Test top-score analysis: Bradman and Lara dominate

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

SNo	HSI	Test #	Year	Inns	BPos	For	TeamScore	Batsman	Runs	1/2	HS1	HS2	Vs
1	6.382	1	1877	1	1	Aus	245/10	C Bannerman	165	Hs1	165	18	Eng
2	4.744	1033	1985	3	3	Aus	308/10	AR Border	163	Hs1	163	20	Ind
3	4.741	846	1979	1	4	Aus	198/10	GN Yallop	121	Hs1	121	16	Eng
4	4.729	1206	1992	3	7	Ind	215/10	Kapil Dev	129	Hs1	129	17	Saf
5	4.692	1863	2008	3	1	Ind	269/ 7	V Sehwag	151	Hs1	151	20	Aus
6	4.648	1481	2000	3	1	Ind	261/10	VVS Laxman	167	Hs1	167	25	Aus
7	4.620	732	1974	3	2	Eng	432/ 9	DL Amiss	262	Hs1	262	38	Win
8	4.559	1414	1998	2	4	Saf	200/10	DJ Cullinan	103	Hs1	103	13	Slk
9	4.046	79	1904	3	3	Eng	103/10	JT Tyldesley	62	Hs1	62	10	Aus
10	4.044	1694	2004	2	5	Eng	226/10	GP Thorpe	119	Hs1	119	17	Win
11	4.034	1327	1996	3	4	Ind	219/10	SR Tendulkar	122	Hs1	122	18	Eng
12	4.000	2038	2012	1	4	Slk	318/10	DPMD Jayawardene	180	Hs1	180	27	Eng
13	3.872	1773	2005	1	4	Win	405/10	BC Lara	226	Hs1	226	34	Aus
14	3.840	1541	2001	4	1	Win	88/ 7	CH Gayle	48	Hs1	48	8	Saf
15	3.802	1171	1991	3	1	Eng	252/10	GA Gooch	154	Hs1	154	27	Win
16	3.792	587	1965	2	3	Pak	307/ 8	Saeed Ahmed	172	Hs1	172	29	Nzl
17	3.730	841	1979	3	3	Win	151/10	HA Gomes	91	Hs1	91	15	Ind
18	3.671	58	1899	3	2	Eng	237/10	PF Warner	132	Hs1	132	21	Saf
19	3.627	631	1968	4	3	Nzl	88/ 4	BE Congdon	61	Hs1	61	9	Ind
20	3.615	130	1913	1	1	Saf	182/10	HW Taylor	109	Hs1	109	19	Eng
21	3.557	226	1933	2	3	Eng	548/ 7	WR Hammond	336	Hs1	336	60	Nzl
22	3.502	1439	1999	3	1	Aus	184/10	MJ Slater	123	Hs1	123	24	Eng
23	3.470	164	1926	3	3	Aus	194/ 5	CG Macartney	133	Hs1	133	24	Eng
24	3.398	1747	2005	1	4	Win	347/10	BC Lara	196	Hs1	196	35	Saf
25	3.372	1939	2009	3	1	Win	317/10	CH Gayle	165	Hs1	165	27	Aus
26	3.343	330	1951	2	1	Eng	272/10	L Hutton	156	Hs1	156	29	Aus
27	3.307	1259	1994	1	3	Win	593/ 5	BC Lara	375	Hs1	375	75	Eng
28	3.299	1271	1994	1	4	Zim	462/ 9	DL Houghton	266	Hs1	266	50	Slk
29	3.290	91	1906	3	3	Saf	138/10	GC White	73	Hs1	73	12	Eng
30	3.283	248	1935	4	3	Aus	274/ 2	SJ McCabe	189	Hs1	189	40	Saf

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

SNo	HSI-1 Inns	HSI-2 Inns	Test #	Year	For	Vs	Batsman	TeamScore-1 Inns	BatScore-1 inns	TeamScore-2 Inns	BatScore-2 inns
1	1.121	1.363	152	1923	Eng	Saf	CAG Russell	281/10	140	241/10	111
2	1.626	1.751	377	1953	Nzl	Saf	GO Rabone	230/10	107	149/10	68
3	1.010	1.804	523	1962	Nzl	Saf	JR Reid	164/10	60	249/10	142
4	1.334	1.613	569	1964	Aus	Pak	RB Simpson	352/10	153	227/ 2	115
5	1.832	1.271	735	1974	Nzl	Aus	GM Turner	255/10	101	230/ 5	110
6	1.333	1.016	736	1974	Nzl	Aus	GM Turner	112/10	41	158/10	72
7	1.025	1.325	873	1980	Win	Nzl	DL Haynes	140/10	55	212/10	105
8	1.076	1.125	1157	1990	Pak	Win	Saleem Malik	170/10	74	154/10	71
9	1.502	1.636	1301	1995	Win	Eng	BC Lara	216/10	87	314/10	145
10	1.307	1.188	1355	1997	Eng	Nzl	MA Atherton	228/10	94	307/ 6	118
11	2.192	1.094	1537	2001	Eng	Slk	GP Thorpe	249/10	113	74/ 6	32
12	1.014	1.287	1562	2001	Zim	Saf	A Flower	286/10	142	391/10	199
13	1.945	1.008	1572	2001	Win	Slk	BC Lara	390/10	221	262/10	130
14	1.583	1.055	1655	2003	Pak	Bng	Yasir Hameed	346/10	170	217/ 3	105
15	1.414	1.095	2086	2013	Zim	Bng	BRM Taylor	389/10	171	227/ 7	102

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

SNo	HSI	Batsman	Runs	Avge	Inns	HSI-T	Gt-1.0	%	GT-0.25	%
1	0.392	DG Bradman	6996	99.94	80	31.3	8	10.0%	34	42.5%
2	0.340	BC Lara	11953	52.89	232	78.9	17	7.3%	75	32.3%
3	0.306	L Hutton	6971	56.67	138	42.2	8	5.8%	41	29.7%
4	0.289	ED Weekes	4455	58.62	81	23.4	5	6.2%	23	28.4%
5	0.289	JB Hobbs	5410	56.95	102	29.5	7	6.9%	32	31.4%
6	0.278	WR Hammond	7249	58.46	140	39.0	7	5.0%	42	30.0%
7	0.267	GA Gooch	8900	42.58	209	55.7	12	5.7%	51	24.4%
8	0.263	SM Gavaskar	10122	51.12	210	55.3	10	4.8%	65	31.0%
9	0.259	Hanif Mohammad	3915	43.99	93	24.1	7	7.5%	24	25.8%
10	0.259	KC Sangakkara	11151	58.08	207	53.6	14	6.8%	57	27.5%
11	0.251	DL Amiss	3612	46.31	88	22.1	5	5.7%	18	20.5%
12	0.248	KF Barrington	6806	58.67	130	32.2	4	3.1%	40	30.8%
13	0.244	V Sehwag	8586	49.34	178	43.5	10	5.6%	35	19.7%
14	0.239	A Flower	4794	51.55	110	26.3	7	6.4%	32	29.1%
15	0.238	Mohammad Yousuf	7530	52.29	154	36.7	8	5.2%	39	25.3%
16	0.238	PA de Silva	6361	42.98	159	37.9	8	5.0%	40	25.2%
17	0.238	RN Harvey	6149	48.42	137	32.6	5	3.6%	37	27.0%
18	0.237	CL Walcott	3798	56.69	74	17.6	3	4.1%	20	27.0%
19	0.236	LRPL Taylor	4178	46.94	98	23.1	4	4.1%	26	26.5%
20	0.233	H Sutcliffe	4555	60.73	84	19.5	3	3.6%	24	28.6%
21	0.233	RA Smith	4236	43.67	108	25.2	7	6.5%	25	23.1%
22	0.230	G Boycott	8114	47.73	192	44.1	13	6.8%	41	21.4%
23	0.230	DM Jones	3631	46.55	89	20.5	5	5.6%	17	19.1%
24	0.228	CH Gayle	6933	42.02	174	39.7	7	4.0%	35	20.1%
25	0.228	Saeed Anwar	4052	45.53	91	20.8	3	3.3%	20	22.0%
26	0.227	IVA Richards	8540	50.24	182	41.4	8	4.4%	47	25.8%
27	0.226	AR Morris	3533	46.49	79	17.8	4	5.1%	16	20.3%
28	0.226	VT Trumper	3163	39.05	89	20.1	5	5.6%	14	15.7%
29	0.225	SR Tendulkar	15921	53.79	326	73.2	12	3.7%	88	27.0%
30	0.224	DJ Cullinan	4554	44.21	114	25.5	4	3.5%	22	19.3%

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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.420	WR Hammond	57	3755	65.88	24.0
2	0.415	DG Bradman	56	5078	90.68	23.2
3	0.347	BC Lara	68	3860	56.76	23.6
4	0.316	GM Turner	69	2887	41.84	21.8
5	0.313	IVA Richards	63	3787	60.11	19.7
6	0.299	DL Amiss	70	3305	47.21	20.9
7	0.298	L Hutton	131	6721	51.31	39.0
8	0.285	JB Hobbs	98	5153	52.58	27.9
9	0.283	Saeed Ahmed	59	2498	42.34	16.7
10	0.281	GA Gooch	189	7990	42.28	53.2
11	0.267	KC Sangakkara	193	10468	54.24	51.5
12	0.267	DA Warner	55	2462	44.76	14.7
13	0.266	AJ Stewart	112	4655	41.56	29.8
14	0.263	SM Gavaskar	199	9442	47.45	52.3
15	0.258	Hanif Mohammad	62	2585	41.69	16.0
16	0.254	VT Trumper	56	1909	34.09	14.2
17	0.253	KC Wessels	55	2333	42.42	13.9
18	0.252	DI Gower	59	2692	45.63	14.9
19	0.249	V Sehwag	169	8166	48.32	42.2
20	0.249	SP 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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.339	BC Lara	163	8079	49.56	55.3
2	0.337	DG Bradman	24	1918	79.92	8.1
3	0.303	ED Weekes	70	3858	55.11	21.2
4	0.301	AD Nourse	60	2940	49.00	18.1
5	0.250	A Flower	104	4364	41.96	26.0
6	0.247	RN Harvey	57	2693	47.25	14.1
7	0.239	LRPL Taylor	96	4142	43.15	22.9
8	0.238	Mohammad Yousuf	151	7378	48.86	36.0
9	0.230	DJ Cullinan	110	4229	38.45	25.3
10	0.230	DCS Compton	116	5422	46.74	26.7
11	0.230	JR Reid	99	3201	32.33	22.8
12	0.225	S Chanderpaul	228	10215	44.80	51.2
13	0.225	SR Tendulkar	325	15809	48.64	73.1
14	0.225	PA de Silva	148	5896	39.84	33.4
15	0.219	Javed Miandad	183	8678	47.42	40.1
16	0.219	PBH May	59	2634	44.64	12.9
17	0.219	GR Viswanath	148	5605	37.87	32.4
18	0.218	RA Smith	93	3566	38.34	20.3
19	0.216	MD Crowe	121	5209	43.05	26.2
20	0.214	JH Kallis	201	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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.516	BC Lara	58	4000	68.97	29.9
2	0.454	DG Bradman	22	2387	108.50	10.0
3	0.295	IVA Richards	48	2531	52.73	14.2
4	0.295	RB Kanhai	44	2869	65.20	13.0
5	0.288	Javed Miandad	60	3730	62.17	17.3
6	0.279	KC Sangakkara	63	3477	55.19	17.6
7	0.260	WR Hammond	46	2691	58.50	12.0
8	0.258	S Chanderpaul	62	3396	54.77	16.0
9	0.258	CL Hooper	42	1791	42.64	10.8
10	0.256	CG Greenidge	49	2455	50.10	12.6
11	0.251	Mohammad Yousuf	42	2060	49.05	10.5
12	0.250	GR Viswanath	45	1688	37.51	11.2
13	0.248	DPMD Jayawardene	71	3695	52.04	17.6
14	0.244	V Sehwag	45	2586	57.47	11.0
15	0.235	KF Barrington	41	2726	66.49	9.7
16	0.234	IT Botham	57	2261	39.67	13.3
17	0.230	SP Fleming	58	2980	51.38	13.3
18	0.228	SR Tendulkar	89	5518	62.00	20.3
19	0.227	GA Gooch	68	3101	45.60	15.4
20	0.223	TT 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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.402	L Hutton	44	2673	60.75	17.7
2	0.323	BC Lara	72	4249	59.01	23.3
3	0.312	DG Bradman	28	2310	82.50	8.7
4	0.302	GP Thorpe	56	2873	51.30	16.9
5	0.286	V Sehwag	58	3823	65.91	16.6
6	0.286	PA de Silva	43	2264	52.65	12.3
7	0.283	KP Pietersen	46	2521	54.80	13.0
8	0.273	SM Gavaskar	62	3552	57.29	17.0
9	0.266	Mohammad Yousuf	46	2977	64.72	12.3
10	0.261	MC Cowdrey	51	2537	49.75	13.3
11	0.254	RN Harvey	42	2266	53.95	10.6
12	0.254	DPMD Jayawardene	69	4598	66.64	17.5
13	0.250	AB de Villiers	48	2638	54.96	12.0
14	0.242	ME Trescothick	40	2192	54.80	9.7
15	0.238	R Dravid	89	4984	56.00	21.2
16	0.228	DI Gower	52	2572	49.46	11.8
17	0.227	KF Barrington	40	2334	58.35	9.1
18	0.223	KC Sangakkara	57	3474	60.95	12.7
19	0.222	SR Tendulkar	106	5692	53.70	23.5
20	0.220	AC 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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.546	DG Bradman	15	1565	104.33	8.2
2	0.361	AR Border	76	3511	46.20	27.4
3	0.325	DL Haynes	41	1938	47.27	13.3
4	0.324	GA Gooch	66	2722	41.24	21.4
5	0.322	KC Sangakkara	59	3161	53.58	19.0
6	0.297	JH Kallis	67	3394	50.66	19.9
7	0.280	VVS Laxman	52	2332	44.85	14.5
8	0.274	DI Gower	62	2287	36.89	17.0
9	0.272	AN Cook	46	2212	48.09	12.5
10	0.270	DC Boon	55	2186	39.75	14.8
11	0.270	BC Lara	56	2264	40.43	15.1
12	0.263	SR Tendulkar	71	2989	42.10	18.7
13	0.260	ML Hayden	41	2152	52.49	10.7
14	0.259	PA de Silva	47	1692	36.00	12.2
15	0.254	BB McCullum	40	1696	42.40	10.2
16	0.249	Habibul Bashar	44	1416	32.18	11.0
17	0.243	Inzamam-ul-Haq	51	2327	45.63	12.4
18	0.242	SM Gavaskar	55	2486	45.20	13.3
19	0.242	G Boycott	51	2085	40.88	12.3
20	0.239	S 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

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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.402	DG Bradman	50	4322	86.44	20.1
2	0.368	BC Lara	111	6217	56.01	40.8
3	0.300	GA Gooch	126	5708	45.30	37.8
4	0.289	RA Smith	62	2631	42.44	17.9
5	0.276	DCS Compton	76	3963	52.14	21.0
6	0.267	Mohammad Yousuf	52	3067	58.98	13.9
7	0.266	DPMD Jayawardene	121	6846	56.58	32.1
8	0.264	PA de Silva	72	3290	45.69	19.0
9	0.262	L Hutton	77	3930	51.04	20.2
10	0.257	RN Harvey	66	2806	42.52	17.0
11	0.250	KP Pietersen	89	4537	50.98	22.3
12	0.248	MJ Slater	57	2842	49.86	14.2
13	0.244	M Azharuddin	66	3412	51.70	16.1
14	0.240	JH Edrich	77	3155	40.97	18.5
15	0.239	DJ Cullinan	59	2363	40.05	14.1
16	0.239	SM Gavaskar	106	5031	47.46	25.4
17	0.237	GR Viswanath	80	3280	41.00	19.0
18	0.236	KC Sangakkara	108	6138	56.83	25.5
19	0.236	PBH May	57	2865	50.26	13.4
20	0.225	S Chanderpaul	119	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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.375	DG Bradman	30	2674	89.13	11.2
2	0.364	WR Hammond	72	4245	58.96	26.2
3	0.361	L Hutton	61	3041	49.85	22.0
4	0.330	JB Hobbs	62	3475	56.05	20.4
5	0.315	BC Lara	121	5736	47.40	38.1
6	0.290	KC Sangakkara	87	4082	46.92	25.2
7	0.288	SM Gavaskar	104	4926	47.37	29.9
8	0.288	KF Barrington	57	3375	59.21	16.4
9	0.272	V Sehwag	91	3930	43.19	24.8
10	0.267	A Flower	56	2307	41.20	15.0
11	0.263	AR Border	118	5154	43.68	31.0
12	0.258	M Amarnath	61	2967	48.64	15.7
13	0.250	SR Tendulkar	176	8705	49.46	44.1
14	0.248	CH Gayle	87	3633	41.76	21.6
15	0.248	R Dravid	166	7690	46.33	41.1
16	0.236	SP Fleming	98	4216	43.02	23.1
17	0.236	G Boycott	93	3758	40.41	21.9
18	0.234	IVA Richards	115	5404	46.99	26.9
19	0.234	Hanif Mohammad	53	2221	41.91	12.4
20	0.232	DI 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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.480	DG Bradman	43	4813	111.93	20.7
2	0.373	GR Viswanath	37	1637	44.24	13.8
3	0.345	GA Gooch	55	2867	52.13	19.0
4	0.317	Saeed Anwar	36	2254	62.61	11.4
5	0.312	WR Hammond	44	2584	58.73	13.7
6	0.302	JB Hobbs	45	2720	60.44	13.6
7	0.290	GP Thorpe	63	3006	47.71	18.3
8	0.284	KC Sangakkara	74	4913	66.39	21.0
9	0.280	GS Chappell	62	3595	57.98	17.4
10	0.274	BC Lara	52	2929	56.33	14.2
11	0.269	Inzamam-ul-Haq	76	4690	61.71	20.5
12	0.266	L Hutton	48	2678	55.79	12.8
13	0.264	M Azharuddin	32	1609	50.28	8.5
14	0.264	DA Warner	31	1608	51.87	8.2
15	0.247	JH Edrich	35	1771	50.60	8.6
16	0.241	KP Pietersen	67	3655	54.55	16.1
17	0.241	RN Harvey	66	3253	49.29	15.9
18	0.240	GS Sobers	46	3097	67.33	11.1
19	0.238	IT Botham	47	1918	40.81	11.2
20	0.238	C 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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.461	L Hutton	39	1700	43.59	18.0
2	0.382	DL Haynes	30	1065	35.50	11.5
3	0.361	BC Lara	126	5316	42.19	45.5
4	0.334	HW Taylor	46	1569	34.11	15.4
5	0.326	GN Yallop	32	1035	32.34	10.4
6	0.304	RN Harvey	30	962	32.07	9.1
7	0.288	Saeed Ahmed	30	1135	37.83	8.6
8	0.283	SR Tendulkar	112	4088	36.50	31.7
9	0.281	GM Turner	35	874	24.97	9.8
10	0.273	RA Smith	52	1734	33.35	14.2
11	0.271	PBH May	30	1215	40.50	8.1
12	0.270	AD Nourse	34	1331	39.15	9.2
13	0.263	B Sutcliffe	46	1222	26.57	12.1
14	0.261	JB Hobbs	42	1889	44.98	11.0
15	0.261	A Flower	66	2372	35.94	17.3
16	0.254	ME Trescothick	40	1467	36.67	10.1
17	0.248	RB Kanhai	40	1340	33.50	9.9
18	0.247	Mohammad Yousuf	65	2393	36.82	16.1
19	0.241	AI Kallicharran	30	937	31.23	7.2
20	0.240	JG 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

SNo	Avge HSI	Batsman	Innings	Runs	RpI	Total HSI
1	0.462	CH Gayle	45	2990	66.44	20.8
2	0.418	DG Bradman	15	1231	82.07	6.3
3	0.356	BC Lara	54	3708	68.67	19.2
4	0.341	Hanif Mohammad	52	2771	53.29	17.7
5	0.340	DL Amiss	34	1643	48.32	11.6
6	0.327	PA de Silva	56	3154	56.32	18.3
7	0.316	SM Gavaskar	103	6101	59.23	32.5
8	0.307	G Kirsten	46	2370	51.52	14.1
9	0.301	V Sehwag	54	3118	57.74	16.2
10	0.299	WR Hammond	60	3614	60.23	17.9
11	0.298	AR Border	99	5217	52.70	29.5
12	0.291	CL Hooper	44	2257	51.30	12.8
13	0.290	IVA Richards	54	3043	56.35	15.7
14	0.283	KC Sangakkara	59	3733	63.27	16.7
15	0.283	Mohammad Yousuf	34	2298	67.59	9.6
16	0.279	KF Barrington	65	3755	57.77	18.2
17	0.272	MP Vaughan	41	2102	51.27	11.2
18	0.271	JH Kallis	72	4337	60.24	19.5
19	0.269	GA Gooch	74	3400	45.95	19.9
20	0.261	KP 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.