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Providing some data for the three point debate: are Bill Self's teams shooting too few?

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538 recently jumped into the debate on Bill Self's use of the three point shot, along with Jesse Newell and John Gasaway. Are there any numbers to support Self?

John Rieger-USA TODAY Sports

I don't want to step on Fetch's toes, since he wrote about this yesterday, so I'll try to keep my article today headed in a slightly different direction. I would ask that you read the full article at my site, BL Analytics, to read through the extended version of my response to 538's recent article on Bill Self and his use of the three. Since this topic relates directly to Kansas, I wanted to link it here, but I would greatly appreciate it if you visit my site to read the whole thing as well.

To dive right in, we all know what the 538 article, written by Matt Giles, said about Bill Self and his reluctance to shoot the three. We also know what accusations of what amounts to coaching incompetence were leveled at Self by John Gasaway and Jesse Newell within said article.

Fetch did a good job yesterday of laying out a case against the accusations, but I wanted to jump in with some supporting data, since data is what's driving the case against Self's coaching. Here are some crucial bits from my full article (which again, I beg you to read in its entirety):

Simple math tells us that attempting a three pointer is, in the long run, simply a better idea than attempting most mid-to-long range two point jump shots. Players don’t see a huge increase in accuracy when shooting, say, a 16 or 18 foot jump shot when compared to a three pointer (approximately 21 feet from the basket). Certainly not enough to merit taking that shot considering that the slightly longer shot is worth 50% points more when made.

It follows, then, that taking a bunch of long two-point shots is generally an ineffective strategy, unless you can make them at a rate at least 50% higher than you can make threes. For the most part, anyone who is good at hitting shots from 16 feet is going to be good at hitting them from 21 feet, so the logical approach to offense is to shoot more threes than long twos.

However, while we’re talking logic here, it’s important to note that the closer you get to the basket, the better your odds of making the shot. When you get close enough to the basket, your odds of making the shot do, in fact, increase by enough to make it every bit as efficient a shot (if not more) than the three pointer, even without the bonus point. Let’s use some real-world data to illustrate this point. According to, the median shooting percentage on shots at the rim this season is approximately 59%. Also, per Hoop Math, the median 3 point shooting percentage is between 34% and 35% (we’ll use 35 just for simplicity’s sake). The median percentage on two-point jumpers sits at about 36%.

To turn this into a concrete example, say a team has 100 shots to attempt in a given game. If this team is average in every way, and they choose to shoot nothing but 2 point jump shots away from the rim, they will score 72 points. If they shoot nothing but threes, they’ll come away with 105 points. Thus, shooting threes > shooting twos, right?

This seems to be the jumping off point for a recent article by Matt Giles, published by a site that I thoroughly enjoy, Giles takes a bit off data, some conventional basketball wisdom, throws in some quotes from ESPN basketball stats expert John Gasaway, and comes away with an article that amounts to a strong back-handed compliment to Bill Self for finally starting to come around on the three point shot and what analysts have known about it for years.

Now, I’m on record as saying that I want Kansas, especially the teams they’ve had in the past two years, to shoot more threes. It does make sense, given what we know about the relative efficiency of the shot. That said, I also know that Bill Self has been an incredibly successful basketball coach at Kansas, winning 11 (likely soon to be 12) straight conference titles, plus a national title and second national championship game appearance.

I’m a huge proponent of the use of analytics in sports. If I weren’t, I probably wouldn’t be investing my free time in doing this type of research. With that said, there are some elements of the "analytics revolution" that concern me, and the message of this article illustrates one such concern. Namely: when data supports x and y, we can’t ignore y and justify it by saying "but look, the data supports x!"

This is what’s being done here. You may have noticed that I stopped short in my example of a team with 100 shots to disperse. Using Hoop Math’s numbers, this perfectly average team would score 118 points by shooting exclusively at the rim. Yes, that’s 13 more points than the team relying on sweet, precious threes! This would seem to indicate that there’s a balance to be found, and that offensive efficiency is more complex than "more threes = good." Obviously in an actual game, you have a team playing defense, likely a style directed at making your best shots the most difficult ones to take. This means that looking at any coach’s track record of three point attempts and wagging fingers for it being too low is a dangerously simplistic approach.

I wanted to kick things off by looking at the effect of 3 point shooting on offensive efficiency. After all, the object of offense at the end of the day isn’t to be able to point to your shot chart and say "look, we shot from where we’re supposed to!" It’s to score points as efficiently as possible. Fortunately, the brilliant Ken Pomeroy tracks a lot of these stats and I used his website (mandatory reading for college basketball fans and intelligent sports fans in general) to pull shooting and efficiency stats for all 351 Division One basketball teams through all games this season. First, I wanted to see if shooting more three pointers has any relationship to what percentage of said shots are made. The following chart illustrates my findings.

3p x 3pa

You can see that, yes, there is a meaningful correlation between the percentage of a team’s shots that come from behind the arc (3PA%) and the percentage that they make (3P%). That’s what we would expect though, right? If you’re a good three point shooting team, you’re probably not going to shy away from shooting threes, though that’s exactly the charge being leveled at Self in the above-referenced article. And to be fair, there’s a point to made regarding Self there. But let’s dig deeper. What relationship, if any, exists between 3 point shooting rate and offensive efficiency? Again, the goal is scoring as many points as possible, so results do matter. The following charts illustrate this relationship, using points scored per 100 possessions as a measuring stick for offensive efficiency.

3pa x oe

Ok, so shooting more threes has a small correlation with scoring more points. Again, nothing surprising here, given that we’ve established the relative efficiency of the three point shot. But doesn’t a .09 correlation seem low? It did to me. That’s why I decided to combine 3 point shooting percentage with the 3 point shooting rate by multiplying the two stats for each team to see if that makes a difference. Since we’ve established that teams shooting more threes tend to make a higher percentage, we should see that shooting a lot of threes and shooting them well has a much stronger correlation. And that’s exactly what you see below.

3px x oe

Case closed, right? A .37 correlation coefficient is pretty definitive evidence that putting together a team of guys who shoot threes well and aren’t afraid to shoot them is going to give your offense a big boost. I think we’ve established that very well. But there’s one thing I’m left to wonder about. What about two pointers? We’ve seen that close two-point shots can be even more efficient than the three. We’ve also seen from Hoop Math’s numbers that not all two point shots are created equal in terms of their likelihood of success. We also can see that almost every single team shoots more (generally far more) twos than threes. So how closely related is two point shot success with offensive efficiency? This is what may surprise you.

2p x oe

Wow! A .74 correlation coefficient? It seems we’re neglecting the importance of the two point shot here, doesn’t it? So to tie everything together, we have a coach under fire for not taking enough threes, countered by the fact that he’s had an almost unheard-of level of success over the last 13 years at Kansas. I wonder if he realizes how important two point shooting is? I wonder if maybe, just maybe, he even gears his offense toward making a large amount of high-percentage twos, given how close the relationship seems to be with scoring. The following chart takes you through each of Self’s years at Kansas, the team’s two point shooting percentage, their national rank in 2P%, and KenPom’s national offensive ranking for the team (bear in mind, this is their rank out of around 350 teams).

Year 2P% Rank KP Off Rank
2015-16 51.6% 70 7
2014-15 46.4% 234 36
2013-14 55.4% 7 14
2012-13 52.9% 15 34
2011-12 52.5% 22 28
2010-11 56.8% 1 7
2009-10 52.7% 19 2
2008-09 52.6% 30 32
2007-08 55.4% 6 2
2006-07 52.8% 32 26
2005-06 50.8% 69 45
2004-05 52.7% 29 13
2003-04 52.0% 27 31

Well, it would seem as though Coach Self has something figured out, wouldn’t it? Yes, last year stands out in a bad way, but it should be noted that despite the two point struggles, Kansas’ offense finished ranked 36th nationally by Pomeroy, and was sufficient to get them a 2 seed in the tournament and a conference title. This was largely done on the back of fantastic offensive rebounding (which is easier to do on two point shots than threes), and getting to the free throw line at a fantastic rate (also something three-heavy teams struggle with, since they aren’t drawing contact by trying to get into the lane). These are two other factors that should be considered when analyzing that strong correlation with 2 point shot percentage and offensive efficiency. Even missed two pointers are more likely to result in offensive rebounds (often near the basket, where shooting efficiency is highest) or free throws (uncontested shots that are made at the highest rate of any available shot in basketball).

My intent here is not to dismiss the idea that Kansas could benefit from shooting more threes; again, I agree with this basic supposition. We’ve demonstrated that a good three point shooting team (which Kansas is this year) shooting an increasing number of threes generally relates to better offensive outcomes. Right now, per Ken Pomeroy’s data, Kansas ranks just 220th nationally in the percentage of their overall shots that come from behind the arc. That’s an awfully low ranking considering they’re 6th in the country in making them (41.7%). Still, the fact remains that this shouldn’t be dwelled upon to the extent that it has, let along used as evidence of some type of coaching deficiency. Coach Self is one of the best coaches in the game, and it’s safe to say he knows all about the percentages. His record of coaching teams with highly rated offenses that score incredibly well inside the arc should suggest that.

The reporting on Self, where his use of the three is concerned, is a prime example of ignoring the facts about y simply because of what you’ve learned about x. Sometimes y can earn you more than a decade of consecutive major conference titles and a National Championship ring.