Sohail Tanvir took plenty of wickets in the IPL, but many of them came late in the innings © AFP

In 50-over cricket, it's more complicated. Taking wickets is still useful, especially early on — you force the batsmen to bat more slowly until later in the innings.

But in Twenty20 cricket, the bowling average isn't important at all. The bowling average is based on wickets, and wickets don't mean much in T20. This fact doesn't seem to be widely recognised, but the whole concept of the 20-over game relies on it. If wickets were important, then batsmen wouldn't blaze away at 8 or 9 an over. So, in T20, the most important simple stat for measuring bowlers is the economy rate.

But of course wickets do help the bowling side a little bit (well, maybe not if Jacques Kallis is on strike), and so in this blog entry I'll try to work out just how much they're worth, and use these to adjust economy rates and give a useful measure of T20 bowling.

*****
Before starting, I'd like to thank commenter Russ, who gave useful criticism and suggestions on an earlier version of this analysis.

There are two ways in which wickets reduce the number of runs scored by the batting side. First, batting teams with less wickets in hand have to bat more slowly — this is a long-term effect over the rest of the innings. Second, the new batsman has to get his eye in, causing a short-term drop in run rate.

To begin, let's look at that first effect. Each scorecard contains the over and ball at which each wicket fell. We also know the score at the fall of the wicket, and the final score made by that team. Collect this data for all the scorecards, and you can plot graphs of runs remaining against balls remaining at each wicket. You can see these graphs, along with other technical details, here. All of the data used is from the IPL.

When you do this, you find that early wickets are worth about two and a half runs each. That's not very much. Wickets only become really important when a team loses lots of them and has the tail exposed early (for example, a seventh wicket with 12 overs left is worth about 14 runs).

A simple method to adjust economy rates would be to work out how many runs each wicket is worth, and give the bowler credit for that. But that's not always fair. Suppose the opening bowlers each take three wickets in their opening spell. They get credited 6 or 7 runs each. Then the change bowlers come on and, bowling at the tail, pick up wickets that are worth over 10 runs each! The opening bowlers surely deserve some of that.

So, what I did was to ignore which number the wicket was, and consider only the number of balls remaining. Doing some graphing and regression gives a pleasantly round result: a wicket is worth (in runs) the number of overs remaining, divided by 6. Keep that in the back of your mind, as we'll come back to it later.

Now let's look at the temporary run-rate drop after a wicket. From the ball-by-ball records, we can find the average run rate in each over, and compare it to the average run rate in each over given that a wicket fell recently.

A couple of features emerge from the results. For most of the innings, a wicket results in a dip of about 2.2 runs, and the dip lasts a couple of overs. After 15 overs, this changes — the dip being smaller and smaller, until there's none at all in the last over.

We now have pretty much all the ingredients necessary to tweak economy rates in T20. There are a couple of subtleties that I go into in the details page.

Now let's look at bowlers in the IPL. In the table below are the top bowlers according to the adjusted economy rate. The columns are balls bowled, runs conceded, wickets taken, average, usual economy rate, the runs credited from the wickets, and lastly the adjusted economy rate. The adjusted economy rate is the runs conceded, minus the runs credited from the wickets, divided by the number of overs bowled.

There is a bit of variation in the runs credited — Tanvir has more wickets than runs credited, whereas Pollock's runs credited is almost twice the number of wickets that he took. This tells us that Pollock's wickets came mostly early in innings, whereas Tanvir picked up many of his wickets near the end of the innings.

name           b    r    w   avg   econ  cred  adj econ

Sohail Tanvir  247  266  22  12.1  6.46  18.4  6.01

SM Pollock     276  301  11  27.4  6.54  20.1  6.11

IK Pathan      318  350  15  23.3  6.60  21.6  6.20

GD McGrath     324  357  12  29.8  6.61  17.9  6.28

AB Dinda       234  260  9   28.9  6.67  15.0  6.28

DW Steyn       228  252  10  25.2  6.63  10.7  6.35

MF Maharoof    216  249  15  16.6  6.92  14.9  6.50

M Ntini        210  242  7   34.6  6.91  11.0  6.60

SR Watson      325  383  17  22.5  7.07  21.1  6.68

M Muralidaran  348  404  11  36.7  6.97  11.7  6.76

Details of the methods and calculations can be found here.

	Ian Botham's heroics against India in Bombay comes out as the best performance by a player in a match © Getty Images

To seek an answer, this article looks at single player performances in a Test match.

Important note: Jeff, Rahul Bose, Sriram et al have mentioned about the bias towards bowling performances, which is true. The consensus is that the 25% upwards valuation of batting performances is too low. Jeff has even suggested 50%. After experimenting with a few figures, I have settled on 40% as the upwards valuation parameter. Since I am unlikely to do a follow-up, I have modified the values and table in this article itself. This means a 55% contribution in batting moves up to 77% which translates to just over 15 wickets. Looks like a very fair normalizing situation.

From this time I have made a significant change. In order for all readers to view my own response to the readers' comments, these responses will be appended at the end of the article. Even though this will make the article longer, this is the best way of addressing what are often overlapping comments. Pl see at the end of the article for these counter-responses.

Let me emphasise that this is not a look at the best all-round performances, although allrounders will be prominent in the lists. I have looked at a method of bringing batting, bowling and fielding performances to a common platform and analyse the results. I will also make due allowances for the fact that bowlers can, on their day, monopolise the team bowling performances, while batsmen cannot. I have also looked at the relative contribution of a player in a Test match rather than the absolute numbers.

Certain criteria have been laid down. Consider the following matches:

• MtId 1138. Ind: 358 for 9, Nzl: 178 for 1.
  
• MtId 0696. Win: 451 for 3, Nzl: 543 for 7.
  
• MtId 1094. Nzl: 512 for 2, Eng: 183 for 6.
  

Hence I will consider only matches in which 20 wickets have fallen. The limit of 20 wickets has been decided after a lot of deliberation. 20 wickets represents two completed innings and there is a fair chance that the match would have gone a reasonable distance. There would be either two completed innings or a third innings. In addition matches in which over 1000 runs are scored are also included to make sure that the really high-scoring matches will be considered.

Just to pre-empt readers who rush to print, let me add that 1769 out of the 1879 Test matches fall under this category. This works out to a very satisfactory 94%.

The only match in which fewer than 20 wickets have fallen and there has been a result is Test # 1483 in which only 16 wickets were lost. This was the Test match with the contrived result and I have left the match in with a lot of reluctance.

Of course, if there is a match with the following [imaginary] scorecard, it would not be included. I can live that. I am sure any reader could.

• Team 1: 100 for 9, Team 2: 400 for 0, Team 1: 200 all out.
  

Now for the difficult task of normalising batting and bowling points.

First the batting. Let us use the batting as the base and assign a point for each run scored. Fairly easy. The only problem is that the batsmen do not have an opportunity to play as much of a dominant role in an innings or match as the bowlers do. The table given below is an eye-opener. The best performances by players as a proportion of their team's performances are outlined below.

Highest share of team performance - Batting

	Innings: A.C.Bannerman 165 (245 all out) - 67.3%

	Match:   Tharanga 165 & 71 (316 & 120)   - 54.1% (Both innings played)

Highest share of team performance - Bowling

	Innings: Laker & Kumble 10 (out of 10)   - 100%

	Match:   Laker          19 (out of 20)   -  95%

Next the bowling. Here only the wickets captured have been considered. Overs bowled is another factor. However, if the batting team score is 400 all out, it is difficult to give any weight to a spell of 40 overs for no wicket against 40 overs for eight wickets. It is quite possible for a bowler to monopolise 100% of his team's bowling effort. Hence no adjustments, similar to the batting adjustments, are done. I will wait for the reader responses to decide whether to give a small weightage, say 10%, to the overs bowled.

It is interesting to note that a bowler has captured 10 wickets or more (50% of or more of the bowling effort), in 361 of the 1879 Test matches.

Look at the following two matches.

• Test # 0028: Aus 116 ao & 60 ao, Eng 53 ao & 62 ao.
  
• Test # 0137: Aus 354 ao & 582 ao, Eng 447 ao & 370 ao.
  

Hence while computing the value of a wicket the bowling and batting figures, for a single match, in terms of runs are equalised. In other words, the value of a wicket in the first match is approximately equivalent to 7 runs and in the second, 46 runs. This will make sure that the proportionate allocation for bowlers is done equitably.

First, the batting and bowling points for a single match are equalised. Then the proportionate allocation takes place.

Now for fielding. Since run-out records are available for very few matches, that is not taken into account. Each catch taken or stumping effected by a player is alloted 20% of the value of a wicket. This figure of 20% is not arbitrary. It has been determined that an average of around 5-6 catches are taken in a match and the total allocation for fielding per match is around a single wicket value, which is very reasonable.

It must be remembered that all calculations are within a single Test match only to determine the contribution of the 22 players involved. Since all these contributions are reduced to % values, there is no chance of wide variations. A batsman scoring 50 out of 100 and another, 250 out of 500 are considered equal. Similarly for bowling.

Finally a recognition that winning is [if not everything] something. Hence the winning team's player points are increased by a nominal 5% and drawing team's player points are increased by 2%.

Summary:

• 1. Only matches in which 20 wickets have been captured or 1000 runs have been scored.
  
• 2. Bowling and Batting points are equalised for the match.
  
• 3. Per wicket points are computed by dividing total runs by total wickets.
  
• 4. Batting points = Runs scored x 1.40 (changed from 1.25).
  
• 5. Bowling points = Wickets captured x Per wicket points.
  
• 6. Fielding points = No of C/St x (Per wicket points x 0.2).
  
• 7. Total points = Batting points + Bowling points + Fielding points.
  
• 8. Player contribution = Total points / Team Total points.
  
• 9. Win factor - 105%, Draw factor - 102%.
  

Match # 1380, India vs England, 1980.
Match total: 785 runs & 30 wickets. Per Wkt points - 26.166.
England: 296 all out and 98 for no loss. (Batting points - 394)
India: 242 all out and 149 all out (England: Bowling points - 20 * 26.166 = 523)
Total England points: 394 + 523 = 917.
Ian Botham
Batting: 160 points (114 runs).
Bowling: 340 points (13 wkts).
Fielding: 0.
Total: 500 points. Indexed by 5% for win. Total: 525 points.
% of Team total: 525/917 = 57.20%, which reflects Botham's outstanding contribution.

I want to emphasise that the batting and bowling equalisation takes place only at the match level and not at the team level. This is done to make sure that the overall match conditions are reflected in this analysis. It is also done to ensure that there are no way-out allocations in completely one-sided matches. An example is given below, the match which can be billed "Brian Lara vs Sri Lanka".

Match # 1572, Sri Lanka vs West Indies, 2001.
Match total: 1306 runs for 29 wickets. Per Wkt points - 45.03.
West Indies: 390 all out and 262 all out (Batting points - 652)
Sri Lanka: 627 for 9. (West Indies: Bowling points - 9 x 45.03 = 405).
Total West Indies points: 652 + 405 = 1057.
Brian Lara.
Batting: 491 points (351 runs).
Fielding: 0.
Total: 491 points. No indexing since West Indies lost.
% of Team total: 439/1057 = 46.48%, which seems very fair.

Note that the West Indian bowlers get less points since they captured only 9 wickets. That allows the batsmen like Lara [and Andy Flower against South Africa] who fought valiantly to get their due.

Now for the tables. Only the Top-10 are listed below.

No Year MtId For Player            RunPts      WktPts  FlPts Total (Team) % Cont

                                       (Runs)      (Wkts)

 1.1980 0874 Eng Botham I.T         160(114r) & 340(13w)  0f 525p ( 917t) 57.20 Won

 2.1899 0059 Saf Sinclair J.H       154(110r) & 143( 9w)  0f 297p ( 529t) 56.08 Lost

 3.2001 1562 Zim Flower A           477(341r) &   0( 0w) 11f 489p ( 903t) 54.12 Lost

 4.1964 0568 Aus Simpson R.B        193(138r) & 105( 4w)  5f 310p ( 580t) 53.40 Draw

 5.1883 0011 Eng Bates W             77( 55r) & 262(14w)  0f 356p ( 668t) 53.25 Won

 6.1985 1029 Nzl Hadlee R.J          76( 54r) & 592(15w)  8f 709p (1342t) 52.83 Won

 7.1974 0734 Eng Greig A.W          242(173r) & 304( 6w) 10f 568p (1078t) 52.68 Draw

 8.1962 0523 Nzl Reid J.R           283(202r) &  88( 3w)  0f 370p ( 705t) 52.53 Lost

 9.1956 0428 Eng Laker J.C            4(  3r) & 474(19w)  0f 502p ( 958t) 52.40 Won

10.1952 0352 Ind Mankad M.H         358(256r) & 192( 5w)  0f 550p (1074t) 51.26 Lost

...

15.2000 1513 Pak Saqlain Mushtaq     45( 32r) & 392( 9w)  0f 445p ( 924t) 48.23 Draw

29.1966 0608 Win Sobers G.St.A      244(174r) & 261( 8w)  0f 530p (1152t) 45.97 Won 

Legend: r-Runs, w-Wkts, f-Fielding pts, p-Player pts, t-Team pts.

Botham's performance is closely followed by Sinclair's all-round performance. Remember South Africa lost the match.

The purely batting back-to-the-wall effort, albeit in a losing cause, by Andy FlowerAndy Flower's great batting performance is now in third place, followed by Simpson's all-round performance. Then come the (predominatly bowling) performances by Bates and Hadlee. Greig's all-round performance is followed by John Reid's batting effort, Lakers's 19-wkt haul and Mankad's predominantly batting effort at Lord's.

There are 3 bowling performances, 4 all-round performances and 3 batting performances in the top-10, restoring the balance between batting and bowling. We have got 6 specialist performances in the Top 10. It will take a truly great specialist performance to get into the top-10/top-20, which is true of Laker's or Hadlee's or Andy Flower's performances.

There are 4 wins, 2 draws and 4 losses. Again no one should have a complaint.

Saqlain Mushtaq just edges Imran Khan's great match-winning effort against India in Lahore for the best Pakistan' performance. Let me add that I myself feel that Imran Khan's 14-wicket haul against India is a far superior performance. However, having laid down parameters I cannot trample over them, just because I do not agree with the results. Sobers' all-round efforts are the best by a West Indian.

Just for information, Gooch's 333 plus 123 at Lord's during 1990, which is the highest compilation of runs in a match, pegged in at around 36.5%.

To view the complete list, please click here.

The brief scores for the concerned matches are given below. Only the concerned players' performances are shown.

==================================================================

Test # 874. India vs England.

Played on 15,17,18,19 February 1980 at Wankhede Stadium, Mumbai.

England won by 10 wickets.

India: 242 all out            (Botham I.T     22.5  7  58  6)

England: 296 all out          (Botham I.T     114)

India: 149 all out            (Botham I.T     26.0  7  48  7)

England: 98 for 0 wkt(s)      (Botham I.T     dnb)

==================================================================

Test # 59. South Africa vs England.

Played on 1,3,4 April 1899 at Newlands, Cape Town.

England won by 210 runs.

England: 92 all out           (Sinclair J.H   12.0  4  26  6)

South Africa: 177 all out     (Sinclair J.H   106)

England: 330 all out          (Sinclair J.H   31.2  8  63  3)

South Africa: 35 all out      (Sinclair J.H   4)

==================================================================

Test # 1029. Australia vs New Zealand.

Played on 8,9,10,11,12 November 1985 at Woolloongabba, Brisbane.

New Zealand won by an innings and 41 runs.

Australia: 179 all out        (Hadlee R.J     23.4  4  52  9)

New Zealand: 553 for 7 wkt(s) (Hadlee R.J     54)

Australia: 333 all out        (Hadlee R.J     28.5  9  71  6)

==================================================================

Test # 11. Australia vs England.

Played on 19,20,22 January 1883 at Melbourne Cricket Ground.

England won by an innings and 27 runs.

England: 294 all out          (Bates W        55)

Australia: 114 all out        (Bates W        26.2 14  28  7)

Australia: 153 all out        (Bates W        33.0 14  74  7)

==================================================================

Test # 428. England vs Australia.

Played on 26,27,28,30,31 July 1956 at Old Trafford, Manchester.

England won by an innings and 170 runs.

England: 459 all out          (Laker J.C      3)

Australia: 84 all out         (Laker J.C      16.4  4  37  9)

Australia: 205 all out        (Laker J.C      51.2 23  53 10)

==================================================================

Test # 131. South Africa vs England.

Played on 26,27,29,30 December 1913 at Old Wanderers, Johannesburg.

England won by an innings and 12 runs.

South Africa: 160 all out     (Barnes S.F     26.5  9  56  8)

England: 403 all out          (Barnes S.F     0)

South Africa: 231 all out     (Barnes S.F     38.4  7 103  9)

==================================================================

Test # 1423. England vs Sri Lanka.

Played on 27,28,29,30,31 August 1998 at Kennington Oval, London.

Sri Lanka won by 10 wickets.

England: 445 all out          (Muralitharan M 59.3 14 155  7)

Sri Lanka: 591 all out        (Muralitharan M 30)

England: 181 all out          (Muralitharan M 54.2 27  65  9)

Sri Lanka: 37 for 0 wkt(s)    (Muralitharan M dnb)

==================================================================

Test # 734. West Indies vs England.

Played on 6,7,9,10,11 March 1974 at Kensington Oval, Bridgetown.

Match drawn.

England: 395 all out          (Greig A.W      148)

West Indies: 596 for 8 wkt(s) (Greig A.W      46.0  2 164  6)

England: 277 for 7 wkt(s)     (Greig A.W      25)

==================================================================

Test # 568. India vs Australia.

Played on 17,18,20,21,22 October 1964 at Eden Gardens, Calcutta.

Match drawn.

Australia: 174 all out        (Simpson R.B    67)

India: 235 all out            (Simpson R.B    28.0 12  45  4)

Australia: 143 for 1 wkt(s)   (Simpson R.B    71)

==================================================================

Test # 1562. Zimbabwe vs South Africa.

Played on 7,8,9,10,11 September 2001 at Harare Sports Club.

South Africa won by 9 wickets.

South Africa: 600 for 3 wkt(s)

Zimbabwe: 286 all out         (Flower A       142)

Zimbabwe: 391 all out         (Flower A       199)

South Africa: 79 for 1 wkt(s)

==================================================================

Test # 1513. Pakistan vs England.

Played on 15,16,17,18,19 November 2000 at Gaddafi Stadium, Lahore.

Match drawn.

England: 480 for 8 wkt(s)     (Saqlain Mushtaq 74.0 20 164  8)

Pakistan: 401 all out         (Saqlain Mushtaq 32)

England: 77 for 4 wkt(s)      (Saqlain Mushtaq 10.0  2  14  1)

==================================================================

Test # 352. England vs India.

Played on 19,20,21,23,24 June 1952 at Lord's, London.

England won by 8 wickets.

India: 235 all out            (Mankad M.H     72)

England: 537 all out          (Mankad M.H     73.0 24 196  5)

India: 378 all out            (Mankad M.H     184)

England: 79 for 2 wkt(s)      (Mankad M.H     24.0 12  35  0)

==================================================================

Test # 608. England vs West Indies.

Played on 4,5,6,8 August 1966 at Headingley, Leeds.

West Indies won by an innings and 55 runs.

West Indies: 500 for 9 wkt(s) (Sobers G.St.A  174)

England: 240 all out          (Sobers G.St.A  19.3  4  41  5)

England: 205 all out          (Sobers G.St.A  20.1  5  39  3)

==================================================================

2. This analysis emphasises only the relative contributions of players and not the absolute contributions. However readers may be interested in knowing who has compiled the highest absolute points on the basis of the parameters used in the analysis. Hence I have given below the top-10 players based on absolute values. Please remember that this table has no real intrinsic value.

Year MtId For Player         RunPts      WktPts  FlPts Total (Team) % Cont

                                    (Runs)     (Wkts)

2004 1680 Ind Kumble A             0(  0r) & 839(12w)  0f 855p (2034t) 42.05 Draw

1976 0781 Win Holding M.A         45( 32r) & 754(14w)  0f 838p (1945t) 43.09 Won 

1997 1374 Slk Jayasuriya S.T     476(340r) & 319( 3w)  0f 811p (1803t) 44.98 Draw

1990 1148 Eng Gooch G.A          638(456r) &  57( 1w) 23f 754p (2070t) 36.45 Won 

1998 1423 Slk Muralitharan M      42( 30r) & 669(16w)  0f 746p (1464t) 50.98 Won 

1985 1029 Nzl Hadlee R.J          76( 54r) & 592(15w)  8f 709p (1342t) 52.83 Won 

2001 1572 Slk Vaas WPUJC          32( 23r) & 630(14w)  0f 696p (1555t) 44.76 Won 

1983 0945 Pak Imran Khan         164(117r) & 484(11w)  0f 680p (1542t) 44.11 Won 

1955 0406 Win Atkinson D.S.t.E   335(239r) & 323( 7w)  0f 671p (1667t) 40.24 Draw

2001 1558 Aus Warne S.K            0(  0r) & 576(11w) 21f 627p (1688t) 37.13 Won 

Counter-responses:

1. I am aware that the increase of batting value by 25% without a corresponding increase in total will be mathematically inaccurate since the sum of allocations will exceed 100.If I increase total by 25%, the whole effect will be lost. However I am ready to live with this mathematical inaccuracy to achieve a parity between batting and bowling in cricketing terms.

8. A good comment has been raised re Hanif Mohd's 337 getting a contribution value of only 37%. The following numbers will justify this allocation.
Total points allocated: 1220 (incl draw bonus of 2%), out of which Batting is 800 and Bowling 420. This itself proves that the batsmen have got twice the valuation in this match. The batting allocation thus works out to 67%.
Out of this, Hanif Mohd, who scored 354 runs gets a contribution value of 37% (incl the 25% extra). Five other batsmen, especially in the second innings, helped draw the match and they have to be given credit. It can be seen that the bowlers are not given any undue allocation.

	Sanath Jayasuriya's 340 was the cornerstone of Sri Lanka's 952 for 6 declared, the highest total in Test cricket © Getty Images

When comparing the biggest team scores in Tests, the results can be a bit messy. This is because cricket often does not allow teams to carry their innings to completion, and big innings are often truncated by declaration or lack of time. We know for sure that the highest innings in a Test match is Sri Lanka’s 952 for 6 in 1997, but an interesting side question would ask if this is also the most ‘extraordinary’ score in Tests. For example, we know that the West Indies once made a score of 790 for 3. Where might such an innings have gone if it had continued? Can we compare it to Sri Lanka’s record?

While we can never know for sure, it is possible to make a statistical estimate. The approach is to look at the way that innings naturally progress over a wide range of scores. Of course, there is plenty of variation between innings [part of cricket’s appeal], but there are statistical patterns. A team that is, say, five wickets down, will on average add a certain number of runs if the innings is played to completion.

This average number of runs added also depends on the starting point. A team on, say, 50 for 5, can be expected to add fewer runs than a team on 500 for 5 before being bowled out. But there is a surprising result to be found here. Contrary to expectation, the number of runs at the starting point is not very important, with only a limited effect on the future progress of the innings. This is shown in the following table, calculated from the outcomes of all relevant Test innings, which gives the average number of runs added by teams with five wickets down, at different starting points.

What we see here is that above a certain level, in this case about 300 runs, there is very little change in the potential scoring of a team. This is surprising, but it probably comes down to the fact that a batsman coming in at a score of 600 for 5 is likely to bat in a riskier manner, or with less intensity, than one who comes in at 300 for 5. This would appear to balance out any advantage from tired bowling or benign conditions. This pattern is also seen at 6, 7, 8 or 9 wickets down.

It should be stressed that these runs added will often be theoretical in practice. For example, the projected all-out score for teams that reach 600 for 5 is 710, but in practice most such innings will not reach 700, often because of declarations. What the projected all-out score gives us is an estimate of where the innings was headed if the limits of time and tactics had been removed – its trajectory if you will.

With modern computer power, the result of this process is an “Innings Projector” that can give a projected estimate for any score. (In practice, it only works for innings with two or more wickets down.) Estimates for extreme innings must remain provisional because of the rarity of the situations, but the fact that trends are so stable, as illustrated by the first table, adds confidence to the results.

So what are the most extreme projected scores? Here is a list of the results:

So Sri Lanka retains the No. 1 position under this calculation. However, the West Indies 790 for 3 moves up to second place, while England’s 849 all out in the Timeless Test of 1930 moves down to seventh.

Another aspect to these scores is that the distribution of the scores around these projections can be calculated, which means that the probability of a specific score can also be calculated. For example, the probability of a score of 790 for 3 actually exceeding the 1028 assigned to Sri Lanka’s record is about 24%.

One other possible calculation here is a re-appraisal of the most one-sided innings victories in Tests. Using the projected score, the margin of victory can be re-calculated and compared more evenly. The most one-sided Tests in this analysis are:

(Please, no comments that the ‘highest’ does not mean the ‘greatest’. No one is claiming that it does. We are just looking at extremes here.)

[Technical note: the trajectory at large scores must be calculated with care, because teams that continue with great success from a high starting point rarely complete their innings. This must be allowed for in the calculation. The way to do this is through an iterative process, where big innings that are declared closed are themselves calculated through to completion, firstly for innings that are nine wickets down, then eight, seven, and so forth, and these results are then fed back into the calculation for end points starting from fewer wickets down.

For example, take a score of 500 for 3. This has occurred 37 times in Test matches. The projected score in this case is 705 all out. However, only three of the 37 teams have actually reached or exceeded a score of 705, while nine have been bowled out for less than 700. The reason that the projected score is above 700 is that many teams continue to do well but declare before reaching 700. Careful iterative analysis of these declared scores produces the average estimate of 205 runs added, or 705 all out for a projected score.]