# Nylon Calculus: What changes when teams go into the penalty?

A couple weeks ago, I wrote about how long teams score and defend in the penalty, and how not all penalty time is equal. The main goal of that post, and any related to the penalty, are to add resources to a phase of the game both fans and analysts bring up, but one with little information to cite. That’s a problem since teams play in the penalty for an average of about 12 minutes per game. But now that we know how much time this situation occupies, we can look at how well teams score and defend with and without fouls to give, and why.

As a reminder, teams enter the penalty after committing or drawing either four team fouls in a quarter (three for overtime), or one within the final two minutes. Team fouls are any fouls outside of those on offense that result in a turnover (moving screens, charges, etc.) and technical fouls. Once the penalty is in effect, every non-shooting team foul leads to two free throws.

I actually wrote a bit about points and other statistics in the penalty last year, but back then too much work was done by hand. It was too time-consuming to continue updating with the same method, or look back at previous seasons. 82games also had a post from what appears to be 2005. They looked at efficiency and several other stats by fouls left to give, which was impressive considering the difference in available data back then compared to today. It’s still a valuable post like so many from the site.

For this post, I worked off play-by-play data from NBA.com, but made a few tweaks to it. The most necessary one was to adjust for rebounds after free throws from the final foul to give. In play-by-play data, there’s usually a difference of a second or two between missed shots or free throws, and the rebound. That meant a team’s penalty phase would start with a rebound, which wouldn’t have made sense when scoring out of the penalty starts with either a jump ball or inbound pass.

A couple other tweaks took out possessions that weren’t vital to team performance. The first one was filtering out end-of-quarter heaves, which are about as likely to go in as a pitcher getting an extra base hit, though any heaves after an offense had eight seconds to get a better shot, or after the defense used their foul to give were included. At that point, it’s bad offense, or in the latter case, it’s good defense. Also, the rare individual rebounds after heaves were taken out. They’re usually credited as team rebounds to the offense.

The other adjustment was end-of-game sportsmanship shot clock violations, when a game is out of reach and the winning team runs out the clock instead of running up the score. These turnovers count as team ones and don’t harm the last player to touch the ball, but unlike team rebounds, they still count towards turnover and possession-based statistics. Because of that, they were removed.

For calculating statistics like true shooting and turnover percentage in and out of the penalty, I also adjusted free throw coefficients to calculate free throw possessions, like in this post. When comparing teams in and out of the penalty, the coefficient when in it was 0.45 to 0.47 while 0.41 to 0.43 was common for when teams had fouls to give.

The aspects of the game to adjust for felt endless, but the changes I made were minor. Below compares league average statistics before and after, with the help of using Basketball-Reference’s possession formula.

What happened when teams entered the penalty was more meaningful. Overall, teams this season scored about 5.2 more points per 100 possessions, tied for the lowest increase since 1998. Below is a look at league-average offensive efficiency in and out of the penalty over the last 20 seasons, as well as the differences between the two marks. You can also look at specific teams and look at defense, but I’ll go over each side of the floor.

## Offense

The shrinking difference in offensive efficiency should be a good sign going forward. Teams appear to rely less on the penalty to aid their scoring chances and more on shooting efficiently from the field, and they seem smarter about excessive fouling. In fact, if you look at the default view of the dashboard, teams in 2017 scored out of the penalty about as efficiently as those in the penalty in 1999 and 2004.

While league-average offensive rating in the penalty this season was the second-highest since 1998, looking at each quarter showed nothing historic in that phase of the game. From first to fourth quarters, this season’s efficiency in the penalty ranked fourth, second, first, and fifth, while marks outside of the penalty were all at the top among the last 20 seasons. Fourth quarters were still surprising as far as scoring in the penalty went. That’s where teams pad their scoring metrics with closing lineups and late-game fouling, but the increase in scoring efficiency was the worst of the last 20 seasons. Most seasons recorded an increase in fourth quarters of 10 to 13 points per 100 possessions, but 2017 ended with the penalty giving a 7.5-point boost.

Regardless of era, just about every team’s offense over a full game was more efficient when the penalty aided them. Only 13 squads since 1998 scored worse, and even then, it wasn’t a death knell to their offense. Most of those 13 were fine overall. The Pacers from 1999 were one of those teams, and they led the league in scoring that season. Also included were this season’s Nuggets, who thrived with Nikola Jokic.

When looking at the most efficient offenses during either foul state, last season’s and this season’s Warriors sat at the top of raw offensive efficiency in the penalty at well over 120 points per 100 possessions, including the latter version reaching 130 when filtering out fourth quarters. Meanwhile, the Seven Seconds or Less Suns and teams with personnel from them covered the top offenses without help from cheap free throws.

Below are the top offenses in each situation since 1998:

Unfortunately, an easy way to overrate the penalty is to not account for, on average, a coin flip for whether the opposition has the same advantage. In the previous post about how long teams play in the penalty, both teams had the same edge and quite possibly cancelled each other’s out 52 percent of the time. Because of this, while offense improves in the penalty, defense typically worsens.

## Defense

Comparing when defenses do and don’t have fouls to give, only 16 teams either broke even or defended slightly better in the latter situation. Unlike when teams score worse in the penalty, this group was mixed with both successful defenses like the 2010 Bobcats and 2017 Pistons, and bad ones, like the 2016 Lakers. To go back to this season’s Nuggets, they ranked 29th in defense with fouls to give at 112.3 points allowed per 100 possessions. In the penalty, they ranked a little better, 23rd by allowing 115.8 points per. As for the best marks with and without fouls to give, the Warriors and Spurs were the stingiest defenses last season at 102.9 and 106.1 points allowed per 100 possessions, respectively. The best raw defensive ratings in each situation since 1998 were the 2004 Spurs and Pistons at 91.4 and 98.2. The top 10 mostly came from 1999 to 2004.

Hopefully it’s worth seeing how historically great (or bad) teams performed with and without the penalty to their advantage. When deciding who’s the best offense or defense ever, should candidates for the former excel in scoring without the help the penalty provides, and should the best defenses have a history of locking up when they have no fouls to give? Regardless, below is a look at every team’s marks since 1998 in a form that allows for comparing and ranking, unlike the dashboard above.

## Overall

So how do teams perform in the penalty overall, at least by net rating? Because more points are typically allowed on both sides of the floor, the net ratings when offenses have this advantage are pretty small. In 2017, teams were +1.8 points per 100 possessions in that situation, compared to -0.6 when out of the penalty. This is probably underwhelming to a lot of people.

The next level was to account for both offensive and defensive foul states at the same, because the real advantage, of course, is when the offense is in the penalty while the defense has fouls to give. In those instances, teams were an average of +3.9 points per 100 possessions, though the margin was larger in the past. The decline was like the scoring increases in the penalty mentioned earlier, with the late-90s and early-2000s showing higher marks overall, first quarters weighing down averages over a full game, and fourth quarters propping them back up.

Below is a breakdown of each in and out of the penalty combo, with their league-average net rating and the percentage of each game they took up this season:

In my last post, the Phoenix Suns and Charlotte Hornets were featured because they were opposites in terms of quality of their penalty time. The Suns led the league in time scoring in the penalty at 13.6 minutes per game, but also on defense at 16.7, good for the worst team by net penalty minutes. As a result, their time scoring with their offense in the penalty was often with no real advantage since their defense often had no fouls to give. Meanwhile, the Hornets led in net minutes, were second in the league in minutes with only their offense in the penalty, and spent the least amount of time with only their defense in that spot.

How did each team actually perform in the best and worst situations, at least by foul state? Below is a season summary, but also with the Golden State Warriors. That’s just to see how one of the greatest teams ever fared in these instances.

While Charlotte certainly performed better than Phoenix when only their offense was in the penalty, the quality of time only helped them so much. Their net rating of +1.4 over 588 minutes was in the bottom 10 this season. Still, the Suns were much worse. Only Brooklyn had a lower net rating this season in what was supposed to be an advantageous spot, ending the season at -11 points per 100 possessions. As for Golden State, their +18.8 net rating led the league comfortably, but the 2013 Memphis Grizzlies had the highest mark since 1998 at +28 points per 100 possessions over 424 minutes.

When only the defense was in the penalty, the Warriors were one of nine teams this season to break even or better. The Utah Jazz fared the best at +9.2 points per 100 possessions over 384 minutes, while Charlotte fell off the grid at -11.9. In general, the Hornets struggled when they had no fouls to give, allowing an average of 121.6 points, three more than 29th-placed Dallas. The best team since 1998 by net rating with only the defense in the penalty was the 2010 Cleveland Cavaliers at +14.4 points over 440 minutes. The worst was the 1999 Chicago Bulls at -24.7, and an offensive rating of just 82.3 over 311 minutes.

## What else changes?

Overall, the samples for the best and worst situations by foul state were small. In a normal season, they’re anywhere from 200 to 800 minutes per team. As we saw with the 1999 Bulls, the results get weird, but we don’t even know why. In 2017, did Charlotte’s opponents simply run hot from beyond the arc? Did Golden State ever miss when their offense was in the penalty? What trends did teams with major differences in offensive or defensive ratings go against once the penalty came into effect? What trends related to the penalty even exist, and what are possible reasons for them?

We can start by using the same statistics used when mentioning adjustments to play-by-play data, and split them by in and out of the penalty. Below are league averages:

Because teams shoot free throws after every team foul once the penalty kicks in, the doubling in free throw rate is the most obvious reason for more efficient scoring. Since 1998, every team’s offense increased their free throw rate by at least 14 percentage points. Before the hack-a-Shaq tweaks banning the strategy for the last two minutes of every quarter and on inbounds plays, the 2016 Clippers had the highest uptick, from 20.8 to 67.4, while this season’s Bulls had the lowest increase in free throw rate, from 22.6 to 36.7. Also, the highest free throw rate out of the penalty, which belongs to the 2006 New York Knicks at 32.3 percent, is lower than the lowest free throw rate in the penalty, which goes to the 2013 Orlando Magic at 33.3 percent. Now you know.

Below were the highest increases since 1998, just to see how weird the Clippers were before the rule changes.

When looking at when only a team’s offense was in the penalty, they almost always ended the season with a positive net free throw rate over those small samples. Only three teams were in the negatives: the 1999 Boston Celtics, 2008 Minnesota Timberwolves, and 2015 Orlando Magic. Turning the tables and looking at when only the defense was in the penalty, the 1999 Spurs, 2012 Lakers, and 2012 Cavaliers are the only teams to have a higher free throw rate than their opponent. The 2012 Cavaliers will now live forever.

Splitting free throw rate by foul state also showed that the decline in this statistic league-wide came when teams were in the penalty. In 2017, that mark was 43.8, which was two to 13 percentage points lower than any other league average since 1998. Free throw rate out of the penalty this season ranked ahead of most recent ones and, randomly, 2000.

To get a better idea about the rest of these trends, I split the statistics up by each minute of each game this season, sorted by when the play started. This was to offer a better look at how quarters end. Watching them in real time, there’s a clear difference in how they play out, and depending on the quarter, anywhere from 66 to 83 percent of those possessions took place in the penalty, by my estimates. Is the final minute responsible for drops in statistics in the penalty, like three-point shooting, while boosting others like pace?

So below is a dashboard with a variety of stats for each minute of a game last season. The 49th to 53rd minutes were all overtimes grouped into those five minutes. There’s a filter for in and out of the penalty while quarters and minutes can be taken out. The minute filter is especially useful to adjust the vertical axis in the case of small sample sizes, typically from the rare possessions early in a quarter when a team was in the penalty. The default view is offensive efficiency overall and no penalty filter. You can also view multiple stats at once.

Even after filtering out heaves, offense declined at the end of quarters without late-game fouling. This made sense on multiple levels. Teams chase the two-for-one even if the first possession needs to be hurried. Some players also sprint up the court before the buzzer to attempt a shot mid-stride, a low-percentage scoring opportunity, but one nonetheless. Looking at the end of games, the cold shooting could come from shots being contested, hero-ball like shots or just iffy 3s trying to complete a comeback.

There’s also the foul to give that disrupted final scoring opportunities. When looking at 320 possessions this season when teams entered the penalty with 20 or less seconds remaining in the first to third quarters, the offense averaged just .75 points per possession. There was also a slow, but consistent decline in efficiency if teams used their foul to give closer to the buzzer.

This matched similar research from last season, but the process is blurry at this point and may have differed from this season’s. Regardless, if a team has a foul to give, they should use it, and especially if they can substitute for more defense on the floor.

And also after filtering out heaves, 3-point rate increased over the final minutes of each quarter. Since 1998, only 13 teams declined in 3-point rate once they entered the penalty, all by a couple percentage points or less. They included the 2017 Bucks, Raptors, and Nuggets. As for the Rockets, their 3-point rate went from 45.4 to 48.3. On the surface, teams play a little more Moreyball with the increase in attempted free throws and 3s, but the end of quarters and a game’s progression play a part.

As for accuracy, 2-point attempts remained similar when in the penalty. That’s helped by an increase at the end of games where 3-point percentage dipped. 3-point shooting peaked in the middle of the first quarter, over 40 percent during that point. Perhaps that’s because of fresh legs, but it’s still odd considering quite a few teams still start two traditional bigs, therefore having less shooting on the floor.

Because shooting is so vital to overall offense, a lot of team examples earlier were outliers here. The 1999 Pacers led the league in offensive efficiency that season, but scored slightly worse in the penalty after a 7.2 percent drop in 3-point accuracy and 5.9 percent decrease in effective field goal shooting. The 1999 Bulls, with their 82.3 offensive rating when their offense was out of the penalty and their defense had no fouls to give, shot just 17.6 percent on their 3s, the worst mark from any foul state. As for this season’s Hornets, opponents improved their effective field goal shooting by 3.5 percent once they entered the penalty, the seventh-highest increase over the last 20 seasons.

Historic shooting was part of why the Warriors dominated in the penalty. In 2017, they led in effective field goal percentage outside of it at 55.8, just barely ahead of Cleveland, but improved by 3.4 percentage points once they entered the penalty, the third-highest improvement since 1998. It’s unfair to have their level of shooting, plus a 20 percent spike in free throw rate once the defense was out of fouls to give. For the Seven Seconds or Less Suns mentioned earlier, their 2007 and 2008 squads hold the highest true shooting percentages without the aid of the penalty at 59 percent.

Looking at other stats, offensive rebounding and turnover rates rising and lowering at similar points, and affecting how they look in and out of the penalty seemed normal. During the final possessions of a quarter, it’s logical to crash the boards when the opposition has a slim chance to respond before time expires. The rise over the final five minutes also made sense when multiple analysts (David Locke comes to mind) have said things along the lines of offensive rebounds at that point carry more weight than those from earlier stages of the game. Taking out defensive rebounds after end-of-quarter heaves could’ve helped offensive rebounding rate in the penalty, but barely.

The drop in turnover rate in the penalty was obviously helped by team fouls leading to immediate free throws and the offense only susceptible to a lane violation or delay of game. And while isolation scoring at the end of quarters can be boring, it lessens the risk of turnovers, the typical small win for wings who attempt a lot of pull-up jumpers.

Pace by minute in and out of the penalty, and by when a play started was too laboring to calculate in the dashboard, but here’s a breakdown by quarter:

The typical reasons for dips or increases in other stats applied here, with team fouls leading to immediate scoring opportunities in the penalty and teams playing faster at the end of games to complete a comeback. The excessive fouling makes a game last longer, but the pace looks faster on paper. The actual differences are also likely closer than the estimated ones because the free throw coefficients in the formulas for in and out of the penalty should be different, but Basketball-Reference’s method is different than NBA.com’s, and wasn’t something I wanted to mess with. Pace is a vague statistic anyway since it averages out each team’s estimated possessions. There could be similar seconds per non-foul possession in and out of the penalty for each quarter, but that’s a project for someone more intelligent.

To back to free throw rate, there’s a steady progression in both foul states, but also the doubling in that mark overall in the final minute of games compared to just about any other point. Teams averaged a free throw rate of 80 percent in the final minute of the fourth quarter this season without factoring in the foul state, and it leapt to 102 in the final minute of overtimes. With the excessive fouling to create more possessions for a comeback, the pace of those situations was 105 and 130.1.

These were mostly just suggestions for why certain stats changed once teams entered the penalty. A common, repetitive theme was the impact of each quarter’s final minute, but it was only one season. I’m sure brighter basketball minds have better reasons for all of these trends, which is great. Combining observations with data is a pretty good combo when the data’s now available. But as stated earlier in this post, it should be good that the advantage the penalty provides has shrunk. Teams are scoring efficiently without that help, though maybe they could adjust their sub patterns so their best players, or foul-drawers play a little more when defenses can’t just stop a play with a cheap foul, and the rip-through ones still lead to free throws.

Next: Nylon Calculus -- The Art of the Finals MVP prediction

For now, we know how long teams score and defend in the penalty, how much parts of the game like scoring improve once opponents have no fouls left to give, and why scoring improves. But every team is different. Below are a couple of dashboards breaking down team statistics by penalty situations on offense and defense. The first dashboard allows for ranking and comparing teams. The second is a line chart focusing on team trends across the last 20 seasons. Both allow filtering by foul state. Selecting ‘Both’ simply means adding ‘In’ and ‘Out’ of the penalty together to get team totals overall.

You can also view single-game penalty time and plus-minus in and out of the penalty here.