I follow your reasoning for n > 1, but why do you say that a team shooting at n=1 will score half the time? The average shot quality is certainly not 1/2; there are many more poor shots than there are good ones, to my way of thinking. How do you justify calling the average shot probability 1/2? It seems to me both theoretically and empirically incorrect.
(It seems to me that even the best shots are not of probability 1! http://www.youtube.com/watch?v=La4PpYnKrNc)
You’re definitely right that my assumption about the average shot quality isn’t very realistic. I only set it to 1/2 to make the numbers nicer. Like I said: this is the comically oversimplified version of the problem! In the paper I linked to I solved the problem for arbitrary values of shot quality mean and variance.
(That video was nice, by the way. Vince Carter can really miss a dunk.)
If only I could jump like him just for a day!
Anyway, the paper is indeed much clearer on what you mean. Neat work, it gives me some thoughts I want to explore.
There’s a good reason why nerds have blogs and pro basketball players have money, women and fame :-D
One thing to add: you need to consider the likelihood of a turnover – sometimes deciding not to take a shot means you’ll subsequently lose the ball and get no shot at all.
You’re definitely right. When considering whether to take a shot, you have to weight its quality against the quality of future shots and the probability that you will lose the ball and never get a chance at all. In the paper I linked to at the end I did take turnovers into account. They have a surprisingly large effect.
So does the probability to draw a foul. Mind the opportunity costs.
Since the shooter used an offensive possession with his two free throw attempts it should count as an offensive possession i.e. a shot attempt for the player..Lets have an example Player 3 takes 15 shots he makes five misses five and is fouled and does not make the shot on the remaining five. Differences in three-point shooting percentage free throw shooting percentage and the frequency with which each player takes various different types of shots can all affect their shooting percentage and whether that shooting percentage should be considered efficient..To accurately compare the offensive shooting efficiency of two players one should look at True Shooting Percentage TS rather than Field Goal Percentage FG as it accounts for three-pointers and free throws..To bring this full circle to our early example Kobe Bryants position requires him to shoot more three-point shots than LeBron James. After all assists are not recorded on passes that lead to shots that should be made but are not.
Your Paper on the arXiv appears to have compiling issue in the Bibliography, nice paper.
Thanks for the heads-up! I’ll fix it.
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