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# Statistical Analysis: Why are Australia ranked higher than South Africa in Tests?

ANALYST
4.14K   //    03 May 2014, 10:10 IST

Graeme Smith (left) and Micheal Clarke (right)

While browsing through the sports news recently, I read an article about the ICC annual rankings update. To my surprise, the number one test team was Australia and not South Africa. That led me to the question: How can Australia after losing 4-0 in India and 3-0 in England last year be the highest ranked Test team?

Well, to understand further we would have to go deeper into how the rankings work?

### How are the rankings calculated?

The rankings are based on the points that a team scores during a series.  These points are calculated based on the ratings of the two teams involved in the series. Then, the points scored divided by the total number of matches gives the final rating of a team.

I would be using the example of the Australia-South Africa series played earlier this year to explain how these points are calculated:

The first step is to determine the series result. This is calculated in the following way:

• 1 point for a win
• 1/2 point for a draw
• 0 points for a loss
• Additional 1 point for a series win (Would be 1/2 if the series is drawn)

So, considering the above criteria, the points for the series result would be:

Australia = 2 (number of wins) + 1 (series win) = 3

South Africa = 1 (number of wins) + 0 = 1

The next step is to convert these into rating points. This calculation is based on the following formula:

Rating Points = (Team’s own series result)  x (50 + Opponent’s rating) + (Opponent’s series result) x (Opponent’s rating – 50 )

Note that the opponent’s rating points being considered for calculation are those before the series. Also, this formula is applicable only if the rating difference between the two teams is less than 40.

The ratings for both teams before the series were as follows:

 Team Matches Points Rating South Africa 30 3988 133 Australia 39 4314 111

Australia’s rating points for the series = 3 x (50 + 133) + 1 x (133 – 50) = 632

South Africa’s rating points for the series = 1 x (50 + 111) + 3 x (111 – 50) = 344

Therefore, the new rating would be:

 Team Matches Points Rating South Africa 34 4332 127 Australia 43 4946 115

Note that the number of matches is incremented by 4 and not 3 (despite it being a 3-match series). This is because in the series result calculation one additional point is considered for the series win.

All this is well and good, but this still does not answer the question why is Australia ranked higher?

For this we need to have a look at one more point: how the ICC annual update works?

How does the ICC annual update work?

The ICC rankings give more weightage to the latest results. As a result, only matches that have been played in the last four years are used to calculate the final rankings. The matches played in the last two years are given 100 % weightage while 50 % weightage for the series before that.

The ICC annual update is used to remove the points due to results three years ago and reduce the percentage of points for latter results. This year’s update removed the results for the 2010-11 season and halved the points for the 2012-13 season. The weightage of points for the 2013-14 and 2014-15 season would be 100% while for the seasons 2011-12 and 2012-13, it would be 50%.

Now, to answer the question: why is Australia ranked higher than South Africa?

I will answer this by comparing both teams based on the following criteria:

1) Points removed during update

 South Africa (2010-11 season) Australia (2010-11 season) 0-0 drawn series against Pakistan in UAE 2-0 loss to India in India 1-1 drawn series against India at home 3-1 loss to England at home

As is visible from the series results that have been removed, the Australian team lost fewer points in the annual update as compared to South Africa. Thus, the removal of poor results from the 2010-11 season helped Australia achieve a higher rating.

2) Points halved during update

 South Africa (2012-13 season) Australia (2012-13 season) 1-0 win against Australia in Australia 1-0 loss to South Africa at home 2-0 win against New Zealand at home 3-0 win against Sri Lanka at home 3-0 win against Pakistan at home 4-0 loss to India in India

The points halved also favor Australia. The points received from their dismal performance in India were halved. On the other hand, South Africa had secured three series wins during this period. As a result, South Africa had much more points to lose as compared to Australia.

3) Rating points gained in 2013-14:

One would argue that the Proteas did not lose a single series in the entire period that the points were calculated apart from the loss against Australia in March. Then how is it that Australia still has a higher rating?

The answer to that is the amount of points Australia have accumulated in their series wins. Consider the case of the Ashes in December, a 5-0 win secured by Australia provided much more points because of their poor rating before the series.

Before the Ashes, Australia had 101 points compared to England’s 116. If we calculate the rating points Australia gained from that whitewash using the above formula:

Australia’s rating points = (5 + 1) x (116 +50)  + 0 = 996

The average rating points per match = 996/6  = 166 (Considering 1 match for the series result)

Whereas, when we consider South Africa’s win over India,

South Africa’s rating points = (1.5 + 1) x (119 + 50) +(0.5) x (119 – 50) = 457

The average rating points per match = 457/3  =  152.33 (Considering 1 match for the series result)

So, there you have it, because of a few less rating points earned as well as the removal of some earlier wins resulted in South Africa slipping in the rankings.

If you are still not convinced and believe that South Africa are a better team, then I can assure you that Australia are not ranked number one by a huge margin. It is only when the points are calculated beyond the decimal point that Australia sneak ahead of South Africa by a whisker.

 Team Matches Points Rating Australia 32 3950 123.43 (rounded to 123) South Africa 23 2831 123.08 (rounded to 123)

Just as an after-thought, if India would have toured South Africa for a three match series, this could very well not have been the case.

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