Category Archives for Cricket – Statistical Analysis

Mental Toughness 5 – How Can It Be Developed?

“I failed over and over, that is why I succeed”

Michael Jordan, who missed 9000 shots including 26 game winning shots, and lost 300 games on the way to becoming a 6 times NBA World Champion.

In this final piece on the subject, having defined mental toughness and why it is important in cricket, we finish the series by determining what the player, the coach and the parent can do to aid the development of mental toughness in young cricketers.

What can the player do?

Let’s start by reminding ourselves of Jones et al.’s definition of mental toughness:

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

Generally cope better than your opponents with the many demands (e.g., competition, training, lifestyle) that are placed on you as a performer

Specifically, to be more consistent and better than your opponents in remaining determined, focused, confident, resilient, and in control under pressure.(Jones et al, 2002)

Key psychological characteristics associated with mentally tough elite athletes – again Jones et al (2002):

• Self-Belief: Having an unshakable belief in your ability to achieve competition goals

• Motivation: Having an insatiable desire and internalized motivation to succeed (you really got to want it)

• Ability to bounce back from performance setbacks with increased determination to succeed.

• Focus: Remain fully focused on the task at hand in the face of competition-specific distractions Able to switch focus on and off as required

• Composure/Handling Pressure:

• Able to regain psychological control following unexpected events or distractions

• Thriving on the pressure of competition (embracing pressure, stepping into the moment)

What can the Athlete Do to achieve these characteristics?

Take control of your own development.  Be the boss of you, control the controlables. If you feel you are weak in a certain area take the responsibility yourself to address the issue.  Be honest in your assessment of your abilities and actively seek out help.

Set effective goals. Set yourself SMART goals. Specific Measurable Achievable Relevant and Timed. Break down these goals so that frequent achievement of smaller goals will provide you with positive feedback.  Review your goals regularly, do not be afraid to change them in the face of changing circumstances, Do not linger unduly on unachieved goals or beat yourself up about not achieving them.

Take control of your internal dialogue. Positively intervene in your own internal dialogue to counter negative thoughts. Visualize yourself performing the way you want to perform. Program your mind for success ahead of time. Expect the best from yourself; affirm what it is you are going to do to be successful.

Practice visualization techniques to imagine successful outcomes. Sit alone in a dark, quiet room, close your eyes, and visualize positive outcomes as clearly as you can, for example, scoring a hundred or taking five wickets in your next game. Over time, your ability to vividly visualize will improve, leading to increased self-confidence.

Bounce back from set-backs. Work harder on your mental training when things aren’t going well. This is especially important specially when injuries prevent you from physical training or playing.

Develop Routine Behaviors. Develop a system. A pre-game routine that turns on the desired mental and emotional state.

• Practice – commit to giving everything you have throughout the practice session.

• During Competition – make an explicit commitment to being mentally tough, and a great competitor.

Be Poised and Composed: If you make a mistake don’t sweat it. Learn how to let go of mistakes quickly if things don’t go well.  Don’t beat yourself up.

Learn to adapt. Key part of toughness is about compensating, adjusting, and trusting

• If plan A does not work, go to plan B or C

• Use “Focal Points” to help focus attention on what needs to be done.

• Don’t allow frustration to undermine your confidence/focus

Look on failure as a stepping stone to future achievement:

Play to win do not fear making mistakes

If you focus on the process of competing well, winning will take care of itself

 What Coaches and Parents Can Do

  • Create an environment where mental toughness can grow.  You can’t ‘teach’ mental toughness as such, but that doesn’t mean that you can’t create an environment where mental toughness can be nurtured and grown.  Look at the earlier posts in this series (in particular, the ‘cricket specific mental-toughness framework’) for details of how what that environment would look and feel like.
  • Rather than seek to grow self-confidence in the player, concentrate on supporting the self-confidence that is already there.
  • Give them the opportunity to take responsibility for their own development.  Don’t smother them.
  • Make sure they spend at least one season a long way from home.
  • Don’t send them to private school.  Mental toughness is a product of environment.  Looking at the toughest England cricketers of recent times, Close, Illingworth, Boycott, Gooch, Botham, Collingwood, – pretty much the only thing they have in common is a state education.

 o0o

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

http://www.livestrong.com/article/169184-how-to-develop-mental-toughness-in-sports/#ixzz2Mqy0TUwV

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.

o0o

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

Cricket Moneyball 3 Assessing Batting Performance in Twenty20 Cricket

Twenty20 cricket gives us a whole new set of problems when it comes to assessing batting performance.  Upper order batsmen are much more likely to achieve ‘not out’ scores in Twenty20 and we have seen in the previous post how that can render the traditional Average score (Ave) close to useless.

 

In Twenty20 scoring rate is of critical importance, a batsman who scores 30 runs off 10 balls, than one who scores 31 off 30. So to accurately reflect the quality of a batting performance we need a measure that takes in both runs scored and the rate at which they are scored.

 

To further complicate matters, runs are scored at very different rates under very different conditions.  It is much easier to score runs quickly on a track with true and predictable bounce under a bright blue sky, than on a green strip in Manchester, or a dead track in Nagpur.  So if possible we need the measure to take into account conditions on the day.

 

Croucher (2000) was the first researcher I have found to deal with the first of these problems. He proposed something he called the “Batting Index” (BI). Which was found by simply multiplying the conventional average by the strike rate per 100 balls faced.

 

BI = AVE X SR

 

Where

 

AVE = R/out

 

R= runs scored

Out = times out

 

SR = 100 X R/B

B = balls faced.

 

Basevi & Binoy (2007) used a very similar measure, which they called CALC

 

CALC = R2/(out X B)

 

Now if you work this out (bear with me here, I only just scraped a low grade ‘A’ level in maths and that was a long time ago), you get

 

CALC = (R/out) X (R/B)

 

In other words this is just AVE X SR again, the difference between that this is runs per ball rather than runs/100 balls, or to put it another way CALC = BI/100.

 

The general feeling among researchers was that this method of simply multiplying average by strike rate over-emphasized the value of strike rate in Twenty/20 games.  Secondly it did not take into account different batting conditions. So how do we account for differing playing conditions when we are assessing a batsman’s performance? One suggestion (Lemmer 2008) is to take the average scoring rate fro all batsmen and compare with that figure. For example if the average run-rate at one particular ground or in one tournament was 124, we could assess an individual players performance against that figure.  This would then give us a good idea of how that individual was performing. The formula for BP (Batting Performance) is as follows;

 

BP26 = e26XRP=e26X(SR/AVSR)0.5

 

Where

E26 = (e2 + e6)/2

E2 = (sumout + 2Xsumno)/n

E6 = (sumout + f6 X sumno)/n

F6 = 2.2-0.01Xavno

AVSR = average strike-rate

SR = Strike Rate

 

In international Twenty20 matches AVSR = 124.03, so that figure can be substituted in to the formula.

 

It is clearly unfair to compare batting performance in differing batting conditions.  So by comparing his performance with the average strike rate of all batsmen playing in those conditions are fairer assessment can be made.

 

Again, Excel is your friend here, it is an initially daunting looking formula, but once you have the formula set up in your spreadsheet, the inputs can be added quickly and the result attained satisfyingly quickly.

 

o0o

Bibliography

 

Croucher, J.S.  (2000)  ‘Player Ratings In One Day Cricket’. Proceedings of the Fifth Australian Conference on Mathematics and Computers in Sport Eds. Cohen G. & Langtry, T. Sydney University of Technology, NSW. 95-106

 

Basevi, T. & Binoy, G. (2007) ‘The World’s Best Twenty20 Players’ Cricinfo cricinfo.com/columns/content/story/311962.html

 

Lemmer, H.H. (2008) ‘An Analysis of Players’ Performances in the first Cricket Twenty20 World Cup’. South African Journal For Research In Sport, Physical education and recreation 2008, 3092): 71-77

 

Lemmer, H.H. (2011) ‘The Single Match Approach to Strike Rate Adjustments in Batting Performance Measures in Cricket’ Journal of Sports Science and Medicine 10, 630-634

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

o0o

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