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
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