Don Bradman's Test Batting Average: Confidence Intervals and Prediction Intervals

Simon D. Angus, Dept. of Economics, Monash University (Feb 2019)

To accompany the online article entitled, How long before we break the two-hour barrier in the men’s marathon? published on 27 Feb 2019 at: https://theconversation.com/how-long-before-we-break-the-two-hour-barrier-in-the-mens-marathon-112505

Which accompanies a scientific report by the author, A statistical timetable for the sub-2 hour marathon, published in Medicine & Science of Sport and Exercise and is available, under open-access, from the publisher's website.

Running the code

We assume MATLAB is installed, with the Statistics toolbox (to get the inverse t-distribution). However, the code is very transparent and could be implemented easily in any mathematical or statistical software.

To run:

>> main

BRADMAN Test Analysis (alpha=0.050) ...
 --> total runs: 6996
 --> n* (all innings): 80
 --> n (minus 10 not-outs): 70
 --> average with ConfInt: 99.9, (71.0 to 128.8)
 --> prediction interval: -143.6 to 343.5

Note: since batting innings are bounded below at 0 (a 'duck'), the lower prediction interval can reported as 0. An extension of the approach would be to calculate non-symmetric intervals, which would likely respect the lower bound.