What happens when a partnership ends

Jaya & Mahana4 August 1997: Roshan Mahanama walked out to the middle with Sanath Jayasuriya at the start of the third day of the Test.  It was the beginning of the second wicket partnership – the first wicket of the innings had fallen to the last ball of the second day.

5 August 1997: The pair walked out together again on day four, having batted throughout the third day – a very rare occurrence.

6 August 1997: An unprecedented feat – batting unbeaten through two full days of Test cricket – the pair started day five still in partnership. At this point they had amassed 548 runs together, surpassing the previous record for a partnership for any wicket in Test cricket by a clear margin.

Sri Lanka batted through day five to reach 952-6, setting the record for the highest total in Test cricket. Opposing captain, Sachin Tendulkar, was full of praise for the Sri Lankan batsmen, but branded the pitch unfit for Test cricket.

Jayasuriya and Mahanama had taken their partnership to 576 on the fifth morning when the latter was dismissed lbw by Anil Kumble. Two balls later Jayasuriya was out caught at silly-point. After twelve and a half wicket-less hours, India had prised out both batsmen in a matter of minutes.

It is a commonly made observation in cricket that after a long partnership, the two batsmen fall in quick succession. Jayasuriya and Mahanama are the archetypes of this phenomenon.

I find the idea that two well-set batsmen will lose their wickets suddenly, one after the other, intriguing. There are conventional cricket explanations – wickets falling to the new ball; an old ball beginning to reverse; or some other change in conditions. But what interests me is that the idea is suggestive of a range of psychological explanations.

There is the simple notion that the disruption in concentration caused by the first wicket makes the remaining batsman vulnerable. More complex is the possibility that the two batsmen during a long partnership have developed an equilibrium, where each has an understood role and has become secure in their relationship. The loss of one wicket and replacement of the established partner with a new batsmen, upsets that equilibrium, making the surviving partner struggle to adapt to a new role and so prone to dismissal. An even more extreme psychological explanation could be that the surviving batsman is grieving for the loss of the established partner and subconsciously wants to re-join them – analogous to the elderly couples whose deaths follow fast upon the other.

But before I indulge in any more psychology, there’s a more basic question to be asked: is there any truth in this cricketing received wisdom that the end of a lengthy partnership often results in both batsmen falling quickly?

To test the theory, I have taken as a sample all Test partnerships of 200 or more since July 2007. I have recorded whether the surviving batsman was the next, the second, third, etc wicket to fall after the partnership ended; how many runs were scored and overs elapsed between the dismissal of the two partners.

I have also taken a control sample of other partnerships (96) to compare the aftermath of a large partnership with randomly selected partnerships (footnote 1).

There were 98 double-century partnerships in this period, 8 of which were unbeaten and so excluded. The fate of the surviving batsman after a 200+ run partnership ended is shown below. 24% (control: 21%) remained not out. 44% (control: 41%) were the next batsman to be dismissed, which is less than the one in two chance of a random result and lower still than the received wisdom of partners falling in quick succession after a lengthy alliance. The results of the control sample are similar, suggesting that the surviving batsman is not much more likely to be the next wicket to fall after a large partnership than any other partnership.

partnerships1-page-001

How long was the portion of the surviving batsman’s innings that remained? 85% (control: 82%) were still batting four overs after the partnership ended; 62% (control: 62%) when ten overs had elapsed. In terms of runs, 84% (control: 86%) added at least 10 runs; 62% (control: 65%) were still batting with the score 30 runs on. The majority of surviving batsmen are not falling hard on the heels of their erstwhile partner. The length of their stay after a major partnership does not differ significantly from the control sample of partnerships

partnerships2-page-001

These figures point to the received wisdom about partners falling one after the other not being supported by the evidence.

I had sought a psychological explanation for a batsman falling soon after his long-standing partner was dismissed, when I should have been looking for a psychological explanation for cricket viewers believing this to be a commonplace. That phenomenon is known as ‘confirmation bias’ and it comes about because our memory is biased to remember the ‘hits’ (Jayasuriya and Mahanama) but not the ‘misses’.

——————————–

Footnote 1: the control sample was drawn from some of the same matches as those involving the double-century partnerships. If the large partnership was for the first wicket, the control figures were those of the other first wicket partnerships in the match.

Acknowledgement: Gabriel Smith (no.1 son) assisted in the collection of data for this post.

Advertisements

Tags: , , , , , ,

About chrisps

TouchlineDad to three sporty kids; cricket blogger and coach; and the alpha male in our pride.

5 responses to “What happens when a partnership ends”

  1. Russ says :

    Good work Chris (and Gabriel). I like your use of a control from the same innings. Very neat solution to a problem. And a neat result. Shows, as usual, that if you model cricket a series of completely independent events (balls) with probability derived from relative skills and the conditions, then you won’t go too far wrong.

  2. Alex Braae says :

    Very interesting post, but I have to ask: If you eliminate evidence for phenomenon in cricket supported by confirmation bias, then what will commentators prattle on about?

    • chrisps says :

      Alex, I have a colleague who, whenever he hears someone say rhetorically ‘chicken or egg?’ interrupts them with the response ‘egg’. It’ll take something similar in the commentary box to stop the ex-players repeating cricket clichés unsupported by evidence. Many thanks.

Trackbacks / Pingbacks

  1. Do breaks in play take wickets? | Declaration Game cricket blog - January 30, 2016

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: