Mental Toughness 4 – Tough Attitudes and Tough Thinking

Mental toughness is a combination of character and attitudes.  It would be entirely possible to produce a player with tough attitudes, but without the tough character attributes such as resilient self-confidence, and independence, those attitudes would not be applied effectively. With that in mind, let’s continue to look at the insights into tough thinking and tough attitudes that Jones et.al. and Stephen Bull’s research gave us.

What are the components of tough attitudes and tough thinking?

 Tough Attitudes

  • Exploit learning opportunities.  A desire to learn and keep learning was evident.  Defeat was not dwelled upon, but was learned from.
  • Belief in quality preparation.  Players believed that a thorough and consistent preparation is vital.
  • Self-set challenging targets. This ties in with the tough character theme of ‘being competitive with yourself and others’. The ability to set challenging goals for yourself and not beat yourself up if you don’t make them is key.
  • “Never say die” mind-set. Many respondents had had a rocky road to cricket professionalism, however they reported that they had brought out their best performances at exactly the moments when their best was required.

“You can throw whatever stones you want at me but I am not going off this course. I am getting there. I am right here. I will prove to you that I am right. It might take me ten or fifteen years but I will get there. I will play for England.”

 

  • “Go the extra mile” mind-set. Along with the ‘never-say-die’ mind-set, this shows a level of tenacity and a commitment to hard work that delivers a strong desire to succeed.
  • Determination to make the most of their ability. Many of the respondents described themselves as not the most naturally gifted of cricketers.  However their determination to succeed allows them to develop an approach to the game that allowed the to excel.
  • Belief In Making The Difference. Players believed that they alone could make the difference to their team’s outcomes.  Players actively sought out that responsibility in key match situations.

“Taking the responsibility on your shoulders is what it’s all about…and the more responsibility I was given the better I reacted…the tighter the situation the more highly motivated I became. I kind of set the challenges to myself that it was up to me to drag us out of this mess”.

 

  • Thrive on competition. Within the confines of the cricket match they tend to focus on the individual challenges they face rather than on the team competition. Surmounting these individual challenges is what motivates them.
  • Willing to take risks. Not just within a game to take advantage of the situation, but with their entire careers. Players are able to change clubs or counties, or even move half way across the world if they feel it would help their career progression.

Tough thinking

 This is the part that sports psychologists dwell upon, as it focuses on ‘match-winning’ thinking.  However I think you will now agree, that tough thinking is a product of everything that has come before, the environmental factors, the tough character and the tough attitudes.  Tough thinking is about the player’s ability to focus the tough character and the tough attitudes to the task at hand in a competitive setting.

 There are two branches to tough thinking that we need to discuss.

 Robust Self-Confidence

 This has been a recurring theme, throughout our discussion; think back to the theme of ‘resilient confidence’ in the tough character section. In this context it refers to self-confidence in in-game performance thinking. It has three key manifestations.

 

  1. Overcoming self-doubt. Not just normal performance anxiety, but also in the field of international cricket when you do not have the evidence to know you can perform at that level.
  2. Feeding-off physical condition.  Loehr stated that in the final analysis toughness is physical.  Certainly the mind-body connection is a key component of self-confidence.
  3. Maintain self-focus. Not selfishness as such, but getting the balance right between the team’s needs, and being self-focussed.

Thinking clearly

 This is about the ability to stay focussed and clear thinking in the face of duress or adversity.  It is a combination of the following three factors;

  1. Good decision-making. Making the correct decisions with confidence at pivotal moments in the game.
  2. Keeping perspective. This is about striking the balance between expressing an attitude of immense importance attached to the competition, while at the same time knowing that it’s no big deal, and at the end of the day it’s just a game.
  3. Honest self-appraisal.  Knowing exactly where your strengths and weaknesses lie, and making performance decisions based on that appraisal.

Conclusion

 So we have seen what makes mental toughness, how tough character and tough attitudes combine to make tough thinking. In the final piece in this series we will look at how mental toughness can be developed in young cricketers, through the actions of the players themselves, their clubs, coaches, schools and parents.

 

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Bibliography

 

Jones, J.G., Hanton, S., Connaughton, D. (2002) ‘What is This Thing Called Mental Toughness?’ Journal of Applied Sports Psychology, 14, 205-218

 

Loehr, J.E. (1995) ‘The New Toughness Training For Sports’. New York Penguin

 

Bull, S.J., Shambrook, C.J., James, W., Brooks, J.E. (2005) ‘Towards an Understanding of Mental Toughness in Elite English Cricketers’ Journal of Applied Sports Psychology, 17:209-227

 

 

 

Mental Toughness 3 – What is to be learned?

In this third piece in the series we look at what Stephen Bull’s paper says are the external environmental factors that may affect mental toughness, and the qualities that represent ‘tough character’ itself.

Environment

 As you would expect, the environmental factors play a major role in developing mental toughness.  Parents can have a good or catastrophic influence on their child’s psychological development depending on how they approach the subject.  In this research every respondent noted a contribution from one or both parents to their success. Exactly what parents should and shouldn’t do to help their child develop will be explored in the final piece on mental toughness.

 The toughest players generally came up through an environment that pre-disposed them to be mentally tough, as one respondent noted:

 

The basic thing is, looking at all these names here,” (the list of top 15 toughest players), “one thing that strikingly stands out is their upbringing. I would say they are probably brought up by the school of hard knocks.”

 Given the English set-up’s pre-disposition to selecting the products of safe private-school educated environments, this may go some way towards explaining England’s perceived weakness in producing tough players.

 Surviving Early Set-Backs (Resilience)

 Many of the players in the study had had a far from smooth ride into professional cricket, however all felt that they had learned massively from the set-backs they had had. These experiences can’t be replicated as part of a coaching program of course, but it’s an interesting insight.

 Playing Cricket Abroad

 All the respondents had played cricket abroad (primarily in South Africa and Australia) during their formative years, and all saw it as a vital part of their toughening up process.

 

“I went to a club where people didn’t know who I was and being an Englishman in Australia you’re always going to be looked to, not so much down on, but you have to prove yourself more than an Australian.”

 

Tough Character

 Now we switch to those factors that are inherent in the cricketer him (or her) self. These tough character traits were seen as universal in tough minded individuals, and are more stable than the more easily acquired ‘Tough Attitudes’ traits.

 Independence

 Respondents showed an aptitude and a willingness to take responsibility for their own career and development, as well ploughing an independent furrow in other non-sporting areas of their life.

 

“What you need to do is to go to Perth or Sydney, anywhere where you’re on your own with no Mom or Dad to look after you.  You’ve got to look after yourself, you’ve got to present yourself to the team you play for and show them what you can do. You’re either sink or swim. You’ll get up and mature, stand up for yourself, think things out for yourself, and work things out on your own.”

 

Self Reflection

 Tough-minded cricketers show a marked ability for self-reflection and self- analysis.  This constant honest re-evaluation of themselves and their performance is seen as critical to their performance and continues throughout their careers.

 Competitiveness With Self and Others

 Tough cricketers have a desire to be the best cricketers they can be. Though players did not necessarily set formal goals, they used competition with other players as well as this desire to be the best to push their development.

 “I want to play against the best bowlers – I want to play against the best – that’s the challenge for me.”

 Resilient Self-Confidence

 Self-confidence alone is not enough to be a mentally tough cricketer. Some players have high levels of self-confidence, but that confidence can be a very fragile thing. Mentally tough cricketers believe they can influence the outcome of every match they play, their confidence is high, and is very hard to undermine.

 This suggests that a key to building self confidence in young cricketers is not so much “how high can we build this player’s confidence?”, but rather “how can we protect the confidence that is already there?”.

 In the next piece we will be looking at those qualities that are a direct result of mental toughness, ‘Tough Attitudes’ and ‘Tough Thinking’.

 

 

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Mental Toughness 2 – The Cricket-Specific Mental Toughness Framework

So having a working definition of mental toughness, and some insights into its genesis, how does mental toughness apply in cricket?  In 2003 the E.C.B.’s Sport Psychology Support Team under the leadership of Stephen J. Bull set out to answer two questions;

1. To develop a deeper understanding of what mental toughness is within cricket.

2. To identify how existing mentally tough cricketers developed their mental toughness.

The research team asked 101 English cricket coaches to name the ten English cricketers they considered to be the mentally toughest of the previous twenty years.  From the resultant list, a total of fifteen of the most mentally tough cricketers were selected for the research.

The methodology used was very similar to that of Jones et al featured in the previous piece. This was another qualitative study, using a mixture of one-on-one interviews and group brainstorming sessions.

I’ll spare you a detailed breakdown of their results, because if you need them you can download the paper for free – here.

What is important to us is the Mental Toughness framework, that they developed based upon their research, which you will notice bears close similarity to the results of Jones et al’s  outcomes.

The framework develops five ‘General Dimensions’, twenty ‘Global Themes’ and four Structural categories.

Here is my reproduction of the framework

Global Dimension Global Theme Structural Category
Development factors Parental influence Environmental influence
Childhood background Environmental influence
Personal responsibility Exposure to foreign cricket Environmental influence
Independence Tough character
Self-reflection Tough character
Competitiveness with self as well as with others Tough character
Exploit learning opportunities Tough attitudes
Belief in quality preparation Tough attitudes
Self-set challenge targets Tough attitudes
Dedication and commitment Opportunities to survive early setbacks Environmental influence
Needing to “earn” success Environmental influence
“Never say die” mind-set Tough attitudes
“Go the extra mile” mind-set Tough attitudes
Determination to make the most of ability Tough attitudes
Belief Resilient confidence Tough thinking
Belief in making the difference Tough attitudes
Robust self-confidence – overcoming self-doubt/feeding off physical condition/maintain self-focus Tough thinking
Coping with pressure Thrive on competition Tough attitudes
Willing to take risks Tough attitudes
Thinking clearly – good decision making/keeping perspective/honest self-appraisal Tough thinking

‘The Mental Toughness Framework’ from Stephen J. Bull et al 2004

This framework is not in itself revolutionary, however it is unique in that it gives a cricket-specific explanation of the development of mental toughness, and it also gives us new insights into how those factors interrelate.

I will discuss the consequences of the framework in the next piece.

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Bibliography

Towards an Understanding of Mental Toughness in Elite English Cricketers, Stephen J. Bull, Christopher J. Shambrook, Wil James, Jocelyne E. Brooks. Journal of Applied Sports Psychology, 17:209-227, 2005

Mental Toughness 1 – What Is It Exactly?

There seems to be almost as many definitions of mental toughness as there have been researchers in the field of sports psychology. It would appear to be one of the most used and abused terms in the entire field of psychiatry.

Looking through the research (of which there is an Everest-sized mountain) we can find the following given definitions…

1.“The ability to cope with pressure, stress, and adversity” (Goldberg, 1998; Gould, Hodge, Peterson, & Petlichkoff, 1987; Williams, 1988);

2.“The ability to overcome or rebound from failures” (Dennis, 1981; Goldberg, 1998; Gould et al., 1987; Taylor, 1989; Tutko & Richards, 1976; Woods, Hocton, & Desmond, 1995);

3.“The ability to persist or a refusal to quit” (Dennis, 1981; Goldberg, 1998; Gould et al., 1987);

4.“An insensitivity or resilience” (Alderman, 1974; Goldberg, 1998; Tutko & Richards, 1976);

5. “The possession of superior mental skills” (Bull et al., 1996; Loehr, 1982, 1995).

6. Loehr (1982), suggested that mentally tough athletes have developed two skills; first, the ability to use energy positively in a crisis, and second, to think in specific ways which gives them the right attitudes to cope with pressure and competition.

To complicate matters further, mental toughness has also been described both as a personality trait (Werner, 1960; Werner & Gottheil, 1966; Kroll, 1967) and a state of mind (Gibson, 1998).

So we can say that pretty much any positive mental ability associated with sport has been characterized by someone as mental toughness at some stage. However reading through these definitions we can see a common theme emerging in mental toughness being associated with an athlete’s ability to cope with stress and anxiety of high pressure competitive situations.

So is mental toughness, something you are born with? Or is a product of your experiences? (The old nature or nurture debate), or is it something that can be learned? Or perhaps something that can be switched on and off at will? Can you learn to be mentally tough?

In an attempt to answer some of these questions Graham Jones of the University of Wales, and Sheldon Hanton, and Declan Connaughton of the University of Wales Institute designed a qualitative study of ten international athletes (none of whom were cricketers I should point out), to determine their attitudes and beliefs in this area.  (Graham Jones et al, 2002)

The study was divided into three phases, a group brainstorming session, in-depth individual interviews and a session where the athletes were asked to rank various attributes in order of importance. The results gave a clear (if somewhat unromantic) definition of mental toughness;

Mental toughness is having the natural or developed psychological edge that enables you to:

  • Generally, cope better than your opponents with the many demands (competition, training, lifestyle) that sport places on a performer.
  • Specifically, be more consistent and better than your opponents in remaining determined, focused, confident, and in control under pressure.

The subjects were also asked to develop a ranking of what they considered key attributes of mental toughness; here they are in descending order of importance;

1: Having an unshakable self-belief in your ability to achieve your competition goals.

2. Bouncing back from performance setbacks as a result of increased determination to succeed.

3: Having an unshakable self-belief that you possess unique qualities and abilities that make you better than your opponents.

4=: Having an insatiable desire and internalized motives to succeed.

4=: Remaining fully focused on the task at hand in the face of competition- specific distractions

6: Regaining psychological control following unexpected, uncontrollable events.

7: Pushing back the boundaries of physical and emotional pain, while still maintaining technique and effort under distress in training and competition.

8: Accepting that competition anxiety is inevitable and knowing that you can cope with it.

9=: Not being adversely affected by others’ good and bad performances.

9=: Thriving on the pressure of competition.

11: Remaining fully focused in the face of personal life distractions.

12: Switching a sport focus on and off as required.

So we have a definition that emphasizes coping mechanisms that allow you to deal better with distractions and stress, and allows you to be better focused, confident, determined and in control when placed under stress.

The key attributes that allow you to develop mental toughness emphasize resilience, focus, “unshakeable self-belief” and an “insatiable desire to succeed”.

So now we have a handle on what mental toughness is, we can go on to look at it in a cricket specific setting, and see how toughness can be developed in aspiring young cricketers.

References.

i. Gould, D., Hodge, K., Peterson, K., & Petlichkoff, L. (1987). Psychological foundations of coaching: similarities and differences among intercollegiate wrestling coaches. The Sport Psychologist, 1, 293–308.

ii. Dennis, P. W. (1981). Mental toughness and the athlete. Ontario Physical and Health Education Association, 7, 37–40.

iii. Goldberg, A. S. (1998). Sports slump busting: 10 steps to mental toughness and peak performance. Champaign, IL: Human Kinetics.

iv. Williams, M. H. (1998). The ergogenics edge: pushing the limits of sports performance. Champaign, IL: Human Kinetics.

v. Williams, R. M. (1988). The U.S. open character test: Good strokes help. But the most individualistic of sports is ultimately a mental game. Psychology-Today, 22, 60-62.

vi. Dennis, P. W. (1981). Mental toughness and the athlete. Ontario Physical and Health Education Association, 7, 37–40.

vii. Taylor, J. (1989). Mental toughness (Part 2): A simple reminder may be all you need. Sport Talk, 18, 2–3.

viii. Tutko, T. A., & Richards, J. W. (1976). Psychology of coaching. Boston: Allyn & Bacon.

ix. Woods, R., Hocton, M., & Desmond, R. (1995). Coaching tennis successfully. Champaign, IL: Human Kinetics.

xi. Alderman, R. B. (1974). Psychological behavior in sport. Toronto: W.B. Saunders Company.

xii. Bull, S. J., Albinson, J. G., & Shambrook, C. J. (1996). The mental game plan: Getting psyched for sport. Eastbourne, UK: Sports Dynamics.

xiii. Loehr, J. E. (1982). Athletic excellence: Mental toughness training for sports. New York: Plume.

xiv. Loehr, J. E. (1995). The new toughness training for sports. New York: Plume.

xv. Werner, A. C. (1960). Physical education and the development of leadership characteristics of cadets at the U.S. military academy. Microcard Psychology, 132. Unpublished doctoral thesis, Springfield College, MA.

xvi. Werner, A. C., & Gottheil, E. (1966). Personality development and participation in collegiate athletics. Research Quarterly, 37, 126–131.

xvii. Kroll, W. (1967). Sixteen personality factor profiles of collegiate wrestlers. Research Quarterly, 38, 49–57.

xviii Gibson, A. (1998). Mental toughness. New York: Vantage Press.

ixx. Graham Jones (2002): What Is This Thing Called Mental Toughness? An Investigation of Elite Sport Performers, Journal of Applied Sport Psychology, 14:3, 205-218

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Q. Does Winning the Toss Matter? A. Not Really

O.K. so you’ve won the toss by fair means or foul, but in the great statistical stream of things, does that matter?  Answer: probably not.

De Silva and Swartz (1997) started from the position that winning the toss was undoubtedly important in multi-day games, but questioned the validity of that assumption in one-day games.  So their study focused on the results of One Day Internationals (ODI’s). They looked at the results of 427 O.D.I. games played in the 1990’s and looked to see if there was any correlation between winning the game and winning the coin toss.  The eight games of the 427 that ended in a tie were discarded.

Four different statistical methodologies were used to compare the performances of the teams that won and lost the toss, I’ll spare you the details largely because I don’t understand them.  The upshot was that no matter which methodology was used no evidence could be found of the coin toss having an impact on the outcome of ODI games.

Interestingly, despite de Silva and Swartz’s presumption of an advantage from winning the toss in multi-day cricket, Allsopp and Clarke (2004) found no evidence of such an advantage.

“It is established that in test cricket a team’s first-innings batting and bowling strength, first-innings lead, batting order and home advantage are strong predictors of a winning match outcome. Contrary to popular opinion, it is found that the team batting second in a test enjoys a significant advantage. Notably, the relative superiority of teams during the fourth innings of a test match, but not the third innings, is a strong predictor of a winning outcome. There is no evidence to suggest that teams generally gained a winning advantage as a result of winning the toss.”

The other interesting point here is the clear advantage Allsopp and Clarke found in teams batting second in test matches, which gives the lie to Shane Warne’s “win the toss and bat” mantra.  Possible reasons for this ‘bat second’ advantage could be that teams batting second tend to bat on days 2 and 3 when test strips are likely to be at their best, and perhaps modern tracks don’t crumble as much or as often as is commonly supposed.This is what Allsopp (2005) has to say on the matter;

“…the dominance of the team batting second cannot be overestimated, and the results clearly describe an unexpected trend that has emerged in Test cricket. The results strongly indicate that to improve their winning chances teams should expose their particular strength, whether that be batting or bowling in the final rather than the penultimate innings.  This puts paid to the mythical notion…that when given the opportunity, teams should elect to bat first.”

So to summarise, in one day games there is no advantage to winning the toss.  In Test matches there is no demonstrated advantage to winning the toss, but that’s only because captain’s consistently choose the wrong option, i.e to bat first.

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Bibliography

Basil M. de Silva and Tim B. Swartz 1997 ‘Winning the Coin Toss and the Home Advantage in One-Day International Cricket Matches’, The New Zealand Statistician 32: 16-22

Allsopp, P.E. and Clarke, Stephen R. ‘Rating teams and analyzing outcomes in one-day and test cricket’ Journal of the Royal Statistical Society: Series A (Statistics in Society) Volume 167, Issue 4, pages 657–667, November 2004

Allsopp, P.E. ‘Measuring Team Performance and Modelling the Home Advantage Effect in Cricket.  PhD Dissertation Swinburn University of Technology pages 273-274

How To Win The Toss

images-2

The Belgian One Euro Coin – The Smart Captain’s Friend

The other day I accidentally caught a few seconds of one of those tedious phone-in political discussion shows on the radio.  The discussion was obviously about the economy, because I heard the caller say;

“Chancellor’s of the exchequer are like cricket captains, you are better off with a lucky one than a good one.”

 Or words to that effect. This set me thinking, what elements of luck are there in a captain’s cricketing career and how can a skipper be judged by his or her luck?

The first element of luck in cricket must surely be the coin toss.

I had always presumed that there was a 50-50 chance of a coin landing on ‘Tails’, which is why, in my short career as captain I adopted the ‘tails never fails’ philosophy, which, as it turned out failed about half the time.  However recent Canadian research shows that coin tosses are anything but random, and that the 50-50 outcomes are a myth.

Matthew Clark and Dr. Brian Westerberg at the University of British Columbia in Vancouver, Canada, asked thirteen medical students to flip a coin 300 times and try to influence the way it landed, cash prizes were awarded to the students who could make the coin land on ‘Heads’ most often. After just two minutes’ practice, the students could make the coin land on the side they wanted 54% of the time. One of the participants achieved heads a startling 68% of the time.

The simplest method of toss manipulation (and the one most relevant to cricket) is simply to note which side of the coin that is uppermost before it is flipped, as this side is 57% more likely to land facing upwards, they found. This is because discs do not spin symmetrically in flight.

But by far the biggest influence on which side the coin lands is the height, the angle of launch and the catch. By practicing to gain consistency, the tosser can have a significant affect on the outcome up to a 68% success rate.

Other studies have suggested that a Belgian €1 coin is significantly heavier on one side of the coin than the other which in theory would give more heads than tails.  However Clark and Westerberg demonstrated that this effect was no more pronounced than on the more routine cheating manipulation demonstrated here.

“The findings of my research show, to statistical significance, that it is easy to manipulate the toss of a coin”, said Clark.

This suggests that when Nasser Hussein lost the toss on fourteen consecutive occasions (16384 to 1, if you are interested), rather than being unlucky he was just not practicing enough.

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Bibliography

 

1. How random is the toss of a coin?

Matthew P.A. Clark, MBBS and Brian D. Westerberg, MD

From St. Paul’s Rotary Hearing Clinic, University of British Columbia, Vancouver, BC

http://europepmc.org/articles/PMC2789164//reload=0;jsessionid=q2o0qzaK5bcjsPYgpwDY.20

 

2. Murray DB, Teare SW. Probability of a tossed coin falling on its edge. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993;48:2547–52. [PubMed]

 

3. Diaconis P, Homes S, Montgomery R. Dynamical bias in the coin toss. SIAM Rev. 2007;49:211–35.

 

4. MacKenzie D. Euro coin accused of unfair flipping. New Sci. 2002. Jan 4, [(accessed 2009 Oct. 22)]. Available: www.newscientist.com/article/dn1748-euro-coin-accused-of-unfair-flipping.html.

 

5. Denny C, Dennis S. Heads, Belgium wins — and wins. The Guardian; [UK]: 2002. Jan 4, [(accessed 2009 Oct. 22)]. Available: www.guardian.co.uk/world/2002/jan/04/euro.eu2.

 

6. Kosnitzky G. Murphy’s Magic Supplies. Rancho Cordova (CA): 2006. Heads or tails; p. 6.

New Methods For Determining Batting Performance In Short Sequences of Games

Cricket Moneyball Two – assessing batting performance over a relatively short period of time.

During the course of an entire career the conventional statistical methods for determining batting prowess work reasonably well. We can for instance determine that with a career test average (Ave) of 99.94 Don Bradman was a half decent test batsman.

The problems arise when we are assessing player performance over a relatively short period of time, when we do not have a large number of innings to sample.  This can for instance become an issue when we are attempting to determine current short-term form, or a player’s performance in a given tournament.

There are a variety of potential problems here, varying game conditions for instance (more of this in a later post), but chief amongst these issues is the batsman who has a high number of not out scores which can distort his (or her) average. High numbers of not-outs may be down to the batsman’s innate brilliance, blind luck, or their position in the batting order, we cannot tell. This can lead to an erroneously high AVE which is calculated by dividing runs scored by times out (AVE=R/W). The most frequently cited example of this ‘not-out bias’ is the case of Lance Klusener who, in the 1999 World Cup scored 281 runs in nine innings while only being out twice.  This gave Lance an Average of 140.5, despite having a high score of only 52! Clearly a nonsense.

The first attempt to deal with this problem that I can find comes from ‘the two Alans,’ Alan Kimber and Alan Hansford (1) who attempted to draw on earlier work in survival analysis (Cox & Oakes 1984) and reliability analysis (Crowder, Kimber, Smith & Sweeting 1991) to produce a more rational means of batting performance indication.

I am reliably informed that Kimber & Hansford “argue against the geometric distribution and obtain probabilities for selected ranges of individual scores in test cricket using product-limit estimators…” (1)

No, I have no idea what that means either, so you will be relieved to know that others [Durbach (3) and Lemmer (4)] have since demonstrated that this system is almost as unreliable as AVE. So we can forget them and move on.

At this point our old friend H.H. Lemmer comes to our assistance again in (4) & (5) he argues that his analysis showes that if a not-out batsman had been allowed to bat on, he could reasonably expect to score twice the runs that he actually scored.  So logically, if we double the not out scores and count those innings as wickets we have a more accurate assessment, right? Well, not quite. Nothing is quite that simple in the wonderful world of cricket moneyball.

The formula derived by Lemmer from his insight is

e6 = (summout + 2.2-0.01 x avno) X sumno/n

where

n denotes number of innings played

sumout denotes the sum of out scores

sumno denotes the sum of not out scores

avno denotes the average of not out scores

However, if you were to simply double the not out scores and call that innings an ‘out’ you do end up with a very similar figure to e6.

 To put that into Lemmer’s parlance, the formula for this simpler method is

e2 = (sumout + 2 x sumno)/n

as you would expect.

Lemmer himself calls this ‘a good estimator’ and that’s good enough for me, this is the formula that I use for day in day out assessment of batting performance in single day games.

Coming to a spreadsheet near you.

There is one caveat, where there is one single very large not-out score the difference between e2 and e6 can become very large (>10), in which case we can use the measure e26 which is found by:

e26 = (e2 + e6)/2

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Bibliography

1) Kimber, A.C. and Hansford, A.R. (1993) A Statistical analysis of batting in cricket. Journal of the Royal Statistical Society Series A 156 pp 443-455

2) Tim B. Swartz et al, (2006) Optimal Batting Orders in One day Cricket, Computers and Operations Research 33, 1939-1950

 

3) Ian Durbach et al (2007) On a Common Perception of a Random Sequence in Cricket South African Statistical Journal

 

4) Lemmer H.H. (2008) Measures of batting performance in a short series of cricket matches. South African Statistical Journal 42, pp 83-105

5) Lemmer H.H. (2008) An analysis of players’ performance in the first cricket Twenty/20 World Cup series. South African Journal For Research in Sport, Physical Education and Recreation 30 pp71-77