Thursday, May 31, 2012

Stats across eras 6 : How did helmets affect the fast bowlers?

The eight part Statistics series by the author was published in Cricketcountry in April to May 2012 

Hendren, Gavaskar and Yallop - Different Headgears

On March 17, 1978, Australians were sent in by Clive Lloyd against Andy Roberts, Colin Croft and Joel Garner on a lively Barbados track. Once Rick Darling had edged Croft early on, a puzzled hush descended on the ground. It looked as if a welder with an oxy-acetylene flame cutter had mistakenly loitered on the cricket field.

Soon Graham Yallop was recognised under the cumbrous white helmet and a transparent face guard and he was booed and jeered all the way to the wicket. The Victorian batted about two and a half hours and scored 42, and started a fashion that changed the game forever.

It was Patsy Hendren who designed his own helmet way back in 1933 – a rubber hat with three peaks two of which fitted over the side of his head – as he faced Learie Constantine and Manny Martindle at Lord’s. But, it took 45 more years for the trend to catch on.

The perception is that ever since the batsmen started donning helmets, fast bowling lost the edge of physical intimidation. Mediocre men could now get behind a Croft or a Dennis Lillee and get away with it.

However, were the pace bowlers really affected by this change?

The figures under helmets

The 1970s and 1980s were known for world class pace bowlers, lightning quicks by the dozen from the Caribbean; fire spewing, swear spitting nasty men from Australia and even a few genuine fast operators from England and Pakistan.  How did they fare when the helmets started butting into the game?

If we look at the 70s till the fateful day for fast men when Yallop walked out under the white contraption, we find men like Lillee, Croft, Garner, Roberts, Jeff Thomson, John Snow, Michael Holding, Bob Willis, Imran Khan – all posing physical threat to batsmen.  On the other side of 1978, over an equal time span till June 1986, we have a sizeable portion of the earlier set appended by Malcolm Marshall, Pat Patterson, a young Courtney Walsh, Rodney Hogg and others.

Considering only the fierce fast men – and subjectively ignoring seam and swing merchants Ian Botham, Richard Hadlee and Kapil Dev – we find:

  • 1971-78: The pacemen took wickets at 25.12 with a strike rate of 52.60
  • 1978-1986: They knocked over batsmen at 24.82 with a strike rate of 53.89.

Hardly any difference. In fact, the average of the second group shows perceptible improvement if Hadlee, Kapil and Botham are included in the analysis.

Putting the figures of all the quick men of the two periods through a statistical test known as Mann-Whitney analysis does not yield any significant difference.

To drill down objectively, let us look at a list of excellent fast men whose careers spanned through the helmet revolution, and try to find out how they battled through the phase. To do this, we look at six years, two before the helmet, two during the first period of its use and two more by which time it grew into a norm. Fortunately, we find nine exemplary men from the period.

March 1976- March 1978March 1978- March 1980March 1980 – March 1982
BowlerWktsAveStr RateWktsAveStr RateWktsAveStr Rate

MA Holding (WI)









CEH Croft (WI)3720.1638.93123.9649.85724.9855.7
DK Lillee (Aus)4721.6344.33526.9157.411921.8147.1
RGD Willis (Eng)7921.1646.75824.9159.55826.2753.7
J Garner (WI)3025.450.13618.2546.85819.6759.6
JR Thomson (Aus)5024.3451.32428.5447.31638.9375.4
AME Roberts (WI)5526.5256.11932.6869.42527.6468.4
LS Pascoe (Aus)1327.9263.51332.6162.003823.1846.6
Imran Khan (Pak)5730.3557.75226.4265.33022.1356

A visual inspection of the data tells us a lot. Holding, Lillee and, to a lesser extent, Roberts, started off with a bang, moved into a steady mode and became lethal again. Thomson was no longer his threatening self by 1980, and the performance of Garner, Len Pascoe and Imran Khan actually improved a lot down the years.

Overall, as a population of bowlers, they remained consistent – a bit of a dip during 1978-80 and then back to best in 1980-82.

What is perhaps more striking is that, with the advent of helmets, the strike rate of these bowlers went down and though it recovered to some extent in the third phase, was never quite the same again.

All these assertions are validated by scientific tests. Mann-Whitney and Kruskal-Wallis Tests do not find significance difference in the three data sets of averages. There is not enough evidence to say that the bowling averages improved or deteriorated during the three phases.

However, Mann-Whitney Test of strike rates does yield a result which loosely means that we can say with 92.2% confidence that the strike-rates deteriorated for this group of bowlers during 78-80 (a p-value of 0.077).

What does this mean in cricketing terms?

      i.        With helmets, scoring runs did not get easier against the fast men of the generation. This has been demonstrated in earlier episodes as well. However, getting wickets became more laborious. Batsmen could resist longer against the quick bowlers, perhaps powered by the protection aided confidence. Batting technique changed. People no longer bothered about moving to the off side of the ball to play the hook shot. The new batsmen were not necessarily inferior to the old brigade, it was the evolution of a different technique with the diminished risk of head injury.

     ii.        When new fast bowlers arrived, they developed new skills to pick wickets at the same rate as their predecessors. With physical intimidation not being what it used to be, they extended their repertoire. In Marshall, Walsh and Wasim Akram we witnessed many splendored munitions in their arsenal. Waqar Younis perfected his toe crushers because no one wears helmets at both ends. In came the slower ball, reverse swing and other innovations.

Cricket is a game that evolves. The appliances and technology come into the game, ammunitions are neutralised, but it does not lead to one sided showdowns. New thoughts fly through the gunnery and out come novel weapons – which may not threaten life and limb, but can be potent enough to make batsmen hop.

The danger today, perhaps, is not protective gear, better bats or benign wickets. It is of this constant flow of thought sinking in the cacophony of Twenty 20 mayhem.

Stats across eras 5 : A detailed look at decade by decade scoring

The eight part Statistics series by the author was published in Cricketcountry in April to May 2012 

In the first part of this series we had gone through the overall average of all Test cricketers decade by decade from 1877 to 2012.

From the figures, it seemed that after the first few decades of dodgy wickets, drastically different conditions and the domination of bowlers, from the 1920s run making became more or less. It was argued that although the popular perception is that with the gradual use of covered wickets, protective gear, shorter boundaries and the decrease in number of fearsome pace bowlers, run making has become easier down the decades, in reality the degree of difficulty has remained constant ever since 1920.

Since only the overall average of all players was considered decade by decade in our analysis, the article did give rise to a number of justified questions.

How can we say that this overall consistency is not a result of balancing out of extreme outliers? What if some decades witnessed increased easy scoring by some sides while it was neutralised by ordinary performances by the weaker teams? Does it not seem too simplistic to look just at the overall average?

Very valid questions, indeed.

In our defence, we have looked at the average of all the Test cricketers who played the game. It seems more reasonable to assume that the degree of difficulty of scoring runs has remained constant, new technical adaptations have developed dealing with the new challenges thrown up by time, with the overall talent pool of batsmen and bowlers over the years remaining more or less consistent. Additionally, it is somewhat difficult to believe that with every decade, each time things got easier, some teams started performing with measured ineptness to keep the overall average unvarying.

At the same time, the doubts continue linger. The cognitive biases of Recency Effect and Rosy Retrospection are always at war, and the debate rages on – as thousands of words are exchanged for and against the present and past generations. The good news is that the results are scientifically verifiable.

At this juncture, let us take the help of cricket-agnostic Chinese wisdom and try to equate ten thousand words to a picture.

Produced above is the graph of the average score of each international cricket side in every decade from the 1920s to 1990s. The different teams are distinguished by colour codes and their movement from decade to decade denoted by broken lines. In the middle of the graph is a solid black line representing the corresponding average score of all Test cricket.

To visually gauge whether there has been significant deviation, we draw a carpet across the picture covering the middle range 25 – 35. We have seen that the average scores in the decades hover around 30, and hence create this rule of thumb to consider an average of over 35 or below 25 as outlier. (The actual global averages across decades are 32.41, 30.51, 33.00, 27.66, 30.91, 30.32, 30.69, 29.21)

To translate this into an intuitive cricket match, a typical completed team innings across eras would total around 300. We raise the outlier flag if the team score is less than 250 or greater than 350. It does seem to make a lot of sense.

Looking at the chart, we find 53 data points across the decades based on the teams that have been active at the time. (Australia, England, West Indies and New Zealand in all eight decades, India in seven, Pakistan and South Africa in six and Sri Lanka in two)

  • Of these 10 turn out to be outliers. That is 81% are within the carpet of normalcy.

  • Four of the outliers are above the chart (exceptionally high average) and six are below.

  • Of the ten, eight (four high and four low) outliers occur during the first three decades (1920s to 1940s).

  • The four high outliers appear in the 1920s, 1930s and 1940s. Twice they are the Bradman enhanced Australians, once the Len Hutton driven 903 for seven amassing Englishmen on marl wickets and once the three Ws powered West Indians. From 1950s to 1990s, none of the teams have crossed the upper level of the carpet.

  • Of the four low outliers, India and West Indies, in their early days, perform poorly in 1930s. New Zealand manages it three times (1930s, 1950s, 1960s) and Sri Lanka once when they appear on the scene in 1980s. The low scores are caused more by the lack of experience or quality of the team rather than an uniform change of bowling standards, conditions or wickets.

  • All the teams go through fluctuations, but remain in one concentrated zone from 1950s to 1990s.
The scientific verification about whether the decades produce different figures or not is done through a statistical test called Kruskal-Wallis. The result (a p-value of 0.667) loosely translates into only 32.3% confidence that the figures from different eras are different, whereas for conclusive evidence, the norm is 95% certainty.

Incidentally even the 2010 data, although there is increase in batting averages, also do not show statistically significant deviation.

And finally, apart from the argumentative points – the chart is an excellent indicator of the improvement and deterioration of the standard of each side across decades with respect to the global standard.

If the picture is anything to go by, it was perhaps the great Don Bradman who benefitted from easier conditions. However, the chasm between him and his peers is so great that there is little doubt that he would have been head and shoulders above the rest in any era.

Gary Sobers, Viv Richards, Sunil Gavaskar and Sachin Tendulkar had battle against similar quality and conditions. How they performed during their respective eras is documented in the second part of the series.

Wednesday, May 30, 2012

Stats across eras 4: Zeroing down on best batsmen across eras

The eight part Statistics series by the author was published in Cricketcountry in April to May 2012 

In the previous part of the series, we had defined a measure - Comparative Index - to find where exactly batsmen stand with relation to their exact contemporaries. We had used the index to determine where the leading Indian batsmen across eras stood were placed when viewed against his peers.

In this episode we take the train of thought to its logical conclusion, by finding out the Comparative Indices of the leading batsmen across time.

Again, we understand that conditions, opponent strength and other influencing factors change from era to era, and hence direct comparison of averages do not make sense. However, in Part 2 we had seen that within any significant period of time, the best batsmen always ended up with the best averages. Hence, our method is to use the Comparative Index to find out where leading batsmen stood with respect to the performance of others during the exact period during which they played the game.

To briefly recap our algorithm:

1. Select a batsman.
2. Find his first and last days in Test cricket.
3. Compute the average of all the players during that period (global average).
4. Consider all players satisfying minimum Test criterion who averaged higher than global average during that period in (2) – to eliminate the chance of varying number of tail enders skewing the rating.
5. Find out the rank of the batsman among all the batsmen in (4).
6. Given the rank, find out how many batsmen he would be ahead of if the number of contemporary batsmen (4) had been exactly 100 (to bring everyone on the same scale). This is the Comparative Index.

We look once again at the positives of this calculation –
  • A player is only compared against his exact contemporaries, and this Comparative Index is computed to contrast players of different eras.
  • This eliminates the problems of fluctuations due to conditions, bowling quality etc.

Demonstrative example:

i. Sachin Tendulkar has played between Nov 15, 1989 and Jan 28, 2012.
ii. The average of all batsmen (global average) during this period is 31.14.
iii. Between the dates in (i), there are 137 batsmen who played 20 or more Tests and scored above this average (ii).
iv. Sachin’s average is 55.44, which ranks 3rd among the 137.
v. That gives him a comparative index figure of 99. For every 100 contemporary batsmen of his era, he would be ahead of 99.
For Sunil Gavaskar, the same computation yields 94. He is ahead of 94 of 100 contemporary batsmen who averaged more than the global average during his playing days.

As noted in Episode 3, Kumar Sangakkara averages higher than Tendulkar during the latter’s playing period, but we cannot automatically conclude that Sangakkara have a comparative index above Tendulkar. Indeed, during the period Sangakkara has played Test matches (July 20, 2000 to April 7, 2012), Tendulkar has averaged more than him. One is thus staying clear of direct comparison of averages and focusing on the index a player achieved during his playing days.

We have carried out this analysis only for batsmen who have played after 1920. The reasons for this are given in the appendix.

The following table lists all the batsmen after 1920 who ended with a Comparative Index of 80 plus.

As we see, Don Bradman (no surprises there), Everton Weekes, Jacques Kallis and Javed Miandad finish in front of all their exact contemporaries. Tendulkar finishes ahead of 99% of players who played in the same period. Big names follow in the form of Ken Barrington, Garfield Sobers, Graeme Pollock, Greg Chappell, Ricky Ponting.

While looking at the table, one should bear in mind that all the batsmen have been evaluated against their peers through their entire career, not only in their pomp. Hence, Vivian Richards, who would have had an index of 100 if he had retired four years before he ultimately did, has to be satisfied with 90. Wally Hammond slips to 87 because of his meagre after World War 2 period.

The ones to just miss getting into the 80+ group are Gordon Greenidge, Mohammad Azharuddin, Bobby Simpson, Virender Sehwag and Rohan Kanhai.




1st Test

Last Test

Global Avg 

# Batsmen 
> Glbl Avg*



1DG Bradman (Aus)99.9430.11.2818.8.4831.85251100
2ED Weekes (WI)58.6121.1.4831.3.5829.19331100
3JH Kallis (ICC/SA)56.7814.12.9517.3.1231.41101100
4Javed Miandad (Pak)52.579.10.7521.12.9330.09811100
5SR Tendulkar (India)55.4415.10.8928.1.1231.14137399
6KF Barrington (Eng)58.679.6.5530.7.6829.8755298
7GS Sobers (WI)57.7830.3.545.4.7429.9794497
8RG Pollock (SA)60.976.12.6310.3.7030.7331297
9GS Chappell (Aus)53.8611.12.706.1.8430.4261397
10RT Ponting (Aus)
11AR Border (Aus)50.5629.12.7829.3.9430.2279496
12BC Lara (ICC/WI)52.886.12.901.12.0630.57105794
13GA Headley (WI)60.8311.1.3021.1.5431.0533394
14A Flower (Zim)51.5418.10.9219.11.0229.6781694
15R Dravid (ICC/India)52.3120.6.9628.1.1231.42110894
16SM Gavaskar (India)
17KC Sangakkara (SL)54.8620.
18H Sutcliffe (Eng)60.7314.
19CL Walcott (WI)56.6821.1.4831.3.6028.739492
20SR Waugh (Aus)51.0626.12.852.1.0430.161061190
21IVA Richards (WI)50.2322.11.7412.8.9130.278990
22Inzamam-ul-Haq (Pak)
23ML Hayden (Aus)50.734.3.947.1.0930.821051488
24WR Hammond (Eng)58.4524.12.2725.5.4731.2124487
25FMM Worrell (WI)49.4811.2.4826.8.6329.0454887
26PBH May (Eng)46.7726.7.5122.8.6128.0138686
27G Boycott (Eng)47.724.6.646.1.8230.12721186
28L Hutton (Eng)56.6726.6.3728.3.5530.5822486
29DPMD Jayawardene (SL)
30S Chanderpaul (WI)49.8317.3.9419.4.1231.241181885
31E Paynter (Eng)59.2315.8.3125.7.3930.5714385
32Mohammad Yousuf (Pak)52.2926.2.9829.8.1031.65921585
33CH Lloyd (WI)46.672.12.662.1.8530.15761384
34ER Dexter (Eng)47.8924.7.5827.8.6830.6242883
35TT Samaraweera (SL)52.8429.
36Younis Khan (Pak)52.4426.
37RN Harvey (Aus)48.4123.1.4820.2.6329.2531181
38KD Walters (Aus)48.2610.12.6511.2.198130.14631381
39Zaheer Abbas (Pak)44.7924.10.6931.10.8530.41681481
40J Ryder (Aus)51.6217.12.2016.3.2931.7311380
41MEK Hussey (Aus)50.823.11.0519.4.1232.78551280

*Criteria for minimum Tests played is 20 for all batsmen other than 15 for careers which ended before 1950.

Note: Home/Away, first innings/second innings etc. have not been considered here. However, this method can be refined for to include those specific details as well

Appendix: Why batsmen before 1920 are not considered ...

i) In the first part of this series, we noted that the batting conditions became standardised only after 1920, from which time the overall average has remained more or less constant. This makes it meaningful to compare someone like Zaheer Abbas (1969 and 1984) with Allan Border (1978 to 1994) in the spans that their careers intersected, because conditions did not undergo statistically significant changes between 1969 and 1994.

ii) Before 1920s, the conditions were unstable. To compare Victor Trumper (1899 to 1912) with Jack Hobbs (1908 to 1930) would make little sense. Although their careers intersected, Trumper played a lot of his cricket in the era of bad pitches, and Hobbs got much better conditions. So, in comparison to Trumper’s total career, the period when Hobbs’ career intersected with the Australian would have a much higher average – although they may have been scoring equally between 1908 and 1914.

This is because Trumper would be handicapped by the 1899 to 1908 played on bad tracks, and Hobbs would be in the happier position of having batted from 1914 to 1930 on much better pitches.

Since conditions of pitches changed drastically during their era, the pre 1920 batsmen cannot be compared on a global level by this method, but we will have to do with a decade by decade analysis as done earlier.
Hence, we don’t consider either Trumper or Hobbs in this analysis although Hobbs did end up with an index of 91.

Stas across eras 3 : Indian Batsmen - Tendulkar, Dravid, Gavaskar - a class apart

The eight part Statistics series by the author was published in Cricketcountry in April to May 2012 

In the first part of the series, we looked at how run making turned difficult or easier with different decades.

In the second episode, we analysed each decade of Test cricket and found that the most renowned batsmen always ended up at the peak among his contemporaries in terms of batting average.

Now, let us use the second finding and try to fit batsmen across eras into one scale. We start by evaluating the extraordinary riches of Indian batting.

Comparison between eras cannot be carried out through simple average analysis. Different eras did have different conditions, and different benchmarks, and the same average scores had different implications.

However, at the risk of repetition, “the best batsmen of a particular period always ended up with the best averages”. So, we will try and compare how different batsmen across time stood in comparison against their exact contemporaries.

To do this we first consider the playing days of a batsman – from the day he made his debut till his last Test.

Next, we find where he stood in terms of average among all the players during that exact period.

Three problems may arise due to this approach.

1. Too many lower order batsmen during an era can skew the figures.

2. A player who has played very few Tests can end up with a very high average.

3. In one period one batsman may rank say 4th among 30 men, and in another era a different batsman may rank 9th among 126. How do we compare them?

To circumvent the problems, we use the following counter approaches respectively.

1. We look only at batsmen who scored at more than the average runs scored during the period

2. We set a minimum criteria of 20 Tests for the modern (post 1950) era and 15 before that

3. We look at comparative index–among 100 exactly contemporary batsmen how many would the particular batsman be ahead of.

So, our algorithm is the following:

1. Select a batsman.

2. Find his first and last days in Test cricket.

3. Compute the average of all players during that period (global average).

4. Consider all players satisfying minimum Test criterion who averaged higher than global average during that period.

5. Find out the rank of the batsman among all the batsmen in (4).

6. Given the rank, find out how many batsmen he would be ahead of if the number of contemporary batsmen (4) had been exactly 100.

The positives of this calculation are that –

  • A player is only compared with his exact contemporaries, and this comparative index is computed to contrast players of different eras.
  • This eliminates the problems of fluctuations due to conditions, bowling quality etc.
For example,

i. Sachin Tendulkar has played between Nov 15, 1989 and Jan 28, 2012.

ii. The average of all batsmen (global average) during this period is 31.14.

iii. Between the dates in (i), there are 137 batsmen who played 20 or more Tests and scored above this average.

iv. Tendulkar’s average is 55.44, which ranks 3rd among the 137.

v. That gives him a comparative index figure of 99. For every 100 contemporary batsmen of his era, he would be ahead of 99.

For Sunil Gavaskar, the same computation yields 94. He is ahead of 94 among 100 contemporary batsmen who averaged more than the global average during his playing days.

Jacques Kallis and Kumar Sangakkara average higher than Tendulkar during his playing period, but therein is the sophistication of this approach. We cannot automatically conclude that Kallis and Sangakkara have a comparative index above Tendulkar, because it may very well happen, and indeed is, that during the period Sangakkara played Test matches (July 20, 2000 to April 7, 2012), Tendulkar averaged more than him. One is in staying clear of direct comparison of averages. Later in the series we will see how Kallis and Sangakkara score on comparative index with respect to their own exact contemporaries.

The table below shows some validation of what we have known for long. Tendulkar leads the charts, with a 99 comparative index. Dravid and Gavaskar end up in the 90s as well, after which there is a large gap.

NoNameAvgDebut TestLast TestGlobal avg

# Batsmen>   Global 

1SR Tendulkar55.4415.11.8928.1.12   31.14   137399
2R Dravid52.6320.6.9628.1.12   31.42   110894
3SM Gavaskar51.126.3.7117.3.87   30.43    78694
4M Azharuddin45.0331.12.846.3.00   29.83    952179
5V Sehwag50.913.11.0128.1.12   32.63    811978
6M Amarnath42.5024.12.6915.1.88   30.44    832373
7VVS Laxman45.9720.11.9628.1.12   31.43   1103470
8DB Vengsarkar42.1324.1.765.2.92   30.09    732665
9PR Umrigar42.229.12.4818.4.62   28.69    572164
10NS Sidhu42.1312.11.836.1.99   30.05    893660
11GR Viswanath41.9315.11.694.2.83   30.28    592460
12SC Ganguly42.1720.6.9610.11.08   30.94    954059
13G Gambhir45.263.11.0428.1.12    32.61    612658
14VL Manjrekar39.1230.12.522.3.65   29.44    472157
15VS Hazare47.6522.6.464.4.53   31.49    261352
16DN Sardesai39.231.12.6125.12.72   30.96    432738
17SM Patil36.9315.1.8017.12.84   29.9    352335
18SV Manjrekar37.1425.11.8723.11.96   30.03    604034
19RJ Shastri35.7921.2.8129.12.92   30.62    634726
20MS Dhoni37.322.12.0515.1.12   32.98    544125
21CG Borde35.5928.11.589.11.69   30.35    463524
22MAK Pataudi34.9112.12.6129.1.75   31.14    574521

*Criteria for minimum Tests played is 20 for all batsmen other than 15 for Hazare.

The only major surprises maybe finding Mohammad Azharuddin high up and Vijay Hazare quite low down in the ranking. Hazare may have suffered from playing in an era of Don Bradman, Len Hutton, Denis Compton, the 3 Ws, Neil Harvey and a roll call of great batsmen belonging to more established sides. Azharuddin’s ranking on the other hand is perhaps an indication that we often fail to recognise greatness when it is right in front of us.


i. Vijay Merchant, the other great Indian batsman, played only 10 Tests and has to be omitted because of low sample size.

ii. Home/Away, first innings/second innings etc. have not been considered here. However, this method can be refined for those specific analyses as well

Stats across eras 2 - Best batsmen by decade

The eight part Statistics series by the author was published in Cricketcountry in April to May 2012 

In the previous episode of this series we dealt with the facts and fables regarding the difficulty of run making across generations. Now, let us turn our attention to some of the best performers across eras.

Batting average is the most commonly accepted metric used to evaluate the merit of a batsman in cricket. However, there are sceptics who underplay its importance as an indicator of quality. While some quote ‘lies, damned lies, statistics’, or the corporate cliché ‘analysis paralysis’,  the more knowledgeable argue that certain confirmed greats of the stature of WG Grace and Victor Trumper ended up with remarkably ordinary figures when compared to current standards. Hence, it does not make sense to attach too much importance to respective records.

Granted, with the evolution of the game, comparison of raw figures of batsmen separated by a hundred or so years may not make sense. However, what happens if we restrict our assessment and analysis to batsmen with their contemporaries?

According to this simple analysis, batting average actually turns out to be an excellent indicator. During their eras, both WG Grace and Trumper, the two players cited most often as counter examples, end up right at the top when measured against their rivals.

It is actually quite intuitive that better batsmen will be more consistent and prolific and will hence end up with better figures.  But, let us not leave it to discussions and debates and move straight the figures.

In the table that follows, the top three batsmen have been identified for each decade (1877-1890 considered the first decade, and every calendar decade from then on). All the usual suspects are there, the ones most would expect to end up on top. From Grace to Jack Hobbs, Trumper to Don Bradman, Gary Sobers to Viv Richards, Sachin Tendulkar to Jacques Kallis.

Considered within an era, average definitely makes a lot of sense.

Of particular interest are two very relevant facts.

1. In the last part, we saw that the wickets started becoming standardised and run making easier and consistent starting from the 1910s and reached a very stable state by the 1920s. Accordingly, we find Victor Trumper’s average tending to figures very comparable with the modern greats in the 1910s.

2. From the 1950s, after Bradman was done playing havoc with reason and ratio, the top averages of every ten years are strikingly similar. Another confirmation of the consistency of run making.

Top averages by decades:

Decade Leading Batsman 1 Leading Batsman 2Leading Batsman 3
1877-1890Allan Steel (Eng)WG Grace (Eng)Billy Murdoch (Aus)
60035.29 63335.16 89632 
1891-1900KS. Ranjitsinhji (Eng)Tom Hayward (Eng)R. Abel (Eng)
97053.88 97644.36 67141.9 
1901 - 1910Aubrey Faulkner (SA)Clem Hill (Aus)Victor Trumper (Aus)
110844.32 216040.75 217336.2 
1911-1920Jack Hobbs (Eng)Victor Trumper (Aus)J.W. Zulch (SA)
174264.51 71054.61 54045 
1921-1930Don Bradman (Aus)CG McCartney (Aus)Herbert Sutcliffe (Eng)
144696.4 116472.75 339666.6 
1931-1940BradmanLen Hutton (Eng)George Headley (WI)
364798.56 134567.25 142164.6 
1941-1950BradmanFrank Worrell (WI)Neil Harvey (Aus)
1903105.7 833104.1 111886 
1951-1960Gary Sobers (WI)Clyde Walcott (WI)Len Hutton
307761.54 298460.89 272855.7 
1961-1970Ken Barrington (Eng)Greame Pollock (SA)Gary Sobers (WI)
575062.5 225660.97 369956.9 
1971-1980Viv Richards (WI)Javed Miandad (Pak)SM Gavaskar (Ind)
362960.48 266357.89 597456.4 
1981-1990Clive Lloyd (WI)Zaheer Abbas (Pak)Allan Border (Aus)
234261.63 234354.48 694053.8 
1991-2000Sachin Tendulkar (Ind)Steve Waugh (Aus)Rahul Dravid (Ind)
582860.08 657856.22 332253.6 
2001-2010JH Kallis (SA)KC Sangakkara (SL)Brian Lara (WI)
904861.97 807058.9 588358.2 
2011-2012Younis Khan (Pak)KallisIan Bell (Eng)
95868.42 70263.81 108463.8 


Minimum runs criteria –

# 500 runs till 1900, 1911-1920 and 2011-2012

#1000 runs from 1901-1910, 1921-1940

#800 for 1941-1950

#2000 elsewhere.

This distinction is required for the varying number of Tests played in the early days and during the decades disrupted due to World Wars.


Other than the top averages given above, the following table lists the top run-getters of each decade along with the other notable scorers who just missed out featuring among the top 3 averages in the above table.

Decade Top run getter, tally & avge Other Notables
1877-1890Arthur Shrewsbury sr (Eng)  993, 31.00P.S.  McDonnell
W Bates
1891-1900Joe Darling (Aus) 1139, 35.59FS Jackson
1901 -1910Victor Trumper (Aus) 2173, 36.20RA Duff
JT Tyldesley
1911-1920Jack Hobbs (Eng) 1742, 64.50Warwick Armstrong
William Bardsley
1921-1930Herbert Sutcliffe (Eng)  3396, 66.60Wally Hammond
Patsy Hendren
1931-1940Wally Hammond (Eng)  4776, 62.80Bill Ponsford
Eddie Paynter
1941-1950Len Hutton (Eng)  2898, 53.70Denis Compton
Everton Weekes
1951-1960Peter May (Eng)   4265, 47.40Neil Harvey
Hanif Mohammad
1961-1970Ken Barrington (Eng) 5750, 62.50Doug Walters
Ted Dexter
1971-1980SM Gavaskar (Ind)  5974, 56.40Geoff Boycott
Greg Chappell
1981 - 1990Allan Border (Aus) 6940, 53.80Javed Miandad
Mohd. Azharuddin
1991-2000Mark Waugh (Aus)  6907, 42.40Brian Lara
Andy Flower
2001-2010Ricky Ponting (Aus)   9953, 55.60Mohammad Yousuf
Sachin Tendulkar
2011-2012Michael Clarke (Aus)  1336, 60.70Early days yet …

Stats across eras 1: Did Sachin Tendulkar have it easier than Sunil Gavaskar?

The eight part Statistics series by the author was published in Cricketcountry in April to May 2012 

In debates that rage in the backrooms and bars, on web forums and beside water-coolers, the general consensus is that batsmen have it much easier today than in the past eras of black and white photographs. Uncovered wickets, fearsome pace bowlers, no helmets, poor quality of bats – the reasons seem to be incontrovertible. On the YouTube, one winces with each scary clip of Michael Holding pummelling the brave, balding Brian Close, of Dennis Lillee and Jeff Thomson terrorising the ducking, weaving, evading batsmen. All the necessary exhibits are there to make the case of the brave and brilliant past, against the mediocre and magnified present.

Cricket is a game where perceptions generally rule over palpability,fallacies over facts. As shown in articles about biased criticism and mythical shortcomings of cricketers, the reality is often vastly different from the reconstruction carried out by our senses influenced by the filtered information fed to us.

Cricket is also one of the most scrupulously-documented of sports, with a data bank that is a goldmine waiting to be tapped. Let us utilise it to see how batsmen have gone about making runs since the inception of Test cricket, whether it has become easier with each decade.


No. of


Avg score
of all



  No. of
Inns per


Stable since the 1920s

Looking at the table, one can immediately derive some logical and correct conclusions and scratch one’s head as other widely held perceptions seem to disappear in the face of facts.

The fourth column is the key here, showing us the average of all batsmen, how the general cricketer scored runs in that decade.

We can see at the beginning, starting with the 1877-1880 and through to 1901-1910, low scores were witnessed, gradually stabilising by the 1910s. It is obvious that before World War 1, the pitches were difficult, not standardised, runs difficult to come by.

However, once the game established itself, tours turned regular, the administration more professional and scoring gradually easier. By the time Warwick Armstrong took his all-conquering team to England in 1921, cricket had evolved to a highly matured state and since then, we see a surprising stability in the decade-wise run scoring. There are variations, but not by any means very significant ones.

In fact, the average scores were the highest during the 1946-50, the period immediately after the Second World War – when Don Bradman bid adieu with a staggering 1903 runs in 18 completed innings, and Frank Worrell, Neil Harvey and Everton Weekes arrived on the scene with huge bangs.

In stark contrast, the decade that followed, 1951-60, saw the most difficult period for batsmen. While this was to some extent driven by a poor Kiwi batting side that averaged an atrocious 18 per innings, the reason is more due to a gamut of phenomenal bowlers arriving on the scene together. In the 50s, Ray Lindwall took 144 wickets at 25.52 and averaged 21st in the list of bowlers who had bagged 30 or more - a testimony to the quality of the times. Jim Laker, Frank Tyson, Richie Benaud, Keith Miller, Brian Statham, Fred Trueman, Alec Bedser, Tony Lock, Wesley Hall, Neil Adcock, Johny Wardle, Fazal Mahmood, Subhas Gupte and a lot of others formed a collection of fast and slow bowlers capable of making any batsman struggle.

What can surprise many is that the two decades of pace bowling dominance, 70s and 80s, don’t really reflect a drastic difference in the figures. Following the cognitive quirk of availability heuristic, we tend to recall the four pronged West Indian attack vividly because of the terror it struck in our hearts. However, we forget the flat pitches of the sub-continent in the same era where draw after draw were played out with huge scores in front of yawning spectators.

The 90s in fact saw a dip in the batting averages, with most of the teams around the world boasting excellent bowling attacks. Australia, Pakistan, South Africa and West Indies all conceded only 25-26 runs per wicket; India, Sri Lanka and England gave away around 30 runs apiece, and contrary to popular belief, it was a more difficult time for batsmen than the twenty previous years.

The first decade of the new century has seen an increase in the runs, and also a reduction in the number of required innings for centuries and fifties. All the teams seemed to develop their batting strength while the bowling did not really scale up adequately. The best bowling sides, Australia and Sri Lanka, conceded around 28 runs per wicket.

However, the figures do suggest that the degree of difficulty for Sachin Tendulkar, Sunil Gavaskar and Don Bradman on the whole were not too different.

Finally, the minnows have played their part in the last 20 years, but they have batted as badly as they have bowled and thus managed to balance things out.

Psychological explanation: Why cricket fans can't accept their idols' failure

This post by the author was published on Cricketcountry on 26.5.2012

During the Indian Premier League (IPL) group matches we saw a 40-year old Sourav Ganguly, way over the hill and struggling with fitness issues, stumbling through the matches, ending with an average of 17, strike rate of 98, his team finishing at the bottom of the table. He consumed balls at the top of the innings, leaked runs between his legs in the field, and for some reason sent free-stroking, in form batsmen like Steve Smith too late in the day to rescue the games.

Yet, in every discussion forum, we find this performance equated with the last fierce roar of a beloved tiger; the initial euphoria of winning matches was reduced to a trickle with nine losses in a row, but somehow the performances always came through as variously courageous, indomitable, against all odds, and exhibits of exemplary leadership.

The reactions seem frozen in time – as Rajesh Ramaswamy put it – in the balcony of Lord’s, 2002. The more graphic the humiliation, the more ecstatic were the subsequent eulogies.

This phenomenon is not limited to his IPL performance, but, as any follower of Indian cricket who does not subscribe to fandom will testify, it has been a feature of a major part of his career.

Results uncorrelated to reactions

This trait is not restricted to Ganguly alone.

With Sachin Tendulkar it works both ways. He averages 42.63 in 12 Tests since 2011 – not low by any means, but a drastic drop from the pinnacles he is known to inhabit. But to his ardent supporters, he still rules the world at the popping crease.

At the other extreme, gems such as his 103 not out against England in Chennai, 214 and 53* versus Australia at Bangalore, couple of VB Series specials and a gamut of other master classes cannot seem to rewrite the perception that he is not a match-winner, clamouring facts and figures notwithstanding.

When we consider Rahul Dravid, fanaticism is perhaps toned down, since the appreciation of his classical batsmanship demands a degree of sophistication. However, he is almost unanimously accepted as the numero uno in difficult conditions, although the numbers reflect that he just about managed to inch his average over 40 in Australia and ended up scoring at 29.71 in South Africa.

Similarly, one section of the populace would attribute every success of MS Dhoni to luck, which can be disproved by putting his captaincy record through basic statistical tests of hypotheses. However, at the other end, he remains the ideal captain for many even after seven consecutive overseas defeats.

It is perhaps extreme in India, especially when it comes to Ganguly and Tendulkar, but not really non-existent elsewhere. Steve Waugh, for example, is widely acknowledged as the crisis man, someone whom you would pick to bat for your life. However, the records show that he averaged 25 in the fourth innings with just two fifties from 31 outings, and scored at 32 in all second innings.

The pattern is similar for each case. A reputation that has been erected in the early days or mid season of one’s career is etched in the psyche of the fan-following, and performance can hardly alter the image after that. In fact, as the IPL debacle of Ganguly shows, when the idol abjectly fails to meet the expectations created by the fumes of fanatical worship, the belief in his esoteric powers is reinforced and grows stronger rather than weaker.

Why belief becomes more fervent when expectations are not met

This curious phenomenon of irrational rationalisation has in fact been studied as a phenomenon of cognitive dissonance.

The path-breaking analysis was performed by American social psychologist Leon Festinger, a faculty member of – among others – Massachusetts Institute of Technology (MIT), University of Michigan and Stanford. Studying the behaviour of large scale cult belief systems, Festinger outlined his results in the path breaking 1956 book – When Prophecy Fails.

According to his scientifically accepted findings, he demonstrated:

# A zealous believer undergoes cognitive dissonance if faced with outcomes which are greatly different from what one expects – feelings of surprise, dread, guilt, anger, or embarrassment.

# In this circumstance, a very natural way to cope with the negative feelings is to become a more fervent believer – provided conditions are favourable for doing so, namely abundant mutual support of similar-minded souls.

The features and the required conditions of the phenomenon are listed below along with their cricket fandom equivalent in parenthesis.

1. The belief must be held with deep conviction and it must have some relevance to how the believer behaves. (In cricket, this equates with the strength of fanaticism and the way the performance of a cricketing idol or villain is linked to the sense well being of the fan.)

2. The person holding the belief must have committed himself to it; he must have made pronouncements or taken actions difficult to undo. In general, the more difficult they are to undo, the greater is the individual's commitment to the belief. (Boasts and predictions in cricket fan communities are common enough, blind faith/dislike for the icon helping things along. Eg. Tendulkar will play a match-winning innings, or Tendulkar will definitely fail under pressure, or Ganguly, the best captain, will surely win the IPL)

3. The belief must be sufficiently specific and sufficiently concerned with the real world, so that events may actually be drastically opposite to the belief. (Axiomatic for the cricket fan who always stands the chance of witnessing his infallible forecasts crashing on the 22 yards)

4. Such undeniable evidence on the contrary occurs and is recognised by the individual. (The fan watches in disbelief as the icon fails to perform according to his expectations. The scoreboard cannot be denied, at least at the beginning.)

5. The individual believer must have social support. It is unlikely that one isolated person could withstand disconfirming evidence.  If, however, the believer is a member of a group of convinced persons who can support one another, the belief can be maintained and the believers are likely to attempt to promote this belief or persuade non-members that the assertions are still correct. (The upset fanatic leans on fan clubs in the physical and electronic world, voices support each other, groupthink leads to mysterious justification of the unacceptable failures, and the entire group re-emerges from the disappointment as an even more impassioned, rabid believers and evangelists.)

Hence, when the uninitiated ends up bemused at the reaction of fan/hate clubs which seem to be at diametric discord with the actual results, he can do well to remember that this is a studied and expected occurrence.

Cricket is a religion here with considerably more than its share of fanatics, and the only way to deal with this is tolerance.