If you were to make a list of the three scariest things on Earth, it’d probably include the following: heights, enormous bugs, and numbers. Math is one of the most frightening things in many peoples’ lives, and for good reason. Nothing can give you a headache quite like a quadratic equation, and there aren’t many things that put me to sleep in high school quicker than my pre-cal homework.
But, believe it or not, math isn’t so scary after all. And sports fans, especially, use it more than most people who aren’t engineers for a living. Everything when it comes to games is mathematical. Heck, a football field is called a “gridiron,” after all. So no matter how many times you had to retake an Algebra 2 test, and no matter how mind-bending a logarithmic curve might appear to be, it’s important we embrace all of it. You can’t really understand a game without most of this stuff.
But before we get into some of the fancier basketball stats out there, let’s simplify the whole thing. Nearly every stat is predicated on the same operation: division. The most common, easiest stats to understand are also mathematically some of the most digestible. The equation for field goal percentage, for example, is (Field Goals Made / Field Goals Attempted). Similarly, the equation for points per game is (Points Scored / Games Played). If Dallas scored 120 points yesterday and the Mavs notch 100 points tonight, to find out their points per game, you’d add 120 to 100 and then divide by two. The result, 110, is their points per game.
Those stats have become ubiquitous over the course of the last several decades, and they’re simple enough to understand that stats like points, assists, per game, and rebounds per game are regularly used at your average bar when fans are debating who’s the best player of all-time. However, these stats aren’t the most reflective of a player’s ability.
Let’s say Dirk Nowitzki plays 36 minutes and grabs 10 rebounds. His teammate, Charlie Villanueva, plays just 12 minutes and pulls down five boards of his own. Which player had the more productive game? This is why many analysts are starting to rely more on per-36 minutes or per-100 possessions stats, as they expand or retract every player’s production across an identical period of time. If we were measuring Nowitzki and Villanueva’s rebounds per 36 minutes in that same scenario, Dirk’s average would stay at 10.0 while Villanueva’s would increase all the way to 15.0. Therefore, on that night, Villanueva was technically more productive while he was on the floor than Nowitzki.
This is just one example, however. There are plenty of other stats floating around out there that might make your head spin, but I promise they’re very simple to understand. Let this be your advanced stats glossary. Refer to this any time you see a phrase or stat you can’t wrap your head around, and hopefully together we can all become smarter basketball fans!
What it means: The number of possessions for a team or player per 48 minutes.
Why it’s useful: Pace is perhaps the most reliable way to measure how “quickly” a team plays. While it has nothing to do with the actual speed the players are moving, pace does factor in how many possessions a team (or player, though it’s more commonly used in reference to teams) plays per game.
The official formula is somewhat of a mathematical estimation because no one sits and officially counts possessions. But the one NBA Stats uses is:
Possessions = FGA + (.44*FTA) – OReb + TO
A “possession” ends with either a shot, defensive rebound, or turnover. If Sam Dalembert grabs an offensive rebound off a Chandler Parsons miss, the initial possession is still in progress. So at the end of every game, both teams will have played at the same exact pace.
A “good” and “bad” example: Last season, the Golden State Warriors played the fastest pace, at 100.69 possessions per game. The Utah Jazz played the slowest, averaging just 92.78 possessions per game. There is little to no correlation between playing fast and winning, however. The Cleveland Cavaliers played the 25th-fastest-pace last season yet made the Finals. Generally, the West plays faster than the East.
What it means: The number of points a team or player scores per 100 possessions.
Why it’s useful: Offensive rating characterizes a player or team’s offensive efficiency more accurately than points per game. Every team plays at a different pace, for example, and if you’re measuring players’ OffRtg, everyone plays a different number of minutes. But offensive rating mitigates the impact of playing time and pace when it comes to measuring scoring efficiency, so it’s therefore more accurate than points per game. For example, Houston finished 12th in offensive rating last season but scored the sixth-highest points per game. One explanation could be the Rockets’ 27th-ranked free throw shooting, which resulted in some extra empty possessions, lowering their offensive efficiency while still adding points to the scoreboard.
A “good” and “bad” example: Last season the Los Angeles Clippers led the league in offensive rating, scoring 109.8 points per 100 possessions. Anything above 107.0 will almost always place you in the league’s top-five, as was the case last season. The 15th and 16th teams ranked by offensive rating each scored 102.5 points/100. Anything below 102.0 will usually place you in the bottom-half of the league. The Philadelphia 76ers ranked 30th by scoring 93.0 points per 100 possessions.
What it means: The number of points a team or player allows per 100 possessions.
Why it’s useful: Just as offensive rating better assesses a team’s offensive efficiency, defensive rating captures a clearer image of just how difficult a team makes things for its opponent. Sometimes the disparity between rankings in points allowed and defensive rating is even wider than what we see on the other side of the ball. For example, last season the Warriors led the league in DefRtg by allowing just 98.2 points per 100 possessions, but they finished 15th in points per game allowed at 99.9. Similarly, Houston finished 17th in PPG allowed but sixth in defensive rating.
A “good” and “bad” example: The Warriors’ league-leading mark of 98.2 is stellar. If you allow fewer than 100 points per 100 possessions in this era, you’re more often than not going to be a top-five defense. And, in fact, no team ranked outside the top-10 in defensive rating has won the championship since the 2000-01 Lakers, per NBA.com, and they finished 18th. The season Dallas won the title, NBA.com had the Mavs ranked seventh. Last season, the Minnesota Timberwolves finished last in DefRtg by allowing 109.6 points per 100 possessions. Just seven teams in the NBA allowed at least 105.0, and none finished with more than 38 wins.
What it means: The difference between points scored and points allowed per 100 possessions.
Why it’s useful: While defensive rating is perhaps the more important half of the formula, net rating still does a good job of showing which teams are the best. Ten of the top-11 in net rating last season won at least 50 games, including the Mavericks. The other team, Toronto, won 49. There was also a clear drop-off from that top-11 to the next group of teams. Eleventh-place Memphis was 3.1 points per 100 better than its opponent, while 12th-place Washington was just 1.9 points better. You might be thinking, “what’s one point across 100 possessions really worth?” Well, the Wizards played in eight overtime games last season, per Basketball-Reference.com, and they went 4-4 in those games. Scoring one extra point (or allowing one less) could have given them an extra win or two, or even more.
A “good” and “bad” example: The Warriors’ 11.4 net rating soared above all other clubs last season, besting the second-place Clippers by 4.5 points per 100. That gap alone — 4.5 points — would have finished fifth in the league in 2014-15. Only one team last season finished with a positive net rating and also a losing record, and zero teams with a winning record finished with a negative net rating. So 0.1 or better is certainly the goal. Meanwhile, the last-place Knicks finished with a -10.1 net rating.
What it means: The number of assists a player records for every turnover he commits.
Why it’s useful: Assist-to-turnover ratio is most useful for point guards and players who spend a lot of time with the ball in their hands. Dirk, for example, has a career 1.44 AST/TO. That wouldn’t be a high mark for a point guard, but because Nowitzki typically isn’t a passer, instead operating more in catch-and-shoot and isolation situations, his ratio doesn’t really matter. This is more of a guard-oriented stat.
A “good” and “bad” example: There really is no “gold standard” for AST/TO. You’d certainly want a point guard with one higher than at least 2.0, because that means the player is capable of operating in an offense and finding teammates without making lots of mistakes. But what’s “elite?” If we’re going to draw the line somewhere, let’s make it 4.0. According to Basketball-Reference, only 37 players in the history of the league have finished with a 4-to-1 ratio while qualifying for the assists-per-game leaderboard. Of those players, only 16 have done it twice, and only six have done it more than two times. One of those is former Maverick Jose Calderon, who’s tied with John Paxson for third-most all-time at six. In second place sits Chris Paul, who’s done it seven times and counting. Leading the pack is Muggsy Bogues, who did it a remarkable 10 times. Paul could catch him, but otherwise it’s going to be a while before someone threatens that mark.
As it relates to teams, the average last season floated around 1.5. Paul’s Clippers were the only team to finish higher than 2.0, and the Mavs finished sixth at 1.74. Charlotte was the only club in the top-11 which did not make the playoffs. The 76ers finished last at 1.16. A team’s assist-to-turnover ratio will almost always be lower than its point guard’s, because while only a few players on a team usually make plays, all 13 who dress are capable of committing turnovers.
What it means: A per-minute rating of a player’s performance. The stat was developed by John Hollinger, who at the time wrote for ESPN but is now the vice president of basketball operations for the Memphis Grizzlies.
Why it’s useful: Many “single-number” metrics — an attempt at boiling down a player’s ability, production, or value to a single number — must be taken with a grain of salt because they are all imperfect, and PER is no different. But of all the single-number metrics out there, PER has had the most staying power and is generally the most accurate when it comes to measuring a player’s performance with some seriously complicated math. PER takes into consideration points, assists, rebounds, blocks, steals, turnovers, free throws, fouls, and more or less every other element of a box score.
A “good” and “bad” example: As the league-average PER is always exactly 15.0, a PER higher means a player produces at an above-average rate, while players below produce at a below-average rate. While this doesn’t mean a player is necessarily “good” or “bad,” it certainly helps. Of the 60 MVPs Basketball-Reference lists PERs for, only six of them had a PER below 20. Of the 28 All-Stars last season (those who were voted or selected in but could not play due to health reasons are still included) only two of them had a PER below 19.2 and eight had a PER higher than 25.
A PER of 30 or higher is basically considered legendary. It’s only been done 18 times in league history: LeBron James and Michael Jordan have done it four times each, Wilt Chamberlain and Shaquille O’Neal did it three times each, and no one else has ever done it more than once. But New Orleans Pelicans forward Anthony Davis finished with a 30.8 PER last season, the 11th-best mark ever, and he’s just 22 years old.
At 28.1, Dirk Nowitzki led the league in PER during the 2005-06 season. The next season, his 27.6 PER was good for second place in the league and he won the MVP award. He’s finished in the top-10 11 times. His 23.3 PER is sixth-best among active players and 18th-highest all-time — and one place ahead of Kobe Bryant — per Basketball-Reference.
What it means: A combination of field goal percentage, three-point percentage, and free throw percentage. True shooting simply measures a player or team’s ability to shoot the ball in all aspects, and it counts each free throw attempt as just less than half of one field goal attempt.
Why it’s useful: A player with a high true shooting percentage is most likely an above-average shooter from both the field and the free throw line. A player doesn’t necessarily need to be a good three-point shooter in order to have a high TS percentage, but it will certainly help. Kyle Korver led all players in true shooting last season at 69.9 percent. DeAndre Jordan, who led all players with a 71.0 field goal percentage last season, had just a 63.8 true shooting percentage — still a very high number, top-five in the league — because of his free throw shooting.
A “good” and “bad” example: Korver’s 69.9 percent is remarkable, and was certainly helped by his nearly shooting 50 percent on threes. It’s the highest by a non-center in the history of the league. The next-closest belongs to Dave Twardzik, who finished at 68.9 percent in the 1976-77 season, but he played before the three-point line came into being.
The Warriors led the league in TS% last season at 57.1 percent. Only the Charlotte Hornets and Philadelphia 76ers finished with a TS lower than 50.0. The Sacramento Kings were the only team in the top-10 in true shooting last season that didn’t make the playoffs.
What it means: How many field goals a player or team scores divided by total field goal attempts. Effective field goal percentage takes into consideration that a three-point field goal is worth one more point than a two-point bucket, so the formula is (Field Goals Made + (.5 * 3-Pointers Made)) / Field Goal Attempts.
Why it’s useful: By accounting for three-point shots, and not bringing free throws into the fold, eFG provides a clearer picture of how efficient a player is when attempting a field goal. Think of it this way: If DeAndre Jordan goes 6-of-10 from the field but doesn’t hit any threes, he’d have the same eFG as Dirk if the German went 4-of-10 but only attempted threes. This is one way of showing how much more valuable three-point shooting can be than two-point shooting. If Nowitzki goes 12-of-20 in a game, including 3-of-5 on treys, his field goal percentage would be a sterling 60 percent. But his eFG would be an even-higher 67.5 percent.
A “good” and “bad” example: The Warriors led all teams last season with a 54.0 eFG percentage. Each of the top-10 teams in the league in eFG made the playoffs, including the Mavericks. Twelve teams in the league had an eFG of at least 50.0. The Charlotte Hornets finished last at 45.6 percent. More or less, taking one glimpse at the eFG list shows you which teams are the best at shooting threes.
It’s best to separate players by position when ranking them by eFG, because centers generally do not shoot three-pointers, and because they typically take much “easier” shots than other players, they typically have much higher field goal percentages than guards and wings. Jordan led the league in eFG last year at 71.1 percent, but Atlanta sharpshooter Kyle Korver posted an otherworldly 67.7 eFG as a wing, although he didn’t statistically qualify by Basketball-Reference’s criteria. MVP Stephen Curry led all qualified non-centers in eFG last season at 59.4 percent.