Stats Guide

League: Four Factors

The "Four Factors Summary" table is the best way to quickly get a read on what the league looks like at any given moment and why. It shows each team's efficiency differential (a good measure of team quality), as well as their points per possession and Dean Oliver's Four Factors for both sides of the ball. This table not only tells you who is playing well or poorly, but importantly it tells you a lot about why.

Studying this table over time can also be very informative about the way the league works as a whole. While each of the Factors help you measure a team in a different way, all of them are connected, sometimes in unanticipated ways. For example, I wrote previously about how you can use these numbers to see how unique the style of defense the Milwaukee Bucks have played under Jason Kidd is — and that these numbers tell us some interesting things about what has succeeded or failed in the league over time.

Below we'll walk through the important columns in this table, with some brief notes on how to think about the Four Factors in general. By default, all of the stats on this page exclude garbage time.

Overall Efficiency (Pts/Poss)click to show/hide

In basketball, a possession starts when a team gets the ball and ends when they lose the ball (or the quarter ends). This leads to an important fact: when two teams play each other, they are guaranteed to have the same number of possessions (with the important exception of the last possession of a quarter). Which means that the best way to compare two teams is on a per-possession basis.

Why? Take a team that plays at a very fast pace and compare it to team that plays at an incredibly slow pace. If we look at what they do per game, we'll be fooled. The fast team gets many more possessions per game than the slow team. But when those teams play each other, they are guaranteed virtually the same number of possessions. So it doesn't matter what they do per game — only per possession.

Imagine if teams in the East played 24 minute games and teams in the West played 48 minute games. We'd never compare what these teams do per game — we'd know that would be silly, since if the teams ever played each other they would, of course, have to play the same number of minutes. It's the same thing with possessions.

That's why we measure a team's offensive and defensive abilities by their points scored or allowed per possession. (CTG displays these stats per 100 possessions so that they're a little easier to read.) You may hear these stats referred to by different names: offensive/defensive efficiency, offensive/defensive rating (ORtg/DRtg), or offensive/defensive efficiency rating (OER/DER), among others. They all mean the same thing: points scored per 100 possessions.

Example: 2016-17 Top 10 teams

These Pts/Poss columns are the two columns highlighted in light gray, one for offense and one for defense. They are the first step in answering the question of how a team plays. How good are they overall on offense and how good are they overall on defense?

You can see that the Warriors had the #1 offense in the league, scoring 116.8 points per 100 possessions played. They also had the #2 defense (just barely, they were essentially tied with San Antonio for #1), allowing 104.0 points per 100 possessions played.

Last year was an interesting season, where we saw 8 of the top 10 teams have an offense ranking in the top 10, but only 5 of the top 10 teams had a defense ranking in the top 10. It's notable from this table that there were a few lopsided teams in the top 10: the Rockets ranked 2nd on offense but 16th on defense, the Cavs ranked 3rd on offense but 21st on defense, the Jazz were 13th on offense but 3rd on defense and the Heat were 17th on offense but 5th on defense.

The Gritty Details

Possessions are counted directly from the play-by-play: they start when a team gains possession and ends when they lose it. There is some trickiness with dealing with the end of quarters — what happens if a team gains possession with 2 seconds on the clock and just has to inbound and heave it? That shouldn't count as a full possession. CTG counts those possessions differently, and by default does not include them in this summary.

Free throws from technical fouls (not counting Defensive Three Seconds violations) are not included in points per possession stats.

Efficiency Differential (Diff)click to show/hide

As mentioned above, measuring a team's offense and defense should be done on a per-possession basis. From there, it's not a big leap to say that a team's efficiency differential is a great measure of the quality of that team. Efficiency differential simply takes a team's points scored per possession and subtracts their points allowed per possession. (CTG multiplies this by 100 to make it easier to read.)

Example: 2016-17 Top 10 teams

This table shows the top 10 teams of the 2016-17 season, ranked by efficiency differential. You can see it tracks pretty well with the team's actual wins. Golden State led the pack by outscoring their opponents by 12.8 points per 100 possessions played, an enormous number. The Spurs had the second best differential at +7.7 per 100 possessions.

The Gritty Details

Efficiency differential is simply points scored per 100 possessions minus points allowed per 100 possessions.

Expected Wins (Exp W)click to show/hide

We can look through history and see how many games teams with various efficiency differentials tend to win. With that and a little bit of math (see the gritty details below) we get a number that tells us how many games we'd expect a team to win based on their efficiency differential.

Example: 2016-17 Top 10 teams

Based on their point differential, we would have expected the Warriors to have won 69 games. They actually won 67. Based on Utah and Cleveland's point differentials, we would have expected them to have won 51 games. They both won 51 exactly.

The Gritty Details

CTG uses Pythagorean win expectation to determine how many wins would be expected of a team with a certain efficiency differential. (CTG uses an exponent of 14.)

Win Differential (Win Diff)click to show/hide

Once we have a team's expected wins, we can then compare how many games any given team actually won to how many we'd expect them to win given their differential. The difference between actual wins and expected wins is what CTG calls win differential.

Why would a team's actual wins deviate from what we'd expect given their point differential? Because of different margins of victory in wins and losses. For example, let's say the Celtics play 10 games, and win 8 of them by 3 points each, but lose 2 of them by 12 points each. They would have a +0 point differential, meaning we'd have expected them to have gone 5-5, but they would have been 8-2 in this stretch instead.

Research has tended to show that performance in close games is more random than most people expect. Using that Celtics example, we probably wouldn't expect a team like that to go undefeated in close games going forward. Very good teams, meanwhile, often win by big margins. Efficiency differential, then, particularly over 10 games, is probably a better measure of team quality than wins and losses. As Daryl Morey once said: "Good teams don’t win close games — they avoid them."

But, over a large sample, performance in close games also doesn't seem to be completely random, as Benjamin Morris has noted. That means if a team's wins are vastly different from what we'd expect, it could be due to good or bad luck, but it could also be due to performance in close games or a higher-than-normal frequency of getting blown out (or blowing teams out). This is particularly true over larger samples.

Example: 2016-17 Top 10 teams

This table shows that most of the top 10 teams ended up winning within 2 games either direction of what their efficiency differential would have predicted. The major outliers were Boston and Miami. The Celtics won 53 games, but their efficiency differential was +2.7. The Win Diff column shows +4.5, meaning that the Celtics won 4.5 more games than expected based on that +2.7 efficiency differential mark. In other words, an average team with a +2.7 point differential would have won around 49 games. Perhaps this overachievement is due to the late-game excellence of Isaiah Thomas, or the coaching acumen of Brad Stevens — but it should be noted that the Celtics actually won fewer games than expected based on their efficiency differential in each of the previous two seasons.

The Heat, meanwhile, were on the opposite end of the spectrum. They had a point differential that normally would have resulted in a team winning around 44 games, but instead they won 41 — a difference that was enough to be cause them to miss the playoffs.

The Gritty Details

CTG uses Pythagorean win expectation to determine how many wins would be expected of a team with a certain efficiency differential. (CTG uses an exponent of 14.)

The Four Factorsclick to show/hide

By looking at basketball on a per-possession basis, we also get another benefit: there are only four ways for teams to increase or decrease the points they score on a per possession basis. These Four Factors (as coined by Dean Oliver) give us a simple-yet-powerful way to further break down a team. They are, in order of most important to least:

  • Shooting: teams can score more per possession by increasing the points they score per field goal attempted. This is measured with effective field goal percentage (abbreviated eFG%).
  • Turnovers: teams can score more by not turning the ball over. If a team doesn't turn it over on a possession that means they get a shot at the basket, and more shots = more points. This is measured with turnover percentage (abbreviated TOV% or TO%).
  • Offensive Rebounding: teams can score more by extending possessions by rebounding their own misses. An offensive rebound keeps a possession alive and gives the team more opportunities to score. This is measured with offensive rebounding percentages (abbreviated OREB% or OR%).
  • Free Throws: teams can score more by getting to the free throw line and converting their opportunities there. This is measured using free throw rate (abbreviated FT Rate or FTR).

As noted above, these factors can be looked at independently, but they all are interconnected. Offensive rebounds frequently lead to high-percentage looks, so teams that offensive rebound better might have better shooting numbers. And, as noted in my Milwaukee Bucks article, there seems to be a tradeoff between shot quality and turnovers.

Overall, this relatively simply framework can tell you a lot about how teams play and what their strengths and weaknesses are. More about each specific stat is below.

Example: 2016-17 Top 10 teams

Styles of teams start to become very clear as you look at this table. The Warriors' offensive success is based all around their incredible shooting efficiency (eFG%): they are #1 by a large margin in this category. That's why their overall offense is #1 despite not ranking above average in any of the three other factors (turnovers, offensive rebounding, or free throws). The Raptors, on the other hand, were kind of the opposite: their eFG% ranked 14th last year but they had the 6th ranked offense because they were 5th in taking care of the ball, 8th in offensive rebounding and 2nd in scoring from the foul line.

Utah's 3rd ranked defense was based on an extreme (but proven) style: they ranked 27th in forcing turnovers but 2nd in shot defense (eFG%), 4th in defensive rebounding, and 9th in preventing opponents from scoring from the line. The Clippers played a somewhat similar style. Houston's league-average defense, meanwhile, was mostly based around forcing turnovers and not sending opponents to the line — their shot defense ranked 20th and their defensive rebounding ranked 21st.

Shooting: eFG%click to show/hide

Let's say Memphis shoots 3 for 6 from the field, all two point shots, and Golden State shoots 2 for 6 from the field, all three point shots. According to regular field-goal percentage (FG%), the Grizzlies shot 50% and the Warriors shot 33% — Memphis seems far more efficient. But they both scored 6 points on 6 shots! That's a problem. We want a stat that corrects for this and shows them shooting the same, since they did. Effective field goal percentage corrects this flaw in FG% by including the extra added value of three-pointers. This stat answers the question: if we account for the added value of three-point shots, what did the team effectively shoot from two-point range? In the example both teams shot 50% eFG% — they both effectively shot 50% from two.

Simply, eFG% tells us: how many points did this team score per field goal attempt? That's why it's used to measure shooting in the Four Factors. (For defense, we just look at opponent eFG%.)

The Gritty Details

eFG% is calculated by simply counting made threes as worth 1.5 times as much as made twos (since three-pointers are worth 1.5 times as much as two-pointers).

eFG% = (two pointers + 1.5 * three pointers) / field goal attempts

Turnovers: TOV%click to show/hide

As noted in the Pts/Poss section, we want to compare teams per-possession. To measure a team's turnovers we simply look at their turnovers committed per possession. That gives us their turnover percentage. (For defense, we just look at opponent TOV%.)

The Gritty Details

Turnover percentage is turnovers divided by possessions.

Rebounding: OREB%click to show/hide

One of the most frequent mistakes made when analyzing team stats is looking at rebounds without looking at missed shots. The only time a team can get a rebound is on a missed field goal or a missed free throw (which is the last of a set of free throws). So when we measure how good a team is at rebounding, we have to take into account how many opportunities they had to get one. Otherwise a team that is great at forcing missed shots will look like a better rebounding team than they are. Yeah, the team got more rebounds, but there were more misses!

The Warriors in 2016-17 were a great example of this: they ranked 3rd in defensive rebounds per game, but as you can see in the tables above, they actually ranked 26th in opponent offensive rebounding percentage. The difference is because the Warriors were elite in shot defense — they forced a ton of misses, so their total defensive rebounds was high. But per missed shot, they actually were poor on the defensive glass.

That's what rebounding percentages help correct: we simply look at how often a team got a rebound per opportunity they had to get one. For offense we look at how many offensive rebounds were collected per opportunity, for defense we look at how many offensive rebounds opponents collected per opportunity.

The Gritty Details

Offensive rebound percentage measures offensive rebounds per missed field goal or reboundable missed free throw. CTG counts this from play-by-play and includes team rebounds from reboundable misses. Note that many other places estimate this from the box score, which can be tricky because not all rebounds are secured by players — a ball that tips off a player's hand and goes out of bounds, for example, is credited as a team rebound. But missed free throws that are not reboundable (e.g. the first of two free throws) are also credited as team offensive rebounds by the NBA. This makes it impossible to get completely accurate numbers from box score stats. By pulling stats from play-by-play, CTG corrects for this issue.

Free Throws: FT Rateclick to show/hide

To measure how well a team is scoring from the foul line, CTG uses free throw rate: free throws made per field goal attempt.

The Gritty Details

It's just that simple: free throw rate = FTM / FGA.