## Learning/thinking about statistics using examples from cricket…

Anantha Narayanan of cricinfo is helping me think through statistics like very few have. His previous two articles trying to figure consistent batsmen and consistent bowlers were superb. The main idea behind both was to look for  measures other than the popularly used  average to measure performances of batsmen and bowlers.

In his third piece, he digs deeper to evaluate bowlers. There is always this criticism that some bowlers top averages by taking most wickets against weak opposition. This is usually targeted against Murali in particular . This is biased in many ways as even Warne took most wickets against English sides whose record against spin was always poor.

So, he tries to figure quality of wickets and even quotes economics:

This is a follow-up to the bowler streaks article published last month. In addition to providing additional analysis on the topic by specifically responding to a couple of very nice queries, I have also attempted to present a new concept to get additional insights to the vexed question of “Wickets – how good are they?” In summary, akin to “Supply-side Economics” being presented as an alternate economic theory, I have tried to present this analysis as the study of bowling from the angle of the dismissed batsmen.

One often repeated query on the article centered on the number of wickets taken by the bowlers. Muttiah Muralitharan’s 800 was said to contain over 160 wickets against the so-called “minnows” while Shane Warne’s 708 wickets was seen to be more valuable since it contained only 17 wickets against these weaker Test teams. This argument seemed quite sound until I pointed out a fundamental error in this assumption. Is the wicket of Shakib Al Hasan less valuable than that of, say, Ishant Sharma? The former is a top batsman of a weaker team while the latter is a tail-ender of a better team. There was no response.

To solve this, I said that I would determine an index using the quality of batsman dismissed. This process will ensure that Shakib would get his due credit as a top-flight batsman with an average of 39.76, while Ishant will be accorded treatment deserving his batting average of 8.89. At one stroke this would solve all problems, including dismissals of batsmen like Bevan Congdon, Ravi Shastri or Roshan Mahanama – average batsmen from top teams.

My first idea was to accord a weight to each wicket and determine a weighted wicket value. I took some steps towards that. Then I suddenly realised that the numbers 800 and 708 are etched in the minds of cricket followers, like 6996, and it would be inadvisable for me to say that Muralitharan has 768.2 wickets or that Shane Warne has 691.1, or that Jerome Taylor has really taken 142.3 wickets, not 130. So I decided not to touch the wickets measure. Rather, I would come out with a new measure called “Weighted Wicket Index” (WWI), which would be an additional pointer.

….

Hence context is important. But I use context mainly in ratings work. So I decided that I would consider only the batting average for determining the WWI. In general, it is important to get the wickets of the top batsmen. However, Ricky Ponting at home had an average of 57 and away, it dropped to 46.4. Brian Lara had figures of 58.6 and 47.8 respectively. Mohammad Yousuf was king at home at 65.3 and a commoner away, at 46. It was far easier to dismiss these top batsmen, and others, away from home. Hence the average I use is location-dependent.

With this lengthy preamble, let me move on to the tables. The methodology is simple. For each bowler, add the location-based average of the batsman dismissed for all dismissals and divide by the number of wickets. Nothing can be simpler.

Context is hugely important. We just take stats results on face value without getting into context.

Interestingly. Mohammed Asif tops the list based on this WWI ranking. For India, Zaheer tops the list:

If anyone thought that this table would be dominated by the Muralis, Kumbles and McGraths of the world, they are in for a shock. Those leading bowlers are required to bowl right through the innings, taking wickets of batsmen of different levels. They have to capture top-order wickets, the settled batsmen in the middle order and the late-order batsmen. So this table is dominated by those bowlers who are not necessarily the leading bowlers. They take top wickets and then leave it to the others to clean up. Only one bowler in this table has crossed 300 wickets.

The table is topped by Mohammad Asif. This one-of-a-kind pace bowler from Pakistan has taken 106 wickets at a fairly low cost of 24.37 runs per wicket. He has complemented this with the quality of batsmen dismissed. His WWI is an amazing 36.64. This is some achievement. That means that the average quality of batsman dismissed by Asif is Denis Compton (away), Mohammad Azharuddin (away) or Ijaz Ahmed (home). I suggest that the readers take a minute or two to digest this fact.

Surprisingly Asif is followed by three very average spinners – Nicky Boje, Paul Harris and Ashley Giles. They have completely forgettable averages exceeding or nearing 40, but have dismissed many top batsmen, most probably those batting in the middle order. I get the feeling that when it came to the lesser and late-order batsmen, the other better bowlers in the teams came to complete the task.

Jerome Taylor, the West Indian fast bowler, is fifth in the table with a WWI of 35.57. On many occasions he was the only attacking bowler in the weakened West Indian line-up. Trent Boult, the New Zealand fast bowler comes in next. His WWI is an impressive 35.34. The low number of wickets helps a lot, in all these cases.

Then come the most important bowlers in this table: Zaheer Khan, Ryan Harris and Andrew Flintoff. They all have WWI values around the 35 mark. Each of these formed the pace-bowling spearhead of their respective teams. That means that each time these bowlers dismissed a late-order batsman, say at an average of 15, they made up with a real top-order batsman, at 55. Mervyn Dillon completes this interesting quartet of pace bowlers.

He further uses variants of WWI and comes up with more rankings.

The crucial lesson behind all this is how different measures tell us different stories. Such is the nature of statistics. So, we should know both strengths and limitations of the measure we use in our analysis. The focus usually is on the pluses which misses the point. No measure can capture the entire story.

Superb stuff.