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March 15, 2014

Test top-score analysis: Bradman and Lara dominate

Anantha Narayanan
Brian Lara is one of only two Test batsmen to achieve a HSI value of 1.5 or more in both innings of a Test. The other one was Geoff Rabone of New Zealand  © Getty Images
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The Tendulkar brace (on Tests and on ODIs), written during late 2013, was a tough pair for me. Not only did I have to put in a lot of effort but also had to face a barrage of (often unjustified) criticism from fans of the great cricketer, who did not want to recognise any analyses that did not sing unrestrained praise. However, one good measure came out of these two articles as a very valuable one for measuring player contributions. In those articles, I had presented a raw version of the HSI (High Score Index). This measure found support from many readers and I had promised that I would develop HSI as an independent measure after incorporating tweaks from many readers. In an earlier article, I have covered the ODI game: an easier one to start with because of the single-innings format. In this article I have covered Test matches. This is far more complicated with many nuances not found in the limited-overs format.

The tweaks suggested can be summarised as below.

- Extend the concept to all batsmen scores, not just the top two scores.
- Incorporate the team score into the computations.
- Avoid the very high range of numbers in the early version: the HSI for an innings went as high as 11.4.
- Look at how the players have performed in various classifications, with HSI as the key measure.
- Look at the possibility of using a GM (Geometric Mean) rather than AM (Arithmetic Mean) because of the significant variations.

A 100 as the top score does not provide enough information by itself. It could be out of a team score of 200 or 500. It could be supported by an innings close to 100, by a 50 or by a 10. It could be part of 300 for 1 or 400 for 5 or 200 all out.

The HSI is a measure of two components for the innings top score. The batsman stands alone at the top and his contribution gets enhanced depending on the support received. On the other hand the second-placed scorer has had the support of a higher-scoring batsman. So it is sufficient to take his and other lower-scoring batsmen's contributions based on the team score. With this background let me show you how it works.

Top batsman HSI = {Hs1/Team score} x {Hs1/Hs2}. This incorporates both components.
Other batsmen HSI = {Batsman score/Team score}.

I worked out that there is no need to multiply the lower scores by {Score/Hs1}. That would lower the values too much. An Hs1 of 100 and Hs2 of 90 (out of 200) would end up with the HSI value for Hs1 well over 25% higher than the HSI value for Hs2, which is incorrect.

Let me try to describe the HSI in a visual manner. If we represent the numbers on a linear scale, the team score is at the top. The batsman score is in the middle and the next highest score is below this. The HSI value increases as the distance between the batsman score and the team score decreases. Alternatively, the HSI value increases as the distance between the batsman score and the next highest score increases. Thus the HSI is dependent on how far away these two values are from the batsman score.

There was a suggestion that an average of the next two (or more) high scores be used to determine the HSI. There is some merit in this suggestion. However, whichever way I work this, I cannot see how a sequence of 100, 90, 80... would be significantly different from 100, 90, 25... For that matter we do not even know whether the 90 batsman has been in partnership with the top scorer or not. That would only complicate things. Now it is possible for readers to work out the HSI of an innings by just perusing the scorecards. I do not want to lose this simple application of the concept.

However one major problem, specifically related to Tests, has to be addressed and solved. It is best explained with an example. Let us say that Australia need 50 to win and they reach 50 for 1 with David Warner scoring 40, Chris Rogers scoring 5 and 5 are scored through extras. Warner's innings will get a HSI of 7.28 (8.0*0.88). Totally outrageous, incorrect and unrealistic. This is higher than the current highest HSI value. But there are also situations such as Len Hutton scoring 30 out of 52 all out or Virat Kohli scoring 105 out of 166 for 3 or Stan McCabe scoring 189 out of 274 for 3 and so on. These have to be taken care of. In the same example I have taken, what if Australia collapsed but still won the match by three wickets scoring 50 for 7 and Michael Clarke scoring 25, with the next-highest score being 5. He would have a correct HSI of 2.75 (5.0*0.55). All these situations have to be taken care of.

I analysed this problem in many ways and tried various options. I even did a customised exclusion of matches based on scores and wickets lost. But that meant that all innings played would not be included. Only when I did an analysis of all 2279 innings in which fewer than ten wickets were lost did I realise that loss of five wickets was the separation point. Loss of five wickets meant that the top order had their say and all support innings would be from the lower order. So I decided that all innings of five wickets or below would have their HSI values reduced by a factor. But what about 274 for 3 or 450 for 2 and so on? So I set a limit of 200 runs to apply this adjustment. It has worked very well.

In the previous examples, Warner's HSI would be multiplied by 0.167(1/6) and Kohli's by 0.5(3/6). Hutton, McCabe and Clarke would retain their values. This is exactly as it should be. It would be tempting for any reader, with a five-minute superficial study of this situation, to punch holes in this algorithm. Before doing that, please do not forget that I have spent well over ten hours solely to take care of this problem. I have analysed each wicket-fall group (0/1/2/3/4/5) of innings separately.

Now that the HSI for every innings has been determined, let us move to the many tables I have created. The first is the basic table of the HSI value itself. I have shown the top 30 HSI values. There is a downloadable Excel file which contains the innings which have HSI values greater than or equal to 0.1. Please download and peruse it before asking about specific innings or player.

Readers should remember that these calculations are scorecard-based, non-contextual and within a team. Hutton's 30, out of 52, will get a much higher HSI (2.795) than Ahmed Shehzad's 147 (HSI-1.039), which, in turn will get a much higher HSI value than Mahela Jayawardene's 374 (HSI-0.679). It does not mean that Hutton's innings was better or match-winning, like the other two. It only means that Hutton contributed more to his team in this specific innings than Shehzad or Jayawardene. The result is immaterial. The key word is "contribution". Please make sure that this point is clearly understood.

A note on the cut-off. I have selected 3000 Test runs as the cut-off for the main table and 168 batsmen qualify. Only three of these batsmen, Harbhajan Singh, Anil Kumble and Shane Warne, have an average below 20 and these three have been kept in. Once the cut-off is set, all players are considered equal. Afterwards, I am not going to say one batsman played in only so many matches and another played in many more matches and so on. The players have met the criterion set and that is it.

For the other 12 tables, there are varying cut-off points. In general 50 innings has been used as the minimum for qualification. However, readers should note that to qualify for the later tables only the appropriate cut-off is needed. A batsman who has scored fewer than 3000 Test runs could very well have played 50 innings at home or 30 third innings and so on.

After getting the HSI values I evaluated on the need to do an alternate mean-evaluation. I decided that it is not necessary to use GM and used AM itself since the distribution pattern revealed a few important facts. The top entry is at 6.4 and the next four entries are 4.7. See how steeply the values drop. Also only 13 innings have HSI values greater than 4.0. So there is really only a single outlier: Charles Bannerman's innings. I did not want to be influenced by this single performance.

A few important facts on HSI.

1. There is one HSI value exceeding 6.0, 12 exceeding 4.0, 37 exceeding 3.0, 180 exceeding 2.0 and 1044 exceeding 1.0. So this is a rather exclusive club. Just to illustrate this: a 100 out of 200, with a next-highest score of 50 will have a HSI value of 1.0.
2. The highest HSI value is 6.382 for Bannerman in the very first innings ever played. More on this later. However, to overtake this value, a batsman would have to score 100 out of 150, with the next-highest score being around 10. As many as 74,856 innings have been essayed since Bannerman's 165 and no one has even come close to this HSI value. Not even within 24% of it.
3. The lowest HSI value for a significant Hs1 innings is in match #786. India scored 524 for 9 v New Zealand. The highest score was by Mohinder Amarnath, with 70. The next highest score was 68 and there were six 50s in the innings. Amarnath's 70 earned him a HSI of only 0.145.
4. The highest HSI value for a significant Hs2 innings is for Javed Miandad. In match #1000 - played in 1984. Pakistan scored 230 for 3. Mudassar Nazar top-scored with 106 and Miandad was close behind at 103. Mudassar's HSI was 0.507 and Miandad's HSI was 0.479. The highest HSI value for a HS2 innings in a completed innings was for Stuart Broad's 169. Only Jonathan Trott's 184 was ahead of him and Broad's innings had a HSI of 0.418.
5. The highest HSI value for a significant non-Hs1-Hs2 innings is for Alec Stewart's 79 in match #1411. England scored 321. The top scorer was Nasser Hussain who scored 106 (HSI-0.452). The next highest scorer was Graham Thorpe with 84 (HSI-0.284). Stewart's 79 fetched a HSI of 0.267.
6. 1044 HSI values are 1.0 and above. This represents 1.3% of the total.
7. 3337 HSI values are 0.5 and above. This represents 4.5% of the total.
8. 26300 HSI values are 0.10 and above. This represents 35.1% of the total.
9.The average Hs1 for 6736 team innings is 88.8. The average Hs2 for these innings is 56.4. The ratio is 1.57: remarkably the same as ODI.
10.The average HSI value for the 74857 innings is 0.125. This average also lets us take a stand on career averages of HSI. Maybe 0.2 would an excellent career average. Fifty-one batsmen have career HSI averages exceeding 0.2. A total of 148 batsmen have career HSI averages exceeding 0.125.

Now for the multiple HSI tables based on various selection criteria. This was one of the main objectives of this exercise. For most tables I have shown the top-30/20 players. It should be remembered that if a batsman qualifies on the specific criterion for the table, he would be included even though he may not qualify on the broad qualification of 3000 Test runs. Needless to say (or more appropriately, needs to be said) that the complete set of entries is available in the downloadable file with 14 tables. Please make an attempt to answer your question by downloading that file before asking me. Since this is by far the longest article I have ever penned (or more appropriately, keyed), I will only provide minimal comments.

I have only one overriding criterion for all tables. Irrespective of the number of innings played, Don Bradman is included in all tables. This is to see what he has achieved in all classifications.

1. Top innings HSI values in Tests
SNoHSITest #YearInnsBPosForTeamScoreBatsmanRuns1/2HS1HS2Vs
16.382 118771 1Aus245/10C Bannerman165Hs1165 18Eng
24.744103319853 3Aus308/10AR Border163Hs1163 20Ind
34.741 84619791 4Aus198/10GN Yallop121Hs1121 16Eng
44.729120619923 7Ind215/10Kapil Dev129Hs1129 17Saf
54.692186320083 1Ind269/ 7V Sehwag151Hs1151 20Aus
64.648148120003 1Ind261/10VVS Laxman167Hs1167 25Aus
74.620 73219743 2Eng432/ 9DL Amiss262Hs1262 38Win
84.559141419982 4Saf200/10DJ Cullinan103Hs1103 13Slk
94.046 7919043 3Eng103/10JT Tyldesley 62Hs1 62 10Aus
104.044169420042 5Eng226/10GP Thorpe119Hs1119 17Win
114.034132719963 4Ind219/10SR Tendulkar122Hs1122 18Eng
124.000203820121 4Slk318/10DPMD Jayawardene180Hs1180 27Eng
133.872177320051 4Win405/10BC Lara226Hs1226 34Aus
143.840154120014 1Win 88/ 7CH Gayle 48Hs1 48 8Saf
153.802117119913 1Eng252/10GA Gooch154Hs1154 27Win
163.792 58719652 3Pak307/ 8Saeed Ahmed172Hs1172 29Nzl
173.730 84119793 3Win151/10HA Gomes 91Hs1 91 15Ind
183.671 5818993 2Eng237/10PF Warner132Hs1132 21Saf
193.627 63119684 3Nzl 88/ 4BE Congdon 61Hs1 61 9Ind
203.615 13019131 1Saf182/10HW Taylor109Hs1109 19Eng
213.557 22619332 3Eng548/ 7WR Hammond336Hs1336 60Nzl
223.502143919993 1Aus184/10MJ Slater123Hs1123 24Eng
233.470 16419263 3Aus194/ 5CG Macartney133Hs1133 24Eng
243.398174720051 4Win347/10BC Lara196Hs1196 35Saf
253.372193920093 1Win317/10CH Gayle165Hs1165 27Aus
263.343 33019512 1Eng272/10L Hutton156Hs1156 29Aus
273.307125919941 3Win593/ 5BC Lara375Hs1375 75Eng
283.299127119941 4Zim462/ 9DL Houghton266Hs1266 50Slk
293.290 9119063 3Saf138/10GC White 73Hs1 73 12Eng
303.283 24819354 3Aus274/ 2SJ McCabe189Hs1189 40Saf

On a cool spring day in 1877, Alfred Shaw bowled the first ball in Test cricket to Charles Bannerman. In all probability a dot ball. The next day Bannerman retired when he had scored 165. Australia scored 245 and went on to win the first-ever Test. Bannerman's dominant hundred has remained one of the best "Ashes" (not called so in 1877) innings ever. This innings has remained at the top of two factors for well over 137 years. This is the highest percentage of a completed innings. And the HSI is a fantastic 6.382 (0.696 * 9.1667). The next highest HSI value is 4.744 for Allan Border's epochal innings of 163 against India which has a HSI value of 4.744, 24% behind. Graham Yallop's 121 against England in 1979 has a HSI of 4.741.

However, the next entry is truly amazing. Kapil Dev walked in at 27 for 5 and sculpted a superlative innings of 129, supported by three scores of 17 by Nos. 8, 9 and 10. The HSI of this unforgettable innings is 4.729, the highest, by a mile, for any late-order innings.

This is followed by two modern classics. Virender Sehwag's 151 out of 269 for 7 and VVS Laxman's SCG blitz of 167 have HSI values either side of 4.65. Then comes the defensive classic of Denis Amiss. His nonpareil match-saving innings of 262 out of England's total of 432 for 9, fetched a HSI of 4.62.

Moin Khan's Sialkot classic of 117, like Kapil's, came batting at No. 7, has a very high HSI value of 2.848. Like Kapil, he entered at 15 for 5 and advanced the team score to 212.

There is another innings which is still more amazing. On a gluepot at the Gabba during the 1950-51 Ashes tour, Australia scored 228. England declared at 68 for 7. Australia countered by declaring at 32 for 7, setting England to score 193 for a sensational win. England were staring down the abyss at 30 for 6 when Hutton, by choice batting at No. 8, walked in. He scored 62 most memorable runs. Freddie Brown supported him a little but England fell 70 runs short. One of the most remarkable innings in Test history and the highest HSI value, for a No. 8 innings, Hutton's 62 gets a HSI of 1.966.

2. Top match HSI values in Tests: Both greater than 1.0
SNoHSI-1 InnsHSI-2 InnsTest #YearForVsBatsmanTeamScore-1 InnsBatScore-1 innsTeamScore-2 InnsBatScore-2 inns
11.1211.363 1521923EngSafCAG Russell281/10140241/10111
21.6261.751 3771953NzlSafGO Rabone230/10107149/10 68
31.0101.804 5231962NzlSafJR Reid164/10 60249/10142
41.3341.613 5691964AusPakRB Simpson352/10153227/ 2115
51.8321.271 7351974NzlAusGM Turner255/10101230/ 5110
61.3331.016 7361974NzlAusGM Turner112/10 41158/10 72
71.0251.325 8731980WinNzlDL Haynes140/10 55212/10105
81.0761.12511571990PakWinSaleem Malik170/10 74154/10 71
91.5021.63613011995WinEngBC Lara216/10 87314/10145
101.3071.18813551997EngNzlMA Atherton228/10 94307/ 6118
112.1921.09415372001EngSlkGP Thorpe249/10113 74/ 6 32
121.0141.28715622001ZimSafA Flower286/10142391/10199
131.9451.00815722001WinSlkBC Lara390/10221262/10130
141.5831.05516552003PakBngYasir Hameed346/10170217/ 3105
151.4141.09520862013ZimBngBRM Taylor389/10171227/ 7102

Since these are Test matches I added a new table here. These are the players who achieved a HSI double in a match. They secured HSI values of above 1.0 in both innings. This is a very tough ask as shown by the number of qualifying entries: a mere 15 in 2122 Tests. Only two players have done this twice in their career. Glenn Turner did the double in two consecutive Tests against Australia, in Christchurch and in Auckland with innings of 101, 110, 41 and 72. The first double helped New Zealand to a rare win over their trans-Tasman giants.

The other to achieve the HSI double is Brian Lara. The first was in England during 1995. Lara scored 87 and 145 in the Old Trafford Test. The two HSI values were 1.50 and 1.63. One of only two instances of the HSI values exceeding 1.5 in both innings. But, as often happened with Lara, in a losing cause. In the two innings the highest score by another batsman was 44. Six years later Lara repeated this during his historic tour of Sri Lanka. The 221 and 130 he scored at the SSC, Colombo, fetched him double HSIs exceeding 1.0. Needless to say, again in a losing cause, albeit with better support this time.

3. Career high HSI values: Min 3000 runs
SNoHSIBatsmanRunsAvgeInnsHSI-TGt-1.0%GT-0.25%
1 0.392DG Bradman 699699.94 80 31.3 810.0% 3442.5%
2 0.340BC Lara1195352.89232 78.9 17 7.3% 7532.3%
3 0.306L Hutton 697156.67138 42.2 8 5.8% 4129.7%
4 0.289ED Weekes 445558.62 81 23.4 5 6.2% 2328.4%
5 0.289JB Hobbs 541056.95102 29.5 7 6.9% 3231.4%
6 0.278WR Hammond 724958.46140 39.0 7 5.0% 4230.0%
7 0.267GA Gooch 890042.58209 55.7 12 5.7% 5124.4%
8 0.263SM Gavaskar1012251.12210 55.3 10 4.8% 6531.0%
9 0.259Hanif Mohammad 391543.99 93 24.1 7 7.5% 2425.8%
10 0.259KC Sangakkara1115158.08207 53.6 14 6.8% 5727.5%
11 0.251DL Amiss 361246.31 88 22.1 5 5.7% 1820.5%
12 0.248KF Barrington 680658.67130 32.2 4 3.1% 4030.8%
13 0.244V Sehwag 858649.34178 43.5 10 5.6% 3519.7%
14 0.239A Flower 479451.55110 26.3 7 6.4% 3229.1%
15 0.238Mohammad Yousuf 753052.29154 36.7 8 5.2% 3925.3%
16 0.238PA de Silva 636142.98159 37.9 8 5.0% 4025.2%
17 0.238RN Harvey 614948.42137 32.6 5 3.6% 3727.0%
18 0.237CL Walcott 379856.69 74 17.6 3 4.1% 2027.0%
19 0.236LRPL Taylor 417846.94 98 23.1 4 4.1% 2626.5%
20 0.233H Sutcliffe 455560.73 84 19.5 3 3.6% 2428.6%
21 0.233RA Smith 423643.67108 25.2 7 6.5% 2523.1%
22 0.230G Boycott 811447.73192 44.1 13 6.8% 4121.4%
23 0.230DM Jones 363146.55 89 20.5 5 5.6% 1719.1%
24 0.228CH Gayle 693342.02174 39.7 7 4.0% 3520.1%
25 0.228Saeed Anwar 405245.53 91 20.8 3 3.3% 2022.0%
26 0.227IVA Richards 854050.24182 41.4 8 4.4% 4725.8%
27 0.226AR Morris 353346.49 79 17.8 4 5.1% 1620.3%
28 0.226VT Trumper 316339.05 89 20.1 5 5.6% 1415.7%
29 0.225SR Tendulkar1592153.79326 73.2 12 3.7% 8827.0%
30 0.224DJ Cullinan 455444.21114 25.5 4 3.5% 2219.3%

The top ten in this table are a testament to the effectiveness and immense value of the HSI measure. Bradman, Lara, Hutton, Everton Weekes, Jack Hobbs, Wally Hammond and Sunil Gavaskar would be in anyone's top-ten table of batsmen. The others do not lag behind. We have already seen that 0.20 is the expected career average of a top-quality batsman. Bradman almost doubles this value and Lara is 70% over. There is no doubt about their value to their respective teams.

The top 11 batsmen have career HSI averages exceeding 0.250. Gavaskar is the leading Indian batsman, with an imposing HSI average of 0.263. Hanif Mohammad leads the field for Pakistan. This shows how valuable these two pint-sized giants were for their respective teams. Kumar Sangakkara's presence in the top ten is a clear indication of his stature in Sri Lankan cricket.

I can hear the phrase "in a weak team" being tossed about, especially for Lara. Of course he played in a weak team for the better part of his career. But what about Bradman, Hutton, Hobbs and Hammond? They were in strong teams. Even Graham Gooch and Sangakkara played for relatively strong teams. Only Lara, Gavaskar and Hanif could be said to have played for relatively weaker teams. Even then Gavaskar had above-average support. So this is not a table filled with players from weak teams. It is a table of quality batsmen.

Sehwag underlines his immense value to the Indian team by occupying a top-15 position. Viv Richards and Sachin Tendulkar played in strong batting teams and this fact is reflected in their top-30 positions. Maybe if we take Tendulkar's 1989-1995 period, he would be placed much higher.

The last two columns are interesting. If we take 1.0 as the hallmark of a world class innings (only 1.3% - once in two Tests), Bradman has achieved this in 10% of the innings he has played. Lara comes next with a creditable 7.3%. Hobbs is at 6.9%. Robin Smith is a surprise at 6.5%. Similarly, taking 0.25 as an above-average level contribution, Bradman clocks in at 42.5% and Lara at 32.3%.

4. Batting Positions 1-3 - Min 50 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.420WR Hammond 57 3755 65.88 24.0
2 0.415DG Bradman 56 5078 90.68 23.2
3 0.347BC Lara 68 3860 56.76 23.6
4 0.316GM Turner 69 2887 41.84 21.8
5 0.313IVA Richards 63 3787 60.11 19.7
6 0.299DL Amiss 70 3305 47.21 20.9
7 0.298L Hutton131 6721 51.31 39.0
8 0.285JB Hobbs 98 5153 52.58 27.9
9 0.283Saeed Ahmed 59 2498 42.34 16.7
10 0.281GA Gooch189 7990 42.28 53.2
11 0.267KC Sangakkara19310468 54.24 51.5
12 0.267DA Warner 55 2462 44.76 14.7
13 0.266AJ Stewart112 4655 41.56 29.8
14 0.263SM Gavaskar199 9442 47.45 52.3
15 0.258Hanif Mohammad 62 2585 41.69 16.0
16 0.254VT Trumper 56 1909 34.09 14.2
17 0.253KC Wessels 55 2333 42.42 13.9
18 0.252DI Gower 59 2692 45.63 14.9
19 0.249V Sehwag169 8166 48.32 42.2
20 0.249SP Fleming 79 3309 41.89 19.7

It is not a surprise that Bradman leads in most of these tables. However in the 1-3 batting position table, Hammond just about edges ahead of him with a very high career HSI average of 0.42. Bradman's average is 0.415. Lara is in third place with 0.347. Turner is a surprise fourth with 0.316. It is clear that Richards out-performed his compatriots quite significantly with 0.313. Readers can see that the 20th entry in this table has a relatively high average HSI of 0.249.

5. Batting Positions 4-7 - Min 50 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.339BC Lara163 8079 49.56 55.3
2 0.337DG Bradman 24 1918 79.92 8.1
3 0.303ED Weekes 70 3858 55.11 21.2
4 0.301AD Nourse 60 2940 49.00 18.1
5 0.250A Flower104 4364 41.96 26.0
6 0.247RN Harvey 57 2693 47.25 14.1
7 0.239LRPL Taylor 96 4142 43.15 22.9
8 0.238Mohammad Yousuf151 7378 48.86 36.0
9 0.230DJ Cullinan110 4229 38.45 25.3
10 0.230DCS Compton116 5422 46.74 26.7
11 0.230JR Reid 99 3201 32.33 22.8
12 0.225S Chanderpaul22810215 44.80 51.2
13 0.225SR Tendulkar32515809 48.64 73.1
14 0.225PA de Silva148 5896 39.84 33.4
15 0.219Javed Miandad183 8678 47.42 40.1
16 0.219PBH May 59 2634 44.64 12.9
17 0.219GR Viswanath148 5605 37.87 32.4
18 0.218RA Smith 93 3566 38.34 20.3
19 0.216MD Crowe121 5209 43.05 26.2
20 0.214JH Kallis201 9896 49.23 42.9

In positions 4-7, Lara edges out Bradman by the third decimal. Then come the middle-order giants: Weekes, Dudley Nourse, Andy Flower and Neil Harvey. Tendulkar has an average HSI of 0.225 in these positions. Barring one innings, this is Tendulkar's entire career.

6. First innings - Min 40 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.516BC Lara 58 4000 68.97 29.9
2 0.454DG Bradman 22 2387108.50 10.0
3 0.295IVA Richards 48 2531 52.73 14.2
4 0.295RB Kanhai 44 2869 65.20 13.0
5 0.288Javed Miandad 60 3730 62.17 17.3
6 0.279KC Sangakkara 63 3477 55.19 17.6
7 0.260WR Hammond 46 2691 58.50 12.0
8 0.258S Chanderpaul 62 3396 54.77 16.0
9 0.258CL Hooper 42 1791 42.64 10.8
10 0.256CG Greenidge 49 2455 50.10 12.6
11 0.251Mohammad Yousuf 42 2060 49.05 10.5
12 0.250GR Viswanath 45 1688 37.51 11.2
13 0.248DPMD Jayawardene 71 3695 52.04 17.6
14 0.244V Sehwag 45 2586 57.47 11.0
15 0.235KF Barrington 41 2726 66.49 9.7
16 0.234IT Botham 57 2261 39.67 13.3
17 0.230SP Fleming 58 2980 51.38 13.3
18 0.228SR Tendulkar 89 5518 62.00 20.3
19 0.227GA Gooch 68 3101 45.60 15.4
20 0.223TT Samaraweera 42 2472 58.86 9.4

In Tests, the first innings is the marker-setting innings. The second innings is more often a reactive taking-stock innings. The third innings is a target-setting one. The fourth innings always has a target. It could be one run to win, 731 runs to win, batting out 200 overs et al. Lara leads the first innings HSI table with a remarkable average of 0.516, one of only two times a batsman has exceeded 0.5 in these tables. Bradman follows with 0.454. And then daylight and Richards and Rohan Kanhai follow with 0.295. Lara's RpI for first innings is a high 68.97.

Gavaskar is conspicuous by failing to make the cut. His HSI average is only 0.194. Milind's father is a big fan of Gavaskar. So he had the right to criticise on the lines "Yeh pyar hai, gila nahin [It is my love, not a complaint]", when he once said that India as a team would have fared better if Gavaskar eked out his second-innings performance in the first innings since the chances of a win were slim at the start of second innings. Well said, Mr Pandit.

7. Second innings - Min 40 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.402L Hutton 44 2673 60.75 17.7
2 0.323BC Lara 72 4249 59.01 23.3
3 0.312DG Bradman 28 2310 82.50 8.7
4 0.302GP Thorpe 56 2873 51.30 16.9
5 0.286V Sehwag 58 3823 65.91 16.6
6 0.286PA de Silva 43 2264 52.65 12.3
7 0.283KP Pietersen 46 2521 54.80 13.0
8 0.273SM Gavaskar 62 3552 57.29 17.0
9 0.266Mohammad Yousuf 46 2977 64.72 12.3
10 0.261MC Cowdrey 51 2537 49.75 13.3
11 0.254RN Harvey 42 2266 53.95 10.6
12 0.254DPMD Jayawardene 69 4598 66.64 17.5
13 0.250AB de Villiers 48 2638 54.96 12.0
14 0.242ME Trescothick 40 2192 54.80 9.7
15 0.238R Dravid 89 4984 56.00 21.2
16 0.228DI Gower 52 2572 49.46 11.8
17 0.227KF Barrington 40 2334 58.35 9.1
18 0.223KC Sangakkara 57 3474 60.95 12.7
19 0.222SR Tendulkar106 5692 53.70 23.5
20 0.220AC Gilchrist 47 2501 53.21 10.3

These are the reactive performances. Hutton leads with a career HSI average of 0.402. Lara follows next with 0.323 and then Bradman, with 0.312. Thorpe is in fourth place with 0.302. Then comes the marauder, Sehwag, with 0.286. Aravinda de Silva, Kevin Pietersen and Gavaskar are also up there.

8. Third innings - Min 40 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.546DG Bradman 15 1565104.33 8.2
2 0.361AR Border 76 3511 46.20 27.4
3 0.325DL Haynes 41 1938 47.27 13.3
4 0.324GA Gooch 66 2722 41.24 21.4
5 0.322KC Sangakkara 59 3161 53.58 19.0
6 0.297JH Kallis 67 3394 50.66 19.9
7 0.280VVS Laxman 52 2332 44.85 14.5
8 0.274DI Gower 62 2287 36.89 17.0
9 0.272AN Cook 46 2212 48.09 12.5
10 0.270DC Boon 55 2186 39.75 14.8
11 0.270BC Lara 56 2264 40.43 15.1
12 0.263SR Tendulkar 71 2989 42.10 18.7
13 0.260ML Hayden 41 2152 52.49 10.7
14 0.259PA de Silva 47 1692 36.00 12.2
15 0.254BB McCullum 40 1696 42.40 10.2
16 0.249Habibul Bashar 44 1416 32.18 11.0
17 0.243Inzamam-ul-Haq 51 2327 45.63 12.4
18 0.242SM Gavaskar 55 2486 45.20 13.3
19 0.242G Boycott 51 2085 40.88 12.3
20 0.239S Chanderpaul 65 2194 33.75 15.5

The third innings sees Bradman with 0.546, although he played only 15 innings. The 270 would have certainly helped. We now have some other names indicating that the requirements are different. Border, Desmond Haynes, Gooch come in. For the first time, Lara moves past the top-ten positions.

9. Fourth innings - Min 25 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.406SM Gavaskar 33 1398 42.36 13.4
2 0.378GA Gooch 29 1121 38.66 11.0
3 0.294DG Bradman 15 734 48.93 4.4
4 0.277MA Atherton 39 1375 35.26 10.8
5 0.274MA Butcher 25 787 31.48 6.8
6 0.263G Boycott 34 1234 36.29 8.9
7 0.263CH Gayle 39 1280 32.82 10.3
8 0.243RN Harvey 30 857 28.57 7.3
9 0.238Inzamam-ul-Haq 31 867 27.97 7.4
10 0.232L Hutton 31 953 30.74 7.2
11 0.231BC Lara 46 1440 31.30 10.6
12 0.229AJ Stewart 39 1136 29.13 8.9
13 0.227GC Smith 41 1611 39.29 9.3
14 0.223IR Bell 29 803 27.69 6.5
15 0.219ME Waugh 27 820 30.37 5.9
16 0.212CG Greenidge 38 1383 36.39 8.1
17 0.208Younis Khan 29 1003 34.59 6.0
18 0.208JG Wright 27 734 27.19 5.6
19 0.205G Kirsten 29 780 26.90 5.9
20 0.196V Sehwag 34 901 26.50 6.7

Gavaskar leads in the fourth-innings table with 0.406. Gooch follows closely. Bradman, with only 15 innings is next. Graeme Smith is in the top 20, with a HSI average of 0.227, but with a very high aggregate of 1611 runs. I wonder whether there was a case for combining the first and second innings as "first" and third and fourth as "second". However, what dissuaded me from doing that was my take that the third and fourth innings are quite different in the challenges faced.

Tendulkar is placed at 28th with an average HSI value of 0.179. Laxman is below average in the first innings but far better in the third and fourth innings while Tendulkar is vice versa. Dravid is better placed in innings two and three. The bottom line is that these three gentlemen worked beautifully as a team.

10 Home matches - Min 50 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.402DG Bradman 50 4322 86.44 20.1
2 0.368BC Lara111 6217 56.01 40.8
3 0.300GA Gooch126 5708 45.30 37.8
4 0.289RA Smith 62 2631 42.44 17.9
5 0.276DCS Compton 76 3963 52.14 21.0
6 0.267Mohammad Yousuf 52 3067 58.98 13.9
7 0.266DPMD Jayawardene121 6846 56.58 32.1
8 0.264PA de Silva 72 3290 45.69 19.0
9 0.262L Hutton 77 3930 51.04 20.2
10 0.257RN Harvey 66 2806 42.52 17.0
11 0.250KP Pietersen 89 4537 50.98 22.3
12 0.248MJ Slater 57 2842 49.86 14.2
13 0.244M Azharuddin 66 3412 51.70 16.1
14 0.240JH Edrich 77 3155 40.97 18.5
15 0.239DJ Cullinan 59 2363 40.05 14.1
16 0.239SM Gavaskar106 5031 47.46 25.4
17 0.237GR Viswanath 80 3280 41.00 19.0
18 0.236KC Sangakkara108 6138 56.83 25.5
19 0.236PBH May 57 2865 50.26 13.4
20 0.225S Chanderpaul119 5630 47.31 26.8

Bradman was king at home. Lara follows closely. And then Gooch and, quite surprisingly, Robin Smith.

11. Away matches - Min 50 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.375DG Bradman 30 2674 89.13 11.2
2 0.364WR Hammond 72 4245 58.96 26.2
3 0.361L Hutton 61 3041 49.85 22.0
4 0.330JB Hobbs 62 3475 56.05 20.4
5 0.315BC Lara121 5736 47.40 38.1
6 0.290KC Sangakkara 87 4082 46.92 25.2
7 0.288SM Gavaskar104 4926 47.37 29.9
8 0.288KF Barrington 57 3375 59.21 16.4
9 0.272V Sehwag 91 3930 43.19 24.8
10 0.267A Flower 56 2307 41.20 15.0
11 0.263AR Border118 5154 43.68 31.0
12 0.258M Amarnath 61 2967 48.64 15.7
13 0.250SR Tendulkar176 8705 49.46 44.1
14 0.248CH Gayle 87 3633 41.76 21.6
15 0.248R Dravid166 7690 46.33 41.1
16 0.236SP Fleming 98 4216 43.02 23.1
17 0.236G Boycott 93 3758 40.41 21.9
18 0.234IVA Richards115 5404 46.99 26.9
19 0.234Hanif Mohammad 53 2221 41.91 12.4
20 0.232DI Gower 90 3713 41.26 20.9

This definition of away included neutral locations. Look at the top five positions. Bradman, Hammond (no doubt helped by the 336 not out), Hutton, Hobbs and Lara: five of the greatest batsmen who ever lived. Gavaskar is also there. Of the modern batsmen, Sangakkara (with considerable help from runs against Bangladesh) and Sehwag (with very little against Bangladesh) are in the top ten.

12. Wins - Min 30 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.480DG Bradman 43 4813111.93 20.7
2 0.373GR Viswanath 37 1637 44.24 13.8
3 0.345GA Gooch 55 2867 52.13 19.0
4 0.317Saeed Anwar 36 2254 62.61 11.4
5 0.312WR Hammond 44 2584 58.73 13.7
6 0.302JB Hobbs 45 2720 60.44 13.6
7 0.290GP Thorpe 63 3006 47.71 18.3
8 0.284KC Sangakkara 74 4913 66.39 21.0
9 0.280GS Chappell 62 3595 57.98 17.4
10 0.274BC Lara 52 2929 56.33 14.2
11 0.269Inzamam-ul-Haq 76 4690 61.71 20.5
12 0.266L Hutton 48 2678 55.79 12.8
13 0.264M Azharuddin 32 1609 50.28 8.5
14 0.264DA Warner 31 1608 51.87 8.2
15 0.247JH Edrich 35 1771 50.60 8.6
16 0.241KP Pietersen 67 3655 54.55 16.1
17 0.241RN Harvey 66 3253 49.29 15.9
18 0.240GS Sobers 46 3097 67.33 11.1
19 0.238IT Botham 47 1918 40.81 11.2
20 0.238C Hill 44 2223 50.52 10.5

In the wins table, Bradman's name is expected. But Gundappa Viswanath's presence is wholly unexpected. That means he played many valuable innings in the 37 India wins. Saeed Anwar's contribution to Pakistan wins is highlighted. Lara is in tenth position, albeit with a good HSI average of 0.274.

13. Losses - Min 30 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.461L Hutton 39 1700 43.59 18.0
2 0.382DL Haynes 30 1065 35.50 11.5
3 0.361BC Lara126 5316 42.19 45.5
4 0.334HW Taylor 46 1569 34.11 15.4
5 0.326GN Yallop 32 1035 32.34 10.4
6 0.304RN Harvey 30 962 32.07 9.1
7 0.288Saeed Ahmed 30 1135 37.83 8.6
8 0.283SR Tendulkar112 4088 36.50 31.7
9 0.281GM Turner 35 874 24.97 9.8
10 0.273RA Smith 52 1734 33.35 14.2
11 0.271PBH May 30 1215 40.50 8.1
12 0.270AD Nourse 34 1331 39.15 9.2
13 0.263B Sutcliffe 46 1222 26.57 12.1
14 0.261JB Hobbs 42 1889 44.98 11.0
15 0.261A Flower 66 2372 35.94 17.3
16 0.254ME Trescothick 40 1467 36.67 10.1
17 0.248RB Kanhai 40 1340 33.50 9.9
18 0.247Mohammad Yousuf 65 2393 36.82 16.1
19 0.241AI Kallicharran 30 937 31.23 7.2
20 0.240JG Wright 46 1365 29.67 11.0

Note the low RpI values of batsmen in this table covering losses. Hutton has performed valiantly in the losses. Haynes and Lara are also there. Many of Tendulkar's losses would have occurred during the early years. Incidentally, this is the only featured table in which Bradman is not present. That is because, in the 22 Australia losses, Bradman averaged only 0.20 in the HSI value measure. His RpI fell to a mortal value of 43.2.

14. Draws - Min 30 inns
SNoAvge HSIBatsmanInningsRunsRpITotal HSI
1 0.462CH Gayle 45 2990 66.44 20.8
2 0.418DG Bradman 15 1231 82.07 6.3
3 0.356BC Lara 54 3708 68.67 19.2
4 0.341Hanif Mohammad 52 2771 53.29 17.7
5 0.340DL Amiss 34 1643 48.32 11.6
6 0.327PA de Silva 56 3154 56.32 18.3
7 0.316SM Gavaskar103 6101 59.23 32.5
8 0.307G Kirsten 46 2370 51.52 14.1
9 0.301V Sehwag 54 3118 57.74 16.2
10 0.299WR Hammond 60 3614 60.23 17.9
11 0.298AR Border 99 5217 52.70 29.5
12 0.291CL Hooper 44 2257 51.30 12.8
13 0.290IVA Richards 54 3043 56.35 15.7
14 0.283KC Sangakkara 59 3733 63.27 16.7
15 0.283Mohammad Yousuf 34 2298 67.59 9.6
16 0.279KF Barrington 65 3755 57.77 18.2
17 0.272MP Vaughan 41 2102 51.27 11.2
18 0.271JH Kallis 72 4337 60.24 19.5
19 0.269GA Gooch 74 3400 45.95 19.9
20 0.261KP Pietersen 52 2831 54.44 13.6

What do we have here? Chris Gayle leads the table. I get the feeling the two 300s, totaling 650 runs, have helped push this value up. Maybe for Lara also, and for Hanif.

The HSI is an excellent measure to capture two important aspects of a batsman score: the support he received (or lack of) and his contribution to the team score. The fact that 30 out of 52 would be rated much higher than 374 out of 756 indicates that the measure is size-independent. As such it has a tremendous value across years and Tests. The other inherent characteristic is the true peer-comparison aspects built in. And the fact that Clem Hill's 188 will be treated in identical manner to Jayawardene's 180, played 122 years later.

To download/view the file containing all qualifying entries of the 14 tables, please CLICK HERE. My take is that many of the questions can be answered if you download this file, and view the contents.

To download/view the huge Excel file (size-10 Mb) containing details of the 26000+ innings with HSI values 0.100 and above, please CLICK HERE. Instead of asking me obvious questions for which the answers are already there in the tables, you could download the file and view the tables.

This article has already raised very justified demands for similar articles, listed below. Some suggestions for performances to be included are already in. I will try and do these after a few days.
: Sub-100 innings, not just forgotten ones.
: Late-order innings.

However my next article will be a similar performance-measuring analysis for the forgotten lot: the Test bowlers.

Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems

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ABOUT THE AUTHOR

Anantha Narayanan
Anantha spent the first half of his four-decade working career with corporates like IBM, Shaw Wallace, NCR, Sime Darby and the Spinneys group in IT-related positions. In the second half, he has worked on cricket simulation, ratings, data mining, analysis and writing, amongst other things. He was the creator of the Wisden 100 lists, released in 2001. He has written for ESPNcricinfo and CastrolCricket, and worked extensively with Maruti Motors, Idea Cellular and Castrol on their performance ratings-related systems. He is an armchair connoisseur of most sports. His other passion is tennis, and he thinks Roger Federer is the greatest sportsman to have walked on earth.

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