Meer Patel writes:
I’m a rising junior in high school and recently completed a study titled “Beyond Averages: Measuring Consistency and Volatility in NBA Player and Team Offense.” I used game-level data to build a new metric for offensive impact and analyzed how player performance fluctuates over time.
From the abstract of his paper:
While traditional player evaluation metrics focus almost exclusively on season-long averages, I propose a framework that incorporates both the magnitude and consistency of offensive impact normalized per minute of play using game-level data from the 2024-25 NBA season. . . . I introduce the Net Offensive Impact (NOI) statistic and use the coefficient of variation of NOI per minute over a fixed, randomly sampled set of games totaling approximately 400 minutes per player to quantify each player’s volatility using a standardized approach. . . . while the league’s top offensive performers tend to be both productive and stable, many players–especially role players and high-variance “wildcard” scorers–display far greater fluctuation. . . . Offensive consistency is closely linked to individual playing time and can also help predict team success to an extent, but falls short in the playoffs. . . . Offensive consistency is a valued but not singularly decisive attribute; both steady and volatile offensive contributors play important roles in shaping NBA outcomes depending on the situation.
I took a quick look at the first version of his paper and wrote that it’s hard for me to evaluate the basketball stuff because I don’t know so much about basketball. But I did have a statistical comment, which is that when your sample size is smaller you will see more variation in the average, and I think that’s what you’re seeing here. So I don’t know that you’re really finding evidence that some players are much more variable than others; you could just be noticing in a different way that some players play many more minutes than others. One way to look at this would be randomly subset your data so that you have the same number of data points for each player.
Patel responded with a revision, writing:
Now, I randomly select the same number of games (20) for each player when calculating volatility. I describe this approach in the updated Data and Methodology section. All results, tables, and figures are based on these random subsets. There were some changes, particularly in the top 5 most consistent and volatile player rankings, where the list changed drastically. That being said, I found that the main findings remained consistent when using equal-sized samples, which gives me even more confidence in the results.
I replied that I’m still concerned about sample size issues. Maybe you should sample equal number of minutes, rather than games, for the selected players? My intuition is still that when you measure volatility, you will find more volatility for players with smaller sample size per game. If you’re measuring game-to-game variability, then players who play fewer minutes will show more variability even with no differences between players, just because fewer minutes is a smaller sample size per game.
Patel replied:
After reading your last email, I revisited my methodology to make sure I’m not unintentionally overstating player-to-player differences in consistency, and updated my paper, which is attached to this email.
For each player, I randomly sample games (from their full season log) until I reach 400 total minutes, then compute NOI per minute for each sampled game, which normalizes all player contributions on the same standardized scale. All volatility statistics, such as the coefficient of variation (CV), are then calculated from this per-minute series, rather than from raw game-to-game NOI.
This adjustment removes the bias where players with fewer minutes per game could appear artificially more volatile, since all rate and variability statistics now reflect offensive production per minute played, regardless of a player’s role or average playing time.
In addition, to further check robustness, I repeated the random sampling with different seeds and confirmed that the volatility and consistency results remain stable across samples.
Enjoy. I have not read the paper in any sort of detail so have no comment on the findings there. (That’s not a negative statement on my part, it’s just the literal truth.) I’m posting here because the general idea sounds cool, issues of implementation aside. Studies of variation in sports are always challenging.
The last time I can recalling sharing someone’s NBA analysis was in this post from 2008. The guy who sent me that earlier item, Eli Witus, had written:
I don’t have any formal statistical training, so I am learning as I go. . . . I am very interested in multilevel modeling–I think it could be very useful in basketball since the game is much more interactive than baseball, and player statistics are heavily dependent on the context of the player’s teammates and coach. I think multilevel modeling could help answer questions about how a player’s statistics are likely to change if he changes teams.
I haven’t heard from Witus in a long time and his blog is no longer around, so I googled his name, and . . . it seems that he’s now the Executive Vice President of Basketball Operations & Assistant General Manager at the Houston Rockets. So all things are possible! In the meantime, if anyone near Edison, New Jersey, has interest in some basketball analytics, there’s nothing stopping you from contacting Meer Patel directly.