Haris Aziz is not a man to let a problem pass him by. Born in Pakistan, he did a Bsc at Lahore University of management sciences, an MSc in maths at Oxford, a PhD at Warwick and is now an associate professor at the University of New South Wales. There he specialises in computational social choice and algorithmic game theory. So far, so on a higher plane.
He also loves cricket. So when, during the recent men’s T20 World Cup in the UAE and Oman, the toss became increasingly problematic and the advantage of winning it and fielding first, when a very heavy dew fell at dusk, became more and more obvious – especially in Dubai where 12 out of 13 games were won by the chasing team – Aziz applied his considerable brainpower. How to, in his words, “ensure that the toss continues to be meaningful but doesn’t have an unfair effect on the outcome of the match”.
“One of the overarching issues that I work on is that many decisions are being made by computers or computer algorithms and one of the overarching themes is how these decisions are made in a fair manner,” he says. “And that was the angle I took when looking at this issue: fairness.”
For Aziz, the toss is not inherently unfair over a long sequence of games as both teams equally have the chance to win it, but it is if you consider it on a match-by match basis. For example, in a one-off game such as the ICC World Test Championship final, the last match of an Ashes series or a T20 World Cup final. The problem is not only advantage to the toss-winning side due to things like the state of the pitch and weather conditions, but also perceived advantage, which can make the losing side feel hard done by and also denigrate the achievement of the winning team.
Aziz’s solution is to move the toss from a two-step formula – toss the coin, winning captain chooses – to a three-step formula: toss, propose, choose. Here, the coin is tossed as normal, then the Unlucky (toss-losing) captain chooses a run handicap to pin to the more favourable option in order to equalise the two choices, before handing back to the Lucky (toss-winning) captain to make the final decision of whether to bat or field. The beauty of the division is that the Unlucky captain will not overestimate or underestimate the runs needed to equal up the decision, as it is the Lucky captain who gets to make the final choice.
“The reason I came up with this method is that it also has really solid mathematical foundations,” says Aziz. “It is inspired by a rule called divide and choose which has been used throughout history to make a very different kind of allocation decision about dividing a divisible resource. Steven Brams and Alan Taylor have written an excellent book on it called Fair Division. Here we don’t have a divisible resource but we do have runs, which are almost a divisible resource, and which we can use to balance things out.”
To non-mathematicians, it is a variation on the age-old solution to squabbling children: let one child cut the cake, and the others choose the slices.
I like the jeopardy aspect of how many additional runs might be worth giving away in order to make the opposition captain opt for what you would like them to do – but it definitely piles added complications on to a game that is already subdivided up to Law 22.214.171.124 (bad behaviour by a runner). But Aziz has thought this through too.
“Cricket already has so many rules such as Duckworth-Lewis and this [the three-step toss] is fairly simple in that respect. How does a captain make the decision? This can be estimated by a very simple thought experiment. Would you bowl first or bat first, then would you bowl or bat first if five, 10, 15 extra runs were added? At some point you would say I’m indifferent between the two options. By doing that, the losing captain cannot say they were disadvantaged.”
There must be a possibility, though, that this will end up being another data-driven decision in a game that sometimes seems it might be eaten up by its own analytics. Can a computer ape intuition? “By careful analysis one can get a pretty good idea of bowling first given two teams at one ground at a certain temperature, but I feel that sports rules should be elegant and simple so my method is not dependent on any calculations on a computer. I think the beautiful rules in sport are those that are timeless and not dependent on technology.”
Though concerns were raised during and after the T20 World Cup by voices as prominent as Sunil Gavaskar, the problem of the toss has been vexing minds for some time. The ICC cricket committee considered removing the toss from the World Test Championship in 2018, but decided instead to urge member nations to produce better pitches. The County Championship went one further between 2016 and 2019, giving the visiting teams the opportunity to bin the toss and bowl first. This was an attempt to stop clubs preparing excessively damp seam-friendly pitches and to encourage spin bowling, but after four years the England and Wales Cricket Board decided it hadn’t worked.
In limited-overs cricket, the captain has had to become something of a gambler, deciding whose over allocation to keep up their sleeve for the crucial final over, the vital penultimate over, that key last over of the power play. Batters have had to reassess their calibration of risk, and DRS means that even in Tests, captains must choose when to play their joker. Aziz’s proposed toss reform is a continuation in the same direction: more risk, but greater integrity. The TV companies would love it. Heads, it’s a goer.