The measure of greatness

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Here's an attempt at a methodology to evaluate a cricketer's efforts fairly and answer that universal question: who was the best of them all?

This is the second article of a multi-part series. Read the first piece >here.



An intro



The great advantage of using a formal system of measuring individual performances is basically twofold. First, all performances are considered for the ratings. Second, all performances are considered according to the same rules. Such rules are not easy to build when one is trying to model any aspect of real life. Economists and other social scientists deal with these difficulties all the time. But when it comes to modeling a game, matters are fundamentally simpler.

This is because games are already based on formal rules. All possible legal moves in a game are precisely and completely identifiable. It follows that all illegal moves in a game can also be precisely identified. Games also have well-defined end conditions. It is always clear at the outset under what circumstances a game will end. It is also always clear who the winner is when this happens. Even in games which permit stalemates, the conditions which constitute a stalemate are precisely defined. In order to exist, games, like cricket, require at least these two conditions to be satisfied.

Cricket obviously satisfies all these conditions. It has formal rules to measure performances and does so using two basic measures — runs and wickets. A tally of the number of balls bowled is also maintained. The rules of dismissal are unambiguous and precise, as are the rules for counting runs, wickets and deliveries.



How to go about it



The systematic method for rating individual performances described here takes into account the strength of the opposition for the conditions in which the match is being played and does not consider the result of the match. The method is designed to evaluate the player’s efforts. For a batsman, this means paying special attention to the period of the match when the batsman was at the crease. For a bowler, it means paying attention to the bowling innings, and the bowler’s participation in it.

The general approach is to consider a player’s performance in relation to that of teammates who were at the wicket with the player. What was the player’s share of the total runs added to the team’s total while the player was batting? How many wickets fell? The intuition behind this is that this is a reliable measure of the difficulty of the situation. For example, some of Sachin Tendulkar’s centuries came in large stands with a single player. Other centuries came while wickets were falling at the other end. The player’s contribution to the overall innings is also considered.

The unit of measurement of the ratings for batsmen and bowlers is runs. Readers familiar with the “wins-above-replacement” measure in baseball will recognise some parallels. It can be used to measure individual match performances, as well as performances over a career, against specific opponents or in specific host nations, in the same way as a bowling or batting average.

The player’s performance relative to teammates against the opposition (the method for measuring the strength of the opposition is described separately below). Full descriptions of the method are given here, so that readers can try this out themselves, review or criticise it, perhaps find ways to improve it, or use it as a point of departure to measure other things which may interest them.





The opposition's strength



Each Test match is divided into two parts: the first match innings (innings 1 and 2) and the second match innings (innings 3 and 4). The rules of Test cricket mandate that each side can bowl exactly once and bat exactly once in the first match innings (and similarly in the second match innings). A Test team cannot, for example, bat in both the 3rd and 4th innings of the same Test, or bowl in both the 1st and 2nd innings of the same Test.

Each participating team’s expected batting and bowling strength in the first match innings and second match innings is calculated. This is given in terms of runs per wicket. It is calculated as follows.

Consider each playing XI separately. Make a list of all the batting innings for each player in the XI before the start of the match. For a player on debut, this list will be empty. Split this list of innings into two, one for each match innings. For each list, complete the following procedure in order to bias it.






  1. Select all innings from the list which were played in the host country of the current match.
  2. Select all innings from the list which were played at the ground on which the current match will be played.
  3. Select all innings from the list which were played against the opponent against whom the current match will be played.
  4. Select all innings from the list which were played against the opponent at the ground of the current match.
  5. Select all innings from the list which were played against the opponent in the host country of the current match.





This means that you now have 10 separate subsets of the main list of innings by the player before the match in question. In order to bias the player’s list of match, add the 10 subsets to the original list. To get a biased list for the first match innings, add the subsets for the first match innings again. To get a biased list for the second match innings, add the subsets of the second match innings again.

So far, each of the eleven players now has a list of individual performances up to the start of the current match which has been biased for the current match. Pick a random innings from each player’s list, and add all the individual runs, and all the individual dismissals (each innings ends in dismissal or in a not out). Calculate the runs per dismissal. Repeat this procedure 100,000 times, and then select the median runs per wicket. This is the expected batting strength for the team for the current match. This is a simple implementation of the >monte carlo simulation. Calculate this for the first match innings and the second match innings.

To calculate the expected bowling score, use the individual bowling performances up to the start of the current match. The expected batting and bowling strength for the first and second match innings is now available.




Calculating the batting rating



To calculate the rating for the individual batting performance, the following information is required:





  • runs scored (r),
  • dismissal (out or not out) (di),
  • team runs in the innings (tr),
  • team wickets in the innings (tw),
  • runs scored by the team while player was at the wicket (pr),
  • wickets lost by the team while player was at the wicket (pdis),
  • opposition’s expected bowling strength for the match innings in question (strength)




The central idea is to measure each performance in relation to other performances while the player was at the wicket. Secondarily, to consider the performance in the context of the overall team innings.






  1. Calculate run share ~ run_share = r / tr
  2. Calculate runs per wicket at the other end while the player was at the wicket [rpwoe] ~ rpwoe = (pr – r)/(pdis – di). If pdis – di = 0 (this is possible if the player is at the wicket for exactly one partnership and is dismissed.
  3. Calculate run_share while the player was at the wicket [raw_share] ~ raw_share = r/rpwoe





The rating for an individual performance is given by:



Batting rating = (r x run_share x raw_share)/strength



A player’s batting rating for the match is the sum of the rating for each innings.


Calculating the bowling rating





To calculate the rating for the individual bowling performance, the following information is required.





  • Balls bowled (bb),
  • runs conceded (rc),
  • wickets taken (w),
  • runs conceded by team (trc),
  • wickets taken by team (tw),
  • balls bowled by team (tbb),
  • the opposition’s expected batting strength for the match innings in question (strength)









  1. Calculate bowling share [bowl_share] ~ bowl_share = bb/tbb
  2. Calculate wicket share [ws] ~ ws = w/10 (since the maximum available wickets is 10)
  3. Calculate bowling average at the other end [bowl_ave_oe] ~ bowl_ave_oe = (trc – rc) / (tw – w). If tw = w, then bowl_ave_oe is simply trc – rc
  4. Calculate the runs conceded per wicket by player [rpw] ~ rpw = rc/w, or simply rc if the player does not take wickets
  5. Calculate the player’s bowling average ratio [bowl_ave_ratio] ~ bowl_ave_ratio = rpw/bowl_ave_oe or simply rpw if bowl_ave_oe is 0.





The rating for each individual bowling performance is given by:



Bowling rating = (ws x strength x bowl_share)/(bowl_ave_share)



The rating formula is designed to value bowlers who bowl a higher share of the team’s overs against stronger batting line-ups and take a larger share of the available 10 wickets. A bowler who achieves this in an innings in which the other bowlers in the team are not able to take wickets is rated even higher.

The bowler’s rating for a match is the sum of the player’s rating for each match innings.

A player’s all-round rating is the sum of the batting and bowling ratings for the player for the match.

The rating is designed to limit the measurement of a player’s performance to things a player might be directly able to control. For a batsman, this means focussing on the progress of the match while the player was at the wicket. The highest-rated match performance using this rating method is not from the last 50 years. It is Stan McCabe’s famous effort against Australia at Nottingham in 1938. The story goes that a number of Australians in the Trent Bridge dressing room were playing card games as McCabe began his innings. Bradman was watching it, and told his players to stop their game and watch, because they would probably never watch anything like it again.

Don Bradman (left) and Stan McCabe (right) resume an innings during an Australian XI versus Western Australia match at the WACA Ground on 26 April 1938. ~ Photo: Wikimedia Commons

Consider the facts of McCabe’s monumental effort. He made 271 runs in the match and was dismissed twice. England batted first and reached 658/8 thanks to centuries by openers Len Hutton and Charlie Barnett followed by a double-century from Eddie Paynter and a century from Denis Compton. McCabe walked in at 111/2 in Australia’s reply after Bradman was dismissed for 51. Things deteriorated rapidly and Australia soon found themselves at 194/6. In just under 4 hours, McCabe made 232 in 277 balls with 34 fours and a straight six off England’s fastest bowler Ken Farnes.

Australia were bowled out for 411. While McCabe was at the wicket, Australia made 300/8. While McCabe was plundering his double-hundred, the batsmen at the other end could muster 7/68 between them in 4 hours.

Australia were asked to follow on. In their second innings, Don Bradman and Bill Brown made careful hundreds. In Bradman’s case, his undefeated 144 came in 379 balls. McCabe made 39 in a stand of 72 with Bradman.

As measured by the method described above, the highest-rated Test match batting performance in history did not successfully avoid the follow-on. But it affected the course of the match spectacularly. It also left the greatest batsman in the history of the game spellbound.

The single-greatest Test match bowling performance is less surprising than the greatest batting performance. Jim Laker’s 19/90 against Australia at Old Trafford in 1956 was a freakish effort, especially when you consider the fact that Brian Statham, Trevor Bailey and Tony Lock made 1/199 between them at the other end while Laker was orchestrating an Australian procession on that admittedly sticky wicket.

The rating is dominated by specialist batsmen and bowlers, as it should be. Cricket is a game for specialists who produce performances of extremely high quality, and raise the standard of the game to an extent which makes it extremely difficult for all-rounders to emerge. Apart from the outrageous skills and ability required to be simultaneously as good as a specialist batsman and as good as a specialist bowler, being an all-rounder is also extremely physically demanding.

Richard Hadlee, the greatest to have handled the red cherry? ~ Photo: Adrian Murrell/Allsport UK

In order to qualify in the all-rounder rating, a player must have taken at least 1 wicket and scored at least 50 runs in the match. This is an admittedly arbitrary condition. The median number of runs scored by an individual player in a single Test match is 28. This would be a more logical cut-off. However, if a Test batsman made 28 runs in a single Test innings, let alone in 2 Test innings, this would be considered a failure. Keeping our cut-off in mind, the greatest all-round performance in Test history, as measured by the methods described above, is Richard Hadlee’s match haul of 15 wickets and 54 against Australia at Brisbane in 1985.

Great all-round performances are extremely rare. Only three players, Ian Botham, Imran Khan and Shakib Al Hasan, have made a century and taken 10 wickets in a match. And only one other player has made 100 runs and 10 wickets in a match. Alan Davidson achieved this feat in the tied Test at Brisbane in 1960.

In summary, this rating method sets each individual performance in comparison to the performances of the individual’s teammates, while also considering the quality of the opposition. It measures an individual’s contribution to a team’s cause. The rating for batsmen and bowlers is produced as a runs-per-wicket measure. This is to say that the formula for batting and bowling innings ratings resolves to a figure which has the unit 'runs/wicket'.

In the next part, we will look at the career rating for the 20 most prolific batsmen and 20 most prolific bowlers, and thus arrive at the top individual match performances. This will help to provide a sense of how performance is measured in the rating.

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