Nylon Calculus 101: Basic Box Score Adjustments
By Ian Levy
One of our missions here at Nylon Calculus is to help make basketball analytics accessible to anyone with interest. A big part of that mission is building a comprehensive and reliable Glossary. The plan is to make this glossary different from some of the others around the internet in two ways. The first is that it will be top-to-bottom comprehensive and sequential. The thing that is often lost in discussions about basketball analytics is that each new statistic or technique is usually an adjustment to a previous model, trying to account for some hole or something that isn’t measured well in existing statistics. All basketball statistics have a lineage of mathematical models and we want to make sure that anyone with the time and interest can peruse the entire family tree. The second thing that I believe will set our glossary apart is that we want to do more than define the statistics. For each we would also like to explain a little about what it says and what it doesn’t say—what purpose it serves in our analytic discussion.
We’re just getting started with our Glossary and there’s a lot more to build. We’ve already looked at The Basic Box Score and Basic Shooting Statistics. Here we will begin looking at how the basics are adjusted to create a more complete picture of what is happening on a basketball court.
Basic Box Score Adjustments
Per Game
The basic box score leaves us with these statistical tools to evaluate and understand a basketball game—minutes, points, rebounds, assists, steals, blocks, turnovers, free throw attempts, field goals and three-pointers. Each of these statistics offers small bits of information about performance. The first way to begin expanding their explanatory power is by looking at each statistic as a rate instead of a quantity. What this means is looking at how a player or team accumulates those statistics within some unit of time. Each of these statistics can be viewed as a ratio to all sorts of units of time but the most traditional, and probably most familiar, is to look at averages per game.
Converting any of those statistics into a per game average requires nothing more advanced than simple division, dividing a season-long total by the number of games played. Although the average fan has become more and more aware of the shortcomings of comparisons and evaluations made on just per game averages, they still represent a more refined version of the information gleaned by looking at simple quantities.
Games are discrete events, each with a winner and a loser. In that way they are the most basic unit of team success in the NBA and there is some value in comparing team and player statistics in the same way (remember the value of a statistic comes from the question you are asking). The benefit of looking at things by per game averages is that it quantifies each statistic by this meaningful unit of basketball understanding. For example, looking at points per game averages for a player gives you a sense of what quantity of scoring can be expected within that comfortable unit of a single game. This naturally includes a lot of variables, hinting at additional information about a player’s role on a team and the amount of time they spend on the floor.
This additional information leads to the shortcomings of per game averages as well. Because so many variables about role and playing time are wrapped up in per game averages, it can be difficult to make comparisons between players for whom those things are different. For example, comparing per game averages between a bench player and a starter is not necessarily an apples to apples comparison since they have a different number of opportunities within each game.
However, there are basic questions that can be answered by per game statistics and other adjustments can begin to help answer the questions for which per game statistics are inadequate.
Per Minute
Per minute statistics are a response to one of the shortcomings mentioned in per game statistics. By looking at basic box scores statistics as a ratio to minutes played, we are a taking a step towards leveling the playing field for comparisons between players who play different amounts of minutes in a game. A per minute ratio would result in a very small and unfamiliar number. For that reason, per minute statistics are usually expressed as per 36 minutes or per 40 minutes, roughly the number of minutes we would expect a starter to play. This converts the ratio into quantities that feel more familiar to us. Comparing per 36 minute averages makes it easier to compare bench players to starters, removing the variable of how much they play, and just giving you information about what they produce when they are on the floor.
The downside is that even these comparisons can smooth over important differences. For a player who plays a small number of minutes per game, it can not always be assumed that their per 36 minute averages would stay the same if they actually played more minutes. For example, a player who has impressive per 36 minute averages in scant playing time may be loading up their statistical resume in garbage time, feasting on inferior opponents.
Although neither per game or per minute box score statistics are perfect, they are an improvement over simple quantities, helping provide context for a player’s statistical achievements. In addition, the problems they present in terms of ignoring variables like the quality of competition or team pace are the impetus for the next levels of statistical models. We’ll continue looking at those more detailed levels in our next few glossary entries.