UC’s media consultant loves cricket and so asked me if I could do something WASPish about the probability of McCullum scoring 300 runs in an innings. The resulting media release is here. (The request came before the start of play today when McCullum was already on 281, but I looked at it from the point of view of the start of his innings.) The guts of the conclusion was that you would only expect McCullum to reach 300 once every 4310 innings if he scored with his career average strike rate and dismissal rate, and that is before taking into account how unlikely it would be that the other batsmen around him would survive long enough to not leave him stranded short of the target.
This was just a bit of fun for a media release. If I was to do the job properly (unlikely, since it is not the sort of thing that results in a peer-reviewed publication), this is what I would like to do:
- Do a Kaplan-Meier estimate of hazard rates out of batting as a function of runs scored, rather than assume that a constant strike-rate and poisson dismissal rate apply at all times.
- Do a monte-carlo simulation using McCullum’s Kaplan-Meier estimates and other players’ dismissal rates to find a combined probability of McCullum and at least one other player surviving until McCullum had scored 300 runs.
- Try to estimate a joint distribution of survival rates and strike rates across games to take into account statistical dependence.