Toss win rates hide how much the toss is worth

Because captains choose sensibly, the numbers comparing coin flip winners with losers systematically understate the advantage.

Somebody publishes a table. Teams winning the toss at this ground have won fifty three per cent of matches. The conclusion drawn is that the toss is worth almost nothing, and everybody relaxes.

That table is measuring the wrong thing, and the reason is a problem statisticians recognise instantly and cricket writers mostly do not. The captain who wins the toss makes a decision. He looks at the surface, the forecast, his attack, and he chooses. Sometimes he chooses well and sometimes badly, and the observed win rate blends the value of having the choice with the quality of the choices actually made.

Suppose batting first at a particular ground is worth a great deal on some days and nothing on others, and suppose captains can tell the difference only half the time. The measured advantage will be modest even though the underlying advantage, on the days when it exists, is enormous. Averaging across the days destroys the signal. Worse, captains sometimes choose against the evidence for reasons of temperament or pressure or the desire not to be blamed, which drags the average down further and makes the toss look even less valuable than it is.

You can separate these. Model the outcome given the conditions, then ask what the toss winner would have been worth had he chosen the option the conditions favoured. That counterfactual number is the value of the toss. The gap between it and the observed win rate is the cost of captains' decisions, which is itself a thing worth knowing and which no board has any appetite to publish.

There is a spin bowling wrinkle here that gets it wrong in the other direction too. On a surface expected to take heavy turn, the choice is not simply about batting last. It is about whether your own attack can exploit the fourth innings surface, which depends on having two quality slow bowlers rather than one. A side with a single spinner faces a genuinely different decision from a side with three, on the same pitch, on the same morning. Pooled toss statistics treat them identically.

So the coin is worth more than the tables say, and it is worth different amounts to different teams.

What a pooled percentage really measures is how good captains are at reading a pitch. That is a lower number than anyone wants to print.