channel4.com - Howzat - Get to grips with the numbers in cricket

A player's performance - both current and career-long – is under constant scrutiny by the statisticians.

Performance in a single match
Assessing a player's career

Performance in a single match

There are certain landmarks that cricketing custom deems significant in a match. These are:

These achievements bring applause from the crowd, although players who score lots of 50s but fail to convert those 50s into 100s are often regarded as somehow under-achieving.

The statistics of a player's career invariably record how many 50s and five-wicket hauls the player achieved. However, the raw statistics rarely tell the whole story. The context of a performance is also important. Take the following innings, for example:

Mike Atherton (England versus West Indies, second innings at The Oval in 2000) scored 108 runs. He has often scored more runs than this, but the commentators at the time described this innings as one of his finest, 'worth a double century in normal conditions'. What did that mean?

So for all of these reasons, Atherton's innings was a truly great one.

There are some cricket statistics that do attempt to mathematically evaluate an innings using more than just the batsman's score, for example:

Assessing a player's career

Players are not usually assessed on the basis of one match, but more on their entire career. There are many ways of rating a Test player. To show this, here are some real statistics for several current Test batsmen as at 1 July 2001:


Runs in career		Runs in career / Inning in career		Runs in career / ('Innings' in career minus Not outs in career)		Runs in 2001 / Completed innings in 2001
Atherton	7507	Tendulkar	51.3	Tendulkar	57.2	Hayden	79.6
Tendulkar	6919	Lara	46.3	Lara	47.7	Thorpe	71.0
Lara	6533	Hayden	38.8	Thorpe	41.4	Laxman	60.4
Thorpe	4476	Atherton	37.2	Hayden	40.2	Tendulkar	55.9
Laxman	1438	Thorpe	36.1	Atherton	38.5	Lara	38.6
Hayden	1085	Laxman	33.4	Laxman	36.0	Atherton	25.2
One disadvantage of this method is that it's clearly easier to score a lot of runs if you play more matches.		This may seem a fairer method, but one flaw in these averages is that they penalise a player who scores 0 not out in an innings when he hasn't done anything wrong.		This is a fairer version of the previous method using completed innings (ie, innings minus not outs).		A simple calculation to rank players according to their current form. Notice this is very different from the ranking according to runs in career!

A more sophisticated ranking needs to make allowances for players who are normally great, but have suffered a setback in their form very recently (Atherton for example). To do this, we need a weighted average that gives more credit to recent form but doesn't ignore past greatness. A simple weighted average can be worked out like this:

Runs in 2001 count 100%
Runs in 2000 count 50%
Runs in 1999 count 25%
Runs before 1999 count 10%

However, it is a little arbitrary to say that 100 scored on 1 January 2001 merits twice as much credit as one scored a week earlier.

The PwC World Ratings use a more sophisticated average that decays each innings by 4% as you go back in time. This smooths out the jumps in the earlier example and works like this:

Most recent innings counts 100%
Previous innings counts 100% x 0.96 = 96%
Innings before that counts 100% x 0.96 x 0.96 = 92.2%
Innings before that count 100% x 0.96 x 0.96 x 0.96 = 88.5%
And so on.

In the PwC system, players' innings are also weighted according to the opposition strength and run levels in the match. By this calculation the batsmen rank as follows:

	Runs in career	Innings in career	Not outs in career	Runs in 2001	Completed innings in 2001
Mike Atherton	7507	202	7	227	9
Sachin Tendulkar	6919	135	14	503	9
Brian Lara	6533	141	4	463	12
Graham Thorpe	4476	124	16	497	7
Venkata Laxman	1438	43	3	604	10
Matthew Hayden	1085	28	1	557	7

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