Bill, I totally now, just now, understand what you are saying. But it is soooo wrong. You suppose that because a person may be able to make 5 consecutive free throws often, they will somehow miss 5 free throws about the same percentage of time.
Why would that be? That is absolutely implausible. Is it simply because the black and white Yen and Yang symbol balances all endeavors? I have some news…
A person who very often make 5 free throws consecutively will almost never, and I mean “never” miss 5 in a row. I didn’t get what you were saying, because what you are saying is so removed from actual outcomes “that it did not compute.”
A person who can rarely, but in a couple hours’ time, can make 10 in a row, will NEVER miss 10 in a row. It is hard to make 10 in a row. The talent is rare. That person, will, I assure you, never ever, ever, miss 10 in a row. Have you shot free throws? This, the coin’s obverse, is not how it works, not even close.
Bill, let me reply to my own reply by saying that the way you explained in detail how you applied normal distribution and shifted the curve by performance was appreciated and well done.
That’s probably hard to tell from what I wrote, and we were at this all night. I did manage to travel 300 miles and shoot a 199, 198, and 196 at 1,000, F-Open. That was good for I believe, about last place in HM. Tough crowd.
My strongest reactions to the bell curve have been when the subject matter concerns one actor’s performance potential, implying an equal likelihood of opposite end performance, that’s far less likely for that person than for any random average person
because that person is in an end.
If a person’s performance range is already at either low probability “end”!of a given bell curve, depending on the subject matter, allowance for crossover to the other end is best case stacking or multiplying fractional improbabilities but worst case overlooks actual diametric opposition between the ends.
I suppose asymmetrical curves with a blunt flange suit me better, especially for certain subject matter.
Respectfully, I don’t think it’s plausible to count both consecutive number of baskets and consecutive number of misses, on one bell curve. I believe that the proper X axis would start at 1 basket and go to say 20, or whatever. The subject heading would be baskets made consecutively, the range would be those numbers and the mode somewhere middle.
I believe that your example sets up two subject fields on one bell curve. We just don’t see that practiced. It permits multiple peaks. A guy could cluster 80% of his baskets at 2 consecutive shots sloping on either side to one and three, but 90% of his total shots are actually misses where he starts over, such that his hits are completely in the graph’s “shadow” (curve) of his miss peak.
I also believe you could graph misses, starting over with hits. I believe that recoding both is simply a scoreboard.
If you don’t separate them, your one graph will overlap yielding an increased chance for both a simultaneous hit and a miss to occur under given areas of curves.