## Wednesday, March 6, 2013

### Declarations and Nightwatchmen

A couple of years ago, I supervised an Honours research paper by Johnny Sharland (now at the RBNZ) on the efficacy of using a nightwatchman in cricket. For the uninitiated, a nightwatchman is a player (usually a bowler**) who is sent in ahead of a better batsman when a wicket is lost near the end of the day in a multiple-day cricket match. The idea is that a batsman is at most risk of getting out at the start of his innings, so the nightwatchman's job is to protect the better batsman from having to start his innings at the end of the day, and then make a fresh start the next morning.

We wanted to compare the cost to a team of changing the batting order to the benefit of a reduced probability of dismissal for a top-order batsman, to calculate when and if the benefits would outweigh the costs. As it turned out, the benefit-cost calculation turned out to be completely uninteresting for an unexpected reason: We could find no evidence in a database of 200 test matches that having to make a second start in any way increases the probability of a top-order batsman being dismissed early in his innings. That is, the key variable that determines a batsman's probability of being dismissed is how many balls he has faced in that innings, not how many he has faced that morning. The cost-benefit calculation then becomes irrelevant, as there is simply no benefit from using a nightwatchman to balance against the costs.

I thought this made the results uninteresting, and so did not seek to write it up for publication. The latest test between Australia and India, however, makes me think that maybe that decision was wrong. The Australian captain, Michael Clarke, has just earned the unenviable distinction of being the first ever captain to declare his first innings closed and then go on to lose by an innings.* Clarke declared the Australian innings closed when they were 9 wickets down with 5 overs remaining on the first day. It seems that his reasoning was that Australia's last two batsmen were probably not going to be able to score many runs anyway, and by declaring he would force the Indian batsmen to start their innings that night and make a fresh start the next morning. Johnny's results suggest that there was no expected benefit to this declaration, only a cost. Maybe a shortened version of his paper concentrating only on the estimate of the second-start effect would be interesting.

* Explanation for non-cricket fans. Each team bats until 10 of its 11 batsmen have been dismissed. The 10th dismissal signals the end of the "innings" after which the other team gets a chance to bat and score more runs. The two teams get two innings of up to 10 dismissals. A captain, however, can choose not to use it full allotment and declare its innings over before 10 batsmen have been dismissed. If a team scores fewer runs in its two innings combined than the opposition scores in its first innings, the opposition does not need to bat a second time and is said to have "won by an innings".

** For an example of a batsman being used as a nightwatchman, check out this match (which is also notable for featuring Bradman's first test century). Batting on a notorious Melbourne sticky wicket, England sent specialist batsman, Douglas Jardine, in ahead of his normal batting position in order to protect superstar batsman, Wally Hammond.

#### 8 comments:

1. Even with no second-start effect it could still have been a wise decision if batting at the end of the day is significantly harder than batting in the morning.

2. I do think it is pretty interesting that there is no second-start effect. I guess if there is no second-start effect from batting a second day there is also no effect from lunch and tea breaks? What about extended rain delays? And do batsmen have better starts in their second innings of a test match?

3. We didn't look at other breaks as we figured that if there was no effect from starting after an entire night's break, there would be no effect for smaller breaks. (I know there is an old adage that the best change bowler is the man who carries the drinks, but I think that is just confirmation bias at work.)

For differences between first and second innings, the effect would be confounded by the very real changes in conditions that occur (in both directions) between innings.

4. I agree, in principle. Nightwatchmen and/or declarations can make sense if the objective is to strategically use varying conditions as opposed to the fresh-start effect. (Another classic case on a Melbourne sticky. Bradman telling is bowlers not to take wickets, England then declaring well behind Australia, and then Bradman opening with his 9, 10, and 11 batsmen (1936 Ashes series).

But I don't think conditions variation would have been significant in the recent India-Australia test. Another possibility is that Clarke thought he would get three new ball overs with fresh bowlers, and then another fresh-bowler set of overs the next morning. (That effect wouldn't exist with nightwatchmen.) But I have to think that the shine, to the extent it has any effect on that pitch, would wear off well before the bowlers tired, anyway.

5. I am interested in your test. From your blog post, I gather you run a linear probability/logit/probit of dismissal explained by number of balls faced, and number of balls faced after the last major interval. Is that correct? In this regression did you include batsman fixed effects? You find that the coefficient on the number of balls since the last major interval is insignificant.

I expect the probability of being dismissed rises with the number of balls faced, due to limited powers of concentration, and the increasing likelihood (with greater numbers) that you get a unplayable ball. But if there is such a thing as the batsman getting in, getting used to the pitch and conditions, there is also a lower probability of dismissal once he has stayed in the crease for a while. Finally, if there is declining bowler performance from tiredness, there should be a higher probability of dismissal after major intervals. How do you model and test these competing effects?

6. Gulati. You are right about the base regression being a probit with both balls faced and balls faced since the interval as RHS variables. We did not include batter fixed effects due to not having sufficient data. I can't recall now everything we tried. The results came out opposite to what we expected, and didn't give us the cost-benefit calculation that we wanted to write about, and so we tried to see whether there were confounding variables getting in the way. One thing we found (and expected) was that the hazard rate is highly non-linear in balls faced, with batters' survival probabilities rising at first as they get their eye in and then declining as tiredness sets in. The nightwatchman theory is all about hazard rates early in an innings, and so we simply dropped all observations after a certain number of balls had been rather than trying to torture the data into fitting a particular non-linear (and non-monotonic) functional form. Finally, we didn't control for bowler tiredness, but if it is a factor, it should show up in the data and we couldn't see it. I suspect that after a wicket, the bowling side's adrenalin picks up momentarily and so creates a similar effect to starting afresh after a break.

7. Another possible line of thought is at the end of the day the batsman will be naturally highly defensive allowing the fielding team to be highly attacking. Sending a night watchman in would at least shield your top order batsman from this. My reading of your comment "We could find no evidence in a database of 200 test matches that having to make a second start in any way increases the probability of a top-order batsman being dismissed early in his innings" suggests this would not be the case though.

8. I agree that the effect you describe would be expected to show up in the data, which it doesn't. But also, from a pure theory point of view, if batting at the end of the day is riskier than the start *because* batsmen become more defensive allowing bowlers to be more attacking, the best response is to simply stop being so defensive!

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