Cricket stats

More or Less from the BBC (hosted by Tim Harford, the undercover economist) is an excellent source of interesting items on statistics. Last week's programme had an item on misleading statistics from the recent Ashes test series. Here's another one, in my opinion, arising from the last test match of the Ashes series:
Almost all commentators regarded Australia's target of 546 to win in their second innings as virtually impossible to achieve. The argument is simply that the previous highest winning total in the fourth innings was 418 (W.Indies vs Australia in 2003). However I believe this is largely a statistical artifact. To register a high winning fourth innings score certain things must hold simultaneously. First, obviously, the target must be big. Secondly, there must be enough time to get the runs. I strongly suspect that the conjunction of these two events is pretty rare (especially when the target is set by the other side, who arguably should not set gettable targets).
It would be interesting to know how many times there has been a target of say over 500 and more than two days left to play (as we just had at the Oval). Confirmation that this is unusual comes from looking at highest fourth innings totals: 17 of the highest 30 in test cricket have occurred since 2000 (8 of these since 2008). Until recently teams scored at a much lower rate than we see these days---there simply wasn't time in a 5 day game to be set a huge target within 3 days if teams score at say 250 a day (when there was no time limit England got to 654 for 5 in Durban before they had to catch a boat back home). Technology and the one-day game seem to have increased scoring rates, so 350 in a day is not unusual. So it is not surprising that few large scores were posted until recently. The point is that at the oval, there was plenty of time and the wicket wasn't that bad. I don't think the records were very relevant. Ricky Ponting made it clear afterwards that he and Mike Hussey were having no problems batting. Arguably it was only the two crucial runouts that turned the game.