Auctioning Off the Toss

BBC cricket broadcaster Christopher Martin-Jenkins gave an excellent talk this week, full of good ideas. One of the ideas (not originally his) is the idea that instead of having a toss to determine who bats first, we could instead have the captains bid runs.

This seems a perfectly logical progression from the Duckworth-Lewis rule, which also uses economic theory to compensate for asymmetric playing conditions. In the case of DL, the asymmetric condition is the number of overs - one team gets more of them, so what's a fair way to adjust the scores in compensation?

Replacing the toss with bids compensates for unequal light, swing conditions, weather and pitch wear. It's particularly relevant in day-night ODI's, where one team clearly has better light to bat in. If it's worth x number of runs to bat first, why not give those runs to the team that bats second? Or vice-versa in some cases.

The original idea for implementing this was to have some sort of interactive multi-round bidding, but the best solution is to have a sealed-bid instant 2nd-price auction (a.k.a. Vickrey Auction). This means that each captain brings an envelope containing his assessment of how many runs it's worth for the choice to bat or field first. The winner is the captain with the higher of the two bids, but the runs awarded to the losing side are what the losing captain bidded. Example: Paul Collingwood bids 40 runs for England and Saurav Ganguly bids 30 for India. Collingwood is awarded the toss, but when India bats, they begin with 30 bonus runs on the board. This is the simplest and fairest type of auction for this, because both sides have the incentive to bid what they think it's worth. If you bid higher than you think it's worth, you might get lucky, but you risk your opponent getting more bonus runs than you think the toss is worth. If you bid lower than it's worth, if you win your lowering the bid does not lower the opponent's run bonus, but if you lose you've lowered your own bonus.

So what happens if both captains bid the same amount (let's say 35 runs)? Then toss a coin and the winner get to choose to bat or field first, and the loser gets the bonus runs which both captains thought the toss was worth (35).

I think this system would be much fairer than the coin toss (especially for limited overs matches), and I applaud CMJ for bringing it to light and cricket coach David Harris of Herefordshire for coming up with the basic concept.

P.S. - One odd side effect of this system would be to introduce the theoretical possibility of an innings defeat to limited overs cricket. If team A is awarded the toss in exchange for 40 bonus runs, and they're bowled out for 38, team B wins by an innings and 2 runs.