APBRmetrics

Ed **Küpfer** · Joined: 30 Dec 2004 Posts: 787 Location: Toronto

Analysis of aging is difficult becase of the noise. In the graphs below, I've taken steps to remove as much noise as possible by regressing player stats to the mean, and also accounting for differences in year-to-year variations, position-by-position variations, and player ability. Here are the stats I looked at:

Mark · Joined: 20 Aug 2005 Posts: 807

Impressive work as usual and rich with information.

Viewing Ed’s graphs, these are my first impressions:

Height. For centers being over 7 foot can aid longevity a little. Not really a surprise. For young shooting guards, outstanding height seems correlated with coming thru or getting you thru the door but by 23-24 yrs many of the tall SGs who don’t have a mix of enough of the necessary skills to compete are perhaps weeded out and average height settles down.

Weight. Heavy centers see a lot of weeding out too by 25 and lighter seems more common among the long serving. I guess the failure rate is higher among the huge guys than the less imposing, who must impress the scouts more with their skill level?

Minutes. For small forwards, perhaps the long careers at big minutes of the Reggie Millers, Scottie Pippens and others give the minute chart more of a tail than for other positions. And maybe it also says something about the relative low quality of young SFs, the difficulty of them to break thru and get on the court over the vets, and /or the multiplicity of young categorized as SFs carried on a roster, hurting their minutes played averages?

Rebounding. You probably don’t want to hold a contract on a rebounder past 31 unless they are quite strong and considered above averge in likelihood of enduring at an acceptable rate?

Turnovers. Seniors improve in taking care of the ball.

In general from the whole collection. Holding players past 33 needs very careful consideration of a player’s unique career curve to date and projected. Age shows many signs of catching up with players, or at least most players. Seems generally in line with past research on age, career curves. Any nuance that breaks from the conventional wisdom?

Ed **Küpfer** · Joined: 30 Dec 2004 Posts: 787 Location: Toronto

Mark, I think the following graphs will be easier to read. They show the same data as above, but as the amount of change from the previous season. The black horizontal line at zero represents no change in the player's stats from the season before. If you can picture a player's career as following an inverted-U shaped arc, that path will be displayed on these graphs as a more-or-less straight line from the top left to the bottom right.

Minutes per game

2-pt percentage.

3-pt percentage

Fouled %

Offensive Rebounding Percentage

Defensive Rebounding Percentage

Turnover Percentage

Steals Percentage

Block percentage

Assist Percentage

Own-Asisted Percentage

_________________
ed

Mark · Joined: 20 Aug 2005 Posts: 807

I understand your explanation of how these new charts are expressed. The first defensive rebounding chart looks like fairly dramatic decline for PF/C but very gradual in second set because the rate of change is relatively constant, not accelerating. Function curve and derivative of that function curve.

And in general the climb to the peak performance level on these stats is quicker in pace and shorter in time than the decline. Before 24 and after 35 seems to show more movement and positonal variation, perhaps affected by smaller groups.

2 and 3 point shooting percentages see moderate dropoff rate between 27 and 30 then the dropoff continues but at a noticeably slower rate.

(I assume each set only looks at those player that persist in the league, letting players drop out without effect on averages rather than assigning zero production stats and keeping them in the dataset).

Ed **Küpfer** · Joined: 30 Dec 2004 Posts: 787 Location: Toronto

Mark · Joined: 20 Aug 2005 Posts: 807

Yes, I editted out the smoothness comment because I recognize that the smoothed lines can seduce to that "line" of thinking when the background data is as messy as you now show.

With your emphasis on the future and prediction, the effort you mention does
sound interesting and expected. League based answers for performance after unusual bounce years, or forecasts for continuing a longer term upward or downward trend would be quite interesting. As you might say, it could give a baseline to compare your player specific assessment against or it could be used as part of building that player specific assessment.

Dean and Dan probably could say some interesting things here about methods, and adjusting methods and experience with these methods if they felt they could without over-relevation.

Ed **Küpfer** · Joined: 30 Dec 2004 Posts: 787 Location: Toronto

I'm not altogether satisfied with the stuff above. I was plotting changes from one season to the next in various players stats against the age in which these changes took place. The idea is fine, but it would have been more useful to use the number of NBA seasons played instead of player age. Also problematic is the lowess regression line I used to summarise the changes. Lowess smoothing always suggests to me a discriptive approach rather than explanatory. To rectify those problems, I'll introduce a different approach below, quantile regression.

Oridnary least squares is pretty much the bread and butter regression approach. I won't bother explaining the method, but I want to say something about the results you end up with. When you use OLS to regress a response variable against a predictor variable, the results will look something like Respose' = Constant + Coefficient*Predictor. The Response' is the expected response given the predictor. This expected response maps closely to the average (mean). What that means is, given an arbitrary predictor P, the average reponse will be Response'.

Nothing objectionable there. But there's no reason to focus only on the mean response. In fact, if you have a skewed distribution, you may want instead to focus on the median response, which is less sensitive to outliers. If you do some median regression, you'll get a result that returns coefficients and a constant that optimises a median response, rather than a mean response. And now, if you're going to the trouble of regressing to the median, you can generalise that method to regress to any quantile -- regressing to the median (50th percentile) uses the same method as regressing to the 75th percentile, or the 95th, or… In my analysis, I'll use the 5th, 25th, 50th, 75th, and 95th percentiles. I'll use the R package 'quantreg' for the calcualtions. (OLS, as the name suggests, uses squared errors to optimise the reponse. Quantile regression uses absolute deviations.)

Right. Let's look back at minutes per game (if it's not obvious, I used YEAR and YEAR^2 to plot these):

MPG

(Once again, clicking the images will take you to a larger sized image.)

The solid line is the median, and it looks a lot like the lowess line in the chart from a previous post. Where this is different is the pseudo-confidence intervals, the quantiles. Look at the column of points over the Year 2 marker. This shows how players' minutes per game played changed after their rookie seasons. The median line is above zero, which means that more than half of all year 2 players increased their MPG. Looking upwards, we see that 25% of all year 2 players (ie players at the 75th percentile) increased their MPG by about 5 or more minutes. Five percent of all players increase their MPG by 15 or more.

What's interesting to me is that while some stats show a clear aging pattern (ie increas -> peak -> decrease), other stats show a negligable or zero aging pattern. Block%, offensive rebounding%, defensive rebounding% in particular show about as much propensity to increase in any given season as to decrease. Even for MPG, which shows a clear aging pattern, there is still a 25% chance that any given player in any given season will see his minutes increase.

2-Pt%

3-pt%

Fouled%

Off Reb%

Def Reb%

Assist %

Own-Assist%

Steal%

Block%

Turnover%

_________________
ed

Mark · Joined: 20 Aug 2005 Posts: 807

I like the additional detail provided by your regression choice and the graphs from it including the background dots. Conveys a strong sense of the diversity in contrast with the mean lines in the earlier sets.

"Even for MPG, which shows a clear aging pattern, there is still a 25% chance that any given player in any given season will see his minutes increase. "

In addition to pure talent evaluation which should increase and decrease minutes based on performance and fit it is probably also influenced by impacts from the salary cap, teams over the cap, budgets, free agent competition and shortfalls filling needs; players changing teams; wanting to get time for young players; injuries/opportunities for others/returns,etc.

Ed **Küpfer** · Joined: 30 Dec 2004 Posts: 787 Location: Toronto