Article Length: ~4,000 words, so a lot of reading.
Table of Contents:
- +/- Stats
- +/- Per 100 Possessions
- Offensive Rating, Defensive Rating, and Net Rating
- On/Off Per 100 Possessions
- Relative Offensive and Defensive Ratings
- Calculating Expected Wins and Net Rating
- Individual Offensive, Defensive, and Net Ratings
Being a modern NBA fan is a daunting task. Not only are there multiple games to watch every single night but analysts also sling advanced metrics like multiplication facts. The latter is what I want to address today because as far as I’m concerned, fans don’t have an on-ramp for learning these metrics. A new fan, besides having to learn names, historical players, and an ever-changing playoff picture, must acclimate him or herself quickly or fall behind at the water cooler (or wherever new fans discuss the NBA. Reddit? Twitter?). Just look at this excerpt from Zach Lowe’s most recent column for ESPN:
They fall apart whenever [Vucevic] sits. Orlando has outscored opponents by 4.5 points per 100 possessions with Vucevic on the floor, but opponents have obliterated them by almost a dozen points per 100 possessions when he rests. The difference — plus-16.2 — is the 11th-fattest among all rotation players, per NBA.com.
This reminds me of the scene in “The Matrix” where Cypher is explaining to Neo that he “no longer even sees the code” while looking at the code for the matrix. To Cypher, it’s as simple as a first language, but to Neo, it’s an impervious wall of nonsense that offers no simple way to decipher it.
Zach Lowe’s multiple references to per 100 possessions stats and +/- jargon acts as the same way: most NBA analysts would breeze through that passage while newer or more casual fans would struggle with this second language.
My goal in this article is to start from scratch to clearly explain what these numbers mean, how they are contextualized, and how it can be applied to evaluating individual players. Hopefully, this can be a skeleton key for those wanting to wade further into the swamps of NBA analytics. Let’s begin at the beginning though, so feel free to jump down to later sections if you find any of the earlier information too simple.
+/- Stats for Teams and Players
The simplest statistic that acts as the base for most NBA analytics is the basic +/- stat that can be applied to both teams and individual players. For teams, it shows by how many points a team wins or loses by while for players it shows by how many points his or her team outscored or was outscored by the other team. Let’s look at an example from yesterday’s Rockets vs. Trailblazers example.
The Rockets won 111-104 meaning that the Rockets’ +/- is +7 while the Trailblazers +/- is -7. After a period of multiple games, we can see start seeing trends about better teams having a higher +/- than worse teams, and it actually becomes a way to differentiate top teams. For instance, if two teams are both 10-2 after the first 12 games, it would be simple to point to them as being equals; however, if team A has an average +/- of +10 and team B has an average +/- of +3, we might draw some different conclusions about which team is actually better and which team has been the recipient of some luck (which we’ll discuss later).
+/- becomes a bit messier when it comes to evaluating players though. What it shows is by how many points a team outscores its opponent while a player is on the floor or by how many points a player’s team is outscored while he or she is on the floor. For instance, take the Rockets’ basic box score from the aforementioned game:
Instead of the boiled down +7 that the Rockets earned during the game, it shows how well the Rockets played when each player was on the court. When P.J. Tucker was in the game, the Trailblazers outscored the Rockets by 17, but when Danuel House was in the game, the Rockets outscored the Trailblazers by 24.
The NBA is all about evaluating sample sizes, and one game is certainly not enough to evaluate teams or players. Does this game mean that Danuel House is the Rockets’ best player and should usurp all of Harden’s minutes? No, but if he consistently scores a higher +/- then his teammates, then it might be time to evaluate what he’s doing on the court to drive this consistent success. This is the sort of evaluation that earned Shane Battier a fruitful career.
The issue with just using +/- is that it’s noisy and favors teams that play a faster pace. Currently, the Hawks lead the league with 105.5 possessions a game while the Grizzlies play at thumping 94.9 possessions a game. Over the course of an 82 game season, the Hawks would have 869 more possessions to rack up a + or -. This is where per 100 possessions comes in.
+/- Per 100 Possessions
Once we have +/- data, we can start playing around with it to normalize it for the league. To evaluate a single game on a per 100 possessions basis, we must take each team’s score, divide it by the pace of the game, and multiply that number by 100. The equation is as follows:
Points Per 100 Possessions = (Team Score/Team Pace)*100
So, if a team scores 103 points at a pace of 100 possessions, its points per 100 possessions would be 103
Let’s look again at the previous Rockets/Trailblazers game. The Rockets scored 111, and the Blazers scored 104. Both teams played at a pace of 91.8 possessions. This means that the Rockets scored 121 points per 100 possessions, and the Blazers scored 113.1 points per 100 possessions.
Rockets Points Per 100 Possessions = (111/91.8)*100
Blazers Points Per 100 Possessions = (104/91.8)*100
Once we have these two new numbers, we can figure out by how many points per 100 possessions the Rockets won by which turns out to be approximately 8, and while this 8 seems too close to the original +7 that they actually won by, this point differential becomes more significant over a longer period of time.
Furthermore, this helps to normalize the score to show that this was a more decisive victory than a much faster-paced game. Let’s pretend that the game was played at a pace of 110 possession. This would make the Rockets’ and Blazers respective points per 100 possessions 101 and 94.5 making this point differential per 100 possessions only 6.5 as opposed to 8. Now we’re beginning to see a difference.
Once again though, this game-by-game analysis provides little insight into a team’s ability. We need two more factors: 1) more data to provide a broader picture and 2) an explanation of how a team is performing on offense and defense. Offensive rating, defensive rating, and net rating provide a better insight.
Offensive Rating, Defensive Rating, and Net Rating
I argue that this is the stage that all NBA fans should aspire towards understanding.
Simply put, here are definitions for each of these terms
Offensive Rating – how many points per 100 possessions a team scores
Defensive Rating – how many points per 100 possessions a team allows
Net Rating – a team’s offensive rating minus its defensive rating (which shows by how many points per 100 possessions a team outscores its opponent or is outscored by its opponent).
In the previous section, we were looking at a team’s game-level offensive and net rating. The Rockets scored 121 points per 100 possessions, so its offensive rating was 121. Since the Blazers scored 113 points per 100 possessions against the Rockets, the Rockets’ defensive rating was 113. When you subtract those numbers, the Rockets’ net rating was 8.
Once again, this is just a single-game statistic, but it becomes immensely more valuable when calculated across many games. The following chart shows every NBA team’s offensive rating, defensive rating, and net rating as of 12/12 (sorted by net rating):
|4||Oklahoma City Thunder||109.2||102.5||+6.7|
|6||Golden State Warriors||115.9||110.1||+5.8|
|10||Los Angeles Lakers||109.7||107.5||+2.2|
|11||Los Angeles Clippers||112.8||110.7||+2.1|
|13||New Orleans Pelicans||114.1||112.3||+1.8|
|14||Portland Trail Blazers||112.3||110.7||+1.6|
|23||San Antonio Spurs||111.4||113.4||-2|
|26||New York Knicks||107.6||114.2||-6.6|
These are some statistics that analysts should start to feel confident about using. They provide some interesting insights and raise even more interesting questions about luck and evaluating teams. For instance, the Raptors currently have the best record in the NBA at 22-7 (75.9% win rate), but the Bucks boast a higher net rating with a worse record (18-8 with a 69.2% win rate). So, which team is currently better? That’s a question that would need to be parsed out by even more specific numbers, but the per 100 statistics show that the Bucks clearly have an edge over the “best” team in the league.
Now, before diving deeper into comparing teams, it’s necessary to take a step sideways to discuss how players can impact offensive/defensive/net ratings with On/Off numbers.
On/Off Per 100 Possessions and Basic Player Evaluation
Earlier in this article, I discussed how players can leave an imprint on a game with his or her +/-. On/Off per 100 possessions takes the same basic principles as before and applies it to how teams perform while a player is on the court versus when a player is off the court. If you take a team’s net rating when a player is on the court and subtract it by the team’s net rating while that player is not on the court, then you have a player’s on/off per 100 possessions. The equation is as follows:
On/Off Per 100 Possessions = Team Net Rating With Player – Team Net Rating Without Player
|LeBron with the Lakers||NRtg|
|On the court||5.9|
|Off the court||-0.9|
|On/Off Per 100||6.8|
This means that the Lakers perform 6.8 points per 100 possessions better when LeBron James is on the court versus when he is not on the court. If we apply this to the team chart above, this difference would essentially transform the 76ers into the Bucks (just by comparing their net ratings). More specifically, we can see that the Lakers perform at the same level as the 4th best team in the league when LeBron is on the court (the Thunder at +6.7 per 100 possessions) as opposed to playing like the 19th best team (the Kings at -.9).
Just like in the previous section though, this provides too broad of an analysis of what LeBron brings to the table, so we can begin parsing this into offense and defense. A player’s offensive on/off per 100 possessions is then how many more points per 100 possessions a team scores while a player is on the court versus when that player is sitting, and a player’s defensive on/off per 100 possessions is how many points per 100 possessions a team is scored on while a player is on the court versus when that player is off the court.
A defensive on/off per 100 possessions is the first stat that we’ll look at that shows value when the number is negative meaning that a lower negative number means that a player contributes more on the defensive end. I will emphasize this throughout.
Let’s take a closer look at LeBron’s On/Off per 100 possessions numbers to see where he’s adding value.
|On/Off Per 100||3.8||-2.9 (Remember, a negative number is a good thing for defensive on/off ratings!)|
According to this chart, the Lakers are about 3.8 points per 100 possessions better on offense when LeBron players and about 2.9 points per 100 possessions better on defense when he plays.
It is important to note that claiming that LeBron adds 3.8 points/100 on offense and 2.9 points/100 on defense would be mathematically dishonest. The fact is that LeBron is just one of five players on the court for his team and just one of ten players on the court at one time. Not only that but the only nine players do not remain consistent throughout, so it’s impossible to parse out exactly what LeBron is adding to the team; however, given enough data points which, in this case, means games in a season and number of seasons, we can start to draw conclusions about individual players if they consistently boast strong on/off numbers.
On/off metrics have a couple of other issues to consider. First, a player who starts will generally be playing with and against other starters most of the time, so they are playing with and against the best competition which is not taken into account by the final numbers. Second, we can only really use on/off per 100 possessions honestly with players who have played in the majority of his or her team’s games otherwise we would be considering games where the player simply doesn’t play in the “off” metrics.
Unfortunately, it’s necessary to switch back over to team analysis before diving into another way to analyze player impact on a team. To see how much of an impact a player has on a team, we need to normalize team performance to show how teams can be compared across a single season and multiple seasons.
Relative Offensive Rating and Relative Defensive Rating
From year to year, average team performance has shifted on both offense and defense. Since the 2000-01 season, four of the five highest offensive ratings came from teams in 2016, 2017, or 2018, and the lowest (best) defensive ratings came from teams prior to the 2005 season. Does this mean that teams are better on offense and worse on defense now?
Well, yes and no. Through various rule and stylistic changes, the NBA is the most efficient that it’s ever been, but it’s also the most difficult to defend. Because of this, the league average offensive rating and defensive rating has sky-rocketed in the last few years meaning that teams are scoring and allowing more points per game.
So, to more honestly evaluate team performance, it’s necessary to compare offensive and defensive ratings relative to the rest of the league. Equations for relative offensive and defensive ratings are as follows
relative offensive rating (rORtg) = team offensive rating – league average offensive rating
relative defensive rating (rDRtg) = team defensive rating – league average offensive rating (once again, negative numbers are better)
As an example, let’s use the team with the league-best net rating: the Milwaukee Bucks. Their Offensive Rating is 114.6, and their defensive rating is 105.1. The league average for both offensive rating and defensive rating is 109.6, so we just need to subtract that from the Bucks’ numbers.
rORtg = 114.6 – 109.6 = 5
rDRtg = 105.1 – 109.6 = -4.5 (remember, smaller and more negative is good)
According to this, the Bucks’ relative offensive rating is 5 which means that their offense produces five more points per 100 possessions than league average, and their relative defensive rating is -4.5 which means that their defense prevents 4.5 more points per 100 possessions than league average. All together this adds up to their 9.5 net rating (another equation for net rating is as following: NRtg = ORtg – DRtg. This allows for negative relative defensive ratings to have a positive impact).
How do these numbers compare to the league? Let’s update the previously posted table with the league’s current team ratings by replacing its information with relative offensive and defensive ratings sorted again by net rating:
|4||Oklahoma City Thunder||-0.4||-7.1||+6.7|
|6||Golden State Warriors||6.3||0.5||+5.8|
|10||Los Angeles Lakers||0.1||-2.1||+2.2|
|11||Los Angeles Clippers||3.2||1.1||+2.1|
|13||New Orleans Pelicans||4.5||2.7||+1.8|
|14||Portland Trail Blazers||2.7||1.1||+1.6|
|23||San Antonio Spurs||1.8||3.8||-2|
|26||New York Knicks||-2||4.6||-6.6|
At this point, this table doesn’t tell us anything new. The Warriors boast the best rORtg and the Thunder boast the best rDRtg, but we knew this information from seeing that the Warriors had the best offensive rating and the Thunder had the best defensive rating. The true value of relative ratings lies in two places: 1) comparing teams from different seasons and 2) comparing player impact on teams (which I’ll discuss in an upcoming section).
The following chart compares the top ten offensive ratings since the 2000-01 season and the top ten relative offensive ratings from the same seasons:
|1||Golden State Warriors*||115.6||2017||1||Dallas Mavericks*||9.2||2004|
|2||Phoenix Suns*||115.3||2010||2||Phoenix Suns*||8.4||2005|
|3||Houston Rockets*||114.7||2018||3||Golden State Warriors*||8.1||2016|
|4||Houston Rockets*||114.7||2017||4||Phoenix Suns*||7.7||2010|
|5||Golden State Warriors*||114.5||2016||5||Dallas Mavericks*||7.7||2002|
|6||Phoenix Suns*||114.5||2005||6||Phoenix Suns*||7.4||2007|
|7||Phoenix Suns*||113.9||2007||7||Sacramento Kings*||7.4||2004|
|8||Portland Trail Blazers*||113.9||2009||8||Dallas Mavericks*||7.1||2003|
|9||Toronto Raptors*||113.8||2018||9||Los Angeles Clippers*||6.8||2015|
|10||Utah Jazz*||113.8||2008||10||Golden State Warriors*||6.8||2017|
While this chart shows an overlap between among five teams (2016 and 2017 Warriors and the 2005, 2007, and 2010 Suns), five new teams arise from comparing the relative offensive ratings. In fact, the 2004 Mavericks rank as having the 31st highest offensive rating while holding the highest relative offensive rating showing that even though they were playing in a year with a low average offensive rating, their offense, while not absolutely better than other offenses this century, was the best offense relative to their season.
(As a quick aside, looking at the top ten relative offensive ratings this century shows an incredible three year run by the Mavericks [2002-04]. It also shows that six of these ten teams were run by Steve Nash).
At the end of the day, we can never truly compare teams or players from different generations (much less years) because of a variety of factors. We can only compare them to their contemporaries, and relative offensive and defensive ratings allow for these comparisons.
Now, from this century’s data on team performances, it’s possible to calculate expected win percentage and net rating, so I’ll do that before explaining individual relative offense and defensive rating to allow for an actual conclusion to this article.
Calculating Expected Wins and Net Rating
Earlier in this article, I referenced luck in terms of teams having a certain amount of wins. With respect to the 2018 Bucks and Raptors, the Bucks should have a better record because their net rating is currently better.
To figure out exactly how many wins equals what net rating and vice versa, it’s necessary to plot every teams’ performance this century. The following scatter plot shows all 536 teams’ wins with their respective net ratings:
Wins correlate well with net rating, but it’s not perfect.
Before calculating it though, let’s do a quick mathematical thought experiment. If a team has a net rating of 0, that means, on average, the team scores the same amount of points per 100 possessions as they allow; however, if this were to hold consistent from game to game, that means the team should end every game with a tie. We know this is impossible, so the most logical alternative is that the team is outscored half its games and outscores its opponent in half its games meaning that they would have a record of 42-42.
Let’s calculate how accurate this has been this century. To do this, we have to calculate the slope intercept of the above graph which means we have to see where the trendline crosses the y-axis. This ends up being approximately 41 meaning that a net rating of 0 has, this century, an expected win outcome of 41 wins in a season. The slope of the line is approximately 2.5 meaning that each point in net rating (either positive or negative) is worth about 2.5 wins. Below is a win expectancy chart based on net rating by a factor of .5 (I have provided data to the theoretical limit of net rating based on possible wins):
|Net Rating||Expected Wins|
When applying this information to the earlier chart listing team net ratings, we can see that the Bucks have an expected win outcome of about 65 wins while the Raptors have an expected win outcome of around 61 wins.
A large number of factors play into this data not correlating perfectly with wins such as blowouts and poor clutch performances, but it might provide a better look at which teams are performing the best.
For instance, based on this information, it’s possible to conclude that 2016 Warriors (who went 73-9 on the season) were actually not the best team this century (or even in their same year). Their net rating ranks 4th, and their expected wins compared to the three other teams with a higher net rating are as follows:
|Team▲||Year||Wins||Net Rating||Expected Wins||Wins Difference|
|Golden State Warriors*||2017||67||11.6||70.3||-3.3|
|San Antonio Spurs*||2016||67||11.3||69.57||-2.57|
|Golden State Warriors*||2016||73||10.7||68||5|
This small bit of data reveals three interesting insights: 1) the 2016 Warriors outperformed their net rating; 2) the 2017 Warriors were actually better than the 2016 Warriors; 3) the three teams who have higher expected wins all underperformed their net rating.
Now that we know how significant even one point for net rating is, we can apply relative offensive and defensive ratings to players to determine how much impact they have on a team.
Individual Offensive, Defensive, and Net Ratings
This is a statistic that I learned from reading Ben Taylor’s magnum opus, and I’m convinced that it’s a solid way to evaluate player impact without diving into the more complex statistics.
In a previous section, I discussed on/off metrics that showed how a team performed with and without a player, but I also addressed some of the drawbacks. This metric provides a different means of evaluating teams with and without players. This is fairly complex and requires multiple pieces of data while producing multiple statistics for individuals.
First, we need to figure out a team’s relative offensive and defensive ratings in games when a specific player plays. For this, we want to use a player who plays significant minutes on a team to ensure he actually has an impact. To walk through calculating this, I’ll use Victor Oladipo since he has played in 17 of Indiana’s 28 games this year. The following chart shows the Pacer’s rORtg, rDRtg, and net rating in games where Oladipo plays versus when he sits, and the second chart shows a new statistic that I’m coining individual relative offensive (iaORtg) and defensive rating (iaDRtg):
|rORtg (positive is good)||rDRtg (negative is good)||NRtg|
|irORtg (positive is good)||irDRtg (negative is good)||irNRtg|
Let’s unpack this.
The first chart shows that when Oladipo has played this year, the Pacers’ offense has performed about 2 points per 100 possessions worse than league average, and their defense has been better than 6 points per 100 possessions than league average. However, when Oladipo does not play, their offense is just .1 points worse, and their defense is 6.8 points better than league average. So, individual offensive and defensive ratings show the net effect a player has on a team.
irORtg = team rORtg with player x in the lineup – team rORtg without player x in the lineup
irDRtg = team rDRtg with player x in the lineup – team rDRtg with player x in the lineup
irNRtg = irORtg – irDRtg
Numbers are a fickle tool, so I am not stating that Oladipo is a bad player, but objectively, the stats show that he has had a negative impact on the Pacers this year. How much of an impact? What do these numbers mean?
Remember from above that each point in net rating equals about 2.53 wins. If you multiply a player’s irNRtg by 2.53, then we’ll get how many wins that player contributes using the net rating model meaning that the Pacers are on track to lose approximately 6 more games this season when Oladipo plays. We can show this through using the expected win model from above:
|Net Rating||Expected Wins|
And we can break this down even more by a player’s offense and defense by applying this same equation to a player’s irORtg and irDRtg:
|irORtg||Expected Offensive Wins Added||irDRtg||
Expected Defensive Wins Added
The issue with using an impact metric like this is that you need to have a player who missed substantial time without other significant players also being out. For example, we can’t evaluate LeBron over the past two seasons because he hasn’t missed any time, and we can’t evaluate Curry from this season because his absences mostly coincided with Draymond’s missed games.
This has been a lengthy and thorough walkthrough of some simple and complex impact metrics. I have covered the following impact metrics:
- +/- Stats
- +/- Per 100 Possessions
- Offensive Rating, Defensive Rating, and Net Rating
- On/Off Per 100 Possessions
- Relative Offensive and Defensive Ratings
- Calculating Expected Wins and Net Rating
- Individual Relative Offensive, Defensive, and Net Ratings
For now, if you use this article as a guide moving forward while evaluating players, I promise that you’ll have a better grasp of advanced analytics in the NBA.