Long two’s are the worst shot in basketball. Shots closer to the rim have a better chance of going in and a higher rate of drawing a foul on the shot, while baskets from beyond the three-point line are worth more points.

Three > Two
3 > 2

Of course, players don’t shoot as well from further away as they do from closer. But the difference between, say, a 19-footer and a 24-footer probably isn’t as big as you’d think in terms of success rate. The difference in expected points from said shots, though, is.

40% on long twos = 0.8 points/shot = 26.7% on threes
50% on long twos = 1.0 points/shot = 33.3% on threes

It’s really not hard to see how taking a step back or focusing your offensive game to be more perimeter-oriented can help an offense by lowering the threshold for makes for an efficient offense. Beyond just that simple math, three-point misses result in a higher rate of offensive rebounds, resulting in more second chance opportunities than two-point shots. There are potentially additional gains, too, from better floor spacing, preventing a defense from doubling or helping as well in the post or on dribble penetration.

This is all fairly logical stuff, but it’s logic that appeared to be lost on the Toronto Raptors last year. While I know their analytic department would prefer those long twos to become threes, their roster includes two players who shoot a high volume of long two pointers in Rudy Gay and DeMar DeRozan. Gay and DeRozan are both mediocre long-range shooters but are fairly adept at creating space and getting their shot off in the mid-range, which could clearly encourage such sub-optimal shot distribution.

But what if Gay and DeRozan made a concerted effort to turn some of their long two-point attempts into three-point attempts? I took a crack at breaking down the numbers to find out what impact this could have on the Raptors’ offense.

Current Shot Distribution
derozan distributiongay distribution

Altered Shot Distribution
It’s unrealistic to suggest Gay and DeRozan could/should have changed all of their twos to threes, but DeRozan was second in the league in attempts from 16-23 feet, while Gay was 23rd as a Raptor. What if we move their proportion of long-twos and threes to that of a more standard distribution?

The median team attempted about a split roughly as follows (percentages are as a percent of all shots longer than 15-feet, since we’re only comparing long-twos to threes, not the overall shot mix): 35% 15-19 feet, 28% 20-24 feet twos, 13% 20-24 feet threes, 24% 24-plus feet.

Rough league Median: 35% 15-19 feet, 28% 20-24 feet twos, 13% 20-24 feet threes, 24% 24-plus feet
Gay: 38% 15-19 feet, 14% 20-24 feet twos, 18% 20-24 feet threes, 30% 24-plus feet
DeRozan: 59% 15-19 feet, 22% 20-24 feet twos, 10% 20-24 feet threes, 8% 24-plus feet

So Gay’s distribution is actually closer to the league median distribution than I anticipated, at least during his time as a Raptor. But let’s ask Gay and DeRozan to move some of their shots from long-twos to threes and see what happens. You’ll notice even in places where a player shoots poorly from three, I’ve moved some long twos to threes, either because of small samples making me think the player may eventually shoot better from that spot and/or the second-generation benefits (offensive rebounding, spacing) of three-point attempts.
gay derozan experiment
As you can see, by making a few tweaks here and there we can add a few points onto DeRozan and Gay’s bottom line. If all of this seems like a lot of work for a small gain, fine, but it’s just an experiment meant to show that the players can make gains if their profile changes to a more efficient one. If I changed ALL the 16-plus foot twos to threes (an extreme and unrealistic scenario), Gay would see a 65 point boost and DeRozan a 14 point boost, so the effect can be very real.

Offensive Rebounding Impact
Depending on where exactly a three comes from, the offensive rebound rate on three-point attempts is anywhere from 22.4% to 25.3%. For mid-range or long twos, that range is from 19.7% to 23.2%. So we can expect roughly a 2-3% increase in offensive rebound rate when we move from a long-two to a three.

In our hypothetical, Gay and DeRozan combined to transfer 152 shots from long-twos to threes. There would also be 10 additional misses thanks to shooting more threes, for a rough total of 162 extra offensive rebounds available. With a 2.5% bump in offensive rebound rate, the Raptors could have been expected to grab an additional four offensive rebounds. Since the Raptors scored about 1.03 points per possession, that’s another four points on top of the gains from Gay and DeRozan shooting a more efficient distribution. The more extreme the distribution changes, the more extreme the second-chance effect would be as well (that is, in the hypothetical where all their long twos become threes, the team would have moved 677 shots from two to three with an additional 61 misses, leading to an extra 18 or 19 offensive rebounds and an extra 20 points or so). Another note: I believe teams score off of offensive rebounds more than in normal sets, but I couldn’t find the numbers to back this up.

Altering the Team Strategy
The Raptors aren’t, or weren’t, equipped with great three-point shooters. But we’ve shown here that making changes to the shot mix can have an impact on point production, even with guys who are decent in the mid-range and aren’t great from outside. If Gay and DeRozan abandoned all twos greater than 16 feet for threes, the team would have gotten an additional 99 points this season. If the change was even a bit moderate, as in the table above, they would have expected an additional 30 points from these two and the change in second chance opportunities.

We also haven’t accounted for floor spacing and the impact that might have on other players shooting in the mid-range or getting to the rim, and we haven’t accounted for the fact that the team could also alter their crashing strategy to get even more value from the offensive rebound effect here.

All of this is highly hypothetical, but I’ll take you back to our original over-simplified math proofs:

Three > Two
3 > 2

40% on long twos = 0.8 points/shot = 26.7% on threes
50% on long twos = 1.0 points/shot = 33.3% on threes

So get in the gym, guys, and fire up those corner threes. Abandoning some long-twos for three-point looks could have an appreciable impact on your scoring rate and the team’s offense.

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  • robertparrish00

    great work. Unfortunately Casey can only draw up isolation “long 2 pt” plays.

  • Bendit

    It would be interesting to know how much they practise the 3pt shots. And what their pctgs are there. That 3pt line can be a psych barrier for most. If you dont do well practising you wouldn’t have the confidence stepping back in a game.

    • It is amazing how much a difference a couple of feet make. Take Chris Bosh as an example. He shot an incredible 53% from 16-23 feet this season, which was the best for any player playing more than 20 mpg, yet his percentage drops to 28% from three.

      One of the reasons it makes such a big difference is often requires a completely different shooting stroke. It’s sometimes not just a matter of extending your range, but of reworking your shot.

      • Bargnani

        Chris Bosh has 3.3 rebound stat against Indiana so far. LoL Check his playing time, than make a big fat article about it, one of those 40000 words that you love so much. Can’t wait for it

      • Wilson

        … What. I’m pretty late to this article, but you’re really going to have to elaborate on “One of the reasons it makes such a big difference is often requires a completely different shooting stroke.” I don’t think I know anybody that shoots differently from three than they do from two. I know I don’t.

        • Shooting from 23 feet and shooting from 15 feet generally take different mechanics. Some guys already have shots (like Dirk) that don’t need to be altered to extend their range. A lot of people may not realize they are altering their mechanics (and some may not be), but most do.

          • Wilson

            That wasn’t an elaboration so much as saying the same thing in more words. For myself, I may use more legs from three and get a little more lift, but my stroke is the same. Seems pretty counterproductive to shoot it two different ways to me. o_O

  • cdub

    the long twos are the result of bad ball movement in all areas. then you throw in a guy like Bargnani who lives to take long twos and yikes. I think derozan can shoot the 3 better. I think he just needs to start going out in games and taking the shot if it is there. normally he would only take the 3 if he had to for the most part and was easily discouraged.
    Gay has shot the 3 decent at times in his career. Many write him off as a poor 3pt shooter but I think he has the potential, he will be hard pressed to replicate last year easily the worst of his career so I think he should be better this year.
    Long twos need to stop though. It’s a really simple thing that has been brutal with casey.

  • bigweeze

    Earlier this year on Grantland, there was a piece on the Raps’ analytics team where it was mentioned they wanted to see infinitely more 3 pointers. Amusing that the Raptors of all teams would be the ones advocating the strategy. The arguments were what you have based this upon – pts per shot and additional 2nd chance pts.

    But as you say, it is important that every player understands where he is effective. I read about Lebron adjusting his play to account for this new information and he now plays far differently than in years past.

    Problems I have with this shot distribution adjustment:
    – corner 3P% for most players is heavily weighted based on spot ups but the type of shot you are advocating more of is off the dribble?
    – opposing defenders are aware of the 3 point line and run shooters off of it, which is so many long 2s are available in the first place. this may already be the optimal distribution
    – a forced shot probably has a considerably lower % than the location average
    – players may become confused/uncomfortable on the court as they attempt to adjust
    – players may lose offensive discipline and other players may follow suit leading to chaos
    – small sample size – 22 total makes over 4 locations, no location with more than 20 attempts

    • BlakeMurphy

      Right, all of those are points that make it hard to predict a jump from point A to point B, especially the corner threes. Like I said, there’s no way to really know, it was just a quick math experiment showing that if the team made a more obvious effort to employ 3s more heavily in the strategy, there are likely gains to be made.

  • J val

    This assumes that they could turn those twos into threes. If they are less proficient at getting open beyond the arc, those shots would be contested and the percentages would likely go down as a result.

  • leftovercrack

    C’mon let’s get this shitshow over with and sign a new GM, then tell Gay and Derozan they’ll be tasered every second contested long two they throw up. Is it just me, or are these NBA semi-finals an indictment of Raptors management past and present? Hibbert coming up big in the paint (Indiana drafted him with the pick we gave them in O’Neill trade), Memphis knocked off Thunder and got to semi-finals after trading the inefficient Gay. Bosh is going for his second NBA title. And the Spurs are the franchise everyone for years has said we should model ourselves after but we never do. I want to wash my hands with past management and start over again building around JV, Ross, Demar, Quincy and giving Lowry one more year to prove he can be the PG

  • Higgins

    What if Derozan and Gay took less shots but still led the team 1st and 2nd in scoring and 2nd and 3rd in assist since they have the ball in their hands most of our possessions. It would be a more potent offense if they created more and set more players up for baskets. Teams are not going to just let those two players come off screens and shoot jumpers all season they have to develop some kind of play making skills to keep the defense honest. Right now they are a one trick pony, they’re going to take half of our shots. Many of which are in Isolation and though they may score a lot we live or die in games with that because other players can’t become a threat and the defense loads up on whatever side Derozen and Guy are on and don’t worry about other players because they are not going to get passes even if they do cut. I did like times when we went inside to Val and he at least passed to some cutters if the double team came. Gay and Derozen may score a lot for us but they are also in the top 3 for us in turnovers maybe because of they’re lack of playmaking abilities.