I’m teaching a graduate-level intro stats course right now, and one thing that struck me as we move from calculating things “by hand” to doing things in R is that there’s no real reason to emphasize the normal approximation binomail confidence interval once you’re using software. Or at least far less reason.
The normal approximation This is the basic interval they’ve taught in introductory statistics courses since time immamorial. Or at least the past few decades, I’d have to know the history of Stats Ed to give the real timeframe.

Alrighty! This post got delayed a bit due to real life as well as some challenges with the data. But it’s also an exciting post because we’re finally on the road to generating player-level counting statistics!
Simple Statitistics This post is focused on simple counting stats or box score statistics that were basically the standard way to discuss NBA players until quite recently. So aggregate numbers of rebounds, assists, steals, etc.

As promised, today we’re going to talk about normalizing by possession instead of time on court.
First, a but of motivation. Different teams play at different paces. Some teams try to score a lot in transition, some teams try to slow the ball down and make sure they get good shots in the half-court. Part of this is related to a team’s defense and how quickly they get rebounds in the hands of players who can push the ball.

Until now, we’ve normalized our data by time. This means we’ve been reporting out stats on a “per X minutes” basis. Today, we’re going to unpack a little bit about why we normalize and why we might not always want to normalize by time in the context of the NBA.
What is “normalizing”? Normalization is the act of putting different observations on a level playing field. (That’s not literally what Wikipedia says, but I think it’s a fair paraphrasing for our application.

Previously on DIY Metrics, we did some remedial cleaning on the full 17-18 play-by-play data set. Today, we’re going to take that clean data, generate full-season five-man plus/minus numbers, and then do some plotting!
Cleaning, again So, turns out there were a few bugs that I didn’t catch the first time we went through the cleaning process. This is fairly typical in my experience: You’ll go through your data cleaning and think everything is Gucci only to find once you start your analysis that there are irregularities or issues you hadn’t considered.

Last time on DIY Metrics, we calculated five-man-unit plus/minus ratings from scratch. If we want to use measures like this to compare performance for these groups of players, its important to consider how much game time we have for each unit. There’s a relevant discussion to be had about whether “number of posessions” or “elapsed time” is the best way to compare these groups, (IMO, it depends on what specific question you’re trying to answer with your metric) but today we’ll avoid that discussion and normalize over time because it’s easier.

Last week, I described how to build a plus/minus score for individual players based on data from NBAstuffer. I enjoyed walking through that process, so lets continue the series and expand our focus.
Five-man units vs. Individual Players One of the first things I talked about on this site was comparing different metrics and choosing the right one for the task at hand. Plus/minus for individual players is a weird metric, because it’s taking a team outcome (net change in score) and applying it at an individual level.

In order to better understand some “advanced metrics”, I figured it’d be useful to build them from scratch. (This is also just a fun exercise in data manipulation, cleaning, etc.)
For starters, let’s do something easy, namely raw plus/minus. For the code below, I’m using the free example play-by-play data set from NBAstuffer. They seem reputable, though I do have concerns about how widely-used their formatting is; one of the challenges with building a workflow is ensuring that the structure of your incoming data won’t change.