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My Name is Ozymandias, King of Kings

Some time ago I started looking into match impact as a way of assessing player performance. I have long had misgivings as regards the usefulness of averages as a means to rate players, as these are obviously impacted variously by runs and wickets gained when the result can no longer be affected – Americans like to refer to this period of a game as ‘garbage time’. Well, while that description may be true of American Football I don’t think there are many who would use such unglamorous terminology in describing a game of cricket meandering even to the most tepid of a draws. That said, one way to skim off this padding of stats is to look at the impact of the various events on the match result, so that more or less credit is given based on the impact on the probability of the match outcome by individual performances.

In order to do that I had to build up enough information from Tests already played as to what the likely outcome was from any given point in a match. That task completed, I could then assess the “worth” of each Test innings, wicket or dismissal, then collect that information together for each player, with an impact performance measure then produced which incorporates each discipline (batting, bowling, fielding).

Does the End Justify the Means?

Is it worthwhile? Frustratingly, it wasn’t possible to determine if all this was worth the effort until it was done. If, for example, there was a direct, very strong correlation between the average match impact and the batting average, this new measure wouldn’t be telling us anything. What I was hoping for was a relationship, certainly, as you would think there should be some positive relationship between a high batting average and match impact, but if the correlation was too high then the match impact average wouldn’t really be any more informative as to identifying impact players than the batting average (which I don’t believe is the case).

In this study I looked at almost 80 England batsmen, from Grace to Pietersen and all points in between. The correlation of match impact average to batting average for this group of players is found to be 0.54, which suggests a moderate correlation. For those of you who care, with 75 degrees of freedom we calculate a t-test value of 5.52. As the probability associated with the calculated t-test value is therefore <0.001, this suggests that the correlation is highly significant and is unlikely to have arisen by chance. In summary, there exists a moderate relationship between batting average and match impact average as we would expect, but not so strong as to render the work uninformative. The Impact of Impact – Gooch and Gower

As an example of the type of information I’ve been trying to unearth, let’s look at two great contemporaries, Graham Gooch and David Gower. Looked at through the magnifying glass of traditional statistics, there doesn’t appear to be much between them:-

GOOCH 118 215 8900 42.58 20 46
GOWER 117 204 8231 44.25 18 39

Gooch has quite a few more runs but in more innings and at a lower average than Gower. Looking at career impact figures, there still isn’t much between them:-

GOOCH 118 1616 13.70
GOWER 117 1314 11.24

Gooch is ahead, but not by a significant margin in terms of average impact per match, plus we’re not directly comparing apples and apples here, as the above figures also include bowling and fielding impact which certainly explains part of the difference. It’s when we look at their career impact profiles, i.e. how their impact on matches has varied over time, that we really see what I’ve been trying to get at with this impact stuff:-

The Impact of Impact - Gooch and Gower

These profiles show a rolling 5-Test match impact average, a number chosen because a per-Test profile has too much variation and a 10-Test average shows too little variation, so neither are particularly informative; the 5-Test average more accurately identifies peaks and troughs, plus it has a certain resonance as five matches was for a long time the de facto length of a Test series. Note also that the strength of opposition is taken into account in these figures.

In profiling David Gower, Christopher Martin-Jenkins wrote “It is curious that the man who briefly held the record as England’s highest ever run scorer in Test cricket should often be remembered as being somehow an insubstantial player”; Looking at his impact profile shown above, when compared side-by-side with that of Gooch, supports that memory. While their profiles look very similar for their first 50 Tests, Gooch took his game to a new level of impact after that, beginning around the time of his 183 to save the match against New Zealand at Lord’s in 1986, and peaking unsurprisingly during the summers of 1990 and 1991. Gower’s profile does show a consistency around the 20% level which not many can boast of, that blue line representing what in my experience is true Test class, but the peak of his rolling average does not approach that of Gooch, who crashed through the green line of 30% which I feel represents the transendance to true greatness in terms of match impact.

So, if we accept that these career profiles represent the actual impact of a player in a way which traditional averages cannot necessarily, let’s look at the England Test batsmen in more detail. The batsmen considered are listed below:-

Leslie Ames Dennis Amiss Mike Atherton Bill Athey
Bob Barber Ken Barrington Ian Bell Geoff Boycott
Mike Brearley Chris Broad Mark Butcher Paul Collingwood
Denis Compton Alastair Cook Colin Cowdrey John Crawley
Mike Denness Ted Dexter KS Duleepsinhji John Edrich
Keith Fletcher Graeme Fowler CB Fry Mike Gatting
Graham Gooch David Gower WG Grace Tom Graveney
Walter Hammond Joe Hardstaff Tom Hayward Patsy Hendren
Graeme Hick Jack Hobbs Nasser Hussain Len Hutton
Stanley Jackson Douglas Jardine Gilbert Jessop Allan Lamb
Maurice Leyland Brian Luckhurst Archie Maclaren Peter May
Phil Mead Colin Milburn Peter Parfitt Eddie Paynter
Kevin Pietersen Geoff Pullar Mark Ramprakash Derek Randall
KS Ranjitsinhji Peter Richardson Tim Robinson Graham Roope
Phil Sharpe David Sheppard Arthur Shrewsbury Reg Simpson
MJK Smith Robin Smith Allan Steel Alec Stewart
Andrew Strauss Raman Subba Row Herbert Sutcliffe Chris Tavare
Graham Thorpe Marcus Trescothick Jonathan Trott Ernest Tyldesley
Michael Vaughan Cyril Washbrook Frank Woolley Bob Woolmer
Bob Wyatt

An admittedly eclectic choice, as I wanted to include some players, like Colin Milburn, who only played a handful of Tests but whom I felt would show as being impactful, and I also included batting all-rounders like Jackson as well as batsmen-wicket keepers like Stewart and Ames, who were selected on occasion on the strength of their batting alone. In any case, all of the top England batsmen have been considered, though all-rounders whose strength was more evenly balanced, or which favoured bowling, such as Bailey, Botham and Flintoff, have been excluded.

A Closer Look at Impact

Looking first at impact average per Test, these are the top ten batsmen:-

19.71 Sharpe
16.80 Hobbs
15.41 Hammond
15.30 Jackson
15.23 Dexter
14.74 Ranji
13.94 Stewart
13.88 Thorpe
13.80 Trescothick
13.70 Gooch

As a boy, I followed the Yorkshire county eleven closely so it’s particularly pleasing to see Phil Sharpe at the top, with brilliant fielding and excellent performances against a strong West Indies side being the main reasons for his high average. However, as he played in only 12 Tests he should give way to the great Jack Hobbs, who is significantly ahead of the next man, Walter Hammond. Another of my boyhood heroes, Colin Milburn, is ranked eleventh with an average of 13.54.

As I mentioned earlier, maintaining a rolling average above 20% is I think a representation of true Test class. In that regard, here is a list of those who have achieved that for the most Tests in their career:-

24 Gooch
22 Stewart
20 Hobbs
19 Hammond
19 Atherton
18 Cowdrey
17 Dexter
15 Hussain
15 Pietersen
14 Trescothick

Gooch stands alone at the top, and it’s interesting to see Atherton and Hussain ranked so highly. Players such as Hobbs and Hammond are penalised when ranked on an aggregate basis by having played in an era of fewer Tests, so here is the same list based on number of Tests maintaining an average over 20% as a percentage of all Tests played:-

33.90 Hobbs
27.87 Dexter
22.62 Hammond
21.05 Woolmer
20.34 Gooch
20.00 Ranji
20.00 Jackson
18.42 Trescothick
17.65 Sutcliffe
16.67 Steel
16.67 Sharpe
16.67 Stewart

By maintaining an average of over 20% for more than a third of his career, Hobbs now stands alone, significantly ahead of Dexter, who is in turn well ahead of Hammond. Gooch still figures in the top five but the surprise here is Bob Woolmer, though his appearance is due largely to two stellar performances in consecutive Ashes Tests in 1977 and the fact that he didn’t play in many Tests, making his percentage above 20 quite high. The same is true of Sharpe, who played in even fewer Tests and who was discussed earlier.

Greatness in Impact

Having earlier established a threshold of true greatness as maintaining an average above 30%, it turns out that of the list of 77 batsmen above, only 13 managed to peak at or above that level. Highly regarded batsmen who didn’t manage to achieve that level of impact include Ranji, Sutcliffe, Compton, May, Barrington, Cowdrey, Gower and Pietersen. Those who did are shown below, ranked on the peak impact average achieved:-

41.52 Hammond
40.10 Dexter
39.00 Cook
38.99 Gooch
37.31 Thorpe
35.73 Stewart
35.53 RA Smith
34.47 Boycott
33.44 Hobbs
33.22 Hutton
32.20 Vaughan
31.94 Bell
30.83 Atherton

There are some players who fare well by traditional measures, while there are those who do not but who we know are greats nonetheless. Ted Dexter, Robin Smith and Michael Atherton fit into the latter category; all three have a conversion rate of only around 25% but have obviously made their runs count when it mattered. I should also point out that the impact we’re measuring here is not only as a result of batting performances, but I wanted to rate those which we would naturally group together under the description “England batsmen”.

Area Under the Curve

If we look at the actual profiles, it is apparent that some players have maintained a higher level of impact – Dexter and Cook, for example, have similar peak values but Dexter’s profile shows a higher level of sustained impact.

The Impact of Impact - Dexter and Cook

One way of assessing that is to measure the “area under the curve”, i.e. the area bounded by the green line representing 30% and the impact profile line, giving us the total impact over 30%:-

35.13 Dexter
26.83 Hammond
22.53 Gooch
12.68 Cook
12.13 Boycott
11.87 Thorpe

No other players exceeded 10%. Dexter is significantly ahead of Hammond, and those two plus Gooch are streets of the next man, Cook. However, when you consider that Dexter played just 61 Tests, compared to 84 for Hammond and 118 for Gooch, I would have to say that England’s most impactful batsman ever is Ted Dexter.

Ted Dexter, a Cavalier among Roundheads

The above description of Dexter was offered by CLR James in 1963, describing him as one who plays “not only against opposing batsmen but against the very soul of the age.” Other comments made by James on Dexter could just as easily have been written twenty years later about Gower – “He is playing his innings in the style of a master expressing a personal vision…[he] is intent on hitting the ball, on hitting the bowler, to the boundary. Then it suddenly begins to dawn on him that this is a Test match and that, worse still, he is the captain of England. He begins to concentrate – on that…I see [him] as engaged in a constant struggle for free individuality in a conformist age.”

This conflict of interests may explain Dexter’s relative lack of century innings. Indeed, Dexter’s two most famous batting performances were scores in the 70s. The first was when he made 76 in even time against the Australians at Manchester in 1961, putting Englasnd, at 150/2 in the driving seat, only for Richie Benaud to snatch back the match and the Ashes with six wickets, skittling England out for 201. After a successful individual campaign in Australia in 1962-63 as captain, Dexter then played an innings which Alan Ross said “defied nature itself”; against the West Indies at Lord’s in 1963, openers Micky Stewart and John Edrich managed just two runs between them, with the world’s two fastest bowlers Wes Hall and Charlie Griffith baying for blood. An hour later, the hundred was up with what Ross described as “violent hitting…that rattled the glasses in the Tavern bar.” Dexter twice in an over crashed half-volleys to the boundary fences before Griffith had completed his follow-through. So utterly dominant was Dexter that Ken Barrington, not known for his sensitivity to the needs of the team, resorted to pushing singles in order to give Dexter the strike. Hall and Griffith were by now “without eagerness and enveloped in fogs of disbelief.” When Gibbs replaced Hall, “Wagnerian thunder gave way to Mozartian melody, the cut and the deflection more evident than the drive”; there was simply nothing the West Indies could do, until finally Sobers was able to disquiet him enough to trap him lbw for 70.

Christopher Martin-Jenkins, as he was with Gower, was similarly guarded in writing about Dexter, but concluded that though Dexter was something of an enigma, “in the right mood he was a batsman playing on a plane so exalted, and with an air of such cool command, that he roused visions of Shelley’s appropriately enigmatic visionary poem: ‘My name is Ozymandias, King of Kings; look on my works, ye mighty, and despair.'”

Or if you prefer, as Dexter’s Sussex teammate John Snow more succintly put it, Dexter was a big-time player – and how.

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