Pappus' plane - cricket stats

Tomorrow I'll be heading to London, where I'll be until the end of the week. For the first time in almost a year, I'll actually watch a day of cricket. I don't mean that I haven't been to a cricket ground for a year (it's been longer than that) — I'm including television as well. It's been a while. So let's hope that the rains stay away on Wednesday for the first day of the Championship, and in particular Surrey v Lancashire.

So before I disappear for a week, here's a quick run-down on what I've done on getting your eye in in the last couple of days. I worked out how to script gretl, so I've now got effective average curves for pretty much all major batsmen (there are a few with really bizarre hazard functions that refused have my curve type fitted to them).

There doesn't appear to be any substantial differences in effective average on nought between openers, all-rounders, and others.

All-rounders might behave differently in terms of how they perform once they're off the mark, but I need to have a bit of a more careful look.

I'm wondering how much of the variation in effective average on nought is due to luck. Looking at batsmen who average over 40, the average proportion of ducks is about 0,061. Using that and applying the binomial theorem with 120 innings (the average number of innings across the dataset), you get an expected standard deviation of 0,022. The actual standard deviation is 0,024. About 60% are within one standard deviation of the mean, a little less than would be predicted (68,7%) by the normal distribution. (I'm assuming there's enough innings for the normal distribution to be a good approximation.) So it looks like there are real differences between batsmen in terms of ducks, but they might not be so big.