This is one of the most significant analyses I have ever done. It is a logical follow-up to the two earlier articles I had done on team streaks. I had used fixed periods in those articles and had mentioned that I would also a dynamic team performance analysis, incorporating floating number of Tests, strength of opposition, recent form and match location. After this article, all suppositions and conjectures should come to an end. The greatest period any Test team has gone through will be identified.

A few important points:

- The article is current up to and including West Indies' comfortable win over Bangladesh in St Vincent.

- Neutral matches are treated as away matches for both teams. This is the correct treatment for these 24 matches.

- Match# 1768 is handled only from the Australian point of view. No adjustments. ICC is treated as a middle-level team.

This is a very difficult article to present and explain. I do not want to give tens of paragraphs of explanations and lose the readers at an early stage of the article. Hence I will provide a basic description of the process, then explain everything about a single Test, and conclude with the important tables. For the first time ever, I have uploaded a detailed FAQs document in which I have answered a number of anticipated reader queries.

A brief explanation of the analysis workings

- For each Test, I will determine the team strength value for the two teams. This will be based on the performance of the concerned team over the past five years. The performances are weighted through a geometric decay basis to ensure that the recent matches carry the highest weight. This weighted average is called FYRAP (Five-Year Rolling Average Performance).

- Based on the Team Strength of the opposition team (FYRAP), TSF (Team Strength Factor) is determined. This varies between 0.80 and 1.20.

- Based on the other team's results during the immediately preceding one year, with a special tweak for the results in the anchor location (current Test's location-Home or Away), the LRFF (Location Recent Form Factor) is determined. This too varies between 0.80 and 1.20.

- The Team performance points are adjusted by TSF and LRFF for each Test. These calculations are carried out for all the 2100+ Tests. I would estimate that in a 198x PC-XT, this process would have taken the duration of a Test: maybe even the Durban Test of 1939. Now I get the results in a minute or so.

- Then the performance of a team is measured over a minimum of 30 Tests played within a maximum period of ten years. For each Test, the best average value is determined. A separate section under the FAQs area explains the reasons behind 30 Tests and ten years.

- The average of the value over 30-plus Tests is called RAAPP (Rolling Average of Adjusted Performance Points). This determines the team performance over the period identified.

A self-explanatory schematic of the complex system is presented below. No explanations are needed.

Everything about Test #1729

All readers should make sure that the four terms are clearly understood. FYRAP is a measure of the Team strength over the previous five years, excluding the current Test. TSF and LRFF are adjustments for the current match. RAAPP represents the best performance period, from the current Test onwards.

Australia and Pakistan played Test #1729 starting on December 26, 2004 at MCG. The complicated analysis forming the base of this article will be explained through this single Test. Every number associated with this Test will be explained. Those who want to know how this analysis is done should first go through it and understand this match. Maybe by reading this section a few times. Please do not rush with questions without going through this explanation. And if you do not want to go through the explanation, then please accept the findings of this analysis.

What is so special about 1729? It is one of my favourite numbers. It is the Ramanujam-Hardy number. The number of the taxi that Hardy took to see an ailing Ramanujam was 1729 and Hardy expressed the view that this was an unremarkable number. Ramanujam instantly responded with: "No, it is a very interesting number. It is the smallest number expressible as the sum of two (positive) cubes in two different ways." namely 1729 = 1^3 + 12^3 = 9^3 + 10^3.

First, I will explain the calculation of respective Team Strength Factors, using FYRAP values.

Australia played 59 Test matches during the five years preceding this match. The geometric decay value for 59, to reach a closing weight of 0.5, is 0.9883205 (in other words 0.9883205^59=0.5). Each of the 59 matches Australia played during these five years is geometrically decayed by this value, so that the weight at the end of 59 matches is exactly 0.5.

Pakistan played 44 Test matches during the five years preceding this match. The geometric decay value for 44, to reach a closing weight of 0.5, is 0.9843705 (in other words 0.9843705^44=0.5). Each of the 44 matches Pakistan played during these five years is decayed by this value so that the weight at the end of 44 matches is exactly 0.5. Please download and go through the document in which complete details are given of this match from the TSF point of view.

So for Australia, in match #1729, the opposition FYRAP is 34.441 and for Pakistan, the opposition FYRAP is 45.072. Note that this is done for every match. These numbers, per se, are not indicative of anything other than relative values since the actual performance points are decayed as the time is moved back. The TSF is determined for each team based on this FYRAP value. The range of the FYRAP is 6.8 to 49.2.

The TSF (Team Strength Factor) for Australia is 1.036 (0.80 + 0.40*(34.41-5.0)/50.0)). The TSF for Pakistan is 1.121 (0.80 + 0.40*(45.07-5.0)/50.0)).

Now, for the Location and Recent Form Factor; These two indices are intertwined and are determined through a complex process. The combined factor is called LRFF. The key limit is that only the Tests played by the teams during the exact preceding year are considered. This is to ensure that only the current form and recent matches are incorporated.

First let us fix the anchor locations for the current Test, which are Australia-Home and Pakistan-Away.

Let us consider Australia. Pakistan played a total of seven Tests during the preceding year. The results are LWLLWLW. However the anchor location for Pakistan is away. The previous Test was played away (anchor). The preceding five Tests were played at home. The seventh Test was played away (anchor). Hence this string is modified to L w l l w l W where upper case indicates an away match (anchor) and lower case indicates a match at home (non-anchor). A higher weight is given to matches in anchor locations. Pakistan's performance during these seven Tests is 43.8% (2*2 + 4*0 + 1*3)/(5*2 + 2*3). Since they played only seven Tests the factor range is narrowed. This is 0.85 + 0.3 * 0.438 which works out to 0.981. So Australia's LRFF is 0.981.

Now let us consider Pakistan. Australia played a total of 14 Tests during the preceding year. The results are WWWLWDWDWWWWDW. However the anchor location for Australia is home. Australia played seven Tests away and seven at home. Hence this string is modified to W W W l w d w D W w w w D W where upper case indicates a home match (anchor) and lower case indicates a match away (non-anchor). A higher weight is given to matches in anchor locations. Australia's performance during these 14 Tests is 82.9% (5*3 + 5*2 + 2*1.5 + 1*1 + 1*0)/(7*3 + 7*2). Since they played more than ten Tests the factor range is complete. This is 0.80 + 0.4 * 0.829 which works out to 1.131. So Pakistan's LRFF is 1.131.

So the final adjustment factor for Australia is 1.016 (1.036*0.981). For Pakistan the final adjustment factor is 1.268 (1.121*1.131). Australia won this Test by nine wickets and secured 71.181 performance points. This is adjusted to 72.33 (71.181*1.016). Pakistan secured 28.819 performance points and is adjusted to 36.54 (28.819*1.268).

Australia faced an above average Pakistan side but coming in with a slightly below average location-recent form. They gained slightly. Pakistan faced a rampant Australia with a strong home (anchor) record and a very strong home (anchor) record and gained heavily.

This calculation is done for each of the following 30-100 Tests, played within ten years and the average arrived at. The highest value for Australia is for 30 Tests between 1729 to 1855 (2008) and works out to 66.138. The highest value for Pakistan is for 31 Tests 1729 to 2098 (2013) and works out to 51.112. It would be easier for lower RAAPP values to be applicable for more Tests rather than higher values since it is tough to maintain higher value average sequences.

Well, my head reels. I am not sure about the status of the readers' heads.

Tables

A careful perusal of the tables indicates that the teams are divided into three groups. The first group consists of teams which have crossed a RAAPP value of 60.0 at some time in their history. Four teams qualify: Australia, West Indies, England and South Africa. No prizes for guessing this. The second group consists of teams which have crossed 50.0, but never reached 60.0. Again four teams comprise this group: Sri Lanka, India, Pakistan and New Zealand, which just about made it. The remaining two teams complete the roster.

I will present separate tables for each group.

Presentation of the data presents its own challenges. There are 152 Test in which Australia's RAAPP values exceed 60.0. England has 44, South Africa 33 and West Indies 32. However many of these are overlapping and I have looked at the table every which way to locate all non-overlapping instances of RAAPP values exceeding 60. Australia has 4, England 3, South Africa 2 and West Indies 2. These 11 performance streaks are, inarguably, the best ever and will form my first table. In addition, the long streaks are identified and presented.

Team Performance Analysis: 4 Top teams RAAPP Team First Test Last Test Weeks Tests 69.261 Australia 1463 (1999) 1629 (2002) 162 38 67.042 West Indies 979 (1984) 1072 (1987) 158 30 67.012 Australia 1721 (2004) 1855 (2008) 161 33 64.693 England 392 (1954) 457 (1958) 187 30 63.085 Australia 198 (1930) 259 (1937) 340 31 62.863 England 1944 (2010) 2044 (2012) 125 30 62.297 South Africa 1985 (2010) 2129 (2014) 186 30 61.567 Australia 275 (1946) 347 (1952) 303 31 61.432 England 9 (1882) 38 (1892) 497 30 61.339 South Africa 1830 (2007) 1951 (2010) 158 30 61.268 West Indies 461 (1958) 588 (1965) 329 30 62.023 Australia 1372 (1997) 1629 (2002) 281 66 60.001 South Africa 1871 (2008) 2111 (2014) 298 51 59.463 England 346 (1952) 457 (1958) 340 51 57.966 West Indies 883 (1980) 1056 (1986) 327 50

Australia's 38-Test streak, bookended by the Harare Test in 1999 against Zimbabwe and Ashes Test in Perth in 2002, had an average RAAPP value of 69.26. West Indies averaged 67.04, a significant 2 points behind, in 1984-1987. This golden period started with the Georgetown Test against Australia, which was a drawn match almost won by West Indies. The last Test in this run was the close loss to New Zealand in Christchurch in 1987. England's best sequence was during the wonderful Hutton-May-Compton-Trueman-Statham days. They averaged a very respectable 64.69 points. South Africa had their two best streaks during the 2000s: the first one between 2010 and 2014 and the second one between 2007 and 2010.

Australia had a way-out 66-Test run over six years during which they averaged 62.02 points. The other three teams had their best sequences around the 60 and sub-60 mark. South Africa's was a third decimal point above 60.

Now we come to the middle-level teams. New Zealand have only two streaks with RAAPP values above 50. India have 130, Pakistan 100 and Sri Lanka 109. However Sri Lanka have the pride of place in this group since they have reached the highest RAAPP value of 58.55. India follow next, with a highest value 57.86 and then Pakistan with 53.15. Looking for non-overlapping and long streaks, I have selected two from Sri Lanka, two from India, two from Pakistan and one from New Zealand.

Team Performance Analysis: 4 Middle teams RAAPP Team First Test Last Test Weeks Tests 58.554 Sri Lanka 1530 (2001) 1699 (2004) 168 33 57.864 India 1884 (2008) 1997 (2011) 150 30 55.384 Sri Lanka 1757 (2005) 1886 (2008) 158 30 53.153 Pakistan 1945 (2010) 2098 (2013) 197 32 52.881 Pakistan 1265 (1994) 1391 (1997) 173 31 52.304 India 1999 (2011) 2130 (2014) 158 30 50.409 New Zealand 950 (1983) 1050 (1986) 178 30 53.974 India 1697 (2004) 1952 (2010) 304 64 53.378 Sri Lanka 1585 (2002) 1839 (2007) 286 50 50.755 Pakistan 1754 (2005) 2034 (2012) 346 56 48.279 New Zealand 1478 (2000) 1790 (2006) 323 51

Sri Lanka achieved a very high average of 58.55 between 2001 and 2004. Inspired by Muttiah Muralitharan and supported by Kumar Sangakkara, Mahela Jayawardene, Sanath Jayasuriya and Aravinda D'Silva to start with. They also had another great sequence between 2005 and 2008. India's sequence between 2008 and 2011 was very close to Sri Lanka's run a few years earlier. Unfortunately, this was cut short by the England debacle. India have repeated this, albeit at a lower level, mostly riding on excellent home form. One of Pakistan's two sequences is recent and the other during the 1994-1997 period.

India had a run of 53.97 over 64 Tests. Sri Lanka were able to get near this value, averaging 53.34 in 50 Tests during the 2000s. Pakistan's sequence is around the 50-mark and New Zealand's, just below the 50-mark. Both are over 50 Tests.

Let me close this with brief comments on the two recent Test teams. Zimbabwe has a 30-Test streak, from Test #1378 (1997) to 1549 (2001) with RAAPP value of 40.03: the only period in which they exceeded 40.0. They had five wins in these 30 Tests, including three against the top Test-playing teams. Bangladesh has a 30-Test streak, from Test #1864 (2008) to 2099 (2013) with RAAPP value of 37.572.

Conclusions

I am not saying that all readers should accept these tables as the final ones. They have every right to plunk for a second or third placed streak as the best but only as a heart-driven decision since all relevant factors such as match locations, opposition strength, recent form and number of matches have been taken into account.

What do we conclude?

First let us summarise the middle-level teams. Sri Lanka's performances are to be admired and appreciated. Their 2000s performance gives them the top billing in this group. India have also been very good in the 2000s. India were the only team to pose any threat to the Australian dominance during the 2000s. However the very poor away performances have let India down. Pakistan have been quite good. In fact I was surprised to see that Pakistan did not reach 55.0. My feeling is that they have been inconsistent and have not sustained their top-level performances for seven to eight series at a stretch. New Zealand have just about managed to make this group.

There is no doubt that Australia, for 38 Tests between 1999 and 2002, were the best Team that ever played Test cricket. All relevant factors have been taken into consideration. Opposition strength, recent results, recent form, location, number of Tests et al. They were truly outstanding and posted a result sequence of 31 wins, three draws and four losses (all away). Let us not forget that this was achieved over 38 Tests. All three draws occurred in a home series against New Zealand. All the four losses were potential wins: two well-known against India in Kolkata and Chennai, one-off against England in Leeds and South Africa at Kingsmead, the normal dead-rubber matches.

Let us look at the second placed sequence of West Indies. During 30 Tests between 1984 and 1987, West Indies were magnificent. They had a results summary of 21 wins, seven draws and two losses. The two losses were to Pakistan, that 53-run-all out disaster in Faisalabad and New Zealand's five-wicket win ainChristchurch, inspired by Hadlee. Maybe one could say these were the days in which a draw could be planned and achieved.

The third best is another recent run of Tests by Australia. However Australian performance in 100 Tests between 1999 and 2008 is something for the Gods. This sequence started with the Lara-inspired loss at Barbados and ended with the 2008 New Year Test against India. The summary was 75 wins, 13 draws and 12 losses. And some of the losses were because Australia went for wins. To me this sequence is probably the most significant of the many Australian achievements. They were truly the most dominant team of all time. For the record this 100-Test streak has an outstanding RAAPP value of 63.066. It is just that there is a better streak of 65.304 for the 43 Tests starting with the Barbados Test.

Data Files: I have uploaded four important files. The first is a special file for Test #1729. It lists all the matches which were played during the five years before this specific match. The second contains the Performance points and adjusted Performance points for all matches played by all the teams, in Team order. The second contains the Performance points and adjusted Performance points for all matches played by all the teams, in Test order. These two are huge files. The fourth is the most important document. It contains the RAAPP values for all the teams, ordered by the RAAPP value for each team.

This is not an article that can be understood by perusing at surface level. It would take multiple readings and downloading and understanding all the documents, especially the FAQs document. Please take your time. Alternatively, if the reader has confidence in my work, he can go straight to the important Tpa_All.txt file.

Please download the zip file containing the four aforementioned files and the FAQs document by clicking HERE.

Some FAQs on the analysis: First time ever I have anticipated some questions from readers and attempted to answer those. Initially I had got these FAQs as part of the main article. However when the number of FAQs exceeded 20, I decided I would create a MS Word document and allow interested readers to download the document and peruse at leisure. Please do so by clicking HERE.