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Not Out Innings and Batting Averages


Wittgenstein’s Suggested


Ludwig Wittgenstein (26 April 1889-29 April 1951), the highly prominent Vienna-born philosopher of language and logic, is well-known for later renouncing the approach taken by his favourably received initial work, the 75 page Tractatus Logico-Philosophicus – so illustrating his propensity to overturn accepted ideas, including his own.  

Wittgenstein became fascinated with cricket and followed the game keenly, having been a student at University of Cambridge and later taught and carried out research there for many years, so being in the company of a number who enjoyed following the game. Analogies with cricket are to be found in many of his writings.

He was serious in all things and determined in argument. Famously, at a meeting of Cambridge University’s Moral Sciences Club in late-October 1946, Wittgenstein argued vehemently with the guest speaker – Karl Popper from the London School of Economics – over whether there existed any real problems in philosophy or merely linguistic puzzles, which was Wittgenstein’s position. About 30 dons and undergraduates were packed into the small room – many more than available chairs – this being around twice the usual number. As the meeting took place deep into an unusually cold autumn evening (starting at 8-30 pm), slabs of coal would have been burning in the fireplace with its decorative marble framework.

At one stage, Wittgenstein seizes the iron poker lying on the hearth so as to emphasise his points, gesturing with it as the argument grew more charged. The poker’s tip is surrounded by ash and tiny cinders. On challenging Popper to state an example of a moral rule, the reply comes: “Not to threaten visitors with pokers”, upon which Wittgenstein throws down the poker and storms out of the room, slamming the door behind him.

Popper, then in his mid-forties, happened to be Vienna-born also, already with a path-breaking book on scientific methodology to his name – The Logic of Scientific Discovery (published in German a decade earlier) – as well as having recently completed a major work on political philosophy, The Open Society and Its Enemies (published in English in 1945). This was to be their first and only meeting.

Coming across a biography on Wittgenstein late on when drafting this essay, set me speculating about what he himself might have come up with if considering how the issue of incorporating Not Out innings in batting averages should be dealt with. I have set this speculation in the context of a discussion at The Oval cricket ground in London with two contemporaries of his, the dashing and innovative England batsman, Denis Compton and the rising cricket statistician, Roy Webber.

To appreciate the type of character that Wittgenstein was and the sort of life he led, the following might be of interest prior to perusing the scenario itself – drawing largely on Alfred Ayer’s book about him published in 1985 (pages 1-16, Biographical Sketch).

  • After two years studying mechanical engineering in Berlin, Ludwig Wittgenstein (LW) enrolled as a research student at Manchester University, then age 19, his studies directed to aeronautics while also taking an interest in the foundations of mathematics and logic. Enthralled by the writings of philosopher Gottlob Frege, LW visited him at the University of Jena (eastern Germany) and took the advice given to study logic under Bertrand Russell at Cambridge. This LW did, having five terms during 1912-13 under the tutorship of Russell who much admired his early work.
  • LW then decamps to do his thinking, mainly about logic, away from the university atmosphere which, he later wrote, “nauseates me….the artificiality, the self-satisfaction of the people”. He lives in exile in Norway in a small village north of Bergen on the west coast, leading a solitary existence until the start of WWI. He did voluntary military service in the Austro-Hungarian army, initially in a workshop and then as a machine-gunner. He was on the front line fighting against Russia and then Italy, and was awarded the Military Merit medal for exceptionally courageous actions.

  • Throughout the War, LW carries notebooks with him, filling these with his philosophical reflections. When on military leave in August 1918 at age 29, he assembles these into the treatise commonly referred to as the Tractatus – being published in 1921 with an English translation coming out the following year. Though somewhat difficult for other philosophers to fully understand, the Tractatus arouses considerable interest among philosophers, and is recognised as a significant work containing a number of original ideas. It exerts a strong influence in a number of quarters.

This work is said to present an exposition of logical truths as sentences which are true in all possible worlds. LW believed it provided the definitive solution to all important problems of philosophy that were susceptible to being resolved, then turning to other pursuits for fully a decade.

  • LW’s father, a leading businessman in the iron and steel industry and shrewd investor, had amassed great wealth, and on his death in October 1913 LW becomes rich. The War was to change him spiritually, denying himself any indulgences; and in late-1919 transfers all of his part of the family fortune to his remaining brother, Paul, a concert pianist (by then, LW’s three other brothers had died, two of them by suicide).
  • After undergoing a teacher training college course in Vienna during 1919, LW becomes a school teacher for a period of six years – doing so at three elementary schools in villages set deep in the countryside south of Vienna, where farmland and forests predominated. This work was in keeping with his family’s long-standing commitment to social work. Although being a strict disciplinarian, typical for those times, LW was mostly liked by his pupils (of ages 6-10) who were the children of poor rural families. He put into practice project-based learning and also composed, with the active participation of his pupils, a 42 page dictionary (having nearly 6,000 word entries) that was tailored to their particular requirements (being published for wider use in 1926 as Wörterbuch für Volksschulen). After a stint as a monastery gardener, LW spent a couple of years assisting in implementing an architect’s design of a “severely functional” house in Vienna for one of his sisters.
  • On reviving his interest in philosophy, LW is drawn into discussion from time to time during 1927-29 with some members of the influential group coming to be known as the Vienna Circle, pursuing the aim of making philosophy scientific. This Circle were intensely interested in the Tractatus. Misunderstandings and tensions were to arise, bringing divisions – with LW accusing a leading figure of the Circle of plagiarism. He is persuaded to return to Cambridge University, doing research and a small amount of lecturing and holding discussion classes during most of 1929-41. This centred on investigating the nature of language, a field encompassing the relations between language, language users, and the world; and also investigating the concepts by which language is described and analysed, both in everyday speech and in scientific linguistic studies.
  • The discussion classes always left LW in a state of nervous exhaustion, usually followed by a visit to the cinema to unwind – his favourites being detective movies and Westerns featuring cowboys, gunslingers, and bounty hunters. He is recollected by some of the participants in these classes as physically short, slender and usually visibly tense; having penetrating blue eyes, and speaking English fluently with very little of a foreign accent.
  • There is a visit to Russia in September 1935 – LW having thoughts about settling there – and an extended break during 1937, retreating to Norway. There, he works on material that would form portions of a book later taking the title of Philosophical Investigations.
  • During WW2, from 1941 to early-1943 LW works at London’s Guy’s hospital as a porter (delivering medicines from its pharmacy to the wards); afterwards, spending a year as a medical research assistant at a laboratory in Newcastle (north-east England).
  • LW resumes at Cambridge University in the spring of 1944, continuing through to summer 1947. After resigning his professorship to concentrate on writing, he spends the autumn of 1947 in his native Austria, before staying in Ireland for eighteen months. There, a good deal of it in solitude in the west of the country, as well as some time in a hotel in Dublin where he found himself able to do some philosophical work. His final two years were dogged by an illness that was to claim his life (prostate cancer).
  • As to the course of his philosophical thinking, by the start of the1930s LW became disillusioned with his earlier mind-set and radically changed his approach to the philosophical issues of language. This culminated in the volume published posthumously in 1953 as Philosophical Investigations. It has been lauded as one of the most important philosophical works of the 20th century.
  • Part I of the Investigations was completed by 1945, Part II being compiled during 1947-9. This offered a new way of looking at language and overturned many of his earlier ideas, repudiating or discarding much of what he had set out in the Tractatus.
  • In the Investigations, LW asks the reader to think of language as a multiplicity of language-games, within which parts of language develop and function. He contends that the “bewitchment” (or entanglement) of philosophical problems arise from philosophers’ misguided attempts to consider the meaning of words independently of their context, usage, and grammar – which he labelled language gone on holiday. Philosophical problems arise, he argues, when language is forced from its proper home into a metaphysical environment, where all the familiar and necessary landmarks and contextual clues are removed.

Instead, philosophers should leave the frictionless ice and return to the rough ground of ordinary language in use. Many examples are given of how the first false steps can be avoided, so that philosophical problems are dissolved, rather than solved. The clarity we are aiming at is, indeed, complete clarity. And this simply means that philosophical problems should completely disappear.

A good deal of the Investigations deals with the concept of Sprachspiel, translating as the language game. In a nutshell, this states that the meanings of words are best understood as used within a game, one similar to chess. To drive home this point, the Investigations is littered with analogies to games. Ironically, LW believed the ideas in the Investigations were widely misunderstood, even by those who claimed to be his followers!

Scenario at The Oval, Kennington

A discussion is taking place in the pavilion during the tea interval on the first day of the 5th Test match against South Africa in 1947. It is Saturday the 16th of August. Wittgenstein, then in his late-fifties, is in earnest conversation with the 29 year old Denis Compton who has made 53 runs in quick time, adding 98 with Len Hutton for the third wicket in this Compton’s 22nd Test match. It would be a high scoring draw, with a Compton century coming in the second innings to add to the seven Test centuries already posted.

The two of them are seated at a smallish round solid oak table, accompanied by Roy Webber (then entering his mid-thirties) who is rapidly making a name for himself in bringing cricket statistics to a wide cross-section of the public, as well as being the BBC’s scorer during live broadcasts. His illustrious Playfair Book of Cricket Records – 320 pages worth – had largely been compiled by August the previous year and would be published in 1951.

After chatting about the early course of the match, in which South Africa made the batsmen work hard for their runs, Wittgenstein mentions he had been at the Wimbledon tennis championships earlier in the year and noticed that before each match began there was a substantial knock-up period, even if the players had been practising on an outside court immediately before being called on to play. Presumably, he reasoned, to start the match “cold” would mean that neither of the players would be likely to do themselves justice in their quality of play, and who gets ahead early on would be largely a matter of chance.

DC: That’s a good convention – it’s probably a regulation that must be applied. Court conditions can vary quite a lot: the effect of the wind, moisture on the court surface…things like that. These take some getting used to, and for many players the knock-up can also help get rid of some nervous tension.

LW: The same thing, a knock-up with one’s opponent, happens with squash – and, I think, with badminton also. Why not with cricket, Denis? Just as important to get a feel for the pitch conditions, behaviour of the ball, the light and so on. Having some net practise shortly before going in to bat hardly compensates; and often a batsman has to sit around for a whole hour or two ready to go to the crease.

DC: I suppose the openers could face some opposition bowling on the pitch for a little while before play gets under way. But difficult to imagine it really happening, and totally impractical I’m afraid for those below them in the batting order. 

LW: In cricket, having to start cold affects all batsmen. Some seem to be affected far more than others, even in Test matches. But I think maybe that’s not much to do with a difference in their actual ability, more of a random factor – the conditions when a batsman starts off, how difficult the bowling is and suchlike.

DC: That’s the luck of the draw – all part of the game!        

LW: Perhaps this good luck-bad luck feature at the outset of an innings could be nullified nach Veranstaltungsende.


LW: My German often slips out when I get intense. What I’m saying is, this could be nullified after the event.

DC: You can’t turn the clock back, Ludwig. Not unless you have got a time machine – have you?

LW: I mean, this could happen by adjusting batsmen’s averages. One could simply ignore the initial, playing-in, phase and take into account only those runs scored and dismissals taking place after that point. Yes… disregard everything that occurs during playing-in.

I have been making notes during my last term at Cambridge on how this could work.


My proposal is as follows:

  1. Ignore all innings terminated during the playing-in phase – exact length to be defined – because surviving this phase usually requires a substantial amount of good fortune. For any individual, survival or alternatively termination when playing-in may be regarded as a random factor.
  2. For those innings in which a batsman survives the playing-in period, take account only of those runs scored after he has reached the end of playing-in.


RW (spluttering): You can’t just monkey around with the averages – that would be sacrilege… also involve a colossal amount of reworking…it’s out of the question!


DC: Well, it’s an idea that could be thought about I suppose. As an experiment, it could be tried out. Not from when Tests first began but, say, since Bradman began – 1928.


DC: We wouldn’t have to replace the already existing averages. An adjusted set could be calculated and put about as a variant, without any special status. Then any particular player could decide which set he prefers – presumably, the one that puts him in a better light in relation to his peers and those of another generation!

LW: Denis, please! Wichtig ist das Prinzip…it is the principle that is important. The consequences follow, whatever they happen to be, and cannot be avoided. A batsman should decide which principle he think is, inherently, the better one, and only then look at how he fares.

RW: All of this is not that easy. Take the playing-in phase. That’s not laid down anywhere. There will be endless arguments about how to define it…this is bound to be bewildering…a veritable nightmare in prospect.

LW: We can set limits. We can agree that it is not as short as four deliveries or three runs, and not as high as 70 deliveries or 30 runs. What do you think Denis?

DC: It varies quite a lot with a batsman’s place in the order and conditions, of course. Though I reckon in Tests nowadays around half a dozen to a dozen runs under one’s belt would be common for getting pretty well settled.[i]

RW: This all needs a great deal more consideration. Sober and thoughtful consideration.

LW: This might help – WAVING ANOTHER SHEET OF PAPER TAKEN FROM HIS JACKET. I have done some arithmetic on the assumption that, typically, a Test batsman has much reduced his risk of imminent dismissal when he reaches 8 runs. It is within the range that Denis has guessed.

And it roughly equates to the five minute knock-up period for tennis. Scoring 8 runs at two and a half an over would mean facing three overs of deliveries in around 11-13 minutes; with the batsman concerned being actively engaged for around half that time, allowing for returning the ball to the bowler and walking back to his mark.

I have looked at what four luminaries have averaged in Test matches when all their innings of under eight runs are excluded.[ii]


Bradman 97.85  becomes  115.30…..plus 17.45

Hammond 58.45  becomes  67.96…..plus 9.51

Hobbs 56.94  becomes  64.13…..plus 7.19

McCabe 48.21  becomes  62.95….. plus14.74

DC: The ranking doesn’t change and Bradman gains the most, getting him past 100. Food for thought eh, Roy?

And talking of foodDC BECKONS A WAITER Three rounds of Cheddar cheese and tomato sandwiches, please. Oh…and a double brandy for Roy, on my right.


[i] Intuitively, a playing-in period that is defined by a certain number of deliveries faced might seem to be most suitable, and is better than the amount of time spent in the middle or even active time at the crease; the latter will tend to be significantly greater if facing fast rather than slow bowling. However, Uday Damodaran (conference paper in 2013) has found that playing-in is more about scoring runs than simply occupying the crease and surviving deliveries. Scoring runs appears to be more important for boosting a batsman’s confidence and giving him an increased probability of successfully facing more deliveries. This accords with the often repeated remark of commentators about the importance of “getting off the mark” and “getting a few runs on the board”.

[ii] OG Stevenson and BJ Brewer (article in 2017) have estimated how a player’s probability of being dismissed – and therefore his batting ability – varies over the course of his innings. Using data for the overall careers of four high profile Test batsmen of modern times, they shown in graphical form that when these batsmen variously reach between the 11 and 20 run mark this risk is virtually on a flat path. And at this stage they are very close to having their eye fully in and being in a state of “batting equilibrium”. In the case of Gary Kirsten he is virtually on a flat risk path when reaching 20 runs, Brian Lara when reaching 18 runs, Steve Waugh when at 14 runs, and Justin Langer (the most cautious of the four) when at 11 runs (the average works out at 15.8).   

It is also shown that the high risk of imminent dismissal faced when each of them starts their innings has been much reduced when reaching an undefeated score of around 6-8 runs. When at 8 runs, Kirsten is already 70% of the way to arriving at his batting equilibrium and Lara is 72% of the way there. When at 6 runs, Langer is already 81% of the way to his equilibrium and Waugh is 83% of the way there.

To tease out this point, taking Kirsten as the example: on starting his innings on zero runs Kirsten is performing with the ability of a player having an average of 14.4 runs – reflecting his relatively high susceptibility to being dismissed very early on – and reaches his equilibrium when performing like a player averaging 54 runs. Hence, the transition from his initial ability to maximum ability is an increase in his “effective average” of 39.6. When on 8 runs, he is batting as though averaging 42 runs, this being an increase of 27.6 on his initial ability.


A.J. Ayer: Wittgenstein. Weidenfeld and Nicholson, 1985.

Spencer Robins, Wittgenstein, Schoolteacher, The Paris Review (quarterly literary magazine), March 2015.

B.J. Brewer: Getting Your Eye In. University of New South Wales, May 2008.

O.G. Stevenson and B.J. Brewer: Bayesian Survival Analysis of Batsmen in Test Cricket. Journal of Quantitative Analysis in Sports, March 2017 (pp 25-36).

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