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The final ranking
Which is the sixth best team in Test cricket today?M J Manohar Rao and Srinivas Bhogle
This is an unusual title. But we have very good reasons for choosing such a title to introduce our novel approach to rank Test cricket teams.
First, because the more obvious question -- "which is the best team in Test cricket at the moment?" -- is hardly interesting, given Australia's undisputed numero uno status in world cricket.
Second, and this is really the crux of the matter, because it is much more difficult to identify the fifth or sixth position than the first.
While working on this article we found at least half a dozen ranking schemes on TV and the Web. Every scheme put Australia at # 1, South Africa at # 2 and Zimbabwe at # 9 (we aren't considering Bangladesh yet), but none appeared to agree on any of the intermediate positions!
This doesn't surprise us because things are quite crowded in the middle. On today's form, India, Sri Lanka and New Zealand appear to be fighting for the # 5 - 7 positions, but a few victories or defeats here and there could also see England and Pakistan (currently vying for the # 3 - 4 positions) joining the fray.
This ranking business is therefore quite tricky, and it doesn't help that most of the existing indices are either too arbitrary and subjective, or too complicated and misleading.
We really need a new, and more objective, index to accurately determine not just the team rankings, but also the the team's relative positions vis-à-vis one another.
"Objective" ranking criteria
What should a Test cricket team do to attain the "Top Gun" status? Most cricket fans would agree that the best teams must:
Towards a "suitable" index
Let's therefore begin our search for a suitable index to measure current Test cricket performance.
We will agree that a win fetches 1 point, a draw fetches 0.5, and a defeat fetches 0 points.
We will further agree to consider the most recent home and away Test series between two countries. So if we are looking at India vs Australia, we will only consider (a) the India-Australia series of 1999-00 in Australia (which India lost 0-3; implying that India get 0 points out of a maximum of 3 in their "away" series, while Australia get 3 points out of 3 in their corresponding "home" series) and (b) the India-Australia series of 2000-01 played in India (which India won 2-1; so India get 2 points out of 3 in their home series while Australia get 1 point out of 3 in their corresponding "away" series).
In this manner, it is quite easy to construct the full "matrix" (see Table A below, updated as on November 3, 2001) of home and away points for all the 36 possible pairs of the nine Test playing countries (remember that we are not considering Bangladesh). This way, we look at a sample of the 209 most recent Test matches (out of a total of 1563 Test matches played so far), making it a fairly "representative" sample.
A "simple" performance index
Table A is extremely informative. For example, if we add up Australia's home and away points we find that Australia have obtained 38 points over the last 50 "home" and "away" matches that they have played against all their opponents. This gives Australia a performance index of 0.760 (= 38 / 50). Similarly, if we add up all of India's points, we find that India have obtained 21 points over their last 48 "home" and "away" matches, giving them a much lower performance index of 0.438 (=21 / 48).
In Table B, below, we provide the current performance indices for the nine Test playing countries.
Table B tells us which team is winning the most matches and corresponds to our Criterion 1. We note that Australia (0.760) and South Africa (0.667) have the two best performance indices while Zimbabwe (0.259) have the poorest. We also note that India (0.438) are languishing in the seventh position, just above West Indies and Zimbabwe.
Opponent-specific "weighted" performance index
It is, however, not appropriate to merely use these simple performance indices to rank the Test-playing countries. This calculation does not take into account the quality of the opposition (recall Criterion 2); as we have remarked earlier, defeating Zimbabwe is not the same as defeating Australia! A victory against Australia must be accorded a mugh higher "weight" as compared to a win against Zimbabwe.
Most analysts recognise this fact, but cannot agree on the opponent-specific "weight" to be accorded under the circumstances. We propose to use these simple performance indices as the "weights". Thus a win against Australia today will have a "weight" of 0.760, a win against India a "weight" of 0.438, a win against Zimbabwe a "weight" of 0.259 ... and so on. This seems a fair way of classifying wins, and implies that a win against Australia is worth almost three wins against Zimbabwe (=0.760 / 0.259)!
In Table C, below, we present the "weighted" performance indices of the nine Test-playing countries (we don't discuss the calculation procedure here, but interested readers are welcome to contact us).
Table C, which combines our Criteria 1 and 2, reveals an interesting quasi-turnaround. Australia and South Africa continue to dominate the rankings; England and Pakistan trade places (England taking the third position). Sri Lanka continue at #5, while India climb to #6, edging out New Zealand. West Indies and Zimbabwe stay at the bottom.
It is particularly interesting to glance at the "difference" column of Table C. Only Australia have a significant positive difference suggesting that they actually perform better against stronger opponents. England is the only other country with an insignificant positive difference -- suggesting that they handle stronger opponents as well as the weaker opponents (one wonders though if England isn't a beneficiary of the charity of Hansie Cronje -- who offered a one-day Test victory -- and, more recently, of Adam Gilchrist).
All other countries, including South Africa, have a significant negative difference; so they are essentially picking off victories from weaker opponents. New Zealand (-0.037), in particular, have picked most of their points only by defeating the weaker teams! Perhaps that's why India could overtake New Zealand to take the sixth position -- the famous wins against Australia are still helping India in spite of the recent losses to Sri Lanka and Zimbabwe.
Opponent- and location-specific "weighted" performance index
The "weighted" performance indices of Table C certainly appear more realistic than the "simple" performance indices of Table B. But we would like to argue that even Table C does not tell the whole story. We still haven't arrived at our "best" index, which must take into account all our three criteria: high win percentage + wins against stronger opponents + wins away from home (Criteria 1, 2 &3). After all, we all agree that defeating Australia in India is not the same as defeating Australia in Australia. We must therefore accord a higher "weight" to "away" victories.
Once again, while most analysts recognize this fact, they cannot agree on what these "location-specific" weights should be. Our formulation, however, offers an easy, and fair, location-specific weight. We propose to "decompose" the simple performance index of Table B into "home" and "away" performance indices and then use these indices as the "weights". Table D, below, shows the decomposition into home and away performance indices.
Table D contains a few notable pointers. For example, Australia's home performance index is an astounding 0.880; so they are practically invincible at home. In our opponent and location-specific index, therefore, defeating Australia in Australia would fetch the opponent an amazing 0.880 points, while defeating Australia when they are "away" (e.g. in India) would fetch the opponent relatively lower (0.640) points for every win. We also note, for example, that defeating England when are playing an "away" series (e.g. in India) is worth 0.433 points. So defeating Australia in Australia is worth two wins against a touring England team.
Home wins against South Africa (0.750), West Indies (0.621) and even India (0.568) are also seen to be lucrative. On the other hand, defeating India (0.327), West Indies (0.192) and Zimbabwe (0.250), when they are on away tours, isn't very profitable!
Our "double-weighted" (opponent- and location-specific) performance index, which we might call the Rao-Bhogle index -- or simply RBI -- is therefore seen to be a very realistic indicator of the "true worth" of Test teams and Test match victories. RBI is essentially computed using the same weighted average procedure that we used for the "single-weighted" (opponent-specific) performance index. Table E, below, summarizes our results (once again we won't go into the calculation details, although readers are invited to contact us if they wish).
Table E, which combines our Criteria 1,2 & 3, reveals no changes in the overall standings. The uniform drop in all the "double-weighted" performance indices shows that every team essentially gains points while playing at home. In particular, the high negative differences in Australia and South Africa's performance indices confirm that they have attained their very high rankings by winning very handsomely at home.
India's low negative difference is a pleasant surprise. This indicates that India's "away" performance is not as bad as it is made out to be -- and in fact, relatively speaking, Indians are among the best tourists! It is true that they hardly ever win a Test match away (and therefore can never win an away Test series), but this is really also the case with most other teams.
Table F, for the record, lists the final rankings as on November 3, 2001.
Table F suggests that Australia is currently very well-entrenched at the top. But, since our performance index (RBI) considers only the most recent home and away Test series, things could change quite quickly. For example, Australia could lose points if they lose to South Africa in their forthcoming Test series, or India's performance could improve if they win the series against South Africa!
After every Test series the RBI's will rise or fall; but they would always be fair estimates of the team's current form. Indeed, because of the dynamic nature of our index, the outcome of every Test series between any two teams will also have a bearing on the remaining seven (non-playing) teams.
Table F, incidentally, also answers the question posed in this paper's title: India is currently the sixth best team in Test cricket.
With the South Africa-India, Sri Lanka-West Indies and Australia-New Zealand Test series about to start, it would be interesting to speculate how the ratings could look like a few weeks later. In particular, Indian supporters would be keen to know how India's performance in South Africa will affect their rating. Table G provides the estimates of the performance rankings and indices corresponding to all possible "end-of-series" scenarios.
Table G indicates that even if India can draw their series against South Africa, they will reach the fourth position, just ahead of Pakistan. A series win of 2-0 would catapult India to the third position!
Remember, however, that India's ranking would also be affected by the "cross-impact" of the parallel Sri Lanka-West Indies and Australia-New Zealand series. Our computer software can easily carry out such cross-impact analysis, although we won't describe it here. Our calculation shows that New Zealand can overtake India only if India lose 3-0 to South Africa and New Zealand win one Test or manage two draws against Australia. We also don't expect a "normal" outcome of the Sri Lanka-West Indies series to affect India's ranking. So it does look as though India cannot drop below the sixth position at least in the near future.
To obtain all the Test match results we used the data available on cricinfo. We are grateful to Pallavi Bhogle and Dhruv Bhogle whose painstaking efforts in tabulating and cross-checking all the entries of Table A made our subsequent work so much easier. Finally, we thank Rediff and Prem Panicker for agreeing to publish this note.
M J Manohar Rao is professor and director, Department of Economics, University of Mumbai, Mumbai; Srinivas Bhogle is scientist and head, Information Management
Division, National Aerospace Laboratories, Bangalore.
Design: Imran Shaikh
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