Re: Which is rarer?
- From: "Wog George" <wog-NotThisBit-george@xxxxxxxxx>
- Date: Thu, 26 Apr 2007 03:16:31 GMT
"tendulkar.com" <tendulkar.com@xxxxxxxxx> wrote in message
news:1177336911.713668.72270@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Apr 23, 8:51 am, linus <lavinia...@xxxxxxxxxx> wrote:
On Apr 23, 5:41 am, Rats <crapats...@xxxxxxxxxxxx> wrote:
6 6s in an over (Gibbs) or 4 wickets in 4 balls (Malinga)
In ODI cricket, one could say that they are equally rare as they were
done only once.
Thats stupid logic. Comparing actual events to get the probability
when you are talking about extremely low probability event
Where does stupid come into it? There has been one example of each.
Historically, they are equally as rare.
Even by crude probability theory,
In an ODI,
MS Dhoni hits a sixer every 32 balls,
Waqar Younis takes a wicket every 30 balls
Iteration 1
Assuming independent* events,
P(Waqar taking 4 wickets in 4 balls) = 1/30 * 1/30 * 1/30 * 1/30 = or
1 in 810,000
P(Dhoni hitting 6 sixers in 6 balls) = 1/33 * 1/33 * 1/33 * 1/33 *
1/33 * 1/33 = or 1 in 1,291,467,969
Therefore Hitting 6 sixers in 6 balls is about 1600 times more
difficult
Wonderful, but Gibbs averages a six every 79 balls (and that's after the
infamous over). You would have us believe that Dhoni is much more likely to
achieve the feat, yet history tells us otherwise. Statistics and
probability are all well and good but not necessarily indicative of what
might happen in the future. If a player has never hit a six, probability
would dictate that they never will, yet it may be just one ball away.
Probability would only really be applicable if each ball was identical. The
probability of hitting a ball for six would depend on numerous factors such
as where the ball pitched, how fast etc. A particular ball might be very
likely to be hit over the stadium, whereas the next may be almost impossible
to hit in the air at all.
Iteration 2
* Of course hitting sixers & taking wickets are not independent
events, they are slightly dependent. However this dependency actually
favors taking wickets than hitting sixers because
a) When a bowler takes a wicket
-A new unset batsman is in, who always has a higher probability of
getting out.
-The bowler is in full control of which ball to bowl.
-More importantly the bowler is still trying to get a wicket.
-All the fielders will move into wicket taking positions
b) If a batsman has hit a sixer,
- he may not want to try another one because of the risk factor.
- The bowler may bowl a really wide delivery or an unreachable
bouncer.
- All the fielders may go on the boundary to create doubt in the minds
of the batsman
All this means is P(6/6) would go even lower compared to P(4/4
wickets)
Iteration 2 is fine. I agree with all of your points.
I can never imagine anyone hitting 6/6 in a non-minnow match, while I
can easily see bowlers getting 4/4. After all many have got 3/3.
Another easy reference point is to look at # of 5 sixers in 5 balls vs
3 wickets in 3 balls. Which is rarer?
Hat tricks are almost commonplace by comparison (although not in any of my
bowling figures). I once managed to sustain hitting sixes at a rate of one
per ball for a total of one ball, yet frequently picked up wickets with
consecutive balls.
Iteration 3
P(5 Sixers in 5 balls) * P(hitting a six) <<<<< P(3 wickets in 3
balls) * P(Getting a wicket)?
An absolutely crap ball can snare a wicket, although it's unlikely that an
absolute gem would be hit for six.
--
George
"In the outside world I am a simple geologist, but in here I am Falcor,
Defender of the Alliance." - Randy Marsh - 4 October 2006
.
- References:
- Which is rarer?
- From: Rats
- Re: Which is rarer?
- From: linus
- Re: Which is rarer?
- From: tendulkar.com
- Which is rarer?
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