Many of you would have seen the statistical exercise undertaken by S Rajesh at cricinfo, where he calculated the standard deviation of some of the top batsmen - showing how much they tend to deviate from their averages - thus trying to find a more balanced understanding of the real value of a batsman. Ofcourse, all this on top of the assumption that statistics still dont ever give the full picture.
I've been thinking about his analysis, and IMO although his Batting Index invention does throw up interesting figures, it still leaves out some obvious facts that can be incorporated.
For example, lets first collect the modern era batsmen that fall in his good and bad list (I won't take the batsmen of past, since its very tough comparing across generations as this batting styles have evolved so much over the time).
Good list : Kallis, Border, Arjuna, Thorpe, Chanderpaul, Boycs and Waugh
Bad list : Atapattu, Abbas, Jayasurya, Lara, Botham, Gibbs, De SIlva, Gooch, Crowe, Fleming
The first thing that struck me was that surely, batting position also plays a role in standard deviation? In the good list we only have Boycs as an opener, while in the bad list Atapattu, Jayasurya, Gibbs, and even Fleming in part, have been test match openers.
Even in the last list of the article, the *bad ones* since 2002, has Smith, Gayle, Sachin, Atapattu (and Fleming) from the openers' club.
An opener is more likely to get a good ball early on, especially on pitches and conditions favourable for batting, as compared to his other team mates. So while his average (runs per innings) are still important, since he, like any other batsman, should score big when he gets in, his standard deviation is going to be less of a factor. As long as he can maintain a high average. Sehwag is an ideal example, but I'm sure many other top openers around the world would fall in the bad list. What say?
Another aspect of the analysis is the real value of the batting index. While it is good way of judging the batsman's value, the question is - how high a value is good enough, and when does it start being *bad*? Hypothetically, a batsman with an average of 50 and standard deviation of 0 should be a great one - for he belongs to the good batsmen's club (averaging 50) as well as a batting index of infinity!
But in reality, this is a batsman who scores exactly fifty runs in every innings he walks out to bat in. How many real test teams, do you think, can afford such a batsman? Because, remember, even if we get this hypothetical genius in, he's the only one of his kind in the team. The others are bound to have their good and bad days. And this bloke would never ever bail the team out even when he's in good touch...since his counter stops at 50. For cricket, in reality is in a way about the inconsistencies of the players, isn't it? Real batsmen are all inconsistent, but the good ones make their good day count.
Consider this batsman, in contrast, to another averaging 35+ and a significantly low batting index. That means he makes those occasional big hundreds, and that gets the team into winning situations. Isn't the value of this player higher than the one above?
And, in a way, this whole equation is already settled in real life through team selections. A batsman constantly giving you 30-40 (or even 50) runs in each innings, time after time, is not really going to last long. For the selectors know that he's wasting away the good chances as well (when he gets his eye in) and sooner or later, the bad days are bound to come.
So...it does seem that no matter how well thought out the formula...statistics still never reveal the full truth!