A Closer Look at 3-pt Defense

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Photo by Brian Georgeson

As the opening weekend of the big dance approaches, and Marquette is finally back in where it belongs, I wanted to dig into a stat that will be very relevant to us in Greenville, SC: 3-point defense.

Our first round matchup is against South Carolina, a team that sports one of the highest ranked 3-point defenses in the nation. I’ve seen some fans on #mubb twitter question whether this ranking is deserved, based in part on the relatively poor 3-point offenses in the SEC. I’ve been playing around with the 2017 NCAA Div 1 Men’s Basketball game data provided by Kaggle this week, so I thought I’d write some code to do a brief analysis on this subject.

My method is as follows: For each game a team played, compute:

  • Opponent’s 3-pt % for that game
  • Opponent’s season 3-pt % after removing games played against team of record

I can then compute basic stats on the differences between those paired quantities, and run a hypothesis test to determine how likely it is that any difference is due to chance.

In the tables farther down, I show the basic stats for the top 25 teams using 3 different rankings:

  • Team’s defensive 3-pt %
  • Average difference between opponent’s 3-pt % against team of record and rest of league
  • T-stat of that difference

The columns in each table are:

  • Team
  • Games played
  • Defensive 3-pt %
  • Average of difference for opponent’s 3-pt % (positive = better than average)
  • Standard deviation of difference for opponent’s 3-pt %
  • T-stat on paired differences
  • Bootstrap-resampled p-value on paired differences*

*Bootstrap resampled p-value is a randomized estimate of the p-value. This method is valuable when the sample size is fairly low. P-value refers to the probability that you might encounter a difference as large as the data, if the team’s defense was simply average. In this case, I’m computing a one-tailed test to determine if the team of record is capable of allowing a lower than average 3-pt %. Lower p-values indicate a higher level of confidence that the team is better than average at 3-pt defense.

One other note: as I said, the data comes from Kaggle, and though I assume it’s clean, I can’t be sure there are no errors. I see slight discrepancies between my 3-pt defensive numbers and kenpom.com, so the data may not be perfect.

A couple observations: South Carolina’s 3-pt defense does appear to be better than average, but probably not quite as good as advertised. They are ranked 6th in defensive %, 13th in opponent’s difference %, and 42nd in statistical significance. The lower ranking in significance comes from a higher variance in defensive % from game-to-game, and suggests some of their outperformance may be due to luck. But look who’s highly ranked in all 3 categories (#1 in difference): Duke, a potential second round matchup for Marquette.

(Also, we suck at this aspect of the game. No surprise there.)

Here are the ranked data:

Table I – Ranked by lowest 3-pt defensive %

Rank Team Games OppAvg Diff Stdev T-stat P-value
1 Morgan St 29 28.0% 5.4% 10.3% 2.822 0.0009
2 Rhode Island 33 29.1% 5.8% 10.9% 3.053 0.0005
3 NC Central 30 29.2% 3.9% 12.0% 1.770 0.0382
4 New Mexico St 30 29.8% 4.2% 11.7% 1.975 0.0224
5 Arizona 34 29.9% 5.9% 9.0% 3.808 0.0002
6 South Carolina 31 29.9% 4.6% 15.8% 1.627 0.0496
7 Duke 35 29.9% 6.4% 12.0% 3.140 0.0008
8 Gonzaga 33 30.0% 6.0% 11.1% 3.122 0.0008
9 Alcorn St 29 30.1% 2.8% 11.2% 1.326 0.0933
10 Wichita St 33 30.1% 5.5% 11.6% 2.719 0.0028
11 Minnesota 33 30.3% 5.5% 11.9% 2.658 0.0050
12 Robert Morris 33 30.4% 3.9% 11.7% 1.928 0.0241
13 Nevada 34 30.5% 4.4% 10.6% 2.428 0.0072
14 Louisville 32 30.6% 6.2% 11.1% 3.144 0.0011
15 St Mary’s CA 32 30.7% 5.1% 9.4% 3.084 0.0011
16 Col Charleston 33 30.7% 3.8% 9.0% 2.444 0.0048
17 Florida 32 30.8% 4.1% 10.0% 2.319 0.0065
18 New Orleans 28 30.8% 4.2% 8.6% 2.591 0.0040
19 FL Gulf Coast 30 31.0% 4.9% 9.0% 2.999 0.0011
20 Villanova 34 31.1% 5.5% 7.8% 4.153 0.0000
21 Colorado St 32 31.1% 3.9% 11.4% 1.918 0.0327
22 Seattle 27 31.1% 2.9% 10.8% 1.395 0.0771
23 Illinois St 32 31.1% 4.7% 7.9% 3.368 0.0003
24 Winthrop 30 31.2% 4.6% 10.8% 2.323 0.0092
25 Furman 30 31.5% 4.0% 9.2% 2.377 0.0070
284 Marquette 31 37.0% -1.9% 11.9% -0.885 0.8154

 

Table II – Ranked by biggest opponent’s difference

Rank Team Games OppAvg Diff Stdev T-stat P-value
1 Duke 35 29.9% 6.4% 12.0% 3.140 0.0008
2 Louisville 32 30.6% 6.2% 11.1% 3.144 0.0011
3 Gonzaga 33 30.0% 6.0% 11.1% 3.122 0.0008
4 Arizona 34 29.9% 5.9% 9.0% 3.808 0.0002
5 Rhode Island 33 29.1% 5.8% 10.9% 3.053 0.0005
6 Villanova 34 31.1% 5.5% 7.8% 4.153 0.0000
7 Minnesota 33 30.3% 5.5% 11.9% 2.658 0.0050
8 Wichita St 33 30.1% 5.5% 11.6% 2.719 0.0028
9 Morgan St 29 28.0% 5.4% 10.3% 2.822 0.0009
10 St Mary’s CA 32 30.7% 5.1% 9.4% 3.084 0.0011
11 FL Gulf Coast 30 31.0% 4.9% 9.0% 2.999 0.0011
12 Illinois St 32 31.1% 4.7% 7.9% 3.368 0.0003
13 South Carolina 31 29.9% 4.6% 15.8% 1.627 0.0496
14 Virginia 32 31.6% 4.6% 12.2% 2.146 0.0169
15 Winthrop 30 31.2% 4.6% 10.8% 2.323 0.0092
16 Nevada 34 30.5% 4.4% 10.6% 2.428 0.0072
17 New Mexico St 30 29.8% 4.2% 11.7% 1.975 0.0224
18 New Orleans 28 30.8% 4.2% 8.6% 2.591 0.0040
19 BYU 33 32.2% 4.1% 11.2% 2.111 0.0182
20 Florida 32 30.8% 4.1% 10.0% 2.319 0.0065
21 Baylor 31 31.6% 4.0% 9.9% 2.251 0.0123
22 Furman 30 31.5% 4.0% 9.2% 2.377 0.0070
23 Robert Morris 33 30.4% 3.9% 11.7% 1.928 0.0241
24 NC Central 30 29.2% 3.9% 12.0% 1.770 0.0382
25 Colorado St 32 31.1% 3.9% 11.4% 1.918 0.0327
267 Marquette 31 37.0% -1.9% 11.9% -0.885 0.8154

 

Table III – Ranked by strongest statistical significance

Rank Team Games OppAvg Diff Stdev T-stat P-value
1 Villanova 34 31.1% 5.5% 7.8% 4.153 0.0000
2 Arizona 34 29.9% 5.9% 9.0% 3.808 0.0002
3 Illinois St 32 31.1% 4.7% 7.9% 3.368 0.0003
4 Louisville 32 30.6% 6.2% 11.1% 3.144 0.0011
5 Duke 35 29.9% 6.4% 12.0% 3.140 0.0008
6 Gonzaga 33 30.0% 6.0% 11.1% 3.122 0.0008
7 St Mary’s CA 32 30.7% 5.1% 9.4% 3.084 0.0011
8 Rhode Island 33 29.1% 5.8% 10.9% 3.053 0.0005
9 FL Gulf Coast 30 31.0% 4.9% 9.0% 2.999 0.0011
10 Morgan St 29 28.0% 5.4% 10.3% 2.822 0.0009
11 Wichita St 33 30.1% 5.5% 11.6% 2.719 0.0028
12 Minnesota 33 30.3% 5.5% 11.9% 2.658 0.0050
13 New Orleans 28 30.8% 4.2% 8.6% 2.591 0.0040
14 Col Charleston 33 30.7% 3.8% 9.0% 2.444 0.0048
15 Nevada 34 30.5% 4.4% 10.6% 2.428 0.0072
16 Furman 30 31.5% 4.0% 9.2% 2.377 0.0070
17 Winthrop 30 31.2% 4.6% 10.8% 2.323 0.0092
18 Florida 32 30.8% 4.1% 10.0% 2.319 0.0065
19 Wyoming 30 32.1% 3.0% 7.0% 2.310 0.0096
20 Baylor 31 31.6% 4.0% 9.9% 2.251 0.0123
21 St Peter’s 32 31.9% 3.2% 8.2% 2.221 0.0119
22 Virginia 32 31.6% 4.6% 12.2% 2.146 0.0169
23 BYU 33 32.2% 4.1% 11.2% 2.111 0.0182
24 Oregon 33 31.9% 3.7% 10.2% 2.067 0.0209
25 Texas 33 32.6% 3.8% 10.5% 2.052 0.0206
42 South Carolina 31 29.9% 4.6% 15.8% 1.627 0.0496
266 Marquette 31 37.0% -1.9% 11.9% -0.885 0.8154