Thursday, October 2, 2014

Why shooting only one free throw would not increase the average value - but slightly change the game


just a short one regarding an idea that was first mentioned here:
The idea is to change the free throw concept to speed things up. Instead of two free throws that are worth two points, we could as well shoot one free throw worth one point. Or three points, if it's for a three-point foul and so on...
The always amazing Nylon Calculus crew spun it a little further
calculating that the expected points per free throw attempt would not change (so basically the mean), but the variance would increase (due to less attempts).
My first reaction was to say 'but what about offensive rebounds!? You cannot rebound the first shot!'
This is true, but it doesn't change the math (too bad, I love to be a nitpicker...)

FT% - Free throw percentage of a player
OR% - Offensive rebound percentage
POR - Points we expect after an offensive rebound
Expected points two free throw situation (resulting points multiplied with their probability):
1       *(1-FT%)*FT% +
1       *FT%*(1-FT%)*(1-OR%) +
2       *FT%*FT% +
(1+POR) *FT%*(1-FT%)*OR% +
POR     *(1-FT%)*(1-FT%)*OR%
0       *(1-FT%)*(1-FT%)*(1-OR%)

Expected points one free throw situation (resulting points multiplied with their probability):
2       *FT% +
POR     *(1-FT%)*OR% +
0       *(1-FT%)*(1-OR%)

So, even this doesn't change.
The aspect of the game that it would really influence is the 'it is late in the game and we lead by three points' situation.
Because the opponent would not be able to make the first shot and intentionally miss the second shot - as there would be no second shot...

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