On Winning the Toss: A Surprising Explanation of an Old Cricketing Conundrum

When Andrew Strauss, captain of England, recently won the toss in the third of a four match series against South Africa, he made a decision which could well influence the outcome of the series. I decided to look more deeply into the factors which a captain has to take into account in deciding whether to bat first. I came up with a surprising conclusion.

‘Every schoolboy knows’ that to win the toss at Cricket confers an advantage. On benign days the opposition will then probably have the worse of a deteriorating wicket later in the game. The Captain sould elect to bat first. But what if conditions are tricky – poorish light, cool, and with high humidity that helps the cricket ball swing mysteriously in flight? The dilemma is plain. Should the captain elect to bowl first. Strauss decided to bowl.

His decision was applauded at the time by the coterie of former captains available to comment on such occasions. Then, a determined innings by the team’s most determined batsman, Jacques Kallis, swung things back in favour of South Africa.

“If you are so clever what would you have done?”

I muttered that Strauss was a good batsman but not a deep-thinking strategist. “If you are so clever what would you have done? The Captain can’t theorise, he’s got to make a decision.” Susan’s question (as so often) forced me out of mutter-mode into thinking-mode. I assumed it would not take long to sort out this little problem. I was wrong. My initial thoughts were that the probabilities could be converted into a version of game theory. This would give some indication of when it might be better to bat first after winning the toss.

Several lengthy periods of thought later, I knew beyond reasonable doubt the extent of my ignorance. That is to say, I did not know how to reach the ‘bat or field’ decision. But the implication went further. I was also pretty sure than no-one else knew the answer either. The decision into the class of indeterminate ones for reason of complexity of factors and lack of adequate information.

The shocking implication and a Leadership Dilemma

The shocking implication of this finding is that a captain who knows the right thing to do on winning the toss, is suffering from a common leadership delusion. It is not a case of ‘knowing more than can be told’, but more a case of believing more than can be known’. The dilemma arises if a Captain feels he loses credibility if he appears to be less than certain of what he is doing. The conclusion applies to more diffident captains like Andrew Strauss, who often appears to recognise the inponderables of leadership. It also applies to the massed ranks of the pundits, be they fearless former England Captains or back-page scribblers.

For the moment take it from me, the uncertainties are of the kind which led Herbert Simon to coin the term ‘satisficing’ for a process through which a decision-maker simplifies the complexities in a situation in order to reach a decision. It may well be the case that someone has done a little analysis of the statistics of winning the toss and electing to field. If so, the results are a carefully guarded secret.

So what should a Captain do on winning the toss?

But Susan’s follow-up remark also hit home. The Captain has to do something in double-quick time. Strauss had had a brief period to anticipate conditions before the toss, and then a few moments to confirm a decision on winning it. Incidentally, he then had less than a minute to justify a decision that can not be arrived at completely by a rational analysis.

Based on this line of reasoning, my considered answer to Susan’s question is as follows: Now that I know my decision is not much better than tossing a coin I would stick with statistics more often than I might otherwise have done. And that means batting first is an advantage. If conditions appeared to favour the bowlers first, I’d think more carefully about it.

I would probably consult, but if I did so it would be with the knowledge that bowlers and batsmen alike would prefer their team to bowl first in tricky conditions, if only for self-interested reasons.

All this would not tell me whether I should bowl, but if I decided to do so, at least the decision to field would then be based on consultation, rather than my trying to maintain face as the captain knows best, and has made the decision on grounds of superior judgement.

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6 Responses to On Winning the Toss: A Surprising Explanation of an Old Cricketing Conundrum

  1. Michael Darby says:

    I looked up the following site (at the bottom) which states that the side winning the toss wins the match 53% and looses 47% (ignoring drawn matches). However, I found the following conundrum. Statistically, should the home team win the toss, they are statistically better off putting the touring team into bat. However, if the touring team win the toss, they are statistically better off electing to bat.

    http://www.howstat.com.au/cricket/Articles/TheToss.asp

  2. Tudor says:

    Thanks Michael. Th e stats for winning for White first in Chess is ca 55% , 45% for Black. That’s the ‘first mover’ advantage. Openings which deviate beyond those stats results get abandoned. Chess players are increasingly big on stats.

    But there’s still the case for playing unusual and slightly weaker openings for surprise value, to upset a much sronger opponent for example.

    Your nice example adds evidence that in Cricket, the bat or field decision is too complex to be worth much though. Be very cautious before deciding to bowl first unless there is evey change of nearly winning the match before lunch on the first day.

  3. Tudor says:

    And an even more recent example from the Australia Pakistan match. Australia win the toss and bat first. Pakistan bowl well and ‘almost’ win the match. Ponting criticised by expert and non-expert alike for not deciding to bowl first. Pakistan maintain advantage until well into the game. Then (after aguably a more significant decision by Pakistan’s Captain to set defensive field) Australia is offered a sniff of victory. As I write they achieve a remarkable and deserved win.

    I’m not arguing that a captain can not influence the result of a match for better or worse. But any post-mortem must look at all the decisions, not one, according to decision theory. That includes multiple decisions, including of course those by the Umpires. Now that’s another thing to think about!

    The blame game is rarely useful, and is mostly a misdirection of focus in sport as in business.

  4. Adil Mistry says:

    Hi Tudor,

    This is a classical delimma which crops up a lot. However, I always though that the descision is made by the team seniors and the coaches along with the captain before he goes in for the toss.

    Also another point to consider is that, the home team captain will have more advantage, as he will have the advice of the curator and will know the local conditions better.

    Adil

  5. The Toss to choose to bat or field should be replaced by The Bid.

    The two captains should bid in runs for the right to elect to bat or field first. The team with the higher bid wins the right to elect.

    The runs bid are awarded to the opposing side as Bid-Byes.

    See “Time to Chuck out The Toss and Bring in The Bid”

    http://goo.gl/cRtki

  6. Tudor says:

    Thanks Warren

    I’m going to think about this creative idea. Any thoughts on new technology to improve decision-making?

    Best wishes

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