I — along with everybody else — have been watching nothing but soccer lately. The World Cup is perfect. It really is. By the time it arrives, the last World Cup is just entering the right age for nostalgia to seep in, and you’re ready for new memories of random Japan-Netherlands games and that one European powerhouse imploding in the group stage (Yeah Spain!). Everyone you know is behind the same team as you. It’s your chance to show the rest of the world what you’re all about — what makes your country unique. And the tournament format allows just enough chaos for hope, without feeling as though mastery of the sport goes unrewarded.
Watching soccer for the first time in so long, after consuming nothing but American sports the past four years, puts my brain in a weird place, though. Everything that happens on the pitch is processed through the lens of basketball and football. Especially basketball. That last second goal Portugal scored against the US to tie the game up? Well, by my count, soccer teams usually hover around 1 or 2 goals a game, so that was basically the equivalent of a basketball team scoring 50 points on one shot to tie the game up at the buzzer. Brutal. Or the US players forcing the ball to Julian Green against Belgium in the final minutes, praying he would work another miracle and allowing the responsibility to fall from their shoulders and onto the 19-year-old forward’s feet? The entire Miami Heat team in the Finals, resigned to the fact that the Spurs were way better and going, “Well, maybe Lebron will go into Lebron Mode and just start barreling through everybody.“
A bunch of comparisons like this have popped into my head while plowing through match after match. One of them — a slightly more plausible one — actually led to an interesting thought.
It happens over and over again. The ball inches closer and closer to the goal, into the danger zone. The offensive team is on the verge of breaking through, but it doesn’t quite have the right angle. And so somebody just rips it, straight at the goalkeeper. He can’t do anything but get his body in front of the ball and allow it to ricochet off of him, but the bounce is unpredictable, and the goalie is now out of position. Somebody else on the offense sprints toward the ball like a wild animal and buries it into the back of the net.
There is no assist on the play. If the initial attacker had pulled back — attempted to find a teammate, to maneuver the ball around until the perfect opportunity arose — maybe someone scores. But more likely something goes wrong. A bad touch, an aggressive defender getting in the way. The unsuccessful shot creates the goal. It’s not a failed attempt.
OK, back to basketball. One of the most popular topics among NBA statheads is “shot efficiency.” Using the word “efficiency” makes it sound super intense, but basically you multiply how many points a particular shot is worth by how often players typically make that basket to see how valuable it is. The most famous example is the comparison of three-pointers to long twos. NBA players make three-pointers about 36% of the time (according to Hoop Data). On the other hand, they make long twos about 38% of the time. Guess which shot the analytics prefers.
Once you do the math, the shots that seem to be the consensus favorites are those taken around the rim, three-pointers (especially the shorter corner threes), and free throws.
All of this, of course, assumes that all misses are worth zero points, which brings me to the interesting thought I promised and have spent over 500 words getting to. Are all missed baskets really created equal, a failed opportunity worth exactly zero points because the ball didn’t go through the net? Or are some misses a little more like the striker pegging the ball at the goalkeeper?
To indulge this mild curiosity, I spent about 800 hours writing a program that went through every missed shot in every play-by-play in every box score of every NBA regular season game on espn.com, and recorded the distance each shot was taken from the basket and whether it led to an offensive or defensive rebound. They don’t call me the homeless man’s Nate Silver for nothing.
The idea itself wasn’t complicated; maybe shots from some parts of the court lead to more offensive rebounds — and thus more chances to attack the basket — than others. Here’s what the results looked like:
Each bar represents a zone of the court shots were taken from, and the height of each bar measures the percentage of rebounds that ended up in the offense’s hands. The higher the bar, the more often missed shots from that area of the floor were grabbed by the offense.
A few things jump out at me. First is the continued dominance of the basketball nerds’ favorite field goals, shots put up from right around the rim. They’re much more likely to lead to second chances than attempts from anywhere else on the floor.
Even better news for the analytics guys: Those long twos they hate so much (from about 16 to 23 feet) are also the least likely field goals to be recovered by the offense. Take a step or two back behind the three-point line and the odds start to increase.
Finally, free throws, considered a staple of a healthy offense, beat out long twos for the Worst Misses For Getting Second Chances Title Belt.
I can only guess why these results are the case. Shots taken close to the hoop — the product of an offense breaking the defensive wall and crashing into the paint — might be more likely to end up in the hands of attacking players already clawing at the basket.
On the other hand, long twos are usually less the result of a defense collapsing in on itself and more the product of an offensive player getting just enough space to launch a shot. But unlike three-pointers — longer shots that result in longer rebounds more likely to reach a guard lurking on the wings — midrange jumpers often fall into the hands of big men positioned comfortably inside the paint. To be sure, the difference isn’t huge. But it is worth noting that while offensive rebounding rates decrease the farther the shooter gets from the basket, they start to pick up just as players begin moving beyond the arc.
That missed free throws are the least likely shot to lead to offensive rebounds is no surprise, considering two defensive big men get to line up on either side of the key just waiting to snag a rebound. The bigger surprise is that free throws aren’t much more likely to lead to defensive rebounds than those long midrange jumpers. Could it really be almost as easy for a defender to position himself for a rebound off of a jumper — taken amidst the many picks, cuts, and passes that comprise a live offensive possession — as it is to ready himself for a board off of a dead ball?
Anyway, I think all this makes for interesting food for thought — that is, as long as you’re the kind of person that spends his free time pondering shot efficiency. But is there a way to factor in this new information when calculating the value of different shot attempts? After all, the point of finding out how often different shots result in offensive rebounds was to get a better idea of how good those shots really are.
Having completed zero stats classes in either high school or college, I can confidently say that I am not the right person to take on this question. But because James’s Blog (Please send me name suggestions. Please) currently has no quality control, I’m doing it anyway.
All right, I already figured out how likely it is for a missed shot to lead to an offensive rebound. But how much is that rebound worth? Well if the offense fails to score again, it’s worth nothing. If it falls to a center right under the basket and he goes back up for the dunk, it’s worth two points. If he kicks it out to Manu Ginobili for the 237th wide-open Spurs three-pointer in the Finals, it’s worth three points and me burying my face in my hands. In other words, the simplest way to measure the rebound’s worth is by how many points it ends up getting the offense.
It seems reasonable then to say that an offensive rebound is worth about 1.03 points, since an offensive rebound provides a second possession, and the NBA league average for points per possession is 1.03. My guess is that number is a little low, considering the potential for put back slams, passes for quick shots before the defense can reset, and the general advantage of receiving the ball close to the basket against a disorganized defense. But since as far as I know there doesn’t exist a stat for points per possession on second chances, I’ll use 1.03 points.
As I said before, one easy way people calculate the “efficiency” of a shot is to multiply how many points it’s worth by how often it goes in. So if jumpers 10-15 feet from the basket went in 50% of the time, then 50% x 2 points = 1 point per shot. The chart below does exactly this.
*I’m defining a “shot” for free throws as when a player steps to the line for two, since this is the most common situation. Obviously, if we were talking about players getting fouled on three-point attempts, the points per “shot” would go up.
Just like the first chart, each bar represents shots taken from a particular part of the court. Now, the height of each bar measures how many points each shot ends up being worth on average. It’s pretty easy to see why advanced stats guys love shots at the rim, three-pointers, and free throws so much.
Again, though, this assumes that all misses are worth zero points. And they’re not. Some are more likely to lead to offensive rebounds, and thus second chance points. So to really get a good idea of how many points a shot results in on average, you have to add in the misses.
Take misses at the rim. A whopping 41% of the time they end up right back in the hands of the offense. And once in the hands of the offense, they’re worth about 1.03 points per possession. So each miss is worth 41% x 1.03 = .42 points per miss. To get an accurate value for the shot then, you have to add up the 65% of the time teams MAKE the shot and get 2 points (65% x 2 = 1.3), which is what I did in the chart above, and the 35% of the time teams MISS and get .42 points per miss (35% x .42 = .15). Adding these together results in a final value of 1.45 points per shot.
The red bars in the chart below measure this new value. The blue bars are the same as before.
As you can see, I’ve named this new stat Cohan Points Per Shot, because calling it “Points Per Shot Including The Value Of Misses By Offensive Rebounding Percentage And Points Per Possession” is too long, calling it True Points Per Shot is to ESPNy, and because it’s looking less and less likely that I’m going to discover a great river or series of islands that I can name after myself.
Quantifying how much each shot is worth in this way leads to one particularly interesting result. While before it seemed that free throws were the best shot by a not insignificant margin, after factoring in misses, shots at the rim and free throws end up in virtually a dead heat.
This makes sense. Shots at the rim are by far the most likely to result in an offensive rebound, while free throws are the least likely. For this reason, shots at the rim were undervalued, and free throws were overvalued, by the original metric. And this doesn’t even account for the fact that offensive rebounds off misses near the rim are probably more likely to lead to put back slams and quick, easy points than typical possessions.
There’s at least one caveat, though, that I can think of. The very chaos under the basket that allows teams to grab rebounds off their own misses near the rim also prevents them from recovering quickly and getting back on defense when they don’t manage to secure the ball. While teams might not collect a huge amount of offensive boards off missed free throw attempts, they do get to prepare themselves to run back down the floor and prevent fast break opportunities. So while they’re less likely to get second chance buckets, they’re more likely to prevent quick baskets by the other team.
None of this is revolutionary stuff. The point though — other than to pass on the Cohan legacy through an obscure basketball statistic known only to people whose newsfeeds I appear in — is that sometimes things aren’t exactly as they seem at first glance. Not all misses are just misses — bad chances, losses for the offense. Some failed attempts aren’t failures at all.
Feel free to take a look at the data/program files here.
If you’re interested in contributing, email me at firstname.lastname@example.org or message me on Facebook.