain had a -4 differential. So, in addition to making up the 3 points, Bahrain would also have to make up 9 goals.
Fast forward to today: November 19, 2014. Bahrain has just concluded the 2014 Gulf Cup. They didn’t score a single goal from 3 matches. 8 of their past 13 matches have been goalless draws. They’ve scored in just 3 of those 13 matches. Since the match against Indonesia, Bahrain has played 45 matches. They’ve scored a total of 34 goals in those matches, for an average of 0.756 goals per game. While Indonesia is ranked by us at #148, since that match Bahrain has played 9 matches against teams outside of our Top 150. They’ve scored 9 goals in those 9 matches… slightly better.
We did a little further statistical analysis on these past 45 matches. It’s a pretty good sample size. Here are the results:
They’ve been blanked on 21 occasions (47%), scored 1 goal 16 times (36%), scored twice on 6 occasions (13%) and scored 3 goals twice (4%). That’s it. They’ve never scored more than 3 goals.
Moreso than their 0.756 average, the standard deviation of these matches is the important part. Over 45 matches, Bahrain’s standard deviation on goals scored is just 0.857. That’s low. Really low. At its simplest, standard deviation is a measure of how different numbers are from each other. How much a number “deviates” from an expected result. If all of the numbers are the same, the deviation is 0. This number can grow inifinitely depending on the numbers you use.
For comparison, in Germany’s last 45 games, they’re scoring at a 2.44 goals per game clip, with a standard deviation of 1.62 goals. This is far more normal, if a little high. Average for a team is around 1.25-1.5.
How It Works
Here’s a little extra math than anyone needs to know. We’re going to use Germany, and even Bahrain, as typical examples. Mathematically, there is a 68% chance that you are within 1 standard deviation of the mean. In Germany’s case, that means the probability they score between 2.44 +/- 1.62 is 68%. Or, in goal terms, the probability they score 1, 2, 3, or 4 goals in a given match is 68%. There is a 95% chance that you are within 2 standard deviations of the mean. In Germany’s case, there is a 95% chance they score 0-6 goals. It makes sense. Anything beyond 6 goals is considered a pretty rare occurrence.
The same applies to Bahrain. Mathematically, there’s about a 68% chance they score 0-1 goals and a 95% chance they score 0-2 goals. Their data above supports these figures. And again, the results from 45 matches make sense. As you get further and further away from the mean, the probability goes significantly down that a result will occur.
In the 3rd minute of Bahrain-Indonesia, Indonesia’s keeper was sent off. Bahrain needed to make up 9 goals to overtake Qatar in goal differential. They scored 10. Despite Qatar getting a draw, eliminating Bahrain in the process, this match immediately came under scrutiny. It was extremely suspicious. The match was still only 4-0 through an hour. Bahrain proceeded to tally in the 61st, 63rd, 71st, 75th, 82nd and 94th. The goal in the 94th was academic, but it was the 5 goal assault over 20 minutes that made things that much worse.
The match was subsequently investigated and no further action was taken. The match was deemed a legitimate result and allowed to stand.
Since scoring 10 goals in one game, Bahrain has scored a total of 34 in their last 45 matches, as indicated above. 10 goals is not just a statistical outlier, it is an EXTREME outlier.
Given Bahrain’s mean goals and standard deviation numbers above, scoring 10 goals in a match is 10.79 standard deviations from the mean. For Germany to be 10.79 standard deviations from their mean, they would have to score 20 goals in a match. Germany just hosted Gibraltar’s police force and only managed to score 3 plus an own goal. Could they really have scored 16 more goals if they wanted to?
Indonesia is not a British Virgin Islands or Kiribati as one of the worst teams in the world. Since that match, they’ve allowed an average of 1 goal per game in 29 matches. For them to concede 10 against a team that has severe difficulty even scoring 1 goal is highly, highly suspicious.
And lastly, you must be wondering what is the probabilitiy of being 10.79 standard deviations from the mean. We’re wondering that too. A normal table stops at 7 standard deviations, where the probability is almost 1 in a trillion. You have a better chance of winning the lottery than being even 6 standard deviations from a mean. To be 10.79 deviations away is mathematically incalculable.
Yes, Indonesia was down to 10 men. And yes, Bahrain had incentive to push forward and score as many goals as possible. But the statistical probability of it actually happening is so impossibly small that one must wonder how it actually happened.
Was there any funny business? We may never know. But one thing is for certain… Bahrain scoring 10 goals is the most statistically unlikely event to occur in the history of sports.