The trouble with answering "no" to that question is that it rules out regarding as "proper" victories many of the great triumphs of the past: does England's legendary Botham-inspired 1981 Ashes series win not count because Australia's best batsman Greg Chappell declined to tour that year? Does England's equally legendary Ashes triumph of 2005 not count because both of their victories (at Edgbaston and Trent Bridge) came in matches where Australia's premier fast bowler Glenn McGrath was absent through injury? Does Australia's 5-0 drubbing in the return series in 2006-07 not count because England were missing Vaughan and Trescothick? That last one is a bit of a stretch, admittedly, but you get the idea. To use a sporting cliché, you can only beat what's put in front of you.
Secondly, hat-tricks. If you have a look at the list of all 39 that there have been in Test history (Stuart Broad's at Trent Bridge being the 39th and latest) a couple of interesting statistical gems can be teased out:
- there were 16 hat-tricks in the 504 Test matches in the 83 years between 1878 and 1961. This includes the only instance of two in the same match; even more remarkably both of those were by the same man, Jimmy Matthews; even more remarkably they were the only six wickets he took in the match, and even more remarkably the third victim in both cases was the same man, Tommy Ward.
- there was then a bleak period of 603 tests and 27 years between 1961 and 1988 during which there was only one hat-trick, Peter Petherick's (on his Test debut) in 1976.
- since then things have reverted to something resembling the pre-1961 frequency with 22 hat-tricks in 893 matches in 22 years between 1989 and 2011.
- Broad becomes just the second man to be a hat-trick victim (i.e. someone's third wicket) and to take a hat-trick himself. Broad was Peter Siddle's third victim at Brisbane just eight months ago; the only other man to achieve the same thing was Shane Warne, who did it in the opposite order, taking a hat-trick in 1994 and then being Harbhajan Singh's third victim in 2001. The only other hat-trick-taker to feature anywhere in another bowler's hat-trick is Darren Gough, who was Warne's second victim in 1994 and then did the hat-trick himself in 1999.
- there must be some scope for analysis of whose was the "best" hat-trick, by some measure of the excellence of the three batsmen involved. I'm not going to do the legwork, but you take total aggregate runs scored by the three batsmen as the metric then if I had to guess I'd say either Irfan Pathan's trio of Salman Butt, Younis Khan and Mohammad Yousuf, or Harbhajan Singh's trio of Ricky Ponting, Adam Gilchrist and Shane Warne would be pretty high on the list. You'd have to decide whether you were talking about total career aggregate runs per batsman, or career aggregate runs at the time of the hat-trick, of course. Tricky stuff.
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