# Nylon Calculus: Possessions have been overestimated lately

In previous posts, I looked at how well players shoot on free throws not overall, but by each attempt in each situation. Players shoot differently on the first of two free throws compared to the second, and those with similar percentages on pairs of free throws can get there in different ways.

What I looked at in this post was not the accuracy on pairs of free throws or fouled three-point attempts, but the totals of each occurrence from NBA.com’s play-by-play data. After weeding out the two and three-free-throw situations from flagrant and clear path free throws, what’s left were legit free throw possessions. They’re important because some advanced-ish stats on NBA.com and Basketball-Reference use a coefficient of 0.44 to estimate free throw possessions instead of using exact totals, and that’s used to estimate all possessions. While that makes it quick and easy to calculate stats (like what I do with drawn foul percentages), the stats themselves are still not totally accurate.

An example of estimating free throw possessions can be found in the formula to calculate all possession totals on NBA.com, as Justin Willard found out here. Possession totals produce other statistics like pace, offensive efficiency, and defensive efficiency. The formula NBA.com uses for estimated possessions is simple and straight-forward. Basketball-Reference’s formula runs longer, but can also be done in a program like Excel with the appropriate statistics:

NBA.com’s estimated possessions: (FGA + (0.44 * FTA) – ORB + TOV) / 2 + (Opp FGA + (0.44 * Opp FTA) – Opp ORB + TOV) / 2

Basketball-Reference’s estimated possessions: 0.5 * ((Tm FGA + 0.4 * Tm FTA – 1.07 * (Tm ORB / (Tm ORB + Opp DRB)) * (Tm FGA – Tm FGM) + Tm TOV) + (Opp FGA + 0.4 * Opp FTA – 1.07 * (Opp ORB / (Opp ORB + Tm DRB)) * (Opp FGA – Opp FGM) + Opp TOV))

If every player attempted two free throws each time they were at the stripe and the defense got the ball on made second shots, NBA.com’s coefficient would be 0.50. The 0.44 considers and-1s, technical free throws, flagrant or clear path free throws, and the extra attempt on fouled missed 3-pointers. One of those four reasons for appearing at the stripe applies to just about every player. Since 1997, only eight players with over 1,000 minutes in a season attempted none of those free throw types. This season’s lucky player was Brandon Rush. Now you know.

But the simplicity of NBA.com’s formula is an issue because while it attempts to adjust for free throw possessions, it does not consider team rebounds. Their possession totals will be higher and scoring efficiency lower than what you’ll see on Basketball-Reference, which at least tries to factor in team rebounds.

And while the 0.44 coefficient itself is typically quite accurate for estimating not just scoring efficiency, but true shooting percentage and turnover rates, it will not work for every team or player, especially those from recent seasons. If we adjusted the coefficient for every year since 1997 by dividing all free throw possessions by all free throw attempts, we’d notice that the league overall is trending downwards:

Since 2005, the 0.44 co-efficient has been higher than league averages. This means estimates for scoring efficiency, true shooting, and turnover rates are slightly lower than they really should be.

What was the reason for this season’s downtick? For starters, there were a lot more fouls on 3-point attempts, 1,046 compared to 696 in 2016. In a great article by Tim Bontemps about fouls on 3-pointers, the number of 3-shot fouls was 1,045, but my best guess for the difference is that filtered one trip with an offensive goaltend. These are rare occasions, but over a full season with all free throw possessions, they’ll add up and become apparent in basic free throw splits. The fouls on 3-pointers are also a reason why four-pointers shouldn’t happen, as fouls on them would throw estimated stats out of whack.

There was also a spike in one-free-throw situations this season, but not just from and-1s. There was something of a crackdown on fouls before inbound plays, which in a typical season only generate a few technical-like free throws. This season, there were 67 such occasions. Overall, one-free-throw situations went over 5,600 for the first time since 2011.

If there are changes over the summer to how fouls on 3-pointers are treated, specifically the ones James Harden is known for drawing, maybe we could approach 0.44 again. Until then, it looks like statistics using estimated free throw possessions instead of actual ones will be overestimating. Below is a look at by exactly how much. Last season was overestimated by 780:

To some, I’m sure the estimates being slightly off and the changes I’ve made further down in this post will come off as minor. That’s fine, but there will be players like Kyle Korver who the coefficient always penalizes. At the very least, the statistics I adjusted are more accurate, if not exactly what they should be. They also rejiggered rankings, and some people love to rank or compare. We have a new best team since 1997 by net rating, and a different player with the best true shooting percentage in a season, minimum 1,000 minutes, for example.

Below are the statistics I tweaked — team possessions, true shooting, and turnover rates — but I also introduced few statistics in some Tableau dashboards like a better version of free throw rate. If you just want to see the Tableau dashboards, scroll down to the bottom of each stat. I would guess that my adjustments are easy enough to read and understand by themselves if you’re familiar with the estimated versions, but I touched on why the results were the way they were.

## Team Possessions

Because of Basketball-Reference’s lower coefficient to estimate free throw possessions and one to adjust for team rebounds, I didn’t bother tweaking their formula. It felt weird using actual free throw possessions in NBA.com’s formula when the results were still off because of team rebounds. They’re at least more accurate now.

While this season was the most efficient scoring one we’ve ever seen, using actual free throw possessions showed it was even better than we thought. The adjustment bumped up NBA.com’s league-average scoring efficiency this season from 106.2 to 106.6. It also remained the fastest-paced season since 1997, even though this season dropped from 98.7 to 98.4. We can probably say the same things for the same metrics on Basketball-Reference, given their formula has stayed the same over some time.

The changes from team to team were slightly larger. Because we’re using exact free throw possessions, it’s possible for a team to have a much higher coefficient on offense, but a lower one on defense, or the other way around. The lowest ones on offense and defense went to this season’s Rockets (0.407) and the 2007 Heat (0.415), respectively. The highest went to the 1999 Hornets (0.459) and 1999 Cavaliers (0.457). That wasn’t too surprising when the table above showed that the highest league averages were from 1999.

Below is a look at the Rockets and Hornets’ pace and scoring since I’ll use them examples for why a team could have a high or low coefficient. I also included league averages just because they’re good guidelines.

Houston had the largest uptick in offensive efficiency because of drawn fouls on 3-pointers. When looking just at three-attempt situations, the Rockets’ 150 at least doubled every team since 1997 but the 2016 Lakers, and that Lakers’ total was bumped up because of Lou Williams, who’s now on the Rockets. Houston even had more three-attempt situations than Dallas had in and-1s this season, at 145.

And-1s for Houston were also worth noting because of Montrezl Harrell, who made 34 of his 69 fouled shot attempts, via Basketball-Reference, and appear further down in this post. Put all of that together, and the Rockets had the lowest coefficient on offense. Every team this season but the Sixers received a slight bump in scoring efficiency, while every team received a slight penalty on defense.

As for the 1999 Hornets and their downtick in adjusted scoring, they made only 15 percent of their fouled shot attempts, generating and-1s much lower than expected. Who is to blame requires guesswork. Play-by-play data didn’t start showing who drew fouls until 2005, which makes Basketball-Reference’s fouled shot attempts up to that season look a little weird. What they have on player pages only goes back to 2001, but it appears that Elden Campbell, David Wesley, and Eddie Jones were average to poor at making their fouled shot attempts. For example, Campbell went a combined 45-for-356 (12.6 percent) on fouled shot attempts in 2001 and 2002. Nothing like Harrell for the Rockets, but it’s hard to complain too much about drawing a lot of shot fouls and getting more offensive possessions in the penalty, which the Hornets were solid at during that era of basketball.

One other note was that Charlotte attempted the fourth-lowest technical free throws that season with 20. The 2001 and 2002 Blazers allowed 110, the most since 1997, which would explain their coefficients of .424 and .417 on defense, respectively. The technical fouls immediately hurt the Blazers’ defensive efficiency because of free points, but it also inflated their allowed possessions. After the adjustments, their defense looks even worse.

Of course, which team benefited or was harmed the most by adjustments depends on what you’re prioritizing. If net rating matters for most beneficial, the 1997 Jazz’s net rating was 0.73 points better than before, the highest bump. Meanwhile, the 2016 Spurs went from third to first in net rating since 1997, becoming the most dominant regular season team in the last 21 seasons by that measure. If you’re looking for the highest leap in rankings, the adjustment pushed the 2017 Pacers up 32 spots in net rating since 1997.

You can find each of those stats in the Tableau dashboard below. It covers each team’s coefficient on offense and defense, NBA.com’s calculated pace and efficiency, adjusted pace and efficiency, and rankings for estimated and adjusted statistics.

True shooting percentage

To see the dashboard featuring adjusted true shooting percentage, scroll down to the bottom of the turnover percentage section.

True shooting percentage on NBA.com and Basketball-Reference considers the value of not just 3- and 3-point attempts, but free throws as well. It’s calculated as follows:

PTS / (2 * (FGA + (0.44 * FTA))

While estimated free throw possessions for teams were usually only slightly off from their actual totals, players were affected a bit more. The lowest coefficient, minimum 1000 minutes, was from Kyle Korver in 2016 at .204. This was because most players like Korver, low-usage sharpshooters who aren’t drawing a ton of fouls except late in close games, are chosen to shoot technical free throws. Of Korver’s 54 free throw attempts, 25 came from technical fouls with an extra 11 from either and-1s or three-attempt situations.

Below is a look at how using exact free throw possessions instead of estimated ones changes Korver’s true shooting marks since 2004:

Korver’s changes aren’t too big since he’s almost always been a low-usage scorer, but they’re certainly enough to move up in rankings. In particular, using actual free throw possessions pushed his 2015 season past Tyson Chandler’s 2012 campaign as the highest true shooting percentage for a player who logged over 1,000 minutes.

The largest increase went to John Stockton in 2001, from 61 to 64 percent. From 1997 to 2003, the Jazz had the six-highest technical free throws attempted per game and seven of the top eight, averaging 1.3 to 1.8 per game. Stockton himself was selected for 84 technical free throws in 2001. That tied for the highest from a player with teammate Jeff Hornacek, who attempted just as many in 1998.

As for bigs, lob threats are similar in usage and efficiency as spot-up shooters, but they’re rarely spectacular free throw shooters. They’ll neither pad their point totals on technical free throws nor draw the occasional foul on three-point attempts. Those who saw increases in true shooting had a high portion of their total free throws originating from fouled shot attempts, plus a well above-average amount of and-1s. That’s where Harrell’s outlier-ish season comes in for the Rockets. His true shooting went up 1.75 percentage points, the highest jump from last season, while Jonathon Simmons saw the largest drop, though it was only 0.6 percent. More on both players in a bit.

## Turnover percentage

The formula below is for turnover percentage, or rate used at Basketball-Reference. It’s somewhat similar to true shooting as it uses the same coefficient and needs shot possessions. It’s as follows:

TOV / (FGA + TOV + (0.44 * FTA))

These changes weren’t as exciting, but were necessary since adjusted true shooting percentage meant for an opposite effect on adjusted turnover percentage. For every 0.5 percent change in true shooting, there was typically only a 0.1 percent bump here. Not terribly thrilling. At the least, this season still finished with the lowest league-average turnover rate ever, from 12.7 to, well, 12.8.

But because we have exact free throw possessions, we can look at how players and teams distributed all their scoring possessions by turnovers, free throws, and field goal attempts. This was done by using the same formula for turnover rate for the latter two stats, for shot rate and free throw possession rate, all adding up to 100 percent. Below is an example of how a spot-up shooter, lob threat, and high-usage playmaker look along with league averages:

However, these types of stats have some flaws. Lowering a turnover rate can happen simply by shooting more, no matter the quality. That would also shrink free throw possession rate, and it doesn’t include potential assists. Regardless, for those who like to cite turnover rate, now there are two new stats like it, and adjusting turnovers felt necessary after adjusting true shooting.

Below is the dashboard including all those metrics for both players and teams. The current view includes just players from this season who played at least 1,000 minutes, and is sorted by lost shooting possessions after adjustments. Harden, who appears first, lost the most  with 44. That was the most not just last season, but all since 1997.

## Free throw rate

Finally, I used free throw possessions to adjust, well, free throw rate (or free throw attempt rate). This simply divides total free throw attempts by total field goal attempts. It’s commonly used to measure foul-drawing, but it’s flawed as it considers all free throw attempts. Surprisingly, the coefficient in true shooting has yet to be thrown in here. Without it, players inflate their rates with trips to the line from technical fouls, the extra attempt from fouls on 3s, and are rewarded for not accumulating and-1s.

So why not replace free throw attempts with free throw possessions? The problem with that is and-1s. While free throw rate penalizes them for the field goal attempt to go with only one free throw, free throw attempt possession rate wouldn’t even acknowledge the free throw attempt since it’s not a two or three-shot situation. If John Wall, an and-1 machine during the playoffs, attempted 15 shots with five of them as and-1s, his free throw attempt rate would be 33 percent. That’s an undercut from what it should really be since going five-for-five on fouled shot attempts is super rare, but it’s better than what his free throw possession rate would be, which is zero.

Drawing any foul should be good, getting to the line should be better, but and-1s should be best and rewarded as so. With that in mind, I made a simple adjustment to free throw possession rate. Since fouled shot attempts only count as actual field goal attempts when made, and players make them at varying rates from inside the arc and beyond it, I put everyone on even ground by converting all and-1s to free throw possessions with the following formula:

(Free throw possessions + And-1s) / (FGA – And-1s)

This tweak propped up players like Harrell, who without the adjustment would’ve been penalized even worse than raw free throw rate. Below is a look at Harrell and Simmons, the latter player who was just 4-of-52 on fouled shot attempts during the season. I also included league averages as a guideline.

Both Harrell and Simmons moved up in the rankings, but Simmons drops back a handful of spots after adjusting for his lack of and-1s while Harrell moved into the top 50.

There wasn’t a strong correlation with team free throw rate and NBA.com’s scoring and defensive efficiency last season. With adjusted free throw rate and adjusted efficiency, the correlations were slightly weaker on offense and slightly stronger on defense. Results were similar when looking at 2012 to 2017, when free throw rates have been pretty stable, and 2005 to 2007, when free throw rates were at some of their highest marks of the last 20 years.

As usual, shooting stays the most important element, but below is a Tableau dashboard of adjusted free throw rates for teams and players, sorted by minutes:

The coefficients used to estimate total possessions or just shooting ones are quite accurate, but not perfect. It’s not reason to panic as most changers are minor, but they’re something to be aware of, especially when ranking and comparing teams and players. It’s obviously important to have a good idea what the stats you cite mean, but knowing the formulas behind is valuable in knowing what’s being included or left out.

Next: 3-point trends in the NBA Playoffs

This was also only one way to measure free throw possessions and scoring ones in general. There’s a decent case that possessions with clear path or flagrant free throws should count as two, and how should we really treat end-of-quarter heaves, among other things? There isn’t really a universal agreement on what is and isn’t a possession. In the future, though, I’ll adjust some statistics for a certain aspect of the game that sometimes occurs for several minutes at a time.

As a reminder, free throw possessions were calculated via NBA.com’s play-by-play data.