Malcolm Marshall emerges as the best of them all © Getty Images

Although I didn’t start out that way, what I’ve ended up with, I think, is a pretty good cross-era ranking of the most efficient strike bowlers Test cricket has known. I don’t claim that it’s definitive: what I do claim is that the method I’ve used is quite interesting, and I’d like to see what other stats mavens make of it.

The first decision I made was to eliminate all minnow matches. Leaving out Bangladesh and Zimbabwe is pretty commonplace but if we’re being realistic, only England and Australia did not have a bedding-in period as minnows before they became a team to be at least reckoned with. It seems essential to eliminate minnow matches because otherwise some bowlers are at a distinct disadvantage: a bowler whose career was from 1970-1980 never got a chance to bowl at a minnow team, whereas Fred Trueman had endless fun with weak Asian teams in the 1950s. Since I use Ric Finlay’s Tastats, this sort of exclusion is very easily accomplished.

There being no formal event which declares a team to have “arrived” in Test cricket, I had to make some arbitrary judgements about when to regard a team as having graduated. I took South Africa’s entry to senior ranks as having occurred when they unveiled their quartet of googly bowlers and comprehensively thrashed the fairly weak England team which toured in 1905-6, after which they were generally difficult to beat. Though West Indies won a series against England in 1934-35, the touring side was again half-strength; I decided that they did not really graduate until 1945. India’s graduation I took to be 1961, Pakistan’s 1965, New Zealand’s 1969 and Sri Lanka’s 1990. One might be able to argue that Zimbabwe were of a reasonable standard from about 1998-2003, but it seemed simpler to leave them and Bangladesh out of all consideration. Since I also have a prejudice against non-Test matches being included, the ICC Superflop game is also left out.

Subtracting those games has a widely-varying effect on a bowler’s career total of wickets. Muralitharan drops from 751 wickets to 588 and Trueman from 307 to 192, whereas Jeff Thomson and Michael Holding’s figures remain untouched.

Next, I decided to find a way to give greater credit for taking top-order wickets, because they are the ones you really want your strike bowlers to be cleaning up.

I was initially tempted to weight them on the basis of the runs scored at each position, but then realised that the top order contribution is exaggerated by declarations and innings cut short by the match being over. I then moved on to using the batting averages at each position.

Adding up the averages for each position gives a total of 307.27. The share for each wicket is given by positional average/total average, so the #3 average of 39.662 is 0.129 of the total. Those shares sum to 1, so if we multiply them by 11, they will sum to 11. This gives us the following weightings:

If the dismissal of a batsman is worth the above number of wickets, then a bowler taking one of each will have a total of 11 wickets, whereas someone with a top-order bias will have more and someone who wipes up tail-enders exclusively will have a lot less. Owing to a limitation in TAStats, whose breakdown of bowler’s victims by position does not differentiate between openers, in practice I used 1.30 for both 1 and 2.

To take three examples, Shane Warne’s total gets adjusted from 685 to 685.2, Glenn McGrath’s from 549 to 605.6, and Stuart MacGill’s from 164 to 159.0. Given that in practice a lot more top-order batsmen than tail-enders get dismissed, most bowlers actually show a profit, so MacGill’s reduction is evidence that he really was a tail-end cleaner.

If we apply this wicket adjustment to the figures for non-excluded matches and remove everyone who played less than 20 relevant games or took under 100 relevant wickets, this is the resultant top ten by average:

The right-hand column shows that there is a wide disparity between bowlers’ strike rates. A strike bowler’s efficiency does not depend solely on runs conceded; his strike rate is also an important factor because of the runs scored at the other end and the overall time taken. If Dale Steyn bowls six overs and takes a wicket but concedes 30 runs while Makhaya Ntini concedes 18 in his six without taking a wicket, the opposition are 48/1 at the end of these spells. If Shaun Pollock bowls 11 overs and concedes 20 runs while taking a wicket, 33 runs get conceded at the other end and the opposition reach 53/1 although the game is ten overs older.

I have for some time been toying with a measure I call the Power Index, which combines the average and strike rate by multiplying them together and taking the square root. Sqrt((runs/wickets)*(balls/wickets)) has a denominator of wickets, so the numerator can be seen as representing the resources used up in taking a wicket.

If we apply that algorithm, we get a new top ten, as follows:

Ambrose and McGrath drop down, Colin Croft rises, and Dale Steyn and Waqar Younis come in instead of Davidson and Trumble.

However, this is deeply unsatisfactory because we know that Barnes and Peel played in a time when scores were lower and wickets fell much more often. Today’s fashion is to bat aggressively from the word go, whereas in the middle of the last century caution was the Test batsman’s watchword. We need a way of equalising for the changes in general pitch conditions and style of play.

This is a well-known problem, and what follows does not claim to be universally applicable.

But the essential aspects of what we are examining here are the balls bowled, runs conceded and wickets taken. If we can find a way of keeing one or more invariant, then we have a fixed point while scaling the others to fit.

I decided to use the first match innings of Tests as the way to fix par. The first innings of the match is the least likely to be cut short by weather, and the least likely to be affected by tactical considerations. A third innings can be anything from a stonewall grind trying to save a match to a hell-for-leather bash while trying to set a target, but a first innings is always going to be played at whatever pace the side think appropriate given the conditions and they will nearly always get as many runs as the conditions allow. The dimensions of the first match innings may change, but its tactical purpose does not.

Across our population of matches, the mean first match innings notches up 327 runs off 678 balls.

What I did was to find out the dimensions of the average first match innings in a particular bowler’s period. I decided not to restrict the sample to matches that the bowler played in, because then his performances are effectively the norm and we don’t see how he stood out (or not) from his contemporaries. I think we are more interested in how their performances stack up relative to everything that happened in their period, so I used all the non-excluded matches played in the cricket years (running May-April) which his career spanned. Somone who debuted on 11th November 1982 and finished on 25th August 1994 would thus have his period defined as 1982 –1995 (Ric Finlay will recognise his “years from and to” filter option).

I then scaled their figures for balls bowled and runs conceded accordingly. So a bowler whose period averaged 340 runs off 650 balls is adjusted to concede his actual runs * 327/340 off his actual balls * 678/650 . We now have adjusted figures for each of balls, runs and wickets and can run through our standard calculations for average, strike rate and PI to come up with our final result, the top ten of which looks like this:

B/I1 and R/I1 are the average first match innings balls and runs for that bowler’s period.

As a dedicated supporter of SF Barnes as the king of bowlers, I am mortified to discover that Malcolm Marshall pips him to the top spot – but if Barnes had to be toppled, I’m glad it was Macko.

On a very contemporary note, Dale Steyn has made an incredible start to his career, since he comes in at number three (with a bullet) on this all-time list. Waqar Younis’s figures at the same stage of his career were even more spectacular, with a PI of 27.29, so we can probably assume that Steyn will also descend the list as his career unfolds.

Of the top ten, only McGrath and Laker were ever really used in a containing role on dead pitches, and they did not do that much. In the full table, those who spend time keeping the runs down without taking wickets lose out, with the result that Shane Warne comes a lowly 55th. But then, this is not a merit ranking but an assessment of how nearly they approached the ideal of incessant lethality.

It’s not an unbelievable top ten. If the model is wrong, it still manages to produce a sensible result.

But it can certainly be challenged on a number of points.

Are the cut-off dates for minnowhood reasonable?

Are the relative batting averages of the positions in the batting order a sound way to weight the value of wickets?

Is the Power Index a sensible way of combining parsimony and frequency to measure attacking prowess?

Is the first match innings a useful point of reference?

Even if comparing first match innings is reasonable, should one average the dimensions thereof for all matches or just the ones the bowler played in?

Whatever those averages are, is it sufficent to scale them in a linear fashion or should some more complex function be used?

So let the debate on those and no doubt other questions commence.

The full table is available here.

	Australia have had plenty of such moments over the last nine years © Getty Images

There are a lot of similarities between the Australian cricket team and Roger Federer. Both dominated their respective games to a level unseen until now. Both had their achilles heal in the Indian team and Nadal respectively. However their overpowering performances during the rest of the period kept them right on top for a long time. They might have been beaten by lesser teams/players once in a while. But that did not make their conquerors World no.1.

When Djokovic defeated Federer at Melbourne, he did not move to (or claim) the No.1 position. Similarly with other players. It took one player, Nadal, to produce consistent top-drawer performances over a long period, across all surfaces, which propelled him to the top, displacing Federer. He won the Monte Carlo Open, Italian Open, German Open, French Open, Wimbledon, Canada Master's and Olympics and only then moved to the top position.

Even then, Federer only moved to No.2 and he showed the fire in him winning the US Open just as Australia have bounced back after their loss to India.

If India or South Africa want to unseat Australia, it is not sufficient that they beat Australia once a while. They have to back this up with consistent wins across the globe and against each other, and that too away. Until then neither team can claim the No.1 spot. Any views to the contrary are hollow and empty words.

Let us look at some tables summarising these 100 matches. These are mostly team-centric analysis with very few individual player references. The format of the tables has been designed to show the years and total horizontally to improve readability.

Summary of series results.

                Total       Won by      Won by
                Played    Australia   Other Team     Draw
All series        32          27           3           2
In Australia      17          15           -           2
Outside           15          12           3           -

The three-Test series played against Pakistan during 2002, at Sri Lanka and UAE, has been taken as an away series. The ICC Test series (one match) has also been included in this table.

Only India have a good record against Australia. Of the five series played between these two teams during this period, two have been won by Australia, two by India and one drawn.

Summary of match results

                2000  2001  2002  2003  2004  2005  2006  2007  2008  Total

All matches        8    14    11    12    14    15    10     4    12    100
Wins               8     8    10     8    10     9    10     4     5     72
Wins %         100.0  57.1  90.9  66.7  71.4  60.0 100.0 100.0  41.7   72.0
Losses             0     3     1     3     1     2     0     0     3     13
Losses %         0.0  21.4   9.1  25.0   7.1  13.3   0.0   0.0  25.0   13.0
Draws              0     3     0     1     3     4     0     0     4     15
Draws %          0.0  21.4   0.0   8.3  21.4  26.7   0.0   0.0  33.3   15.0
Inns wins          3     2     5     3     1     0     2     1     1     18
Inns wins %     37.5  14.3  45.5  25.0   7.1   0.0  20.0  25.0   8.3   18.0

Home matches       5     6     5     8     7     7     5     4     5     52
Home wins          5     3     5     5     5     6     5     4     3     41
Home wins %    100.0  50.0 100.0  62.5  71.4  85.7 100.0 100.0  60.0   78.8
Home losses        0     0     0     2     0     0     0     0     1      3
Home loss %      0.0   0.0   0.0  25.0   0.0   0.0   0.0   0.0  20.0    5.8

Away matches       3     8     6     4     7     8     5     0     7     48
Away wins          3     5     5     3     5     3     5     0     2     31
Away wins %    100.0  62.5  83.3  75.0  71.4  37.5 100.0   0.0  28.6   64.6
Away losses        0     3     1     1     1     2     0     0     2     10
Away loss %      0.0  37.5  16.7  25.0  14.3  25.0   0.0   0.0  28.6   20.8

During this period Australia have lost only three Tests at home. The first was the dead rubber Test (at 4-0) against England during 2003. The other two have been against India during 2003 and 2008 respectively, both in live situations. This is an imposing record.

Away from home, the maximum losses have been against India (5 times) followed by England (3 times). Overall Australia's draw % has been a low 15%. Barring recent times, they have always gone for a victory, risking a loss.

Australia's best years have been 2000, 2006 and 2007 when they had a 100% all-won record. Their worst year has been 2008 when they have won less than half the Tests, the only such year during this golden period. Another measure of their dominance has been the number of innings wins they have achieved, 18 in all, an amazing 18% overall. However it must be seen that 11 of these wins (nearly 25%) were achieved during the first four years and the numbers have fallen off recently. Important to note that, during these nine years, not once did Australia lose by an innings.

If one looks at Australia's recent record, say during 2007-08, they have played 16 Tests, won 9, lost 3 (all against India) and drawn 4 matches. This is not the sign of a dominating team, especially the high proportion of drawn matches. The South African series will be a clear pointer to the Australian revival from this minor slump. If they win 3-0 or 2-0, they would have established their dominance. If they win 1-0 or draw the series or lose, there will be a clear sign of fall.

Now let us look at possible contributing factors, both for the dominance and the (possible) fall from such a dominating position.

Summary of partnerships

                2000  2001  2002  2003  2004  2005  2006  2007  2008  Total

Aus:Innings       13    25    17    21    27    29    18     7    22    179
Aus:Op >100        2     5     4     1     4     2     0     1     3     22
Aus:Op >100 %   15.4  20.0  23.5   4.8  14.8   6.9   0.0  14.3  13.6   12.3
Aus:Op <10         6     8     4     5     3     6     5     0     5     42
Aus:Op <10 %    46.2  32.0  23.5  23.8  11.1  20.7  27.8   0.0  22.7   23.5
Aus:Op runs      438  1546  1060   776  1458  1365   602   498  1015   8758
Aus:Op avge     33.7  61.8  62.4  37.0  54.0  47.1  33.4  71.1  46.1   48.9

Opp:Innings       16    27    22    24    28    30    20     8    24    199
Opp:Op >100        0     2     1     2     2     3     0     0     2     12
Opp:Op >100 %    0.0   7.4   4.5   8.3   7.1  10.0   0.0   0.0   8.3    6.0
Opp:Op <10         8     7     6    11     9     7     5     3     7     63
Opp:Op <10 %    61.5  28.0  35.3  52.4  33.3  24.1  27.8  42.9  31.8   35.2
Opp:Op runs      232  1031   778   784   732  1077   534   196  1031   6395
Opp:Op avge     17.8  41.2  45.8  37.3  27.1  37.1  29.7  28.0  46.9   35.7

The opening failures have also been reasonable, at 23.5%. This compares favourably with the all-Test average for failures which is 28.7%.

Let us look at what the Australian opening bowlers have done. The opposing teams have missed playing only one of the second innings (during a rain-affected match against New Zealand during 2001) and have had only 6% of opening partnerships exceeding 100, below half of the Australian numbers and well below the all-Test figure of 8.1%. The failures have been similarly higher, at 35.2%, much higher than the all-Test value of 28.7%.

We have successfully identified the first two reasons. The success of the Australian opening batsmen and bowlers.

Late order batting

                2000  2001  2002  2003  2004  2005  2006  2007  2008  Total

Aus:Last3wPtsh     8    17    12    12    22    22    11     3    18    125
Aus:Last3wRuns   491  1139   591   507  1093  1468   664   165  1090   7208
Aus:Last3wAvge  61.4  67.0  49.2  42.2  49.7  66.7  60.4  55.0  60.6   57.7

Opp:Last3wPtsh    16    25    20    22    26    27    18     8    20    182
Opp:Last3wRuns   613  1301   759  1018  1187  1246   819   347  1000   8290
Opp:Last3wAvge  38.3  52.0  38.0  46.3  45.7  46.1  45.5  43.4  50.0   45.5

Team batting and bowling summary

                2000  2001  2002  2003  2004  2005  2006  2007  2008  Total

Aus:BallsBwled  6909 12768  9420 11146 15176 14458 10076  3744 13252  96949
Aus:RunsScored  3942  8042  6279  7596  8994  8944  6125  2436  7300  59658
Aus:WktsTaken    160   248   215   224   257   281   191    80   211   1867
Aus: RpO        3.42  3.78  4.00  4.09  3.56  3.71  3.65  3.90  3.31   3.69
Aus: BpW        43.2  51.5  43.8  49.8  59.1  51.5  52.8  46.8  62.8   51.9
Aus:DiffBatRpO  0.57  0.60  0.98  0.95  0.58  0.47  0.55  1.00 -0.02   0.58
Aus:DiffBowS/R  23.9  27.4  30.7  48.4  -0.5  14.1  28.8  59.7   8.7   22.0

Opp:BallsBwled  6780 14286 10289 13738 13693 14487 10355  4047 13666 101341
Opp:RunsScored  3226  7554  5176  7172  6795  7833  5340  1962  7568  52626
Opp:WktsTaken    101   181   138   140   234   221   127    38   191   1371
Opp: RpO        2.85  3.17  3.02  3.13  2.98  3.24  3.09  2.91  3.32   3.12
Opp: BpW        67.1  78.9  74.6  98.1  58.5  65.6  81.5 106.5  71.5   73.9

The overall bowling strike rate has been an excellent 52 balls per wicket, as compared to 68 overall. Once every 8+ overs means they were looking at dismissing an opposing team within a day's play.

The opposing teams have also been quite good with an overall RpO figure of 3.12. However they have been way below par in their strike rate value which is more than 70. However remember this includes 6 Tests against Bangladesh and Zimbabwe.

I have also introduced couple of other factors, differential in nature. One is the difference between the Batting RpO values of Australia and the opposing teams. Australia have exceeded the other teams by an overall substantial value of 0.58. Only once, during the current year, have the other teams matched the Australian figures. Similarly Australia have consistently captured a wicket every 22 balls more frequently than the opposing teams. Only during 2004 have the other teams managed to better Australia's BpW figure.

Summary of innings scores

                2000  2001  2002  2003  2004  2005  2006  2007  2008  Total

Aus:Comp Inns      7    13    10    10    19    18     8     2    16    103
Aus:Inns<100       0     0     0     0     1     0     0     0     0      1
Aus:Inns<100 %   0.0   0.0   0.0   0.0   5.3   0.0   0.0   0.0   0.0    1.0
Aus:Inns          13    25    17    21    27    29    18     7    22    179
Aus:Inns>500       1     3     4     6     4     3     4     2     3     30
Aus:Inns>500 %   7.7  12.0  23.5  28.6  14.8  10.3  22.2  28.6  13.6   16.8

Opp:Comp Inns     16    19    21    20    24    26    17     8    18    169
Opp:Inns<100       1     0     3     1     3     0     0     0     0      8
Opp:Inns<100 %   6.2   0.0  14.3   5.0  12.5   0.0   0.0   0.0   0.0    4.7
Opp:Inns          16    27    22    24    28    30    20     8    24    199
Opp:Inns>500       0     3     0     1     1     0     1     0     3      9
Opp:Inns>500 %   0.0  11.1   0.0   4.2   3.6   0.0   5.0   0.0  12.5    4.5

The opposing teams have been dismissed below 100 4.7% of the innings completed, slightly above the 3.84% overall. They have also exceeded 500 4.5% of the innings played, way below the overall 6.5%. Incidentally 7 of these 9 innings above 500 have been scored by India.

Finally the summarised reasons for the Australian domination. I would appreciate it if the readers do not write to me that these are obvious. These are not off-the-cuff subjective conclusions, as normally made. These are based on a thorough analysis and have been derived in an objective manner.

1. The success of the opening partnerships - both in terms of increased successes and considerably reduced failures.
2. The way the Australian opening bowlers have reversed the above trend, not allowing successes and the high number of breakthroughs very early in the innings.
3. An overall very high scoring rate.
4. A very high bowling strike rate despite the presence of the slightly lower-striking Shane Warne (57 bpw) throughout.
5. Rare batting failures and frequent batting successes in terms of innings scores.
6. The only reference to an individual in this team-centric analysis: one of the major reasons for Australian domination during these 9 years has been the performance of Adam Gilchrist, who scored 5130 runs at an average of 46.64 and effected 397 dismissals. That sort of all-round performance meant that Australia had invariably been able to play with an extra bowler/allrounder through the luxury of having Gilchrist bat at No.7.

What does the future hold for Australia. It is possible for Australia to lose their No.1 position, provided India maintains its very competitive recent Test performances, both home and away. They have to win away consistently and win at home comfortably. Similarly for the South Africans, with a lower degree of possibility. I am not certain whether any other team has the resources to test Australia over a long period. Pakistan lack a dynamic captain while England lack top-quality players.

Australia will go through a phase of re-building and will come back stronger. However the days of domination are probably over. The No.1 position will swing between 3-4 teams.

The same thing applies to Federer. He will win around 15-16 Grand Slam titles and probably go back to No.1, but not at the dominating level as exhibited earlier. So the similarities between Australian team and Federer will continue.

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December 6, 2008

The optimum age for a cricketer

Posted by Ric Finlay at in Trivia

	According to this graph, experience outweighs youthful exuberance more times than it doesn’t (Click here for a bigger image) © Ric Finlay

Our CSW database has the capacity to analyse data by age, so I decided to use it to investigate what age(s), if any, provided significantly better performances.

My sample was Sheffield Shield data since 1977, when the newest state, Tasmania, entered the competition. This provided reasonably homogenous data, with little of the cultural variation that might be obtained using Test match data. The sample thus analysed over nearly 950 matches, involving 800 players.

The results are in the table below:

Age-wise averages with bat and ball in Sheffield Shield since 1977

Age	Batting average	Bowling
<20	28.34	34.01
20	26.66	35.78
21	29.08	36.45
22	30.55	36.92
23	30.31	36.10
24	31.23	34.93
25	30.77	33.22
26	31.67	33.56
27	30.99	32.75
28	31.53	32.86
29	32.41	31.45
30	33.96	30.58
31	32.35	32.19
32	34.63	30.42
33	31.64	29.93
34	30.71	31.19
35	32.72	33.32
>35	33.06	34.97

What, if anything, can be deduced from the results? Well, clearly, both batting and bowling averages improve as one gets older, but the extent to which this happens after the age of 30 surprises me. The picture of the young, virile cricketer in his early-20s emerging triumphant over the aging has-been is not sustained by this data, and it would seem that experience outweighs youthful exuberance more times than it doesn’t. For both batsmen and bowlers, the ages of 32 - 33 are the vintage years, and perhaps we are too keen to write players off as they move through their early-30s.

I would be most interested to read of the comments by others in relation to this data, and data from other spheres of cricket.

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