# Nylon Calculus: The college prospect growth curve

Pretty much any NBA fan who follows the draft knows that age is a big factor in evaluating prospects. If two players are close in productivity, but one is younger than the other, you obviously favor the younger player. But, if the older player is more productive the question of how big that gap has to be in order to favor the older player is a bit more tricky

The most direct way to look into that is to generate the descriptive statistics of how college players perform at different ages. Too often we skip the step of showing descriptive data, that is often easier for people to understand with just a little context. Also, beyond the overall one-number metrics, we can break down which statistical measures improve the most and which ones are less affected by age.

I used the database I got via Will Schreefer also used to build my “NBA Player or Not” model. The database has just under 7,000 unique college players who went on to play in some professional capacity since 2005, and over 22,000 individual seasons played. I rounded each player’s age to the nearest year then average each stat by rounded age to get a sense of the typical difference in performance by age.

First I used Box Plus Minus (BPM) as the one number metric to get an overall sense of the growth curve, including the offensive and defensive breakdown.

As the table shows, the BPM estimate of productivity increases pretty significantly as players mature over their college career, and by the BPM estimate, at least, most of that increase is on the offensive end. I don’t want to put too much stock into that breakdown since we know how difficult it is to capture defensive value with box score stats and how incomplete those measures are. However, when we look inside the box score measures, it becomes apparent why the BPM estimates’ growth skews to the offense.

Here are the advanced box score stats that get attributed to the offensive side by age, with the difference between the age 19 seasons and age 22 seasons highlighted at the bottom:

As the table shows there’s a clear upward trend by age for all of the offensive statistics except for offensive rebounds. The difference between the age-19 season and age-22 season is highest for the creation and ball-handling as assist percentage increases 15 percent while turnover percent falls 13 percent.

By contrast only defensive rebounds show any increase, and then a relatively modest one.

These numbers are for all of the players in the database, if I separate out only the players that eventually make it to the NBA, the growth between the age-19 season and age-22 season is larger almost across the board. The only exception being rebounds, where there is actually more growth for non-NBA prospects. Assist percentage increases 25 percent for the future NBA players and Usage% increases 14 percent. It appears that developing the skills to handle the ball and create offense are significant separators for getting into the league.

I would note that fouling rate, which is not in the “Advanced” box score and doesn’t figure into BPM, does show improvement with age, with fouls per-40 minutes falling 10 percent from 19-year-olds to 22-year-olds.

Lastly, I filtered the stats based on the player’s height, using three tiers as approximate height groups for player positions as guard height up to 6-foot-3, wing height at 6-foot-4 to 6-foot-8 and bigs at 6-foot-9 and taller. I used height as a stand in for position because I didn’t have a good outside source for all 7,000 players and I didn’t want to develop a position estimate based on the same stats that I was going to be tracking changes by for. It is not uncommon for a 6-foot-8 college player to play more of an interior role early in his career but to take on more of a wing role as his skills and offensive responsibilities change. I wanted to keep them in the same tier for stat tracking even if their role changes later.

I will just highlight a couple of things from the height tiers. Guard height players show the largest improvement as measured by BPM ( +3.1), then Wing height (+2.3) and then Bigs (+1.7). This is consistent with what I have seen in draft models and NBA development models, backcourt players have a longer development curve, at least as measured by box score stats. The difference in statistical growth for future NBA vs future non-NBA pros is maybe less than I would have thought, +.2 for NBA bound Guards, +.5 for Wings and +.3 for Bigs, which maybe in part due to negative selection bias the best young NBA guys going into the league early.

Below is the increase or decrease in average performance comparing year 19 year old season to 22 year old seasons in individual stats categories. To be clear, these are the percent changes to the base value, so an average 25% increase in AST% by Bigs is starting from a lower base value 6.2% for 19 year old Bigs vs 18.3% for guards.

The big standouts, to me, are how much TOV% falls for Guard height players, and how little for Bigs, as well as the fact that DRB% does increase for 6-foot-9 and over players in a somewhat significant way, most likely a reflection of increased strength and weight.

Keep in mind that these are changes in the averages, the progression of individual players is much, much more noisy, and that’s not just true of shooting percentages. These also cannot just be transferred over whole to NBA projections. There are very clear selection issues based on when player’s try to go to the NBA or even go pro overseas, and the competition and team environment is, of course, very different.

That said,I think we can see clear enough patterns development to give us some useful priors to take into prospect valuation. If you’re looking at two wings where the older player has much higher steal and block numbers, don’t assume the younger player will catch up. If the only advantage an older guard shows is fewer turnovers there’s probably a decent chance of the younger player closing the gap and moving ahead, all other things equal.