Friday, January 25, 2008

Openers and falls of wicket

Samir Chopra asked me a question about openers: what is the average wicket that they're dismissed at? For example, suppose an opener is the first wicket to fall in one innings, the second in another, and the first again in a third innings. His fow-average would be 1,33. (I can't think of a better name for this; it's not really the fow, since that refers to the runs the team has scored when the wicket falls.)

You'd expect that a player would do well on this statistic if they bat slowly or if they're a good batsman in a bad top order.

There's a tricky question here about what to do with not-outs. The way I treated them is as follows.

Suppose the batsman was not out, with the team n wickets down. If he'd never been not out at so many wickets down, I assigned him n+1 for that innings. In particular, this means that an opener who carries his bat gets a "score" of 11.

If the batsman had lasted longer than n wickets, then I replaced the not-out with his fow-average for all the times he lasted longer. An example:

A batsman is dismissed at wickets: 1, 1, 3, 5, 9.
A batsman is not out with the team have lost: 3, 6 wickets.

The "6 not out" is replaced by a 9. Now the two rows of data look like:
FOW's: 1, 1, 3, 5, 9, 9
nots-outs: 3

The 3 is now replaced by (5 + 9 + 9)/3 = 7,67.

So, the opener's fow-average is (1 + 1 + 3 + 5 + 7,67 + 9 + 9) / 7 = 5,1.

Right! With that out of the way, here are the openers with the highest fow-averages, the lowest, and some selected examples in between the two extremes. Qualification of 15 innings. (Edit: The original version of this table had some errors. These have been fixed.)

name inns fow avg
Russel Arnold 15 3,22
Raman Subba Row 16 2,97
Ravi Shastri 26 2,95
Bill Woodfull 43 2,90
Glenn Turner 66 2,87
Bruce Mitchell 48 2,78
Arthur Shrewsbury 18 2,78
Jackie McGlew 58 2,74
Dennis Amiss 69 2,66
Chris Tavaré 33 2,63
Jack Robertson 15 2,60
Billy Zulch 28 2,57
Geoff Boycott 188 2,56
Desmond Haynes 191 2,54
Alec Bannerman 46 2,53
John Wright 145 2,29
Mark Taylor 186 2,27
Mike Atherton 197 2,25
Graham Gooch 184 2,18
Matthew Hayden 164 2,18
Herbert Sutcliffe 83 2,09
Jack Hobbs 97 1,97
Gordon Greenidge 183 1,94
Justin Langer 113 1,89
Michael Slater 131 1,85
Trevor Franklin 37 1,68
JJ Lyons 16 1,50
William Shalders 18 1,50
George Ulyett 15 1,47
Bob Catterall 18 1,44
Mushtaw Ali 16 1,44
Boeta Dippenaar 18 1,39
Syed Abid Ali 21 1,38
Bruce Pairaudeau 16 1,38
Alan Turner 26 1,35
Saleem Elahi 19 1,21

I would have set the qualification at 20 innings, but I think that Russel Arnold deserves a moment in the sun. He started his Test career as an opener, and really did nothing wrong. Indeed, he averages over 50 as an opener (where he scored all three of his Test centuries), compared to under 30 overall. He carried his bat once in a low-scoring draw against Zimbabwe. But those muppets headed by a joker decided that Atapattu was a better opener instead. And he did all right, of course, six Test double-centuries.

Anyway, make what you will of the list above. It's a bit of a mixed bag.

Bang on David on Russell... he has always been badly treated in spite of fabulous performances for his side. Your numbers as usual brought out yet another startling fact. BTW where do you get your info for all the stats?
I built myself a database of all Test scorecards, mostly from Cricinfo but fixing some occasional errors. I can then write programs to search through it all and pick out what data I want. It's nowhere near as easy to use as Statsguru, but it means I can do more complex analyses.

I eventually plan on building a database of first-class matches as well, from CricketArchive. I've started with the matches from 19th century England.
Hi David,

Thanks very much. I was trying to get a handle on how much an opening batsman holds an innings together. So, besides batting slowly, I'd say its their limpet-like qualities (holding one end up as it were) that could contribute to a higher FOW. It might also be useful to see what the average score was when they got out?
Simply Awesome David!
David, I guess it would be too complicated to extend this for say those who come in after x or y wickets have fallen?

Great stuff...I keep learning something here.
Samir and Soulberry: I will generate the stats you want in a few days.

Doing the same thing for non-openers will require a bit of adjustment, since middle-order batsmen would (I think) be more likely to see more wickets fall, because they bat with the tail more often. But this shouldn't be too hard to deal with.
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