A couple of weeks ago I wrote an article in which I asked, is a miss always just a miss? If you want the gory details, you can find them here, but I’ll try to sum up the idea quickly.

For some time now in the NBA, people have been trying to figure out the quality of different shots. One easy way to do this is to look at how often a shot goes in, and how many points it gets you when it does. For instance, three-pointers count for, surprise, three points, and they find their way into the basket about 36% of the time, making them worth 36% x 3 points = 1.08 points per shot. Looking at shots in this way paints a pretty accurate picture of their value.

There is, however, one problem with this method: It ignores the most common outcome of the shot, a miss. After all, 64% of the time players launch three-pointers, the ball doesn’t land gracefully in the net. Instead, it bounces off the rim into a mass of bodies and *something* happens. The question is, what exactly is that something?

After scraping together the data, I found that misses from certain areas of the court were much more likely to lead to offensive rebounds — and thus, presumably, second chance points — than others. As it turned out, not all misses were equal.

I attempted to factor in this new information to create a new, more accurate “points per shot” statistic. Obviously, the 36% of three-pointers that went in were still worth three points. But what about the 64%?

Well, the new data I had said those misses were recovered by the offense about 25% of the time. And assuming those second possessions were worth 1.03 points, the league average for points scored per possession, then each miss was worth 25% x 1.03 points = .26 points per miss. Putting it all together, I added up the 36% x 3 points for made baskets, and the 64% x .26 points for missed baskets to get a final value of 1.25 points per shot.

Shots at the rim — being the most likely to lead to offensive rebounds — got the biggest boost from this new way of looking at things. Free throws, on the other hand, fared the worst, with long twos not so far behind.

Cool, you’re saying. You discovered something of very, *very* marginal interest.

Thanks. If you wanted to nitpick, though, you might point out that I made one big assumption. And that is that I assumed all offensive rebounds were worth the league average for point scored per possession, 1.03 points.

I had my doubts using that number. After all, second chance possessions are inherently different from regular possessions. Wouldn’t it be easier to score after grabbing an offensive board — gifted the ball within striking distance of the basket, facing an exhausted defense with no chance to brace itself for the attack already within its gates?

And if certain misses are more likely to result in offensive rebounds than others, isn’t it also possible that certain offensive rebounds are more likely to result in second chance points?

To *really* get an accurate idea of how much shots are worth, then, I’d need to replace that 1.03 figure with a real number, or even better, real numbers, one for each type of shot.

To get the those numbers, I wrote another program that went through the play-by-plays in the 2013-2014 regular season schedule on espn.com and figured out how many points were scored off every offensive rebound. It sorted the points scored by where the missed shot was taken. Then, it could calculate the average points scored after offensive rebounds off misses from each zone of the court.

My reward, the following chart.

The different bars represent the different locations from which shots were missed, and the height of the bars equals the average second chance points scored after offensive rebounds.

As you can see, the difference between shots appears minimal. At the high end are misses at the rim, with 1.07 second chance points after offensive rebounds on average, while at the low end sit free throws, with an average of .99.

Only .08 points between them, hardly a significant margin. Right?

Well, play that out over 100 possessions and it’s the difference between scoring 107 points and scoring 99. That’s just a slightly smaller margin than the difference between the Clippers’ league best offense — 109 points per 100 possessions — and the 76ers’ D-League offense — 97 points per 100 possessions. So there is a difference, likely explained by the fact that offensive rebounds collected off shots near the rim are the most likely to turn into high percentage putback shots.

The thing is, though, offensive rebounds are infrequent enough that this difference barely registers when it comes to determining the end goal, points per shot.

As you can see in the chart above, there’s virtually no difference between the statistic I created last time, Cohan Points Per Shot, using 1.03 points as the value of an offensive rebound, and the updated statistic, Cohan Points Per Shot 2.0, using the new average second chance points data.

Think about it. If you only miss shots at the rim 35% of the time, and you only get rebounds off those misses 41% of the time, those shots are only leading to second chance points 35% x 41% = 14% of the time. If second chance points only come into play on 14% of shots, then it isn’t going to make a massive impact whether you score 1.07 points or 1.03.

Good thing I spent all that time getting that new data then, right? I mean, nothing quite gets the people going like reading an article whose conclusion reads, “Nothing significant to see here.”

Luckily, there was ONE interesting result, at least to me. After noticing that the range for average points scored after offensive rebounds seemed to be wrapped awfully close around the original number I used for points per possession, 1.03, I decided to run my program again, this time calculating the average points scored after offensive rebounds for ALL misses. The number I got back … 1.03.

How about that. My suggestion that second chance possessions might be worth a little more than regular possessions was completely wrong. In fact, there’s no difference at all. So while a miss isn’t always a miss, a second chance possession is, in fact, just a possession.

*Feel free to take a look at the data/program files here.*

**If you’re interested in contributing, email me at james_cohan@brown.edu or message me on Facebook.**

Photo credit: Andrew Morrell Photography via photopin cc

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