I think I got this one. Sometime after I posted yesterday about the free throw shooter with the remarkable neurosis, someone tweeted at me that they agreed with me, and that they couldn’t figure out how so many people were getting 50.5%. It seems that Ollie at 538 had tweeted this:
The speculation is that the highest bar (which Ollie confirmed represents the correct answer) is 2/3, the 2nd highest is 50.5%, and who knows what the other two answers are. I’d really like to know. (BTW, if that chart is a Harry Potter Sorting Hat, then the houses are: Ravenclaw, Slytherin, Gryffindor, and Hufflepuff, respectively. Fight me.)
I can fully understand how so many people could get 50.5%. It all comes back to that #define statement from my previous post:
#ifdef THE_WRONG_WAY // This code might seem correct but will not correctly "prune" the // tree of possibilities shots++; made++; #else // now ensure that we make the "seen" shot (eg 99) if(SimShot(shots, made) != NS_Made) return NS_Invalid; #endif
I showed that code to a colleague and it took some convincing that “throwing out” half the trials because they resulted in a missed 99th shot really was the correct method. Yes, each path is equally likely, but the fact that we know the 99th shot was made indicates that it is much more likely that the player has had more success in the past.
I can imagine people taking several paths to an answer for this one. Some percentage would immediately say “2/3, easy” and not think anything of it, and it would turn out they are right. Another group would write some sort of simulator and would get to that 99th shot and just credit it to the shooter, and they’d get 50.5%. And still another group would take the approach I’ve outlined and come up with 2/3 again.
Then there’s the other two answers, and I have no idea what happened there. Gryffindor and Hufflepuff, what can you do, amirite?
(Having said that, I still won’t be 100% sure I am right until I see a better explanation.)