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Originally posted by A Pennsylvania Coach
Quote:
Originally posted by Dan_ref
Quote:
Originally posted by A Pennsylvania Coach
Quote:
Originally posted by Dan_ref
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Originally posted by A Pennsylvania Coach
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Originally posted by ref18
I think that a future rule change should allow a penalty of 3 shots for any technical foul which interferes with a 3-point attempt.
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End of game situation like this, more than 3 FTAs are needed. A 70% free throw shooter is going hit 3 of 3 only 34% of the time.
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Well...not quite, but this is close to what they teach in statistics 101.
If you're in Honesdale over the weekend Chuck will be happy to buy you a diet coke and I'll bore you with my explanation. 
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Feel free to explain here.
I will say that I've seen a team down by three in the last three seconds of game shooting three shots exactly (yep, you guessed it) three times in my career and (of course) three of them made three of three.
One was in OT of a state final, and the kid who was something like a 60%er made three with NO time on the clock and his team won it in double OT. Unreal.
Another was my team, when I was an assistant. We had a 55% shooter hit three of three with :03 left in regulation as we came back from 18 down with 5:45 left. We won on a double OT buzzer beater by a freshman who was only in because four others had fouled out. The girl who made the three-of-three only missed one more FT all year and finished at 67%.
The last was as a head coach, we fouled a three-point shooter with :01 left up by three. (Ugh.) She hit them all but we won in overtime.
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In a nutshell: you make assumptions concerning the validity and the uniformity of the FT shooters prior statistics that are generally not valid when you did your simple calculation (.7 X .7 X .7 = 34%). Based on your own experience, using these same assumptions, we could just as easily conclude that *any* shooter will *always* (probability = 1) make 3 of 3 FTs when the game is on the line.
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My experience is invalid due to small sample size.
If you are referring to the "streakiness" of shooting, may I refer you to:
http://www.psy.utexas.edu/psy/FACULT...onomicBR(1995)
http://www.hs.ttu.edu/hdfs3390/hothand.htm
and especially
http://www.hs.ttu.edu/hdfs3390/hh_1998.htm
I was also looking for a piece of work about FT shooters. It took NBA players with long careers and compared their percentages of second shots made when either making or missing the first, and it was remarkable how a career 75% guy, on the second shot of two after a miss on the first would make 75%, and on the second shot of two after a make on the first would also make 75%.
I stand by my 34%.
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Sigh. By using your experience we have shown conclusively that simply stating
End of game situation like this, more than 3 FTAs are needed. A 70% free throw shooter is going hit 3 of 3 only 34% of the time. is inaccurate at best, regardless of the sample size. Again, you are ignoring simple well known concepts. Start here:
http://mathworld.wolfram.com/BayesianAnalysis.html
then go here
http://mathworld.wolfram.com/topics/...ributions.html
to see what I mean by some types of distributions (your references might or might not be useful in determining THE distribution for A particular shooter, BTW, as might many other physical & psychological factors). Next go here to see why I say your original statement is inaccurate at best
http://mathworld.wolfram.com/topics/Moments.html
paying attention to links concerning variance & deviation. BTW, the outcome of the 3 FTs might end up with a probability distribution looking a lot like this:
http://mathworld.wolfram.com/NormalDistribution.html
And finally go here
http://mathworld.wolfram.com/topics/ErrorAnalysis.html
to see how the uncertainty of this is dealt with.