FanPost

Fun with Small Sample Sizes (SSS) and Dribble Drives

A few weeks ago, I made a post comparing the outcomes of driving to the basket vs. taking a 3-pointer. At that time, I had to make some assumptions about certain values about dribble drives: % being fouled, % made and % fouled+1.

I usually enjoy watching my Mizzou sports while I am on my treadmill. But I was not feeling very well, so I had to resort to my recumbent bike while watching the LBSU game. I had my hands free, and I decided to tally the stats for our main dribble penetrators: Clarkson, Brown and Ross.

Here is the data on the number of drives to the basket:

Attempts

Made

Miss

Fouled

Fouled+1

TO

Clarkson

10

3

2

3

0

1

Brown

5

3

0

1

1

0

Ross

6

2

0

1

0

3

Total

20

8

2

5

1

4

Attempts is the sum of all possible outcome of driving to the hoop.

Made is 2 pt baskets made, and miss if it clanked out, not counting being fouled.

Fouled is ] a defensive foul.

Fouled+1, is when a 2 pt basket was made + a foul.

TO is all types of turnovers including offensive foul.

I computed percentages from the table above.

% being fouled (not including + 1) = 5/20 = 25%

% made after a drive = 8/20 = 40%

% fouled+1 = 1/20 = 5%

The expected value of a drive to the basket is then:

2*40%+2.78*5% (I used a FT% of 78%)+1.58*25% = 1.33

I omitted the TO and misses because the resulting value = 0, so no sense in multiplying with % occurrence.

This is way higher than I had expected. Compare this number with the expected value of a 3-pointer of 1.07 (assumes an average 3pt% of 35.8% which is a bit dated).

Conclusions

1. I know that this is fun with small sample sizes, i.e. a single game data.

2. In stat classes, the joke is to use n=20 as minimum. In reality, the adequacy of the sample size is dependent upon the distributional characteristic of the population and the accuracy required. I have no clue what the sampling distribution even looks like in this case.

3. It’s too bad that such micro game data is not tallied and made available. I don’t know if the Mizzou couching staff enumerates and tallies such outcomes by individual plays. Even if they did, I doubt they would share them with us. Would they? :)

4. The SSS empirical result suggests that the expected value of driving to the basket is quite a bit larger than taking a 3 pointer. I hope Clarkson and Ross could forgo some of the poorer 3 pt attempts in favor more drives. Expected value represents averages, so I am in no way advocating that all they do is drive.

5. This SSS exercise has many weaknesses and omissions. For example, driving to the basket resulted in 20% turnover rate (4/20) which I assume is the negligible when a 3pter is taken, and there is a small chance for the unaccounted for 4 pt. play.

FanPosts may be posted by any RMN member and may not reflect the views of the management staff of Rock M Nation or SB Nation.

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