# Nylon Calculus: Revisiting penalty time

There’s one aspect of a basketball game that can completely change the dynamic of player for several minutes at a time. Fans and analysts often mention it, but rarely with exact measurements because there’s not a lot of information out there. It’s when a team goes into what’s called either the bonus or the penalty. I’ve actually covered this situation a couple of times over last summer (here and here), but this is the start of a series looking at that aspect of the game with more depth. Hopefully by the end of it, those that mention the penalty will have useful resources at their disposal. They’ll be able to add more to their discussion other than simply describing it as important. For this post, I looked at how long teams scored and defended in the penalty this season, but also why similar marks from two teams overall might not be equal in quality.

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 outside of offensive and technical fouls, and once the penalty is in effect, every one of them leads to two free throws. Every edge matters when efficiency is stressed now more than ever.

It might seem obvious, but over a large sample, the earlier a team uses their fouls to give, the more likely they’ll enter the penalty. Below was a team foul chart I made for a post last year, using seasons from 1998 to 2016 to look at the likelihood a team enters the penalty with over two minutes left, depending on when they committed or drew their first to third team fouls. Unfortunately, I lost the code and couldn’t even find the document that produced this screenshot, so I wasn’t able to add this season or create a separate one for just 2017, but I’d bet the latter chart would’ve looked unusual anyway given the small sample sizes in a single season for several time slots.

This season, the most time spent scoring in the penalty in a single game was from

Denver against Toronto

, back when they had both

foul-drawing machines

in Danilo Gallinari and Jusuf Nurkic. The Nuggets logged about 31 minutes of penalty time and attempted 35 free throws overall. There were also two shutouts for entire games this season, both coming from Chicago in the same week, spending zero seconds with an advantage on offense against

Charlotte

and

Detroit

. There have been

27 shutouts

since 1998.

Single-game totals can be viewed here. Below is a look at team averages throughout this season. You can also look at each year since 1998 and filter by first to fourth quarters:

There were two historic teams by penalty time this season, but I’ll touch on them later. As for league averages, they’ve been mostly the same over the last four seasons, about 11.5 minutes per game with nearly two minutes from first quarters, three in second and third quarters, and three and a half in fourth quarters. As you might expect from those marks and the team foul chart, fouls aren’t distributed evenly from each quarter, which gets overlooked. Either more contact is allowed early in games or teams are less aggressive.

Regardless, those numbers were all down compared to over a decade ago. Back then, teams averaged between 13 and 14 penalty minutes over a full game. Intentionally fouling over the last few years has done little to effect league-average marks over several months. In fact, the Los Angeles Clippers scored in the penalty over a minute per game longer this year than the previous couple.

The decline league-wide also coincides with the decline in free throw rate, since it rewards teams with more ways to visit the stripe. Below is a dashboard looking at team penalty time and free throw rates. This is more just to show the correlation between the two stats and not to show something like which teams draw the most fouls when they know their opponents have no freebies left. It does give something of an idea of what that would look like, but definitely not a complete one. The current view highlights just teams from this season.

However, not all penalty time is equal in quality. For example, if both teams of equal talent faced off and were always in the penalty at the same time, it’s possible that the benefit it provides for their offenses are cancelled out since the defenses have no fouls to give. To use a hockey term, the teams would still be at even strength.

But because teams are in the penalty less often in recent seasons, one related stat that’s gradually increased is the percentage of time teams spend with only their offense in it. League-average minutes in the penalty this season was 11.5, but teams averaged 5.5 of them, or about 48 percent, with their offense in it and their defense still having fouls to give. The difference is small compared to over a decade when the percentages were from 42 to 46, but today’s teams are still experiencing an actual advantage more often, even if it’s harder to reap the benefits because of foul-averse defenses.

This was where teams that excelled or suffered in net penalty minutes look great or bad, respectively. The Charlotte Hornets and Phoenix Suns from this season were decent examples. By penalty time on defense, the Hornets were historically great and Steve Clifford’s squads have typically excelled at foul-related (and rebounding) metrics in general. Both their raw minutes defending in the penalty per game and adjustments for league averages this season were tops since 1998, and their net minutes per game was seventh-best. The 2013 Lakers were first with +6.8 minutes.

Meanwhile, after adjusting the Suns’ time defending in the penalty by league averages, their marks were the worst of the last 20 seasons. In particular, Alex Len and Marquese Chriss were in the top five in fouls committed this season per 36 minutes, minimum 1,000 minutes. It’s the first time two teammates finished that high since Golden State in 2013 with Draymond Green and Festus Ezeli.

Because of the Suns’ marks on defense, they may have spent two more minutes scoring in the penalty than the Hornets overall, but their advantage on the end of the floor was negated by often defending in it at the same time. That’s where Charlotte made up ground, spending a good chunk of their offense in the penalty while their defense had fouls to give. Below is a look at each team’s splits:

Charlotte’s three minutes with only the defense in the penalty was second-lowest to only the 2013 Lakers. Meanwhile, Phoenix’s minutes with only their offense in it was sixth-worst, and their time with only their defense in it was the highest this season by over a full minute. In their two matchups this season, the Hornets’ offense combined for 10 more minutes minutes in the penalty. However, Phoenix won one of the games. The most minutes in a game this season with only the offense in the penalty came in a Heat-Hawks matchup with Atlanta having that edge for 20.7 minutes, but they lost by 18 points.

We could also look at when it’s best or worst to have only the offense in the penalty, since teams are whistled for fouls less often in the first quarter compared to the other three periods, but this could be team-dependent. For example, the Los Angeles Clippers averaged 2.1 minutes with this advantage in the first quarter, the most in the league and the fourth-highest mark for any of the four quarters. If they had a choice, would they rather keep it that way to help their bench-heavy lineups early on even if it’s unlikely there’s excessive fouling in the first quarter, or have that two-minute advantage in the middle of the second or fourth quarter with their starter-heavy units?

As with shooting, there’s also some luck involved in penalty time. This could be measured in several ways, and some more complicated than others like measuring no-calls not found in play-by-play data. One method I used was looking for when teams entered the penalty even though, if not for the under two-minute rules, the defense would’ve had two or more fouls to give. Under the two-minute mark, teams have one foul to give at most, even if they committed none for 10 minutes.

Below was how much penalty time teams accumulated in this fashion, though the totals are small because this involves only the end of quarters:

Unsurprisingly, the teams with the highest penalty time in these situations were usually those that drew less fouls on offense, or were foul-averse on defense. Charlotte’s defense was an outlier with 14 percent of their total time on defense coming from these “unlucky” spots when teams typically average five to seven percent. Over the years, the Spurs were frequently at the top defensively. It’s certainly not enough information to determine if they’ve used their foul to give most often when they’ve had the option, but their results were interesting.

Despite all of this, penalty time only tells us so much. How important is this aspect of the game if we don’t know what actually changes when teams score or defend in it? In another post, I’ll look at how the penalty alters some commonly used statistics in box scores and others calculated with the help of possession formulas.

Next: Nylon Calculus -- The NBA Finals and clustering team offensive styles

Until then, below is a dashboard looking at team averages for penalty time with all the additional statistics featured in this post.

Statistics were derived from NBA.com’s play-by-play data.