T C A Srinivasa-Raghavan: Where should we meddle?

OKONOMOS

What should cricket captains do after winning the toss?

There is a wonderful term in Tamil that describes what economists often do: korangu cheshtai. It is used to describe the habit that monkeys have of fiddling around, justu wonly. Here are two wonderful examples of this tendency amongst economists, both sent to me by my friend Niranjan Rajadyaksha.

The first paper*, by Peter Dawson, Bruce Morley, David Paton, and Dennis Thomas uses econometric analysis to tell us the effect of the toss on outcomes in limited over games in cricket. The second**, by some Israeli economists, is about why goalkeepers jump this way or that in response to a penalty kick when it makes more sense to stand still.

First cricket. "The tradition of tossing a coin to decide who bats first in a cricket match introduces a randomly-assigned advantage to one team that is unique in sporting contests," say the authors, not entirely accurately. They then see what this does to the result in the day-night games, as distinct from the day version alone.

They have studied all day-night games between 1979 and 2005 by using conditional logit models of the outcomes. "Other things equal, we find that winning the toss and batting increases the probability of winning by 31 per cent. In contrast, winning the toss does not appear to confer any advantage if the team chooses to bowl first."

So if he wins the toss, should the captain always decide to bat first, even if there is a 69 per cent chance of losing? Posed this way, the analysis loses its appeal somewhat. The more relevant fact, surely, is that regardless of the toss, the win-lose average for any team fluctuates between high of 52 per cent and a low of 46 per cent. A great deal also depends on against whom you play, not to mention other things that have a bearing on the progress of the game, such as umpires who can't be modelled.

The authors say that "cricketing authorities should seriously consider the implications at both international and domestic level" largely because of knockout matches and bad scheduling in tournaments.

The latter can make a difference if some teams get more day-night games than others. This has been known to happen. Since day-night games are commercially more popular, the authors have got this bit right, at least.

So what should the ICC do? "One seemingly obvious policy recommendation would involve each team batting/bowling for two 'half-innings' of fixed overs during balanced sessions, with order determined by the toss of a coin, ensuring that both teams (potentially) experience both lighting conditions." But it seems that where this has been tried, several matches have ended prematurely, which can annoy the commercial interests.

"Another possibility might be to determine the choice of batting order according to pre-match rankings, and whether the weaker team is playing at home" so that the contest becomes more even. "Unless key matches are to be played wholly in daylight, a major final (and possibly semi-finals) could be played over two legs (preferably at the same venue) with order of batting reversed from the first to the second, allowing both teams to experience batting first in a match. The batting/bowling choice would then be determined by the toss of the coin in the first match only."

Turn to the football paper now. The following excerpt is from the Atlantic Monthly.

"A group of Israeli economists studied 286 penalty kicks and found that most goalkeepers decide to jump right or left before they can really see where the ball is going. Based on the distribution of kicks, the researchers concluded that the smartest choice would be to remain in the middle of the goal....The economists explain their finding by citing "norm theory," which holds that people's actions are more likely to be guided by convention "" and the fear of looking foolish "" than by pure reason. Adherence to norms typically favors inaction: when facing a choice with potentially negative outcomes, people often prefer to do nothing, on the theory that a harmful outcome looks worse when it's the product of action rather than inaction. In soccer, the authors argue, this pattern is reversed. Goalies would look awfully bad just standing and watching the ball zip by, so they resolve to do something, however irrational the action turns out to be."
Well, what can one say.

*IASE/NAASE Working Paper No 08-01 "To Bat or Not to Bat: An Examination of Contest Rules in Day-night Limited Overs Cricket",  February2008econpapers.repec.org/paper/spewpaper/0801.htm
**Action Bias Among Elite Soccer Goalkeepers: The Case of Penalty Kicks," Michael Bar-Eli et al., Journal of Economic Psychology