# Nylon Calculus: Calculating penalty time for players

A few months ago, I published penalty time/time spent in the bonus for teams. While I’d discussed and published penalty time multiple times two seasons ago, this summer’s posts were the first time I adjusted for whether or not a team’s defense had fouls to give, too. Now, with only days away from the start of the season, it’s a good time to publish similar measurements of penalty time for players.

As a reminder, the penalty happens when a team either commits four team fouls in a quarter, three in overtime or one in the final two minutes of either a quarter or overtime. From that point on, every team foul leads to two free throws.

Unfortunately, player penalty time only covers last season, but it’s better than nothing. Penalty time requires accurate lineups for all events in play-by-play data, which I didn’t have pre-2017. We could ballpark player penalty time based on subbing patterns on NBArotations.info that go back further than this dashboard, but it wouldn’t be close to 100 percent accurate. There was also a temptation to use percentage of shots, rebounds, assists, etc. in and out of the penalty to estimate penalty time because some stats had strong correlations, but this seemed too risky given the statistical trends in the NBA over the last 20 years. In a follow-up with shooting stats split by penalty situation, those will go back to 1998.

This was not a normal blog post as far as how it was written. Because I’ve explained in an earlier post about how the penalty affects offense and defense, and some of the columns and rows were used in previous dashboards, I’ll post the player penalty dashboard right off the bat and follow up with a glossary that explains the rows, columns and filters in case there is indeed some confusion. After that, I’ll explain what well-known aspects of the NBA and stats penalty time is supposed to impact, and end with caution when using this dashboard.

## Glossary

Rows

Player – NBA means league average.

Tm – NBA means league average. All is used for Season Total in the Total Type Filter, which takes a player’s numbers like DeMarcus Cousins’ over an entire season instead of splitting stats by team before and after a mid-season trade.

Qtr – Good for seeing which quarters players never have the chance to score in the penalty or spend a ton of time in. For example, reserves will generally spend a big portion of their minutes in the first quarter with one or both teams having no fouls to give. More on this later.

Off. In/Out of Penalty

Def. In/Out of Penalty

Hopefully self-explanatory if familiar with previous posts related to this topic, but if not, I’ll use some player examples of what in/out of the penalty means. Offense or defense in or out of the penalty means scoring or defending in or out of the penalty. It can also be looked as a player’s opponent (offense) or their own team (defense) having some fouls left to give (out of the penalty) or no fouls left to give (in the penalty). If we used ‘Both’ for both offense and defense, there would be no filtering at all, and player results would just be their season totals.

Below are player examples of some offense/defense combos.

Off. In/Out of Penalty: In, Def. In/Out of Penalty: Both.

Scoring in the penalty/bonus. The player’s opponents had no fouls left to give, while ‘Both’ on defense means there’s no adjustment for whether or not the player’s team had fouls left to give. This is good for the player and his scoring statistics.

For example, Andrew Wiggins played 37.2 minutes per game last season. Of those 37.2 minutes, 11.1 were when opponents had no fouls to give, time when there was a scoring advantage for Wiggins and the Timberwolves. He was scoring in the penalty for 11.1 minutes per game, the most in the NBA on a per game level.

If we flip-flop offense and defense to make it so the defense was in the penalty, Devin Booker would be the leader in minutes per game in this situation. Of Booker’s 35 minutes per game, 12.5 happened when the Suns had no fouls left to give and were at a defensive disadvantage. Booker defended with no fouls to give or defended in the penalty for 12.5 minutes per game.

Those examples only filtered one side of the floor by foul state. Below are some examples when applying filters to both sides of the floor.

Off. In/Out of Penalty: In, Def. In/Out of Penalty: Out.

The power play of the NBA, sort of. The player’s team has fouls to give, but the player’s opponents do not. Teams had a net rating of +3.9 points per 100 possessions in this situation last season, though it was as high as +5.8 in 2015, and in the +6 to +9 range from 1998 to 2003.

The player who had the most minutes per game in this spot last season was Blake Griffin. Of his 34.1 minutes per game last season, 5.8 were spent when the Clippers had fouls to give but his opponents did not. I’ll get a little more into this later, but while scoring in the penalty is great for Griffin’s individual stats, this spot in particular is helpful for Griffin’s net rating, on-off statistics, etc.

Flipping offense and defensive situations, Booker spent 6.2 of his 35 minutes per game playing against opponents with fouls to give while the Suns had none remaining. Sad times.

Off. In/Out of Penalty: In, Def. In/Out of Penalty: In.

Getting into the bonus is nice, but sometimes the other team is in it as well and neither team has any fouls left to give in a quarter. Outside of late-game fouling, you could probably characterize this as an even-strength situation.

Booker was the leader in minutes per game in this filter at 6.4. For example, of Booker’s 12.5 minutes when defending with no fouls to give, 6.4 came when Booker’s opponents had no fouls to give either, negating what would otherwise be a disadvantage for Booker and the Suns. It’s possible the 6.4 minutes per game were rounded up because that time, plus the 6.2 minutes on the floor when the Suns had no fouls left to give but opponents did, adds up to 12.6 instead of 12.5.

You could also look at Booker’s 9.9 minutes scoring in the penalty, or when opponents had no fouls to give, and say that 6.4 came when the Suns, unfortunately, had no fouls left to give either. Subtracting 9.9 from 6.4 meant that Booker spent 3.5 minutes on the floor in the best situation, when the Suns had fouls to give, but their opponents did not.

Off. In/Out of Penalty: Out, Def. In/Out of Penalty: Out.

When neither team is in the penalty or when both teams have fouls to give. The true even-strength situation. The players at the top of the leaderboard in minutes in this situation play a ton of minutes in general, but they are also ones with unusual sub patterns, subbing out early-ish in first and third quarters to play with bench-heavy units in the second and fourth quarters. They are part of a staggered sub pattern so either them or a teammate of equal value are on the floor at all times.

The leader in minutes per game in this situation last season was Kyle Lowry at 27.9 minutes per game. Three-fourths of his 37.4 minutes per game were spent when both the Raptors and their opponents each had fouls to give.

Hopefully this makes sense. If not, you can bug me on Twitter. These rows can be tweaked in the Offense-Defense In-Out of Penalty Combo filter.

Columns

Total MP

Total MPG

Season totals. Good for context and filtering.

MPG in Off/Def Combo

% of Total MP in Off/Def Combo

These are the minutes played in the foul situations selected. Minutes per game will affect players on the floor a ton while percent of total minutes balances that out.

MPG in Off/Def Combo per 36 TOTAL MP – Like other per-36-minute stats, this scales penalty time to where it would be if every player played 36 minutes per game. For example, a player who logs six total minutes per game but scores in the penalty for one of them would average six penalty minutes per 36 total minutes played. When scaling on a per-36 level, Wiggins’ 11.1 minutes scoring in the penalty per game last season decreased to 10.7 per 36, since he averaged 37.2 total minutes per game.

% of Off/Def Combo MP vs. Tm Avg – The first of the team comparison stats. Not every player on every team plays the same percentage of their minutes with the penalty to their advantage or disadvantage. It also adjusts for teams who draw or don’t draw, commit or don’t commit a ton of fouls.

For example, Marquese Chriss of the Phoenix Suns spent 25 percent of his minutes on the floor with the offense in the penalty, above the league-average of 23.7. This should be given some weight when viewing his overall scoring efficiency.

However, the Suns led the league in time scoring in their penalty or when their opponents had no fouls to give, with 28 percent of their total minutes. In this column, Chriss gets a mark of -3.1 percent, meaning he was on the floor with opponents out of fouls to give less often than his teammate averages. (The Sun on the opposite spectrum is Alan Williams at +8.3 percent.) That should be given some weight when measuring on/off, plus-minus metrics.

Team averages were calculated by team penalty time in games when the selected player played.

Off/Def Combo MP Per 36 TOTAL MP vs. Team Avg – Scales team averages to a per-36-minute level and then subtracts from the player’s per-36-minute totals. In the above example, Chriss’ 9.0 minutes scoring in the penalty per 36 total minutes, subtracted by the Suns’ 10.1 per-36-minute average in games he’s played, yields a result in this column of -1.1.

That’s super wordy, but it’s just comparing team and player per-36 rates. The rankings in this column are the same as % of Off/Def Combo MP vs. Tm Avg.

Tm Off/Def Combo MPG

Tm % of MP in Off/Def Combo

Tm Off/Def Combo MP Per 36 TOTAL MP

Team stats for games when the player selected played. For transparency and context, I included these. They should also make it easier to understand the vs. Tm Avg stats. Hopefully.

GP

GS

Games played and games started. Overtimes were not included because of multiple overtimes in the same game.

GS% – Percentage of games played when the player started. For quarters, this is percentage of games played when the player started the quarter. Overtimes were not included because of multiple overtimes in the same game.

Filters

Players – NBA is for league averages.

Qtr – View single quarters or overtimes.

Tm – NBA is used for league averages. All is used for Total Type -> Season Total.

Total Type – Season total is good for season-long totals, regardless of the team the player played for. This does not account for mid-season trades.

Team Total splits player stats by team they played for, factoring in trades. It also allows for viewing penalty time from rosters of teams.

Offense-Defense In-Out of Penalty Combo – The wordiest filter in NBA history adjusts for penalty situation on offense and defense. For no filter on a side of the floor, select ‘Both.’ ‘Both/Both’ is not an option simply because that would just involve season-long totals with no adjustments. The more specific the combo becomes, the likelier the sample size will be smaller.

The default setting is ‘In/Both,’ which is basically how long a player was on the floor when their offense was in the penalty or when their opponents had no fouls left to give. Because of ‘Both’ for defense, it does not adjust for how many fouls left to give the player’s team had.

GP – Games Played.

GS% – Percentage of games when that player started. For quarters, it’s percentage of quarters the  player started.

Total MP

Total MPG

Both are season-long minutes played with no penalty adjustment. Good for filtering out penalty-related results from small samples that are unsustainable with more playing time overall.

## What Penalty Time Impacts

Penalty time on the surface should affect:

Starters versus reserves – Reserves generally play a higher percentage of their minutes scoring in the penalty. This makes sense for a couple reasons. At the least, they’re closing out first and third quarters, but the best reserves also close out games and sometimes chip in before halftime. Reserves aren’t playing most of the first quarter, either, which has the lowest amount of penalty time when comparing the four quarters.

Below is a look at percentage of minutes a player plays with their offense in the penalty and the percentage of quarters a player starts.

Staggering – Similar to above, and mentioned earlier, staggering impacts the penalty time of a star who carries a bench unit through the early stages of the second to first quarters.

Below is a look at the time with the offense in the penalty from Kyle Lowry, Andrew Wiggins, Klay Thompson and LeBron James with a fellow teammate or two. We’ll clearly see the effect of staggering and playing with bench-heavy lineups in the beginning of second and fourth quarters while missing out on the penalty time at the end of the first and third quarters.

In a follow-up with shooting metrics split by penalty situation, we’ll be able to use those splits to determine the best candidates to play with bench-heavy units this season.

Player efficiency – On average, players shoot slightly worse when in the penalty/bonus partly because end of quarters are more about having the last possession than the best shot, but they get to the free line at nearly double the frequency. Players also turn the ball over less, whether it’s because of end-of-quarter possession hoarding and low-efficiency, low-risk isolation players or late-game fouling.

Below is a look at the averages of statistics when in and out of the penalty.

A player who spends a lot of time in the bonus/penalty on offense should, at the least, get a decent boost in free throw rate.

On/Off, Plus-Minus metrics  Some plus-minus formulas account for starters/reserves by rewarding players who play more minutes. That could balance out the effects of penalty time when reserves typically score in the penalty more than starters. However, some players log a higher portion of their scoring penalty time than their teammates, while others benefit from scoring in the penalty while their team’s defense still has fouls to give. Both situations would impact on/off, plus-minus metrics.

## Caution

In general, don’t look at any metric and assume it’s perfect.

For metrics related to penalty time, it’s good to note that teams generally score more efficiently when scoring in the penalty or when their opponents have no fouls to give. In 2017, teams scored 113.0 points per 100 possessions when scoring in the penalty compared to 107.8 out of it. They also have a higher net rating when they score with the penalty to their advantage while they themselves still have fouls to commit on defense,  a mark of +3.9 per 100 possessions on average.

However, over one single season, samples for in the penalty/out of penalty combos are small and some teams perform worse with the advantage the penalty is supposed to offer. This would impact on/off statistics, but not in the way intended.

There are also some players whose penalty time looks better or worse because they draw a lot of fouls or commit a ton. Over a large enough sample, a foul-drawing machine like Joel Embiid’s time scoring in the penalty, especially when the Sixers’ defense still had fouls to give, should not be used to penalize him because he’s responsible for the majority of the team’s drawn fouls. He’s creating that penalty time on offense for the 76ers. On the flip side, hackers like Marquese Chriss and Alex Len should be penalized even if their penalty time already looks poor, because it’s likely they’re responsible for putting their team’s defense in the penalty.

Next: Nylon Calculus: NBA Iron Men of 2017

And as we’ll see in the scoring splits for players when in and out of the penalty, the difference in efficiency between the two situations is larger than normal for some players while a few showed little change.