It’s been a spring of attrition for Colorado basketball.
Those hurt, but neither Thomas nor Hopkins will leave a hole in their team the size of the one that Arielle Roberson will in the women’s team. The redshirt junior is graduating in May with a degree in communications and won’t return for her final year of eligibility.
Roberson led the Buffs in scoring and rebounding as a sophomore, then tore her ACL in offseason workouts and missed all of last season. Colorado has experienced life without her, and it wasn’t pretty — the Buffs’ defense cratered. They finished 15-17 and missed the postseason entirely.
Anyone who has seen Roberson play can understand why she’s a good defender; she is tall, lanky, athletic and tenacious, she has outstanding lateral quickness, and she can guard four positions. Anyone who looks at the box score can see how far Colorado fell in her absence — the Buffs dropped from fourth in the Pac-12 in scoring defense in Roberson’s final season to last in the conference without her.
Still, box scores don’t tell the full story. I wanted to go beyond that and use advanced stats to quantify Roberson’s defensive contributions. First, I threw points per game out the window. Although the Buffs fell precipitously in that stat without Roberson, it’s a poor overall measure of a team’s defensive performance.
For example, the Golden State Warriors and the Utah Jazz have, by all acclamations, two of the best defenses in the NBA. The Jazz allow 94.7 points per game, which is best in the league, but the Warriors allow 99.3, which is 14th. So, why is Golden State’s defense as highly regarded as Utah’s?
Because points per game doesn’t consider that different teams play at different paces. The Warriors are the fastest team in the league. The Jazz are the slowest; they play fewer defensive possessions each game, so they allow fewer points. To accurately compare their defenses, we must look at how many points they allow per 100 possessions.
Points allowed per 100 possessions, or defensive rating, is simple — if a team plays defense 100 times, how many points will they allow? Golden State’s defensive rating is 97.8, which is best in the NBA. Utah’s is 102 — the Jazz are still good, but not as stingy as their points-per-game average would suggest.
Back to Colorado. I calculated the Buffs’ defensive rating for the last two seasons. In 2013-14, Roberson’s final year, Colorado’s defensive rating was 91.3. Last season, without Roberson, it was 99.3. That eight-point bump may not seem drastic, but it’s equivalent to the difference between Golden State’s NBA-best defense and the Orlando Magic’s fifth-worst.
I used this formula to get those totals:
Points allowed x 100/(.96 x (Opponent field goal attempts – Opponent offensive rebounds + Opponent turnovers + (.475 x Opponent free throw attempts)
It’s pretty simple. The denominator is the equation for calculating the number of possessions a team had over a game or a season. Ken Pomeroy explains here why you multiply free throw attempts by .475. You multiply the entire denominator by .96 to account for team rebounds — say, if a shot gets blocked out of bounds without anyone collecting the board, the shooting team is still credited with a rebound. The .96 multiplier compensates for that; the shooting team isn’t gaining a new possession, they’re extending one.
So, if the Buffs allowed 91.3 points per 100 possessions in 2013-14 and 99.3 last year, then each opponent possession was worth .913 and .993 points, respectively — teams were eight percent more likely to score against Colorado on a given possession without Roberson than with her.
I also computed Roberson’s defensive win shares for her final season, which, simply, is a rough estimate of how many wins she added to Colorado’s total through her defense. And I mean very rough. The calculation calls for the average pace of the league (or, for college basketball, the country). Because of the limited data available for women’s college basketball, and because there’s no way I would do the math for 300-plus teams, I substituted the Pac-12 for the nation at large.
Roberson had about 2.7 defensive win shares in 2013-14; her defense, by itself, won the Buffs nearly three games. Last year, that would have been the difference between a winning and losing record. Again, these stats are estimates, but their impact is the same — Roberson held Colorado’s defense together, and the Buffs are desperate for a stopper without her.
Note: advanced stats are readily available for the NBA and men’s college basketball, but not for women’s ball. You can find every formula I used in this article here if you want to make the calculations yourself, because you’re probably better at math than I am.
Contact CU Independent Staff Writer Tommy Wood at firstname.lastname@example.org