I decided to break out a random number generator again, and ran 29 games with a 45% shooter who took a random number of shots, from 1-7.
Originally Posted by
superdave
In games where Andre attempts three or fewer 3-point attempts he shoots .375 (6-16). In games where Andre shoots more than three 3-point attempts, he is .457 for the season (53-116).
I ran the simulation a few times -- here are the first 10 results of this random "shooter":
Code:
<=3 >3
1 45.45% 51.92%
2 45.00% 45.63%
3 48.39% 54.22%
4 46.15% 51.72%
5 51.52% 52.33%
6 44.83% 56.25%
7 50.00% 37.50%
8 42.11% 56.52%
9 40.00% 59.21%
10 52.00% 57.32%
There's often a substantial departure between the percentage.
Originally Posted by
superdave
Here's another way to look at it that is far more telling: In games where Andre shoots .500 or better, he shoots .636 (42-66). In games where Andre shoots under .500, he shoots .258 (17-66).
This analysis is a very clear cut case of sampling bias. You're really not saying anything more than "games where he shoots well, he shoots well."
To illustrate that, here is my random "shooter":
Code:
<50% >=50%
1 15.38% 60.00%
2 14.81% 62.39%
3 5.88% 63.37%
4 10.71% 62.07%
5 10.00% 62.37%
6 7.14% 61.47%
7 0.00% 60.87%
8 8.70% 60.53%
9 8.33% 61.29%
10 7.69% 64.20%
Note, these are 20 different simulations, so the two outputs don't correspond.