Testing the Four Factors

For a beginner's guide on the four factors discussed in this post read this.

The four factors certainly work effectively to determine a team's offensive/defensive ability. In order to take a closer look, I decided to "build" an expected offensive efficiency for each team in 2009-2010 based solely on the four factors. The major problem was determining how to weight each factor. For the NBA, Dean Oliver recommended 40% shooting, 25% turnovers, 20% rebounding, and 15% free throws. However, these numbers are somewhat arbitrary. When using those weights, the correlation coefficient between Dean Oliver's weighted four factors and actual offensive efficiency was .94. I then decided to play around with the weights. I was able to raise the correlation coefficient to just barely over .99 by using the following weights:

1. Shooting: 58%
2. Turnovers: 23%
3. Rebounding: 16%
4. Foul Shots: 3%

(NOTE: The spreadsheet used must have been created slightly before the end of the '09-'10 season. Stats for individual teams are slightly off, but the overall study remains useful.)

Why this weighting system correlated so well to offensive efficiency is a bit of a mystery. Getting to the line is barely accounted for, but this is what worked. The next step was to turn my new four factors rating into an expected offensive efficiency. The results were good. Every team's expected offensive efficiency was within 4.7 points per possession of their actual offensive efficiency. Prairie View A&M was the most inaccurate projection (91.8 expected OEff vs. 87.1 actual OEff).

The Expected OEfficiency tends to underestimate highly efficient teams and vice versa for inefficient teams. Here is a look at the teams most undervalued and overvalued:

Note: Final column may appear off by a tenth due to rounding.

• From top to bottom these teams ranked 1, 5, 3, 13, and 4 in unadjusted OEff.
• All five teams shot two pointers, three pointers, and free throws well above average with the exception of Duke's well-documented two pointers.
• As expected, excellent ball control is a common theme among these teams.

• From top to bottom these teams ranked 343, 342, 341, 345, and 336 in unadjusted OEff.
• Each team was 330 or below in eFG%.

Clearly, the four factors work. The weights that seemed to work the best are the interesting part. It would definitely be interesting to see other work on this topic.

Varying Impacts - Jimmer Fredette

A while ago, we did a post on the varying impacts an efficient basketball player can have. In order to explore this subject further, we have conducted a series of interviews. We have discussed three different types of players with team specific bloggers. This final post features an interview with Mountain West Connection (twitter: @JeremySBN) on Jimmer Fredette.

Hoop Vision: Jimmer Fredette was 63rd overall in offensive rating, but 1st overall for players with at least 28% of possessions used. Excellent shooting percentages, assist to turnover ratio, and ability to get to the line were the driving factors. Where (on the floor) and when (transition, end of shot clock, etc.) did Fredette's shots occur in 2009-2010?

Mountain West Connection: Jimmer is actually a good enough player to be able to beat defenders of the dribble with his quickness, but if defenders back off and give space so they are not beat Fredette is good enough to drain a deep shot. He is very difficult to handle one on one and in a man defense. A zone can work better since it is more difficult to penetrate a zone off the dribble. Basically he was good enough to score from all over court and was the guy to take a shot as the shot clock was expiring which is why he had 10 games of 25 points or more which included a season high of 49 over Arizona in Tucson.

Hoop Vision: As the point guard for BYU, Fredette was not able to hide on the court. How much of Fredette's solid TORate (15.0%) was due to his ability to rely on his teammates and how much was due to his decision making ability?

Mountain West Connection: He had to rely on his teammates to an extent because there were times when opposing defenses would throw everything his way, but Fredette was able to get out of it by just controlling the ball or finding the open teammate. Plus, the team was so good they knew where to be to help out any player. Fredette's decision making of taking on a defender to get to the foul line was key in keeping the number low.

Hoop Vision: Fredette's 3% has gone up from 34% to 38% to 44%. What can we expect from him shooting the ball in 2010-11?

Mountain West Connection: It is hard to get to much better then 44% from three point range, but who knows. Fredette is on the USA Select team where is playing with current NCAA stars while going up against NBA players who are on the National team. Fredette, as hard as it seems to be, may have to take on more of an offensive presence in the offense due to the loss of a few key players. Fredette's goal is to get to the NBA but being a 6 foot two point guard in the NBA will require him to keep up that deadly shot, because it will be very difficult for him to beat guys who are five inches taller and outweigh him by 25 pounds. In general he will do what it takes to score whether it shooting deep threes or taking players off the dribble to get to the free throw line.

Hoop Vision: BYU has proven to be a quality team throughout Fredette's career. However, would Fredette be having the same success in a top conference and with equally great teammates?

Mountain West Connection: Excellent question and I do not think any player who is the stud on their team would be as good if they played with an equally good player. I think Fredette will be one of those guys that you hear about that were great college players, but never really made it in the pros. I think with much stiffer competition like the ACC or Big East Fredette would struggle to beat guys off the dribble on a consistent basis, however he is such a good shooter that he would perhaps be a number two option on any team in the Big East or ACC with the occasion to take over game. I could be selling Fredette short since he did put up big numbers against NCAA teams such as 49 over Arizona, 37 over Florida in the first round of the NCAA tourney, and consistently scoring 20 plus points against UNLV, San Diego State, and New Mexico.

Hoop Vision: What can we expect from BYU as a whole in 2010-11?

Moutain West Connection: I expect BYU to contend for the conference title again, but the Mountain West is a really good league and the title will come down between BYU, San Diego State, and UNLV. There is a possibility of New Mexico being in the mix but they lost Darrington Hobson, and are more of a darkhorse then a title contender. The Cougars should make the NCAA tournament and anything less is unacceptable, but they do lose Jonathan Tavernari, Michael Loyd, and I believe Tyler Haws is leaving on a church mission for two years so the talent will be gone from last year. A top three finish in the regular season and an NCAA berth is a reasonable goal.

Varying Impacts - Jon Scheyer

A while ago, we did a post on the varying impacts an efficient basketball player can have. In order to explore this subject further, we have conducted a series of interviews. We have discussed three different types of players with team specific bloggers. This second post features an interview with Duke Hoop Blog (twitter: @DukeHoopBlog) on Jon Scheyer.

Hoop Vision: Jon Scheyer was 10th overall in offensive rating, but 3rd overall for players with at least 20% of possessions used. Solid shooting percentages and an excellent assist to turnover ratio were the driving factors. Where (on the floor) and when (transition, end of shot clock, etc.) did Scheyer's shots occur in 2009-2010?

Duke Hoop Blog: Jon took over half of his 531 shots in 2009-2010 from deep (287). His two-point attempts usually came at the rim or just inside the arc due to Duke’s offense. Once in the half-court, Jon would primarily play off the ball with Nolan running the point. Jon took most of his shots at the beginning or very end of the shot clock. Because of the personnel of the 2009-2010, Duke did not run in transition that often. If Duke couldn’t get a quick shot in transition (beginning of the shot clock) Coach K liked to run the clock all the way down, causing Jon to take shots at the end of the shot clock. Jon also took quite a few shots after an offensive rebound and a quick kick-out, causing the shot to come at the beginning of the shot clock.

Hoop Vision: As the point guard for Duke, Scheyer was not able to hide on the court. How much of Scheyer's phenominal TORate (11.4%) was due to his ability to rely on his teammates and how much was due to his decision making ability?

Duke Hoop Blog: Half and half. He wasn’t able to hide on the court as a point guard, but after bringing the ball up, he often played off the ball. That obviously helped his TORate. He was also, arguably, the smartest player in college basketball. There were too many examples of his basketball IQ and decision making ability to single out one from last year, but a great example from 2009 sticks out. In the second round game of the NCAA tournament with 15 seconds left he dives to save a ball and throws it up in the air as high as he can to the other side of the court to waste time. A foul by Texas occurred and Duke ended up winning the game because of the spectacularly intelligent play by Jon.

Hoop Vision: Would Scheyer's style of play have seen as good of results on a team inferior to Duke? Were his assist numbers and efficiency largely dependent on his team's ability to make shots?

Duke Hoop Blog: That is a tough question. On a team with less talent, Jon would have had to take most of the shots, causing his assist numbers to drop and, most likely, his turnovers to increase. Jon is not a John Wall type player who can slash through a defense and get teammates wide open layups time and time again. But, what he can do is command defensive attention for himself and then get the ball to his teammates for open shots.

Hoop Vision: It is hard to criticize a national championship team, but did Scheyer best utilize his talents in Duke's offense or could he have played a more prominent role while keeping his excellent efficiency?

Duke Hoop Blog: No I don’t think he could have played a more prominent role and kept his efficiency as high as it was. As I have said, he often played off the ball after bringing the ball up; this let him maximize his talent as a shooter and a more natural 2-guard. He was also able to develop his skills as a passer and game manager while playing the point guard position. If he had been expected to carry the load offensively his numbers would have suffered.

Hoop Vision: What can we expect from Duke as a whole in 2010-11?

Duke Hoop Vision: Duke will be more talented in 2010-2011 because of the arrival of freshman point guard Kyrie Irving, transfer Seth Curry, the return of Kyle and Nolan, and the emergence of the Plumlees. Duke has all the tools to repeat as national champions, but they will certainly miss the decision making and leadership of guys like Jon, Zoubek, and Lance. If a leader can emerge (most likely Kyle or Nolan) and Kyrie can make good decisions with the ball, the Blue Devils will be extremely successful. Duke will look very different next year than they did this past year. They will be a more traditional Duke team on defense, using pressure man-to-man and stepping in passing lanes. This is possible because of the speed and agility of the added personnel. On offense, Duke will look to run. The Plumlees are built to be agile and athletic big man who can run the floor and finish at the rim. Kyrie is a lightning quick player (he will challenge Kemba Walker as the quickest player end to end in college basketball) who can get the ball up the floor and either finish in transition or put a teammate into position to finish. Expectations are very high for the Blue Devils in 2010-2011, but they are achievable.

Varying Impacts - Blake Hoffarber

A while ago, we did a post on the varying impacts an efficient basketball player can have. In order to explore this subject further, we have conducted a series of interviews. We have discussed three different types of players with team specific bloggers. This first post features an interview with The Daily Gopher (twitter: @TheDailyGopher) on Blake Hoffarber.

Hoop Vision: Blake Hoffarber was first in the nation in offensive rating. Outstanding shooting percentages and quality turnover prevention were the driving factors. Where and when did Hoffarber's shots occur in 2009-2010?

The Daily Gopher: The easy answer is that Hoffarber's shots came from behind the arc. 75.8% of his shots were threes. I'm not sure where that stat compares to the rest of SGs around the country but 5.2 three-point attempts per game compared to just 1.7 twos is a pretty significant ratio. More specifically he was most proficient in transition. The Gophers turned their opponents over at a pretty high rate, especially early in the season. Hoffarber is very good at running wide, finding an open spot on the wing and then draining the three when receiving the pass. In the half-court the Gophers really were not very good at running offensive sets to get him some open shots. His shots in the half-court set usually would come on a ball reversal when the defender would fall asleep and choose to not close out on him.

Hoop Vision: Was Hoffarber's low turnover percentage more from his overall timidness in the Gopher's offense or quality decision making?

The Daily Gopher: I'll say a little of both and a lot of neither. Hoffarber's low turnover rate is largely due to the fact that he does not put the ball on the floor that often. He is a great shooter and a great passer, but he is not athletic enough to create shots with penetration. He is smart enough to know that and rarely did he put the ball on floor, putting him in position to turn the ball over.

Hoop Vision: Hoffarber shot 47% from 3 and 59% from 2, both excellent marks. However, he shot more than three times as many 3's as 2's. How big of an impact did Hoffarber's three point efficiency have on the other Minnesota players? Did his range open up space for Westbrook, Johnson, Joseph, and company?

The Daily Gopher: Yes, yes and yes. Not only was everyone better but the Gophers were 13-1 when Hoffarber scored 11 points or more last year (19-2 over the last two years). The problem is he doesn't hit that magical 11 point mark nearly enough. For a guy with his shooting ability, he really should be more of a focal point and be taking at least two or three more shots per game. This gets back to an earlier point that the Gopher offense doesn't do nearly enough to run him off screens and run offensive sets exclusively for him. He really should not be 4th on his own team for shots attempted. When you break it down by minutes he would take a shot every 4 minutes, 7th on the team for guys over 300 minutes. Lawrence Westbrook led the team taking a shot every 2.7 minutes.

Hoop Vision: Did Hoffarber best utilize his talents in the Gopher's offense or could he have played a more prominent role while keeping his excellent efficiency?

The Daily Gopher: I think if he was more of an offensive focal point, you would obviously see his efficiency drop off a little but not by much. The thing is that defenses already focus on him at all times. So if the Gopher offense were to run more of their offense through him, it is not like defenses would adjust and spend more time trying to slow him down. They already put one of their best defenders (usually a longer and more athletic one) on him and that defender typically is not responsible for helpside defense. Maybe fatigue would be more of a factor if he is running off screens and not allowed to sit out behind the arc quite as much. But that would go both ways as his defender would be taxed more as well. In the end, the Gophers need to at least find out how much his efficiency would drop. He isn't the most athletic player on the floor and he won't create his own shots, but he is savvy. Give him the opportunity to come off screens and trust him to make good decisions with the ball. Putting the defense in more situations where someone has to choose to leave their man to guard Hoffarber or let him have an open three is exactly the kind of situations the Gopher offense needs to get itself into.

Hoop Vision: Hoffarber was not nearly as efficient during his sophomore season. His turnover percentage was 22.6% and he only shot 34% from long range. Will the tremendous strides made from sophomore to junior year remain for 2010-11 or is regression due to occur?

The Daily Gopher: His sophomore year was the abberation. I do not think you will see great statistical improvement from his JR to SR year, but I'd be shocked to see him regress to anything near his Sophomore year numbers. His sophomore year was a year where he could just never get on track. Shooters go through droughts but his was started in January and lasted through the NCAA Tournament loss to Texas.

Hoop Vision: What can we expect from Minnesota as a whole in 2010-11?

The Daily Gopher: There is plenty of talent on this roster but there are a number of question marks. Two key players are still in limbo as to whether or not they'll be playing this year, both starters and key positions for this team. Al Nolen missed half the season due to academic issues and Trevor Mbakwe missed the entire season due to pending legal issues (UPDATE). If both issues are resolved then Nolen is our starting PG and Mbakwe is our starting PF. So step one is getting everyone eligible, adding those two completely change the outlook of the 2010-11 season. After getting those guys on the roster it comes down last year's sophomores and freshman improving. The soon to be juniors are the nucleus of the team. Devoe Joseph, Ralph Sampson and Colten Iverson have all been solid but they need to be better and more consistent. Rodney Williams showed flashes of great athleticism in his freshman season but he needs to grow by leaps and bounds in his sophomore year. He is capable of being our most dynamic player but he needs to understand his role in the offense and how to play Tubby's demanding defensive system. Assuming Mbakwe and Nolen play, and assuming even just moderate improvement from the rest of the roster I believe this team will fighting to finish anywhere from 3rd to 5th in the Big Ten. There is the talent to compete for a conference title but the starts kind of have to align for that to be realistic possibility. If guys do not become eligible and Williams doesn't figure out how to get himself on the floor, this team will miss the NCAA Tournament and could finish way down in the Big Ten pecking order.

Varying Impacts

On the court, not all players contribute to a team equally. Naturally, the best player(s) are going to have the most prominent roles offensively. The goal of a team offensively is to score as many points per possession as possible. Each shot taken has a risk and a reward. Essentially, the probability of the shot equaling or exceeding the team's average offensive efficiency should be greater than the probability of it not.

However, players have different talent levels. This contested shot is going to be more efficient than this contested shot because of the individuals who are shooting them. Depending on talent level, players can be more involved offensively than others and still be efficient enough to help their team. Finding this balance (between usage and efficiency) is key in maximizing a team.

The below graph is of the most efficient players from 2009-2010. The x-axis is usage (% of possessions a player is used while on the court) and the y-axis is offensive rating. I circled four of the best players at each of the four levels of impact.


There will be more on these four players and their respective regions on the graph later.

It is interesting to compare the graph above to the NBA one. The stars in the NBA (high USG) are nearly as efficient as the top role players. This is very different from the NCAA. It is hard to tell why this is. Maybe NBA teams are better at recognizing who exactly should be taking varying shots on the court. Or maybe the stars in the NBA are just that much better at their craft.