Advanced Stats in Basketball: An Explainer Series

Part One: On per-36 minute, per-possession, and per-100 possession stats

So, let’s say you’re comparing stats of two players who played last night. Player A scored 25 points in a game that went to 58 minutes due to double overtime, and Player B scored 22 points in a standard, 48-minute regulation game. Who had the better game, scoring-wise?

The raw stats, free of context, would point to Player A. 25 is more than 22, after all.

However, with some context, it’s clear that Player A has an advantage in this comparison. More minutes mean that there is literally more time to score, by virtue of the additional 10 minutes afforded to Player A. In fact, if you were to divide the number of points Player A scored by the number of minutes Player A could have played, you would divide 25/58, or .43 points per minute. Player B, at 22 points in 48 minutes, scored .45 points per minute. In this way, you could argue that Player B actually had a better scoring night.

By figuring out how many points per minute each player scored, we’re taking the first step in doing something that is common in statistics and mathematics: normalization. In simple terms, normalizing is to place data (in this case, the points each player scored) on a scale that is the same, even when the data itself isn’t. To put it another way, in order to account for the fact that Player A had more minutes available to him to score, normalizing the stats makes the comparison more fair. You bring Player A down to Player B’s level, or Player B up to Player A’s level. It doesn’t really matter as long as the two players are on an even scale.

The first level of advanced stats in basketball is an attempt to normalize stats, on a few different levels. The first is per-36 minutes, which is the easiest to calculate, but the most imprecise.

In order to calculate per-36 minute stats, you divide 36 by the number of minutes the player actually played, then take that number and multiply all of the player’s stats by it. 36 minutes is commonly considered an average number of minutes for an NBA starter, so by normalizing a player’s stats for 36 minutes, you can get a sense of how a player might produce as a starter.

As an example, on March 28th, 2016, Henry Sims of the Brooklyn Nets played 13 minutes against the Miami Heat, recording 4 points, 6 rebounds, and 1 assist.

Another Nets player, Sean Kilpatrick, played 21 minutes, scoring 14 points while collecting 3 rebounds.

By normalizing these player’s stats to 36 minutes, we can better compare their stats for the game, which is important when a minutes disparity is so large.

Henry Sims played 13 minutes, and, when you divide 36 by 13, you get 2.77. When you multiply 2.77 by Henry’s points, rebounds, and assists, you get 11 points, 17 rebounds, and 3 assists.

Kilpatrick’s 21 minutes go into 36 1.71 times, which gives us 24 points and 5 rebounds.

Now, as I said at the beginning of this section, this is the most imprecise version of any of these types of normalized stats, and there are a few different reasons why. The first is the issue of sample size. Imagine Sims played 1 minute and in that 1 minute scored 2 points and grabbed 1 rebound. If you normalize that for 36 minutes, Sims winds up projecting out to 72 points and 36 rebounds, stats that would be unheard of in the NBA and obviously unrealistic. By starting with such a small set of data (the “sample size”) projecting it out to a larger set is very unstable. To cross sports, a player who hits a homerun in his first baseball game is not likely to hit one in every game, so projecting 162 home runs (one per game) is silly.

So where are per-36 minute stats helpful? Typically, I find them useful when players play more than 36 minutes. In our very first scenario, we would normalize Player A’s actual minutes played to 36 and Player B’s actual minutes played to 36, and compare their scoring numbers. This would give us a more accurate sense of how their games’ compared.

The second issue with per-36 minute stats is that minutes aren’t actually the most accurate measure of activity in a basketball game. You’re probably looking at the screen very confused right now, so I’ll explain.

In basketball, teams trade possession of the ball after a few different types of what we’ll call “events.” So, when the ball is stolen from a player and the other team takes possession, this “event” is labeled as a turnover. When a player misses a shot and the other team grabs the rebound and takes possession of the ball, this “event” is a defensive rebound. Scoring a basket or making your second free throw while shooting foul shots is also an “event” where possession changes. In the NBA, a possession can theoretically take up an entire quarter (if a team keeps missing shots but getting the ball back on an offensive rebound) or barely any time at all (if they immediately pass it to the other team), but in most cases, teams switch possession of the ball (due to an aforementioned “event”) every 15–20 seconds. But this number can vary wildly from team to team and game to game. A team that has a lot of young, fast players may want to rush up the court and take quick shots against a team of old, slow players, for example.

More possessions mean more “events.” So, in one minute where a team has 3 possessions, they have more opportunities to score, because they’ve theoretically taken more shots. Because they’ve taken more shots, the other team has more opportunities to get rebounds, and because of the number of possessions in that minute, there are more opportunities for things like turnovers and fouls.

So, 36 minutes in one game can mean something wildly different than 36 minutes in another game. How do you combat that?

This is where per-possession stats come into play. Using per-possession stats allows you to measure the game at its smallest-possible unit of measurement that takes both teams into account. By this I mean that every possession is essentially counted equally for both teams, as by definition a change in possession can only happen when the other team gets the ball. So, even if a team somehow holds the ball for two minutes, that’s still one possession, and when the other team gets the ball, that’s one possession for them as well, even if they only then have it for fifteen seconds before giving it back.

In different eras of basketball, the pace of play has varied wildly due to league trends. In the 60s and 70s, basketball was an uptempo game, often featuring scores in the 130s and 140s due to the number of possessions each team had during the 48 minute game. The 80s, 90s, and early 2000s all favored slower play, where teams would score half of what they did in the 60s and 70s, with far fewer possessions per team. In the last half of the 2000s to now, the pace of the game has steadily risen, though it’s still nowhere near where it was in the 60s and 70s.

By normalizing stats to a per-possession basis, we take out the differences in pace of play and in doing so can get closer to crafting real comparisons between players and teams.

The per-possession stat crafting is pretty similar to the per-36 minute stat. Instead of taking the number of minutes a player played and projecting it to a 36-minute number, you compare the number of possessions a player was on the floor for to the stat in question. For example, if a player scored 10 points while on the floor for 50 possessions, then that player scored .2 points per possession. The number of minutes it took to get that many possessions is irrelevant. That player could have played in 20 minutes to get to 50 possessions, or 10; his actual output per possession is the same. This stat is very important when considering players from different eras, considering what we know about them.

In the 1998–1999 season, for example, the average NBA team had about 89 possessions per game, compared to 2015–2016’s 96 and 1969–1970’s 117. Since there were so many more possessions in 1969 compared to 1999, a player who scored 20 points per game in 1998 was a lot more rare, and, therefore, more valuable, since he had far fewer opportunities to score, even though the game has always been 48 minutes long.

To reiterate, more possessions mean more events, which is more opportunities to accumulate stats. As an example, in 1969–1970, when the average team had 117 possessions per game, the average team attempted 99 shots (the disparity here is due to free throws and turnovers), while in 1998–1999, the average team with 89 possessions per game attempted about 78 shots per game. That’s 21 fewer opportunities to score per game per team, on average. This was reflected in the scoring, as teams in 98–99 scored about 92 points per game, and in 69–70 that number was 116.7.

Drilling down to per-possession stats eliminates all of these discrepancies. A possession in 1969 is the same as a possession in 1999. This is why per-possession stats are far more precise when comparing players, especially across eras. Per-possession stats are subject to the same sample-size problems as 36-minute stats, as a player who scores 2 points in 1 possession on the court is in no way guaranteed to score 100 points if he played 50. This is not how these stats work.

Finally, a quick word about per-100-possession stats. Again, this is a normalized stat. In order to calculate it, one calculates the per-possession number and multiplies it by 100. It’s really easy math and a pretty good estimate of how many possessions are in a basketball game, which is why statisticians chose it, I think. Whenever you hear team stats referred to as “defensive rating” or “offensive rating,” the person speaking is referring to a team’s (occasionally a player’s, but usually a team’s)per-100-possession statistics. From what we know about pace of play, the number of possessions in a game, and how that skews the resulting stats from that game, normalizing team stats would seem to make sense, right? If a team, due to their pace of play (which, remember, is a measure of both teams’ possessions) gives up 105 points per game on 100 possessions per game, that’s the same as a team giving up 100 points per game on 95 possessions (about 1.05 points per possession). But, if you didn’t know that one team played at a much faster pace than the other, you would think that its defense was worse, when in reality it was about equal.

The mid-to-late-2000s Phoenix Suns are credited, in part, with speeding basketball back up. They are referred to as the “seven seconds or less” era Suns because their offensive philosophy was to get a shot up within seven seconds of getting the ball.

Because of this increased pace of play, they often gave up more points on defense than other teams. in 2006–2007, they gave up 102.9 points per game, much more than a team like the New Orleans Hornets, which gave up about 97. People thought that, based on this raw number, that Phoenix’s defense was worse than New Orleans, and many other teams. However, when adjusted for pace (Phoenix’s games had about 96 possessions compared to New Orleans’ 90), Phoenix was actually slightly better defensively (106.4 points per 100 possessions compared to 106.5).

Per game stats can be useful, but we have the tools now (check out the excellent basketball-reference.com for stats from just about every year of professional basketball there has been) to better understand the game. What I hope to accomplish with this series is to demystify, and, indeed, argue for the importance of, so-called “advanced” stats. Please drop me a line on Twitter or in the comments and let me know how you enjoy it.