When to declare?

One of the unique things about test cricket is the prospect of declarations.

While there's situations in motor racing where a driver might go slow in order to conserve fuel or in sailing where a racer might give up the lead in order to get in a more favourable position, there's not really any other sport where a team or individual can opt to stop scoring to ensure that they get a win.

The prospect of a draw encourages positive play from the team that is on top, and allows an out for teams who are losing.

Deciding when to declare also provides interesting talking points for fans and commentators alike, and the decisions are much easier in hindsight.

However, it's essentially a statistics problem. There are two variables, and a whole lot of historical data. The key variables are the overs left at the start of the innings and the target to win. 

While there are other issues (the "throw out a carrot" theory - if the target is close enough, teams will take more risks) and no two teams are the same, we can build a model based on that data and use that to predict the chances of winning, based on when a team declares.

I've built a very basic model, based on the 130 most recent matches where the target was under 400.

Given that data, the optimum declaration point changes based on the runs per over that the team scored.

In the end they set West Indies a target of 312 in 85 overs, which was too much, and the model suggested that it would be. It output the probabilities of 9.8% for a West Indies victory, 27.5% for a draw and 62.6% (all values rounded - which is why they don't add to 100%). The most likely outcome is what happened.

Part of the fact that England had such a good chance of success was that they scored so quickly. 92 runs in 11 overs gave them an excellent chance of success. However, a declaration a couple of overs earlier might have given them an even higher chance of success. They would have had a 64.4% chance of winning if they had declared a couple of overs earlier.

I put together a graph showing the impact of the scoring rate on the chance of winnings and the optimum time to declare. It's often said that strike rate isn't relevant in test matches. But this match proved the value of scoring quickly in tests.