Averaging averages
Daniel Vettori has just now been dismissed for 134. That is a stunning return on the decision to promote him. And it’s not just his own score of 134 that is worth celebrating. Vettori came in with the score at 136/4, with a first-innings lead in the balance, and departed with the score at 408 and a humongous first innings lead of 185. At 6 he can not only save an innings, he can also build big innings. This also allows Tuffey to fill the roll shepherding the lower order.
This 134, by the way, has pushed Vettori’s average over 30 for the first time (excepting his first few matches). It also pushes his average in the no. 6 spot up to above 40.
An average in the 30s is great for a bowler, good for an all-rounder, but pretty average for a batsman. So it is disheartening to note that 4 of the 5 batsmen that bat above Vettori have averages in the 20s. (Taylor, currently the world’s 9th best batsman, is the exception).
Of course, all of the junior batsmen have played so few tests that their averages are pretty volatile. Daniel Flynn for example has only dropped below 30 in this series and would be back up again if he scored a century in the next innings. Though the more innings they have, the more confident we can be that their average reflects their ability.
There is a statistical value that can measure how confident we can be about an average, called the standard error of the mean. The larger the sample size (in this case, the number of innings), the more accurate the mean (batting average in this case). The standard error of the mean is calculated (assuming several things about the statistical distribution) by dividing the mean by the square root of the sample size. So we should be able to get a measure of the reliability of a batsman’s average by dividing it by the square root of the number of innings played.
So Daniel Flynn’s average of 28.7 off 29 innings has a standard error of about 5.3. My very rudimentary and rather naive interpretation of this sort of standard error is that we can be only 63% certain that he is not batting at an average of 30 or higher and has just been unlucky.
For Guptill (avg. 23.5, 14 innings) we can be only 93% certain that his average shouldn’t be 30. Whereas for McIntosh, we can be only 79% certain that he is not hiding an average of 30 behind his current average of 26.41 off 18 innings.
Now, B-J Watling, this test’s debutante, has scored a mere 18 runs, giving him a disappointing average of 18. However, the standard error of this average is itself 18. This means that even with this poor start to his career, we can only suggest with 83% certainty that he won’t score 30 runs in every innings here on in.
(Any of this make sense?)
By the way, we can be 99.8% certain Flynn shouldn’t be averaging 40, but only 96% certain for Watling. Two ways of saying “definitely” I suppose.
