The cricket season starts soon, so I was interested to read this article on ESPN Cricinfo, arguing to change the way that the toss is decided at the start of each match:
In cricket, the fairness of the pre-match coin toss is the subject of perennial debate. And rightly so.
The toss is random but its impact is not. Over a long series of games, the impact of the toss is neutral, but if it is meant to offer both sides an equal shot at winning any one game, it fails. Our analysis of more than 40,000 professional matches suggests as much: the team that wins the toss wins the game 2.8 percentage points more often. And if that were not sobering enough, in day-night one-day matches, the advantage of winning the toss is a whopping 5.9%...
Auctioning off the ability to choose whether to bat or bowl first is a better idea. Instead of awarding the decision to the captain who correctly calls the face of the coin left staring at the sky after landing on the ground, we should ask teams to use their knowledge and experience to price the value of getting to pick whether to bowl or bat first.
After giving the teams time to inspect the playing surface, each team should simultaneously bid the number of runs that should be added to the other team's score. The team that puts in the higher bid - proposes more runs be added to the other team's score - wins the right to choose whether to bowl or bat. (If the bids are tied, which suggests that teams price the ability to choose the same, an actual coin toss can be used to decide which team chooses and the runs would be added to the other team's score.)
It's an interesting suggestion. If both team captains are equally skilled (which is a heroic assumption), then the coin toss as currently practiced confers a random advantage to one team. Auctioning that advantage to the highest bidder would cost the team winning the toss some runs (because they would have to score additional runs in order to win), reducing the size of the random coin toss advantage. If both teams are equally adept at bowling first (or batting first), both captains are equally skilled, and both captains have complete information about the state of the pitch, then both would be willing to bid the same number of runs.
However, I see three problems here. First, as highlighted in the article:
Cricket teams already heavily use data to help guide decisions on who they draft, what to pay for each player, what tactics to use against each bowler and batter. And the decision on what to do when a team wins a toss is probably already guided by the analytics companies. So yes, teams with more money and better analytics obviously have a leg up.
So, it isn't fair to assume that both captains are equally skilled, because analytics matters. And that leads to the second problem, which is the winner's curse. Consider the two team captains. If both are rational then they will each bid the number of runs that they think fairly represents the advantage they would get from winning the 'coin toss auction'. They won't bid less than that number of runs, because that reduces their chance of winning the auction. They won't bid more than that number of runs, because that reduces their chance of winning the game, if they win the auction. This rational bidding behaviour is what would make this auction format attractive to many economists. However, the captain's estimates of the advantage they get from winning the auction is subject to some random error. They might overestimate the advantage, or they might underestimate the advantage. Since both captains are bidding at the same time, the one that overestimates the advantage by the most will win the auction. And they will likely have bid too many runs for the true value of winning the coin toss. That is the winner's curse. The auction format is good in theory, but it might simply change winning the coin toss from a likely advantage to a likely disadvantage. [*]
A third problem arises when the two teams are mismatched. How many runs should Afghanistan or Kenya bid when playing Australia or India? Could they bid negative runs? And, knowing that, would Australia or India be willing to bid many runs at all? It seems to me that this proposal would ensure that top teams always win the toss when playing against teams that are far below them.
As an economist, it would be interesting to me to see how this would all play out. However, as a cricket fan, the status quo is much preferable because at least the randomness gives the underdogs a chance. For that reason alone, I hope that we never get to see this in practice.
[HT: Marginal Revolution]
*****
[*] The winner's curse is a problem in an auction with many bidders. In an auction with only two bidders (such as this), it is possible that both might underestimate the size of the advantage, and whichever captain underestimates by the least will win. In that case, the winning captain does bank an advantage for their team, but the advantage is smaller than it would be based on a pure coin toss.
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