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