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Evaluation of match-winning — the tale of farcical analysis

Sachin Tendulkar averaged in excess of 80 in Test wins overseas © Getty Images
Sachin Tendulkar averaged in excess of 80 in Test wins overseas © Getty Images

In a misguided abuse of statistical pseudo-analysis, the average of a cricketer in victorious matches is sometimes cited as an indicator of his match-winning ability. Arunabha Sengupta demonstrates why this method of evaluation is wrong and why match winning is too complex a factor to be measured by this simplistic variable.

Misguided Method

“Player A averages more than Player B in won matches and therefore is a better match-winner. Look at how they have averaged in overseas wins; if you are not convinced, QED.” How many times does this argument do rounds in cricketing discussions?

Cricket the game leaves in its wake a fascinating array of numbers — with perhaps only baseball comparable in this respect in the entire world of sports.

To look at the figures from the past and present is a rewarding experience — for proper analysis, evaluation and  as well as unmasking of  the many quaint fiction, fables and legends often recounted in the guise of fact. Numbers can also ensure verification, and often falsification, of several expert opinions taken as gospel. Immensely satisfying insights can be obtained by perusal of the charts of batting, bowling and match results, provided proper analytical tools are used to make inferences. The only shortcoming is perhaps that numbers cannot tell us of the joy of watching a particular performer, the hush that descended on the ground as a batsman walked out with his mighty bat, and the raucous cheers at each stroke.

At the same time figures sometimes render us susceptible to misinterpretation, wrong conclusion and fallacies — and this forms a very interesting area of study in its own merit.

When analysis is restricted, as it is in most cases, to putting a greater than or less than sign between the batting averages of two players – there are several pitfalls when evaluating the most complex scenarios. One can fall prey to oversimplification to the point of rendering the study farcical. This especially holds true when we indulge ourselves in our favourite pastime of gauging the impact of one person on the outcome of a match.

The batting average in won matches is a much abused parameter when trying to gauge a cricketer’s match-winning ability. In cricket, 22 players are involved in a game, and the result of the match is a complex function of the performance of each one of them. The value of one batting average being more than the other is definitely not a measure of who the greater match winner was. The problem is far too complex for that, and way more sophisticated statistical techniques are necessary to test any such claim.

Unfortunately, tests of hypotheses using multiple complex parameters are not really meant for wide readership and understanding.

Why, the Duckworth-Lewis method employs just two variables – overs and wickets, and the resulting curves and target resetting leave most of the fans suspicious and unhappy about the robustness of the system. This is it is a shortcoming of the D/L method, it is the best rain-rule available. Whenever the number of parameters in question becomes more than one, basic arithmetic is seldom enough for analysis and the answers cease to be intuitive. And much dismay as it may cause, the effect of 22 variables cannot be approximated by the batting average of one person.

Reduction ad absurdum

While a discussion on the methods of analysis of match-winning performances may be too technical for these pages, what we can do is show why batting average in won matches is not a valid parameter for evaluation.

A few months earlier, we had laid to rest another hilariously inept measure for evaluating effective performances summed up by the argument — ‘team has always won when he has scored a hundred, or team has never lost when he has scored a hundred’. We had assumed the claims to be true and were thereby struck with absurdities which showed people like Gautam Gambhir eclipsing some slightly more illustrious names like Garry Sobers and Alec Stewart and Sourav Ganguly leading the field ahead of Don Bradman. The technique we had used was reductio ad absurdum.

Now let us see for ourselves what the claim ‘better batting average in wins implies better match-winner’ produces.

Filtering for batsmen boasting more than 1000 runs in wins, and ranking according to average, here are the first 15.

Best averages in won Tests

Batsman T R Ave
Don Bradman (Aus) 30 4813 130.08
Graeme Pollock (SA) 9 1178 84.14
Cheteshwar Pujara (India) 11 1117 79.78
Clyde Walcott (WI) 12 1113 79.5
Inzamam-ul-Haq (Pak) 49 4690 78.16
Garry Sobers (WI) 31 3097 77.42
Jackie McGlew (SA) 11 1156 77.06
Shoaib Mohammad (Pak) 12 1055 75.35
Kumar Sangakkara (SL) 49 4913 74.43
Frank Worrell (WI) 18 1483 74.15
Greg Chappell (Aus) 38 3595 70.49
Wally Hammond (Eng) 29 2584 69.83
Jimmy Adams (WI) 21 1534 69.72
Hashan Tillakaratne (SL) 24 1534 69.72
Steve Waugh (Aus) 86 6460 69.46

There is no surprise at the top of the table as the legendary names stares back at us, and perhaps we can still digest Cheteshwar Pujara’s presence at number three given the phenomenal start to his Test career. However, as we proceed down the rows, the absurdity hits one by one. Jackie McGlew is apparently the best match-winning batsman produced by South Africa. Shoaib Mohammad suddenly appears, ahead of some better known compatriots like Javed Miandad and Zaheer Abbas. What is more, Shoaib and McGlew are both ahead of Wally Hammond and Greg Chappell. Down the rows, Jimmy Adams and Hashan Tillakaratne join Shoaib and McGlew, ending up ahead of people like Jack Hobbs, Len Hutton, Viv Richards, Herbert Sutcliffe, Ricky Ponting, Neil Harvey, Rahul Dravid, Sachin Tendulkar and the rest of the pantheon of batting greats.

Let me quietly add here, that had the minimum runs scored been limited to 500 instead of 1000, as it will be in case of away matches, it would not have been Don Bradman leading the table but Zimbabwean Brendan Taylor.

I think this sufficiently shows why this analysis is totally misleading.

Given the huge number of people prone to this error by over-simplification, one can wonder why we get this sort of weird result. Let me answer that with a counter question that I generally pose when this method is brought up for discussion.

Suppose Player A averages more than Player B in won Test matches, and Player B averages more than Player A in lost ones. What does it mean? Is it that Player A is a better match-winner? Or is it that he is a fair-weather batsman who performs only when the opponent is at a disadvantage and his team is winning? Is Player B not a match winning batsman? Or is he the one who stands up and delivers in difficult circumstances when the opposition is winning?

There is no simple answer, certainly not an axiomatic one. This is simply because this way of evaluation is fundamentally flawed. We are looking at the wrong metric, which does not give us any indication of a batsman’s worth. To use a statistical cliché, correlation is not necessarily causation. A high batting average in wins does not automatically lead to the conclusion that the wins were due to the high batting average.

As explained, to evaluate the match winning abilities of a batsman, we need to put the individual performances and the statistics of the players involved in the matches through complex statistical procedures to come up with any meaningful conclusion.

There is another widespread belief — especially in the subcontinent — that home performances amount to little. It is only how the cricketers performed overseas that matter. Batting in home Tests is almost akin to taking a penalty kick. One is expected to score and all hell breaks lose if he does not. (Although the caveat is that generally only players of the subcontinent are put through this home game filter.)

So, let us look at the best averages in victorious Tests played at away venues. Limiting the eligibility criterion to 500 runs, here is the table:

Best averages in won Tests overseas

Batsman T R Ave
Jimmy Adams (WI) 8 670 111.66
Younis Khan (Pak) 17 2025 106.57
Alastair Cook (Eng) 11 1496 99.73
Don Bradman (Aus) 9 1452 96.8
Wally Hammond (Eng) 14 1816 95.57
Jackie McGlew (SA) 5 667 95.28
Steve Waugh (Aus) 34 2802 84.9
Sachin Tendulkar (India) 20 2017 80.68
Bill Ponsford (Aus) 4 551 78.71
AB de Villiers (SA) 17 1559 77.95
Ken Barrington (Eng) 9 841 76.45
Gautam Gambhir (India) 8 757 75.7
Kevin Pietersen (Eng) 12 1285 75.58
Frank Worrell (WI) 9 875 72.91
Mike Gatting (Eng) 5 503 71.85

Jimmy Adams upstages Don Bradman. Need we say more about the method?

Hilariously, based on the eternal myths that do the rounds in the cricket world, many may be convinced that this is an incorrect method by looking at the table and finding the name in the eighth position! Yes, many will thus arrive at the right conclusion by taking a number of wrong logical turns on the way.

Of course, just these tables may not be sufficient to debunk the fallacy of averages in won matches.

There are many clichés which come to the rescue of long-held beliefs, and one of the primary ones is “one cannot compare eras.” Generally this phrase is used as a gospel. Although we often look at the trends of inflation, price, salary structure, migration, habits, climate, temperature and other measures across different ages in other fields of more serious analysis, somehow it supposedly cannot be done in cricket: unless, of course, the output verifies our perceptions.

There are actually excellent methods of comparing and contrasting players of different eras, mainly by defining relative indices through intra-era comparison and then moving to inter-era analysis based on the indices. Besides we have shown earlier that the conditions have remained more or less constant from the 1920s, with the balance between bat and ball swinging in manageable oscillations since then. However, let us assume this much is true. Perhaps it is also not right to compare players of different teams …

Let us see where that gets us. We will now compare the supposed match-winning quotient of players of the same sides who played more or less in the same period, who remained teammates for considerable while.

So this is what it gets us. The following is just a short summary of nonsense produced by the analysis.

The wrong Jacques — a cornucopia of nonsensical results

For England, Joe Hardstaff Jr. was ‘way more of a match winner’ than Wally Hammond.

For Australia, Dean Jones, David Boon and Kepler Wessels end up ‘ahead of’ Allan Border. Limiting Australians to overseas matches, Adam Gilchrist and Darren Lehmann ‘score over’ Ricky Ponting, Phil Hughes over Michael Clarke.

For West Indies, Jimmy Adams ‘towers above’ Shivnarine Chanderpaul while Brian Lara brings up the rear. And outside the Caribbean the gap between Adams and the other two is even larger. Jeff Dujon incidentally turns out to be ‘better at winning matches’ than Richie Richardson.

Outside South Africa, Jacques Rudolph proves ‘more effective’ than Jacques Kallis in this regard.

Similarly for New Zealand, away from the nation, Daniel Vettori is a ‘better bet’ than Nathan Astle in terms of match-winning batsmanship.

Turning to India we find a mixed result for the legendary all-rounders. Vinoo Mankad turns out to be a ‘better match-winning batsman’ than Vijay Hazare and Polly Umrigar. And well, Syed Kirmani is ‘ahead of’ Kapil Dev! Away from home, Gautam Gambhir is ‘better at winning matches’ than Rahul Dravid.

For Pakistan Shoaib Mohammad ‘upstages’ Javed Miandad. And overseas, Taufiq Umar streaks ahead of Mohammad Yousuf.

Well, the above results should amount to enough absurdities to last a lifetime.

In conclusion, numbers tell a very poignant tale, but only if evaluated in the proper way. And computing the contribution towards match-winning is not as simple a technique as comparing averages.

The game is far too complex for that, and therein lies another of those facets that make cricket the charming sport that it is.

(Arunabha Sengupta is a cricket historian and Chief Cricket Writer at CricketCountry. He writes about the history and the romance of the game, punctuated often by opinions about modern day cricket, while his post-graduate degree in statistics peeps through in occasional analytical pieces. The author of three novels, he can be followed on Twitter at http://twitter.com/senantix)

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