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 |