Thursday, March 26, 2009

Cricket: the "nightwatchman" strategy

I don't understand cricket all that well, but I think I get the gist of this New Zealand article about the "nightwatchman."

Cricket fans reading this, please correct me if I'm wrong, and forgive my use of the wrong terminology. (For instance, when a cricketer bats, can you also say he "hits"? I hope so.)

The idea, I think, is this:

In cricket, a batter will hit until he makes an out, and which point he is replaced and will not bat for the remainder of the innings. Batters hit in pairs. Once ten of the eleven men are out, that leaves only one, who can't bat alone, and the innings ends.

Outs can be infrequent; typically, a batter can hit for 25 runs or more before making out, and good batters occasionally hit for 100 runs or more. Therefore, an innings (or game) can go on for several days.

The best batters normally come to bat first. Sometimes, one of the better batters will go out late in the day. When that happens, the team will sometimes send up a worse batter to end the day. That batter is called the "nightwatchman."

Why would they do this? According to Wikipedia, the idea is that the end of the day is a bad period in which to hit – the next batter may be tired, or the light may not be good. Also, if they do send up the good batter, and he is quickly put out, the psychological effect might hurt the team.

And so, they sometimes put in an inferior batter, who can waste some time between now and dusk, so the better batter can be saved until tomorrow.

Now, if all this is correct, what would be the strategic advantage? Every batter has to hit eventually, and there is no inherent benefit of putting good batters together as in baseball, because every batter comes up in the same situation (the equivalent of "bases empty"). And the psychological rationale seems weak to me.

That leaves the "hard to hit in the dark" hypothesis. If the dim light causes all players drop by the same percentage, then it makes sense to put in the batter who normally bats for 10 runs than the one who normally bats for 35 runs. Better to lose X percent of 10 then X percent of 35. But isn't it also possible that it's the other way around? Maybe the better the batter, the more able he is to handle the adverse conditions.

Also, you have to keep in mind that every batter gets the same chance to bat, except the one who's left after ten men have gone out. The longer you wait before putting in your best batters, the greater the chance it'll be one of those good ones who doesn't get to finish. So, generally, you'd want your better batters first.

So which is the better strategy? This seems like a good problem for cricket sabermetrics. The original article points to a study by Charles Davis, who (I get the impression) is cricket's foremost sabermetrician.

In that study, Davis finds that teams who used the nightwatchman strategy (late in the day after two men had gone out) undershot expectations by 25 runs over teams who didn't. It wasn't because the nightwatchmen didn't do well – they did about the same as their career average lower in the "batting order." So it must have been ... what? Maybe stranding a better batter after the last out? That still seems like a lot; the difference between a good batter and a bad batter might be ... what, 50 runs? And there are still 8 outs (wickets) left in the match. So the fraction 25/50 seems too large under the circumstances.

But look at Davis's graph: an increase of 100 runs scored in the first two wickets leads to a final score only about 35 runs higher. That shouldn't be the case, should it? Wickets are independent except for the identities of the players involved. Consider a baseball analogy: if the Houston Astros score three runs in the first two innings, wouldn't you expect their final score to be three runs higher than if they scored zero runs in the first two innings? Why isn't that happening in Davis's study? The only thing I can think of is that if you score more runs in the first two wickets, it's because you've used up your very best batters, and all that's left is your weaker ones. In that case, it means that team strategy is a huge factor in the distribution of scoring. And so, when you divide innings into "nightwatchman" and "non-nightwatchman," you can't assume the two groups are identical, as Davis did.

Again, please correct me if I've assumed something incorrectly, and I'll update this post.

P.S. Here's one intro to how cricket works. There are lots of others.

Hat Tip: Rod Nelson of SABR



At Thursday, March 26, 2009 9:45:00 PM, Anonymous Anonymous said...

One thing you might be missing is the impact of time. Assuming that this is a Test Match (top-level full international match), then the game lasts fifteen sessions over five days. If the game hasn't been completed by then, regardless of the score, it's a draw.

What that means is that if your first batsmen score a couple of hundred runs, they'll occupy the crease (be in) for a long time - easily several hours - and the remainder of the side will often find themselves under an obligation to score faster, and thus play more riskily, in order to avoid the game petering out to a draw.

You can actually choose to end your team's innings at any times: that's called a declaration. If you've got a big enough lead that you think you can't be overhauled, then it's good tactics to give yourself as long as possible to bowl the other side out.

As for tactics, another significant factor is the state of the ball and the pitch. The pitch will get roughed up over the course of the match by the batsmen's feet, which will make the bounce less even and will help the slow bowlers spin the ball further: even within an innings, the ball is only replaced per eighty overs (540 deliveries).

When the ball's new, hard, and shiny it favours fast bowlers, who'll often aim to hit or intimidate the batsmen by bowling balls which bounce towards their heads at 90mph - there's no rule per se against striking batsmen in cricket. However, when the ball's old, it'll sometimes swerve dramatically for the faster bowlers ("reverse swing"), and it'll spin off the pitch more effectively for the slow bowlers (leg- and off-spinners). Where batsmen play in the side often depends on what sorts of bowling they play best against. Opening batsmen (lead-off hitters) are good against hostile fast bowling; middle-order batsmen (between maybe 5 and 7) are typically more aggressive and often play better against spin.

Another factor: nightwatchmen are usually specialist bowlers. A typical cricket team consists of five or six specialist batsmen, a wicketkeeper (think catcher, and these days they all have to be effective specialist batsmen too), and four or five specialist bowlers, but it's like the National League: everyone bats, and some bowlers - Monty Panesar for England, say - are really horrible batsmen.

So here's a potential scenario which might explain some of this. If you're batting down to seven (have seven good batsmen), and you promote a tail-ender - your ninth, tenth or eleventh batsmen (average maybe 10, maybe worse; Matthew Hoggard would be a good example of a recent one in international cricket) to three or four as a nightwatchman, you're pushing one of your effective batsmen down from seven to eight, where there are only three wickets (outs) left, and the batsmen there are likely to only get thirty runs or so between them. That could easily cut ten runs off what you'd expect (assuming your number 7 averages 40 - which is a bit generous, but about the right size).

On top of that, the nightwatchman is going to survive by playing defensively - blocking, because in cricket if you don't want to run, you don't have to - which slows down the scoring rate, forcing the rest of the team to play faster and more riskily.

Players who can both bat and bowl well, like South Africa's Jacques Kallis or England's Andrew Flintoff (both fast bowlers), or New Zealand's captain Daniel Vettori (a left-arm orthodox spinner, in other words a left-handed slow bowler), are disproportionately valuable as a result - they effectively give you the bowling you need while giving you extra batting firepower.

Cricket's a really complex game.

At Thursday, March 26, 2009 9:51:00 PM, Blogger Phil Birnbaum said...

Good stuff ... thanks for the explanation! I did consider the "declaration" (but didn't know what that was called), but the Davis study only considered games that were "all out." I assumed that meant everyone batted ... is that correct?

It now occurs to me: wouldn't that rule out games where the winning team batted second, and the match ended when it took the lead in the last innings? That would explain why the scores were so low even after a 200 in the first two wickets -- selection bias omitted the games where the team played well enough to win without going "all out."

Do those explanations make sense?

At Thursday, March 26, 2009 10:11:00 PM, Anonymous Anonymous said...

I suspect you're onto something there.

You're going to underselect teams who have good second or fourth innings, and over-select for teams who do badly going first or third; as well as eliminating any innings where a side go 600-4 dec or whatever and win dramatically - innings victories (when a side doesn't even need to bat twice, because they got more in their first innings than the other side got in two goes)'d be knocked out too.

It wouldn't amaze me if that wound up meaning that middle-order collapses (where the batsmen after the openers, but before the tail, temporarily lose the ability to find their backsides with both hands, let alone anything more complex; if you follow England, you get used to it...) were systematically over-represented in his dataset, which'd give you this kind of result.

At Friday, March 27, 2009 5:06:00 AM, Anonymous Anonymous said...

As both a cricket and stats geek, wonderful post!

Just one little bit, which I don't have any data for: "there is no inherent benefit of putting good batters together". I see where you're coming from with this, but there is certainly a perceived wisdom that it's a good idea to have two good batsmen batting at the same time: if there's a good batsman and a poor batsman batting at the same time, the opposing team will tend position its fielders defensively (trying to prevent runs being scored, rather than to get the batsman out; unlike baseball, the effect of field placings certainly is significant on runs scored/wickets taken) for the good batsman, but become more aggressive for the bad batsman (who isn't likely to score so many runs whatever). The idea is that this has the effect of getting the bad batsman out without too many runs being scored by the good batsman.

Whether this is a good idea from a game theory point of view or not, I don't know, but it's definitely a tactic which is often employed.

At Friday, March 27, 2009 10:03:00 AM, Blogger Phil Birnbaum said...

Jorallan: thanks! But the way you're describing it, it seems the strategy depends only on the batter and not his partner. Am I misunderstanding? If you have a weak batter, won't you play him aggressively regardless of how good the other batsman is?

At Friday, March 27, 2009 12:42:00 PM, Blogger Philip Kendall said...

If you've got a weak batsman, you attack. The question is what to do if you've got two strong batsmen: setting defensive fields isn't going to win you the match. There's a well known idiom in cricket that you have to get the other side out twice to win - many matches are "saved" by the team in a losing position by playing out time, converting a loss into a draw. In some situations, a draw may be fine - one obvious one is you're 1-0 up in a series with one match to play - but in others, you may need to win.

In the situation where you do need to win, if you've got one weak batsman and one strong one, you can attack the weak batsman and hope that the strong batsman "runs out of partners", thus finishing the innings with the strong batsman having a lower score than he would have otherwise. However, this obviously isn't going to work if you've two strong batsmen, so the tactics you apply to one batsman can vary with their partner.

Another example of this is "farming the strike": if you reach the situation where you've got one strong batsman and one weak batsman trying to play out time, you obviously want to bowl as many balls as possible at the weaker batsman. The crucial point here is that overs are bowled from alternating ends of the ground, but the batsmen change ends only when they score an odd number of runs. If you're bowling to the good batsmen, for the first few balls of the over you'll put the fielders a bit deeper to encourage the "easy single" and get 3 or 4 balls at the weaker batsman. For the last couple of balls, you try to prevent the single so you can get a whole over at the weaker batsman when the next over is bowled from the other end of the ground.
With two good batsmen, you wouldn't go through any of that.

(The previous paragraph is based on the assumption that the weaker batsman won't score any runs at all. The same still applies to a reduced degree in the more realistic situation that they're less likely to score a run on any particular ball than the good batsman).

Hoping this makes some kind of sense: as anonymous said at the top, cricket can be really complex at times.

At Friday, March 27, 2009 3:03:00 PM, Blogger martin said...

The reason that the nightwatchman seems like a reasonable idea is the concept of 'getting your eye in'.

When a batsman first comes to the crease he is quite susceptible to getting out cheaply. But as he gets used to the bowling, the bounce of the ball, the seeing conditions etc he gets better. This is an accepted fact in lay discussion and is also backed up by statistics (see discussions about 'getting your eye in' at

When you come in for a short time at the end of the day you risk your good batsman getting out for little gain and then he has to come out the next day and get his eye in again.

The theory is that bad batsman and good batsman are about equally good at not getting out in a short time period.

I am against the nightwatchman for other reasons though. If he makes it to the next day then he usually takes up time that your better batsmen could be using, runs poorly between the wickets, costing runs and possibly wickets. And as mentioned above, your number 6/7 batsman who are good players are pushed down the order and are often stranded. Especially New Zealand, who have Dan Vettori (averages 40 recently) batting at 8 and Chris Martin (averages about 2) at 11 can't afford to push their good batsmen even further down.

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At Saturday, March 28, 2009 8:37:00 AM, Anonymous Anonymous said...

Just digging around a bit this morning, a different analysis ( comes out at the nightwatchman making pretty much no difference at all. Just throwing it out there.

At Thursday, April 02, 2009 6:18:00 AM, Blogger philistine said...

Just been directed here by

One other apparent advantage for the nightwatchman is that he is expected to take as much strike as he can which has the benefit of protecting the established batsman.

Again this seems highly dubious as a tactic as at any other stage of the game, the senior batsman would be expected to protect the lesser player. It's as if the batting team is trying to lose another wicket and score as few runs as possible for the rest of the day.

With two wickets down and less than half an hour to play, all of a sudden your number 10 batsman becomes completely expendable? If they had 8 wickets down, they would be trying to eke out every run they could.

At Tuesday, June 30, 2009 7:12:00 AM, Anonymous Jeff said...

Just come across this blog - excellent stuff !!

Regarding night-watchmen, I believe that one of the main reasons for using them is to avoid having the main batsman make "2 starts". It's well known that batsmen are most vulnerable early in their innings (even the best batsmen make a fairly high proportion of very low scores (eg Bradman, the best batsman (sportsman??) ever, who averaged 100 runs for each out, scored less than 10 runs in 26% of his innings.) This is usually put down to having to "get their eye in" - ie get used to the bowling, the conditions etc.
If a batman has to start his innings late in the day, even if he survives until the close of play, he will have to start over again the next morning - therefore doubling his most vulnerable time "at bat".

Using a nightwatchman helps to improve the chances of your better batsman only having to make one start per innings.

That's the conventional theory as I understand it.

The key to me, is "when" you should use a nightwatchman - ie how many balls should there be left in the day to optimise the benefit (if any) of nightwatchman.

This could depend on the individual batsman "at risk" - how good is he at making starts? For example, another great batsman of the past, Walter Hammond, only had 22% of his scores under 10 - so you might be less inclined to protect him than Bradman (for example.) Ideally you'd look at how many balls faced rather than runs scored - this data is available for modern cricketers (although wasn't in the early days - typical of the poor cricket stats available.)

In reality, I believe that night-watchmen tend to be used too early and are asked to survive too many balls.

I've not looked closely, but if I were a captain/coach I wouldn't use a nightwatchman until very late in the day (if at all), particularly as if a wicket falls in the final over (6 balls) of the day, then typically play will be called to a halt anyway.

Sorry to have rambled for so long...


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