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