August 13, 2014

Horse 1734 - The Declaration: A How To Guide

Cricinfo is useful because of the myriad of statistics it carries. No doubt it probably has complete scorecards for every Test Match going back to 1877. Of the 2135 matches to date (as at 10th Aug 2014), there is one statistic which it can not possibly determine and that's simply because it is based on future expectations - the declaration.
The question posed about making a declaration is almost never one of what has been successful but what will be successful. I believe I have the perfect guide to making a declaration in a Test Match and surprisingly, it has nothing to do with the number of runs anyone has.

The problem with Cricinfo's stats is that they deal in things like runs, overs and averages; they almost never deal with that specter at the feast - time. Time though is one of those things which a Test Match runs on. The crowd is certainly aware of it and if you look at the number of wickets which fall immediately before the end of a day's play or just before the end of session, the stats kind of also hint at this unacknowledged fact.
Having said that, it should be obvious to all that the only way to win a Test Match is to have the opposition complete two innings. That usually requires taking twenty wickets but if they have declared their either or both of their innings, that might not follow.
Making the opposition complete those two innings requires a handle on that elusive one thing about a Test Match which is known, time. It is known from the outset that there are five days in a Test Match and as such, the timetable for when you should make a declaration follows very nicely.

First Innings:
Score as many runs as possible.
The declaration should come on Day 3 and on the 45th over of the day. At that point there are exactly two-and-a-half days of play left. A first innings declaration will require the bowlers to bowl the batting side out twice and that time will be needed. If the opposition's first innings is a flop and the follow-on can be enforced, do so; a follow-on results in victory 92% of the time and not doing so only results in victory 68% of the time.

Second Innings:
Score as many runs as possible.
The declaration should come on Day 4 and on the 67th over of the day. At that point there are one-and-a-quarter days of play left. A second innings declaration will only require the bowlers to bowl the batting side out once and that time will be needed.

Third Innings:
Score as many runs as possible.
The declaration should come on Day 4 and on the 67th over of the day. At that point there are one-and-a-quarter days of play left. A third innings declaration will also only require the bowlers to bowl the batting side out once and that time will be needed.

Fourth Innings:
All fourth innings are only chasing down the target set for them. Unless the captain for some reason actually wants to lose the match, there is no reason to declare a fourth innings. I couldn't find any evidence that anyone had ever declared a fourth innings in Test history; I suppose that any captain who is foolhardy to do such a thing would immediately be investigated for match fixing.
There is an argument that it could conceivably be done at county or provincial level but only really if you wanted to rig a league table to make an impending knockout phase of a competition easier for yourself*.

Making a declaration as I see it is almost entirely dependent on time. A team which is in the place where a declaration seems like a good idea, should leave sufficient time to allow their bowlers to take the necessary wickets for victory, bearing in mind that every single batting side in theory is only ten balls away from total collapse.
If there are 450 overs in a Test Match, then there should be roughly 112.3 overs in an innings. Actual start times will vary from country to country and even venue to venue depending on if the ground has lights installed or not. The number of actual overs remaining is materially less important than time. Because cricket is very much a mind game, the declaration itself is a weapon and I think that if a side which is batting, leaves a whiff of victory lingering in the air for the opposition, that they're likely to start biting. If a declaration is left too late, then the whiff dissipates and the whole match has the danger of turning stale.
If you do happen to care about runs scored, then the average for all batsmen in test matches is 2.83 runs per over which works out to be 254.7 runs per day. The test of how many runs are needed is really a material test against that standard; which by the way is up from 2.61 runs per over and only 234.9 runs per day, thirty years ago. The question of how many runs are needed should then be drawn up against that.
The thing is that I can make wild judgements like this because I'm not actually out on the field of play during a Test Match. I am a cold number cruncher who has the benefit of looking at what works on paper; cricket is not played on paper, it is played on a green oval, by players with better skills than I... at cricket... but maybe not at maths... unless they like a really good maths person.

*In the 1954 FIFA World Cup, I think that West Germany deliberately threw their match against Hungary and lost 8-3. Hungary topped the group and met Brazil in the knockout round; whilst West Germany would go on to play Hungary and subsequently win the tournament.

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