Losing early wickets and chances of victory

I have a general hypothesis which I will be exploring throughout a series of blog posts in this season, and it is this: batting teams start with two resources (balls and wickets), and they spend those resources as efficiently as possible to convert them into as many runs as possible. Thus Twenty20 cricket isn’t just about scoring runs as fast as possible. You want to preserve enough of your wickets to be able to play a riskier game at the tail-end of the innings “spending” those surplus wickets to give you the capacity to score at a faster rate.

In today’s post, I want to explore the role of losing early wickets in determining how many runs a team scores, and their chance of victory.

As a taste, this graph shows the likelihood of victory for teams based on how many wickets they have lost after five overs:

Teams that have maintained all of their wickets have roughly two-thirds chance of winning. Teams that are down one wicket are still favoured to win, but the chance of victory drops gradually further. A team which has lost four wickets has less than 20% chance of winning. There have only ever been six innings where a team had lost six or seven wickets after five overs, and in all six cases that team went on to lose.

Obviously this is a simplification: I haven’t separated out first and second innings matches, and it doesn’t take into consideration how many runs the other team will score – if both teams lose a lot of wickets they may cancel out these effects. But when you zoom out to the entirety of men’s Twenty20 cricket over the last sixteen years, the trend is clear.

Here’s another version of the same graph, but showing the state of play after ten overs:

Any team that has lost no more than two wickets after ten overs, but any time down five wickets or more has a slim chance of winning.

Finally, the same metric at fifteen overs: by this point you expect teams to have lost wickets. There aren’t many cases of a team lasting fifteen overs without losing a wicket, but when they do they are almost guaranteed of a win. Out of 53 cases, that team won in 50 cases, along with two losses and one tie.

Finally here is the same information for the fifth, tenth and fifteenth over, split between the two innings for both men and women:

Now obviously this gives you a general idea of what is a “normal” loss of wickets at a particular point in the game, but it doesn’t tell you how many runs to expect to score when you’re trying to calculate your chance of reaching a particular target.

It’s time for some box plots. If you’re not familiar with box plots, the box represents the middle 50% of cases in the sample – the upper end of the box is the 3rd quartile, and the lower end is the 1st quartile, so 25% of samples are above the box and 25% below. The thick line in the middle represents the median point – if you line up every score in a row, the median is the one in the middle. The dots represent outlier cases.

I measured this in two ways. Firstly: at a particular point in the innings and having lost a certain number of wickets, how many runs (as a raw number) are left to be scored in the remainder of the match. Secondly: at that some point, how many runs are left to be scored as a proportion of the runs scored so far. If a team has scored 50 runs and will end up on 185, then the first metric will produce a score of 135, and the second metric will produce a score of 2.7. I’m not really sure which metric is the best at this point in time.

The chart above shows how many more runs are scored in the last fifteen overs of the match relative to the runs scored in the first five. What you see is that the ratio of runs is roughly the same for teams who have lost between zero and five wickets, with slight evidence that teams who have lost a handful of wickets actually do better than those who have avoided losing any.

This chart also shows the five-over mark, but shows the number of runs to come in the remainder of the match as a raw number. When you look at scores this way, teams steadily score less runs if they have lost more wickets. If you assume that teams who have lost a handful of wickets will have scored less runs in the same period than those who haven’t lost any (a reasonable assumption), then it makes sense that the ratio of runs to come over runs scored is roughly the same but the raw numbers of runs is higher for those teams who haven’t lost a wicket.

For the sake of completeness I’ll end with two charts, showing how many runs are scored in the remainder of the innings (as in the above chart) broken down by wicket at the 5-over, 10-over and 15-over point in the innings, both for men and women.

So what can we conclude from this? Firstly, there is a clear trend that teams which lose more wickets in the early and middle parts of their innings have less chance of winning the match.

Secondly, teams that have lost up to four-five wickets usually have the ability to score a similar ratio of runs in the remainder of the innings as teams that have lost no wickets. Roughly, this means a team who has lost these number of wickets will score four times their score at the 5-over mark, double their score at the 10-over mark, and 40% more than their score so far at the 15-over mark. Teams that have lost more than 5 wickets at the 5-over mark, 6 wickets at the 10-over mark or 7 wickets at the 15-over mark are capable of scoring less runs in the remainder of their innings.

When you look at raw numbers of runs, every subsequent lost wicket reduces your power to score more runs, with the drop-off becoming particularly dramatic at the points outlined in the previous paragraph.

Overall none of this is probably very surprising, but it makes it very clear that the loss of early wickets in a Twenty20 match can have an impact. A team that comes into the end of their innings with plenty of wickets in hand is capable of scoring more runs, and thus having a greater chance of winning.