Pappus' plane - cricket stats

Russ pointed out a couple of things in the previous post. For those who missed the comments thread, here are the revised formulas for calculating uncertainties.

Batting: 0.9 * average / sqrt(# innings)
Bowling: 0.9 * average / sqrt(# wickets)

So, e.g., Mike Hussey becomes 68.4 +/- 9.5. About 68% of 'true' averages will lie within the range given. You need to double it to get it up to 95%.

I haven't made much of an effort to work out the underlying distribution of Australian players that Hussey comes from. To get a rough idea of what should happen, I found the mean and standard deviation of averages of Australian batsmen at batting positions 1 through 7, over the last ten years. There's a bit of a problem about what to do with players who only played a couple of Tests and averaged (say) 5 — clearly they could have averaged up around 20 or 30 if given more opportunities.

Anyway, I bumped those guys up to 20, and the result was something like mean 42, standard deviation 12. So, carrying on with the Hussey example, we crunch the numbers like this:

regressed average = (68.4/9.5² + 42 / 12²) / (1/9.5² + 1/12²)

uncertainty = 1 / sqrt(1/9.5² + 1/12²)

to estimate Hussey's 'true' average as about 58 +/- 7.

Let's just hope that he can score runs in India.