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.



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


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.




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



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.

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.






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



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.





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