I think nearly everybody will be at at least slightly suprised by these results. You would think that there are periods where a team hits good form for a year or two (happens to England and India quite often for example) and in this period the fast bowlers are not getting injured so there is a sense of constisency and stability. But the teams are hardly as consisent as this analysis shows.
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Gizza
I cannot really do an in-depth analysis as I don't have the time.
Just to take an example of Indian team under Gangluy recently or under Dhoni, the opening was fluid until Sehwag/Gambhir settled in. There might have been stability at 3-7 although Ganguly/Yuvraj swapped places. Spin might have been in the hands of Kumble and Harbhajan, but not outside. And finally the pace attacks have kept on changing.
So it is not easy for the same eleven to keep on playing.
Ananth:
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I'm also surprised by these results. I would have thought that Steve Waugh's team would have played more than nine consecutive Tests, but I think that shows the relative lack of pace-bowling support for McGrath and Gillespie (of course, in that period Australia tried several others such as Lee, Bichel and Kasprowicz). That must also have been very shortly before Mark Waugh's retirement (I think he retired at the end of that Pakistani series).

I am also surprised at the rarity of XIs lasting more than three Tests also. I think either injuries or knee-jerk selection policies must be to blame for that.
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Marcus
I have started some preliminary work on the 2-3-... player groups. There is no doubt that the Australians are tops in, say, the 2-player groups. However the 11 player group is quite tough. For Australia the third pace bowler, the sixth batsman and the opening combinations are the culprits.
Ananth:
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Impressed with the algorithm you used to arrive at the results. Correct me if I am wrong but I think it is a slight modification of string matching algorithms used in computer science. Keep up the good work.....

I think the algorithm you have followed is very complicated .There is a simpler logic.See there are only 2^11-1 combination of player sets you need to consider. That is 2047 in approximately 1800 test matches,each test match giving 2 teams,so totally you need to see 2047*1800*2 combination sets only.Increase the count for each set when they appear together.I did this for n=2 to n=10,Here is the top 3 in each set
n=2
R Dravid(India),SR Tendulkar(India), 122
A Kumble(India),SR Tendulkar(India), 122
JH Kallis(SA),MV Boucher(SA), 116

n=3
R Dravid(India),SC Ganguly(India),SR Tendulkar(India), 103
A Kumble(India),R Dravid(India),SR Tendulkar(India), 97
R Dravid(India),SR Tendulkar(India),VVS Laxman(India), 96

n=4
A Kumble(India),R Dravid(India),SC Ganguly(India),SR Tendulkar(India), 86
R Dravid(India),SC Ganguly(India),SR Tendulkar(India),VVS Laxman(India), 80
A Kumble(India),R Dravid(India),SR Tendulkar(India),VVS Laxman(India), 73
contd..

continuing from previous post
n=5
A Kumble(India),R Dravid(India),SC Ganguly(India),SR Tendulkar(India),VVS Laxman(India), 65
CG Greenidge(WI),DL Haynes(WI),IVA Richards(WI),MD Marshall(WI),PJL Dujon(WI), 58
IA Healy(Aus),MA Taylor(Aus),ME Waugh(Aus),SK Warne(Aus),SR Waugh(Aus), 55
n=6
CG Greenidge(WI),DL Haynes(WI),IVA Richards(WI),MD Marshall(WI),PJL Dujon(WI),RB Richardson(WI), 43
AC Gilchrist(Aus),GD McGrath(Aus),JL Langer(Aus),ML Hayden(Aus),RT Ponting(Aus),SK Warne(Aus), 40
DPMD Jayawardene(SL),KC Sangakkara(SL),M Muralitharan(SL),MS Atapattu(SL),ST Jayasuriya(SL),WPUJC Vaas(SL), 39
n=7
AC Gilchrist(Aus),DR Martyn(Aus),GD McGrath(Aus),JL Langer(Aus),ML Hayden(Aus),RT Ponting(Aus),SK Warne(Aus), 30
CA Walsh(WI),CG Greenidge(WI),DL Haynes(WI),IVA Richards(WI),MD Marshall(WI),PJL Dujon(WI),RB Richardson(WI), 30
DC Boon(Aus),IA Healy(Aus),MA Taylor(Aus),ME Waugh(Aus),MJ Slater(Aus),SK Warne(Aus),SR Waugh(Aus), 28

n=8
AC Gilchrist(Aus),DR Martyn(Aus),GD McGrath(Aus),JL Langer(Aus),JN Gillespie(Aus),ML Hayden(Aus),RT Ponting(Aus),SK Warne(Aus), 23
AB de Villiers(SA),AG Prince(SA),DW Steyn(SA),GC Smith(SA),HM Amla(SA),JH Kallis(SA),M Ntini(SA),MV Boucher(SA), 21
AL Logie(WI),CA Walsh(WI),CEL Ambrose(WI),DL Haynes(WI),IVA Richards(WI),MD Marshall(WI),PJL Dujon(WI),RB Richardson(WI), 21

n=9
AL Logie(WI),CA Walsh(WI),CEL Ambrose(WI),CL Hooper(WI),DL Haynes(WI),IVA Richards(WI),MD Marshall(WI),PJL Dujon(WI),RB Richardson(WI), 18
AL Logie(WI),CA Walsh(WI),CEL Ambrose(WI),CG Greenidge(WI),DL Haynes(WI),IVA Richards(WI),MD Marshall(WI),PJL Dujon(WI),RB Richardson(WI), 17
AL Logie(WI),CA Walsh(WI),CEL Ambrose(WI),CG Greenidge(WI),CL Hooper(WI),DL Haynes(WI),MD Marshall(WI),PJL Dujon(WI),RB Richardson(WI), 17

n=10
AL Logie(WI),CA Walsh(WI),CEL Ambrose(WI),CG Greenidge(WI),CL Hooper(WI),DL Haynes(WI),IVA Richards(WI),MD Marshall(WI),PJL Dujon(WI),RB Richardson(WI), 14
[[
Sumant
You are finding fault with my algorithm for determining 11 players and then showing 2-10. I have not even published anything on 2-10 players. I have done the preliminary work on 2 players and the numbers match. So your algorithm is correct.
However you have a limited objective, finding the top 3 (or 5). I do complete articles. When I present the 2-player combinations, I will present the top-5 for each country and so on. Anyhow you do not know anything about my 2-10 methodology to pass any adverse comments.
I make sure that the readers, from wherever they are, be it Melbourne, London, Bulawayo, Calcutta, Lahore, Dunedin et al get to know of their countries and player combinations.
Ananth:
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Excellent Analysis. Really surprised that at the few times top teams have played from Australia and West Indies. Also the Indian number was less than what I would have guessed if asked.

The Best Part: There can be no comments that this analysis is flawed as a certain player is not on top. Or am I underestimating the cult followers of the players?
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Raghav
One thing is certain. This is only a team analysis and will attract one-tenth of the comments which individual analysis would have elicited.
Ananth:
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Very thorough on the concept as always. These strings of a settled combination will now be more and more unlikely with injuries, IPL and indifference to Tests in the FTP.

Ananth,
It would be very interesting to see who averaged more / scored more runs, Dravid or Tendulkar, in the 122 matches they played together. I suspect it's Dravid.
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X
Possible. Although it would be unwise to put any money on one since Dravid went through a bad patch after 2007. However his last 7 matches have yielded 800 runs at a high average. Tendulkar has maintained an average around 55 during the last 30 tests.
One thing is certain. At the beginning of 2007 Dravid was 4 ahead of Tendulkar (58 vs 54). Now touch and go.
Ananth:
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I saw the document you have uploaded about the complexity of finding this solution and I admire how much mathematical your approach is. But at the same time, there was perhaps, another approach to go about this. Assuming that you have a table with all test records, you could try programatically populating a table called TEST_PLAYER (say) with 11 fields, one for each player ID such that PLAYER_1_ID is always numerically less than PLAYER_2_ID and so on. Then, you could get your desired results by writing a simple SQL statement which groups tests by player IDs. The SQL would be:

Select PLAYER_1_ID, PLAYER_2_ID,.... PLAYER_11_ID, COUNT(*)
From TEST_PLAYER
GROUP BY PLAYER_1_ID, PLAYER_2_ID,.... PLAYER_11_ID
HAVING COUNT(*) > 1
ORDER BY COUNT(*) DESC

This solution could also help in getting 10-player combinations and so on by using SQLs with UNION clause across different 10 player combinations e.g. (1,2,3,4,5,6,7,8,9,10), (1,2,3,4,5,6,7,8,9,11). I know this is a tedious approach
My 2 cents
[[
Akshay
Pl see my reply to Sumant.
Ananth:
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ananth,No I am not finding fault with your algorithm or passing adverse comments,I am merely saying that this is a simple way,I have just presented top3 for lack of space,I can give you the entire list as well by country basis,or on overall basis.The algorithm took about 2 mins to complete.I can see in your algorithm that you take something to do with squares of player id which is not required.Anyways I was just thinking aloud.Keep up the good work
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Sumanth
I use Excel for my personal database and for some rare needs (such as the Sehwag article in CastrolCricket.com) and am not wholly familiar with it. My methodology is to spend time on a notebook, do the preparatory work and then move on to a C program to process my proprietary database. There are many reasons.
1. I can do, virtually, anything by this method.
2. I save all the C programs and can re-use.
3. The reports come out in ordered tables which are the basis for my articles.
4. Adding further analysis bits is easy. For instance what Xolile has asked for, which is to compare the averages of the concerned set of 2 players. I would just have to add 10 lines of code.
I am certain that your solution is the right method to do a one-off analysis and I like the thought process which has gone into it. But you are probably an Excel-wiz, which I am not. On the other hand, I can claim to be a C-wiz.
Thanks for all your inputs.
Ananth:
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Nice article, Ananth.
Do you have plans to combine the analysis to get the stability of the teams? I mean, publishing list of tests for 11 test players, 10, 9 etc, doesn't give much insight. If you could do a weighted average of this, it would indicate the stability of the teams, right? (may be the timefactor also will pitch in).
I'm wondering how this is related to the article S.Rajesh published sometime back in this blog.
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Unni
That is a good idea worth exploring further. For the time being I am going to post the basic tables. Once I complete the other huge analysis you know about I will look at this again to do a weighted analysis.
Ananth:
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Hi Ananth,
Another Masterstroke from you...grt analysis & thanks for taking it up..With due respect to Aussies...heartening to see a list in which Aussies are not on top....but in honourable second..Interestng to note that for most countries, the same XI seems to have played in the same series...may be an evidence for reluctance to change winning combination..As mentioned correctly.. SAF is a well settled Test side now...if only the guys deliver the promise they are serious contenders to #1 spot in tests..If Sumant's analysis is also considered. #11 to #5 is dominated by WI and by Aussies... a reflection of their might...WI would be in the favourite list of any true cricket fan...it is fun to watch the guys who play with the best spirit..grt to see their fight in Aus last couple of weeks..After that #5-#2 dominated by most famous Indian middleorder along with the Gladiator - Kumble..If only India managed to find a grt Quickie(still hunting) India would hve achieved greater laurels
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Sesha
Thanks to you for asking a nice question. The 2-10 players' tables will be posted in the next few days. I will use Sumant's work.
Ananth:
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Good stuff once again Ananth.

I agree that the results are surprising. Not necessarily with who the teams are (ie 80s Windies, 00s Aussies etc) as you would expect winning teams to be more consistent.

The suprising thing is the low numbers of matches and also the fact that the top 2 teams had worse than average results with their most Settled line ups.

Also not surprising is that most examples are recent given the sheer volume of matches in the past 10 or 20 years. Previously, the lack of matches per year and the more "amateurish" selection policies would have had a big negative impact on consistency.

I agree with Pankaj Joshi that the trend may well reverse in coming years, with the bigger emphasis on the shorter game.

Finally, in reponse to Xolile, in the 122 matches they played together, Tendulkar has (just about) outscored Dravid 10245 runs to 10113, and also has a better average, 55.38 to 54.08

I read somewhere that the much-touted pace quartet of Roberts/Holding/Garner/Marshall only played together for 6 Tests.

The norm was for any three out of those four, with the fourth being a short-termer like Croft, Daniel, Baptiste, etc.

I'm also surprised that 11 matches is the "record" for the same 11 players in a team. Just a quick query re the England results: the summary shows won four, drawn one and lost one. The list of results shows four wins and two draws.. Kind of leads on to the question of which team benefits the most from consistency of selection...

It is a good one. It will be interesting to see for the ODI and T20I. Is it possible to publish the source data and run the query of the web?