Post by Deleted on Mar 23, 2021 13:42:11 GMT -5
Devious Deviations 2: Categorical Uncertainties
by JZ (TMBSL Nets GM)
by JZ (TMBSL Nets GM)
Introduction
Last time, we looked at some examples of standard deviation for players within a single season, and across an ensemble of 100 seasons. This short entry will bring the analysis of digging into the standard deviation of each statistic itself.
Methodology
For this experiment I took the same 100 seasons that were simulated, and looked at the standard deviation, and two times the standard deviation to get a better estimate of how accurate an individual test sim can be to the expected value from a given player. Only players with more than 20 minutes per game (on average over the 100 seasons) were considered for this study.
Results
Without further ado here is the chart, which we will discuss further:
For the purposes of keeping the chart a semi-wieldy size, players 76-189 (as ranked my average mpg) are hidden in the chart, but are included in the standard deviation averages.
Discussion
The first thing you will notice is that for some players, the standard deviation can be quite wide. Player 39 (Brain Winter) had a point standard deviation of 2.4. Using two times the standard deviation is often called the “95% uncertainty”, which means that 95% of the time your values will fall within two times the standard deviation. For Brain Winter, that means you can only know that your average points for any given season is within plus or minus 4.8 points! That means one season he could see 24 points per game, and another season you could see 32 points per game, and these would be entirely normal variations.
Fortunately, most other player’s don’t have this high amount of variance, which you can see in the bottom two rows of the chart. The average standard deviation for points is 1, and the 95% uncertainty is 2 points. However, this includes players who aren’t very high volume in the averaging formula.
Points is just the tip of the iceberg though, we see many of the other stats are fairly predictable season to season. Three pointers, Steals, Blocks, Turnovers, and Fouls are all pretty consistent with 95% uncertainties around 0.3. However, for some statistics like Blocks, 0.3 is a fairly large swing, with 1.2 and .6 blocks per game being within the 95% uncertainty probability for a player that shows .9 blocks on average.
Additionally, Rebounds show a 95% uncertainty of .8, which means someone’s rebounds could fluctuate up to 1.6 rebounds and still be considered an entirely “normal” season, all with 0 changes to any depth charts or league composition.
Conclusion
I suggest to use these “error” values when doing any test sims for rookie players who you manage to get a significant amount of playing time (20 minutes per game, 70+ games). So if you simulate a season to see how Kevin Durant will do, keep in mind his point total from one season to another could vary by a significant amount. These error values should be helpful to people that won’t simulate a ton of seasons for this reason, as you could simulate a smaller number (say 4 or 5) and average together the stats of the player across each season, and then use the error bars derived from this reporting. As always YMMV with differing league files and player builds than the one I used here, but I think this is a good general ballpark estimate of categorical uncertainty moving forward.
Future Work along this vein won’t be heavy, but may include analysis by position and by mean totals (i.e. we expect to see more variation in points for Brain Winter who typically scores ~26 than for Catfish who score ~9). New uncertainty values would be derived for each position and point total range (i.e. PG who scores ~25 should expect 95% uncertainty of +-5, while a C who scores ~9 should expect a 95% uncertainty of +-2).
