The Cricket Monthly recently asked 25 experts to vote on the 50 greatest Test performances of the last 50 years. We also asked four cricket statisticians to complement the jury's pick by coming up with their own lists, based on their algorithms and databases. The two are not connected in any way.

Allrounder supremacy
By Anantha Narayanan

There are two ways of compiling such an elite list. I could use one or more of a number of analytical processes I have available to measure player performances. This is not necessarily a good method since analysis reflects the mind, not the heart. Bare numbers and derivatives do not often tell the story. The other method is to do a personal selection.

I adopted a method that combines both options. I used my Performance Analysis methodology to shortlist 25 to 30 performances. Then I selected the top 10, using rigorous standards. I selected six of the top seven, and then three more from within the top 20. Only one entry came from outside the top 20, for very justifiable reasons.

The performance analysis is structured as follows.

The cornerstone of these computations is that the two teams would be accorded 50-50 performance points only when a Test was tied. Everything else flows from this base. The point spread for wins varies between a one-run win (Test #1210 scored 50.08-49.92 for West Indies) and a 675-run win (Test #176 scored 92.82-7.18 for England). The total points for a draw depend on the extent of completion of the match. It could range from 0.38 points (Test #1907) to 99.89 points (Test #2019: India-West Indies near-tie).

There are two ways of selecting player performances. The first method is to use the absolute performance points received by the player. However, this would mean that the selection is too much in favour of wins, and among these, big wins. We are also interested in great performances in draws and losses. So I used the percentage of contribution (player's to team's) as the base. Of course, meaningless high-percentage contributions have been weeded out. Here are the top 10.

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

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Hadlee for the win
By Ric Finlay

The biggest challenge in determining the "greatest" Test match performances is to find the numerical balance that equates runs to wickets, so that performances over an entire match can all be rolled into one statistic. I decided the best way to do this was to attribute to each wicket the value of 33.05, which is the average number of runs scored between wickets in the 50 years of Test match cricket under review. I also attributed a run value of 9.91 to each catch taken, calculated by working out the proportion of wickets that fell to catches (roughly 60%), and sharing equally that run value with the bowler. For those who bowled, I deducted one point for every run conceded.

Doing this for all match performances gave me the following ten qualifiers, without regard to conditions or strength of the opposition:

(Points = Runs + 33.05*Wickets + 9.91*Catches - Runs Conceded)

For those who think that the list is dominated by batsmen to the detriment of bowlers, it should be noted that the next three positions were filled by those with significant bowling performances: Imran Khan, Narendra Hirwani and Bob Massie. It was a close-run thing.

To determine a final ranking, I decided that some match context was needed to moderate the differences in conditions. To do this, I calculated the proportion of the match runs and wickets each player above achieved, added the two together, and re-ranked them. This gave me my final listing for the ten greatest Test match performances in the last 50 years.

Ric Finlay is a statistician, historian and data provider based in Tasmania

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Botham, followed by the rest
By Andrew Samson

The primary idea of the methodology is to calculate a "standardised" value for batting and bowling performances in each match. This needs an assessment of the quality of the pitch and the quality of the bowling attack faced for each innings played, and the quality of the batsmen dismissed for each innings bowling performance. This system rewards performances that really stand out within the context of a particular match and not just those performances where lots of runs were scored or wickets taken.

Virender Sehwag in Galle, 2008: the best match batting figures © AFP

The calculation is done as follows:

• Each batsman's career average is divided by the average runs per wicket totalled over the matches he played in to give a "batting index". For example Peter May and Ken Barrington each have a batting index of 1.77 although May averaged 46.77 compared to Barrington's 58.67, having played in much lower-scoring matches than Barrington.
  
• Similarly a "bowling index" is calculated by dividing the total runs per wicket in the matches he has played by the bowler's career average.
  
• A "pitch quality" value is calculated, which is the average runs per wicket in each match.
  
• A team bowling index is calculated by adding the individual bowling indices for each bowler in each innings proportioned by the number of overs each bowler bowled in that innings.
  
• For each individual innings a standardised score is calculated by dividing the actual score by the pitch quality and multiplying it by the team bowling index for the attack faced.
  
• The batting score for each player for each match is this standardised score added up for both innings.
  
• The bowling score for each match is the sum of the batting indices of the batsmen that the bowler dismissed in each match, minus the runs conceded/pitch-quality figure.

The leading bowling performance of all time is Jim Laker's 19 for 90 against at Old Trafford with a score of 15.87, followed by Hedley Verity's 15 for 104 against Australia at Lord's in 1934, at 11.49. The best match batting figures are Virender Sehwag's 12.07 (for 201 not out and 50 against Sri Lanka in Galle in 2008), followed by Graham Gooch's 34 and 154 not out versus West Indies at Headingley in 1991. So the scales for batting and bowling performances are very similar and the final score is the sum of the batting score and the bowling score.

The top 10 performances by this measure since January 1, 1966:

Andrew Samson has been the official statistician for Cricket South Africa since 1994

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Gooch lords it over the giants
By Charles Davis

One challenge in judging the most remarkable cricketing performances lies in putting batting and bowling on the same scale, without using arbitrary conversion formulas or weighting factors. But it can be done.

To properly rank bowling performances, we must take into account both wickets taken and runs conceded. For example: while standard lists would rank a return of 11 for 150 above 10 for 30, most would agree that the latter is the more remarkable. I have found a way to quantify this statistically, based on the observation that bowling returns follow a "normal distribution" or bell curve.

For each specific number of wickets, there is a separate bell curve, and the remarkable thing is that each of the curves has much in common; at five wickets or above, they all peak at 110-135 runs and have similar spreads or standard deviations of around 35-40. The difference is in the height of the curves, reflecting increasing rarity as the number of wickets climb.

King of Spain: Mushtaq Mohammad made 121 and 56 and took 8 for 97 against West Indies in Trinidad in 1977 © Getty Images

Using these observations, different bowling performances can be matched according to how rare they are. The analysis of all Tests since 1966 shows that the following match returns are similar in terms of rarity: 7 for 35, 8 for 50, 9 for 65, 10 for 80, 11 for 100, 12 for 125, and 13 for 150-plus. These are equivalent, in terms of rarity, to a batsman scoring about 225 runs in a match. (Note that taking 14 or more wickets, regardless of runs conceded, will always have a rarity value higher than 225.)

By expanding this analysis, any bowling performance can be matched with its batting equivalent, based on rarity value. The calculation can be reduced to a statistical formula based on normal distributions. Batting and bowling can now be ranked on the same scale. Batting performances are untouched, a simple total of runs scored. Using these methods, performances like Narendra Hirwani's 16 for 136 in Madras in 1987-88, and Bob Massie's 16 for 137 at Lord's in 1972, are equivalent to a batsman scoring just under 400 runs.

It must be stressed that these are pure statistical assessments, with a minimum of adjustment factors or arbitrary weightings. If you are looking for "the greatest", there are many other factors to consider: too many, perhaps. For now, it might be feasible to build on these rankings by bringing in some of these factors.

Once batting and bowling are on the same scale, all-round performances can now be evaluated, simply by adding up the totals. The final list looks like this:

For those interested in earlier performances, the highest rating of all goes to Jim Laker's 19 for 90 at Old Trafford in 1956, equivalent to a runs total in the region of 550. This is not surprising, given that no one else has taken more than 17 wickets in a first-class (11-a-side) match.

Charles Davis is a Melbourne-based statistician and author who had developed a large ball-by-ball database for Test matches

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