Recently one of my regular readers, Ganesh Mani, made a good suggestion on the tricky topic of evaluating allrounders. The traditional methods of either subtracting the bowling average from the batting average (in my analysis, the Weighted Batting Average) or dividing the WBA by bowling average have a number of holes in them. Values of 50 and 40, and 30 and 20 will produce the same difference. Similarly, values of 30 and 20, and 45 and 30 will produce the same quotient. Chalk-and-cheese situations providing the same indices means that even as back-of-a-napkin calculations, these methods lack credibility.

Ganesh suggested I take a value "1200/(bowling average)" as the bowling component, which could then be compared against the batting average. A bowling average of 20 results in a quotient of 60, somewhat equivalent to a top-five batsman. A bowling average of 24 results in a quotient of 50, somewhat equivalent to a top-25 batsman. And so on. He also made the interesting point that the crossover bowling average value of 34.6 (nearly the square root of 1200) is comparable to the mean of top-order batsmen's batting averages. This idea made a lot of sense and I decided to explore it further.

First, a pertinent question: who is an allrounder?

A high-bar definition of an allrounder is someone who could be selected as a batsman, batting at six or higher, or a bowler - one of the top three choices. I would say, a rough quantitative definition of this, give or take 5-10% either way, would be a WBA of 35-plus and a bowling average below 30. Let me go through the list of allrounders to see which players qualify based on these criteria.

Keith Miller's Weighted Batting Average (WBA) is 35 and bowling average 23.

Shakib Al Hasan could be considered as well, since he plays for a weaker team (37.1 and 31.1).

For all others, some sort of compromise has to be made.

Imran Khan and Ian Botham can only play as Nos. 7-8 batsmen (WBA 31.6 and 32.5). Garry Sobers could play only as a fourth pace bowler or a second spinner (bowling average 34). Jacques Kallis could be selected only as a fourth pace bowler (bowling average 32.7); same with Tony Greig and Ben Stokes (bowling average around 32).

There we end. Not really a satisfactory list. It is clear that this is too lofty a definition.

A more general definition will do: an allrounder is a player who has performed consistently well in both disciplines across his career. Now to convert this subjective statement to measurable steps.

Let's lower the bar to 100 wickets and 2500 runs. This too is too high; only 20 players make the cut. Many are excluded because their careers were during a period when the number of Tests played was not very high. We need to be pragmatic and, for example, ensure that Wally Hammond, who scored a lot of runs but only took 83 wickets, is included, as is Chris Woakes, who has taken over 100 wickets but not scored many runs.

So for my first level of selection, I included players who have scored over 1500 runs and taken 50-plus wickets, or scored over 1000 runs and taken 75 or more wickets.

This got me a substantial number of players. To avoid including bowlers who have played enough Tests to have accumulated a fair number of runs, like Anil Kumble, Shane Warne, Chaminda Vaas and Stuart Broad, I have set a limit of 22.5 as the lower cut-off for WBA (which roughly amounts a batting average of 25). And to avoid classifying Chris Gayle, Mark Waugh, Asif Iqbal, et al as allrounders, I have excluded those who took fewer than a wicket per Test - which is a poor return, indeed.

There was a temptation to set the upper limit for bowling average at 40. I have resisted that since it would mean the exclusion of a few players who are normally perceived as allrounders, prominent among them being Ravi Shastri and Carl Hooper.

A total of 51 players qualified. All countries, barring Sri Lanka, are represented. This is understandable, considering that among Sri Lanka's players, only Vaas comes closest to being an allrounder.

How do we rank these allrounders? We have to be fair to the batting and bowling functions. We have to recognise performance. We have to recognise the all-round impact of the players.

After a few days of work, I confirmed the folly of adding or subtracting actual batting and bowling average values. Let's face it: 50 minus 40 and 35 minus 25 both lead to values of 10. The latter averages are far more valuable to the team as an allrounder. I realised that my tried and trusted formula of assigning weights and determining the parameter values based on actual metrics was the solution. I was also determined that almost all the metrics used should be performance measures and not longevity measures. No one becomes an allrounder because he takes more wickets overall or scores more runs overall than another player. I also wanted equal weight assigned to batting and bowling on the one hand and a career span and individual Tests on the other. Finally, I wanted to recognise impactful performances.

I have worked out the following formula.

Allrounder Index =
Batting Index (25 points) +
Bowling Index (25 points) +
All-round Contribution per Test Index (20 points) +
All-round Impact Index (20 points) +
All-round High Impact Index (10 points)

Batting Index
Since I am a strong proponent of the Weighted Batting Average, I will use that value to determine the Batting Index. Overall I want the top score on any of the above parameters to be around 90% of the maximum points available. Hence, a maximum of 25 points will be allotted for a WBA of 57.5. The WBA for Sobers is 51.47, the highest in this group of 51 players. His Batting Index is 22.4, which is quite close to 90%.

Bowling Index
Since the bowling average is, arguably, the strongest of player measures, I will use that value to determine the Bowling Index. Here I will use Ganesh's suggestion, suitably tweaked. Since I have used the WBA, which produces lower numbers than the batting average, and I am normalising to a lower value, I will use 500 as the numerator. This will provide the maximum of 25 points for a bowling average of 20.0. The bowling average for Richard Hadlee is 22.30 - the lowest in this group. This leads to a Bowling Index of 22.4, matching the batting maximum.

Contribution per Test Index
This recognises the contribution the player made in each Test he played, in terms of runs and wickets. I have used a simple method of deriving the base value: "Runs scored + 25 * Wickets taken". The maximum of 20 points will be allotted to a Contribution per Test (CpT) value of 180. A big surprise here: R Ashwin has the highest CpT value of 165, which results in an Index value of 18.3. This method ensures that the value realised is a fair indicator of the player's contribution whether he is a bowling or batting allrounder. He could make up for one with the other.

All-round Impact Index
The All-round Impact Index is based on the player's performance in individual Tests. The player might have delivered a true all-round performance in a game (scored 75-plus runs and taken three or more wickets). Alternatively, he might have provided a batting-centric performance (scored 100-plus runs and taken two or more wickets), or he might have provided a bowling-centric performance (scored 50-plus runs and taken four or more wickets). If he scored fewer than 50 runs or took fewer than two wickets, it is fair that he is not deemed to have made an all-round impact. The number of such instances of all-round performance is divided by the total number of matches played to derive an AR Impact percentage. This is a better method of working than looking at the frequency value, which could go quite high for low numbers of matches played. An AR Impact per cent of 45.0 realises the highest value of 20 points. Shakib has achieved the feat in 23 of the 57 Tests he has played in, which gives him an Impact percent of 40.4 and an All-round Impact Index of 17.9, the highest.

High Impact Index
Some of the All-round Impact performances are virtually once-in-a-lifetime performances. Hence these are recognised separately. A very high bar is set for this. To qualify, the player should have scored 100-plus runs and taken four or more wickets in a Test. There is only one batsman who has crossed 100 runs per Test over his career, Don Bradman. (Steven Smith is almost there.) Only five batsmen have even crossed 90 runs per Test. Only 64 bowlers have taken four wickets per Test. A High-Impact per cent of 17.5 leads to the highest value of ten points. Shakib has achieved this in nine out of the 57 Tests he has played in. Hence the High-Impact Index value is 9.0 for him.

I can hear murmurs of "double counting". Of course, yes. However, these are performances at such high levels that double counting (or even "triple counting") seems perfectly justified. You might see a similarity with tennis here: Roger Federer has won 103 titles. Out of these, 20 are Grand Slams. When one does any serious analysis, the 103 and the 20 have to be independent parameters. For Rafael Nadal, the numbers would be 86 and 20, while, for Novak Djokovic, 82 and 18.

Thus, it can be seen that the highest values in all five categories are around 90% of the maximum points.

To start with, my objective was to have the Bowling Index and Batting Index within 10% of each other. Let us see whether I have achieved this. The average Batting Index value for the 51 qualifying players is 13.85. The average Bowling Index is 16.0. The total batting component average is 24.4 and the bowling component average is 28.2. (The batting component includes the Batting Index, the Runs per Test (RpT) part of the CpT Index, and 50% of the Impact Indices. The bowling component includes the Bowling Index, the WpT part of the CpT Index, and 50% of the Impact Indices.) It can be seen that all these are reasonably close to each other, with a slight edge to the bowling discipline. Hence the basic objective has been achieved.

A few other overall numbers. The average WBA for the 51 selected players is 31.8 and the bowling average 32.33. The average allrounder in this group scored 3135 runs and took 161 wickets. The average WpT is 2.62 and the average RpT, 51.1.

In the graph below, the batting and bowling totals are graphically highlighted to let the reader get a clear idea as to whether the player is batting-centric (Sobers, Kallis, Bob Simpson) or bowling-centric (Imran, Ashwin, Hadlee) or balanced (Shakib, Greig, Stokes).

You could say there's a huge surprise at the top, although maybe not to a clinical follower of the game. To have followed Bangladeshi cricket is to have followed Shakib. He is truly a giant. In both disciplines, in almost equal measure. Despite the fact that he has played only 57 Tests, his run tally and wickets tally are excellent. A very good WBA of 37.1, a competitive bowling average of 31.2 and an outstanding CpT value of 161 form a strong foundation. However, what really tips the scale for Shakib are the very high AR Impact % (over 40% of Tests) and a superlative 15.8% of High-Impact performances - that means that he scored over 100 runs and took four wickets once every six Tests.

Sobers has excellent batting numbers, acceptable bowling numbers, and very good impact numbers. His WBA of 57.5 is the highest among these 51 players and his bowling average is a passable 34.0. His AR Impact per cent is 36.6 and he has produced a High-Impact performance once every six Tests. Sobers is a truly great allrounder and fully deserves his high placing.

Aubrey Faulkner of South Africa, who played mainly before the First World War, comes in in third place. Let us examine his credentials closely. A WBA of 38.7, bowling average of 26.6, and a substantial CpT of 151 are, overall, better than Shakib's numbers. It is only in the Impact figures that Faulkner lags marginally. The net impact is a well-deserved third place. We are now seeing the wisdom of assigning zero weightage to longevity-related numbers.

Miller is some distance behind Faulkner. He has a sub-23 bowling average, which is among the best ever. His WBA is that of a top batsman - around 35. And the impact values are reasonable. Jack Gregory is another example of an old-timer making it to the top ten because we are able to treat a 25-Test career at par with a longer one. His numbers are quite good, especially his delivering impactful performances once every three Tests. Then there is another surprise: Chris Cairns has leapfrogged other, more fancied, contestants to sixth place. A near-33 WBA and a sub-30 bowling average and very good Impact performances have earned him his high rank.

Botham, one of the most charismatic players, is next. His figures almost match Cairns'. The fact that he played a lot more Tests than most others in the top 20 pushed his Impact values down slightly. Imran Khan, whose figures resemble Botham's on the batting front but are way better on bowling, comes in next - mainly because of the lack of high-impact performances. Maybe the presence of explosive bowlers in many teams in his era caused this.

Ashwin's batting credentials are just above par - a WBA of 24.7. However, his bowling average is very good - it stands at an impressive 24.7. But the real clincher is the CpT value of 165 - the best among any player here. His five high-impact contributions help him a lot, especially as he has played only 78 Tests.

Kallis completes the top ten, due mainly to his batting numbers. His WBA is a very high 48.6.

Greig, Hadlee, Ravindra Jadeja, Vinoo Mankad Trevor Goddard form the next group of five players. All are very good allrounders, having done enough in either discipline. The presence of Jadeja on the list, in addition to Ashwin, is an indicator of India's Test strength currently, especially at home.

Now we come to the second part of the article. Here I will look in depth at ten selected allrounders. This list is the top 12 above minus Gregory and Greig. Gregory's 24 Tests work against his selection, and Hadlee gets the nod ahead of Greig because of his pre-eminent position as the best bowler in this collection.

The graphs below are complicated and some explanations are in order. You will get the hang of the presentation after perusing a graph or two. (Please right-click the images and open them in a new tab to be able to see them better.)

1. The strip in the middle is used to show the Test number and year.
2. The wickets, represented by stumps, are shown in the top half of the graphs and the runs, grouped in rounded ten-run segments (33 displays as three segments and 47 as 5), at the bottom.
3. The AR Impact Tests - 75r/3w or 100r/2w or 50r/4w are shown as black squares.
4. The High-Impact Tests - 100r/4w are shown as blue squares.
5. The best performance of the player, in terms of the contribution he made, is highlighted by a double line connecting the batting and bowling sides of the graph.
6. The career of each player is split into three equal parts and the Mean Wickets and Mean Runs for each career segment are represented by the line that runs across batting and bowling parts horizontally. This will let the reader understand how the career progressed. The career segments have widely varying number of Tests. But that cannot be helped.

Let us now move on to the individual player graphs. The career-best performance is based on a normalisation of wickets taken to runs scored, with each wicket being equated to 25 runs.

Shakib's excellent career progression is depicted in the graph. Look at how close the three career segments are - the middle segment is just a little above the other two. His best performance of 143 runs and ten wickets came in this segment. Despite a poor start, Shakib has delivered consistently. Look at the splashes of blue, the Impact performances. In the past 15 Tests, Shakib has delivered impact performances in ten Tests. His ban for not reporting a bookie approach derailed his career somewhat, but he still ought to have at least five fruitful years ahead of him. Truly, Shakib is the greatest allrounder ever.

Sobers in the second spot is like Lewis Hamilton moving to second - it does not happen often. Sobers' first career segment was poor on the bowling front. He averaged just above one wicket per Test. But the 365 ensured that his batting numbers were good. The second segment was quite different. An average of over four wickets and nearly 100 runs per Test - the hallmark of a great allrounder. He dropped a little on both fronts in the third segment, although his career-best performance (247 runs and six wickets) came in this phase. In more than a third of the Tests Sobers played, he made an impact as an allrounder, and over 10% were high-impact performances. In summary, a truly great batsman and a good bowler, metamorphosing into a very good allrounder.

Faulkner was a legspinning allrounder who had a magnificent career on both batting and bowling fronts. All his Tests bar one were played before the First World War. He fought for the Allies in the war and was awarded the Distinguished Service Order. In the first career segment, Faulkner was primarily a bowling allrounder, averaging over four wickets per Test. In the second, his batting took off and he averaged well over 100 runs per Test while still taking four wickets per Test. This segment is among the best of all allrounders in history. His batting fell off as he came towards the end of his career. He made an impact in nearly a third of his Tests - almost all in the golden middle segment. He is one of three allrounders who have delivered career-best performances of 400-plus runs: in 1910, he took 8 for 160 and scored 201 against England.

Miller was a truly magnificent allrounder and was key to Australia's dominance during the post-World War II years. He delivered impactful all-round performances in over a quarter of his Tests. His first career segment was bettered in the second and third segments on the bowling front. As for other players, Miller's middle segment was his most effective one. However, his best Test performance came towards the end of his career.

Cairns is the real surprise in this collection. After an indifferent start, he quickly moved on to deliver stunning all-round performances. In his second segment he was more of a bowling allrounder and his batting dipped. However, his best career segment was his third one, unlike the other allrounders featured here. Nine wickets in his last Test makes one wonder if he retired too soon; but it is also true that he was plagued by injuries throughout his career.

Botham is the quintessential high-performing aggressive allrounder. The first half of his graph is astounding. In his first segment he averaged over five wickets per Test - more than many great bowlers; and he was a competent late-order batsman. In the second segment, his bowling fell off slightly, to be made up by a corresponding batting increase. The third segment was weak - an average of three wickets and well under 50 runs per Test. His struggles were all too visible (and similar to Kapil Dev's). Maybe he played a dozen Tests too many. But he was a king in his earlier years, which housed the greatest all-round performance ever - 114 runs and 13 wickets against India in 1980.

Khan follows Botham closely. A bowling-dominated first segment, true all-round performances in the middle, and a drop-off, especially on the bowling front - though accompanied by a rise in his batting numbers - in the last segment. Look at his bowling in the middle segment: over five wickets per Test. Let us not forget that he also was a successful captain from early in his career. His best performance of 11 wickets and a hundred came right in the middle of his career.

Ashwin's presence is also a surprise. However, he qualifies and fully deserves to be featured here. When we look at the graph, it is clear that Ashwin is a bowling allrounder. He has taken well over five wickets per Test in his career - either side of five all through his career. These are numbers close to Muttiah Muralitharan's. However, Ashwin's overall tally of runs per Test is only around 40 and even that has dropped off in the third segment. But it must be said that many of his runs have been invaluable late-order contributions. His best performance of nine wickets and over 100 runs was in his third Test, against West Indies.

Kallis was a batting allrounder - in sharp contrast to Ashwin. His first segment produced under two wickets per Test and not-so-great batting numbers. He improved as a batsman in the second segment and almost reached 100 runs per Test. A la Botham, he dropped off in the third segment, but he was able to produce quite a few batting-centric all-round performances in this phase. His Impact per cent was just over 20 and there were only three High-impact performances. A true batting allrounder, as evidenced by his wickets per Test value of 1.75.

Hadlee is, almost inarguably, the best bowler in this august group. A career accumulation rate of just over five wickets per Test, strike rate of 51 balls per wicket, and a bowling average of 22.3 are testaments. He was a colossus in bowling as Sobers was in batting. Like Ashwin, his three-segment wickets-per-Test figure is in excess of 4.5. His batting was competent for someone playing at No. 7 or 8. The overall impact figures are sub-par mainly because of the lack of batting contributions. Hadlee's best-ever performance was something for the ages - from a bowling point of view. He took 15 wickets and just about crossed the batting bar of 50 runs. This included 9 for 52, the greatest bowling performance in Test cricket.

Unfortunately Kapil Dev is in 24th place, making it difficult for me to feature him. His WpT of 3.31 does not compensate enough for the RpT value of 40. Nor does the fact that the bowling average is higher than the WBA. He also has only 23 AR-Impact performances (17.5%) and only one high-impact one. He joins Richie Benaud, Shaun Pollock, Stokes and Mankad among allrounders unlucky not to be individually featured.

Conclusion
I will say with conviction that the parameters for this analysis have worked very well. The top three allrounders - Shakib Al Hasan, Garry Sobers and Aubrey Faulkner - stand over 10% clear of Keith Miller. They surely deserve their places. And let us not hesitate to give Shakib the respect he deserves, especially considering he plays for a relatively weak team.

Finally, I have made available for the readers the Excel sheet containing the data for all the players, which you can download here.

Email me your comments and I will respond. This email id is to be used only for sending in comments. Please note that readers whose mails are derogatory to the author or any player, will have their mail ids permanently blocked.

Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems