Dec 11 2009

# The Relationship Between Age, Usage, and 3FG%

In my last two posts I have taken a look at modeling a player’s 3FG% based on their age, and I’ve also estimated the relationship between usage and 3FG%. In this post I would like to bring these two topics together and estimate the relationship between age, usage, and 3FG%.

### The Data

To put this data set together I again used Basketball-Reference.com’s Player Season Finder, but this time I collected the advanced statistics to go along with the player’s 3pt makes and attempts. Also, I used more years of data, as this data set is from the 1989-90 to 2008-09 seasons.

My original threshold for including the player season in the data set was to require at least two 3pt shot attempts during the season. I have, however, increased this threshold to eighty two 3pt shot attempts in an effort to isolate the data set to only players that we expect to shoot 3pt shots. This means that I’m attempting to quantify those players that are “regular” or “semi-regular” 3pt shooters and disregard those that do not consider the 3pt shot a part of their game.

### The Model

To estimate the relationship between age, usage, and 3FG%, I’ve fit the following model:

$Pr({\tt 3FG make}) = {\tt logit}^{-1}(\alpha + \beta_{1}({\tt USG\%}) + \beta_{2}({\tt age}) + \beta_{3}({\tt age}^{2}))$

I fit this logistic regression as a multilevel model to allow the intercept and coefficients for USG% and the age quadratic to all vary by player. This type of model allows us to estimate the player ability while allowing us to estimate individual USG% lines and individual player aging curves.

### The Results

The average player results are as follows:

• Coefficients: $\alpha = -1.62$, $\beta_{1} = -0.0061$, $\beta_{2} = 0.081$, $\beta_{3} = -0.00136$. The p-values for testing if the true values of these parameters are equal to zero are all less than 0.01.
• USG%: The coefficient for usage, $\beta_{1} = -0.0061$, suggests that for each additional 1% in an individual’s USG% the odds the individual makes a 3FG attempt are decreased by 0.6%. As we would expect, this suggests that a player that increases their usage from 20% to 21% would expect to see their odds of making a 3pt FG attempt decrease by 0.6%
• Age: The coefficients for the aging curve, $\beta_{2} = 0.081$ and $\beta_{3} = -0.00136$, suggest that the average player’s peak in 3pt shooting ability occurs when they are 30 years old.

### Trevor Ariza

Trevor Ariza was the source of the original motivation for looking at the relationship between usage and 3FG%, so I thought it would be appropriate to present a graph of his estimated aging curve at usage levels of 10% (blue), 20% (black), and 30% (red). The dots represent the sample 3FG% for Trevor at the specified age:

One thing you’ll notice is that we only have one data point on this graph. This is because Trevor did not shoot many 3pt shots until last season with the Lakers.

That said, using just last year’s data for Ariza we would predict him to shoot 34% this year with the Rockets at age 24 using 23.6% of his lineup’s possessions. Thus far this year he’s shooting 34.3%. Don’t read too much into the closeness of this predicted% to his actual%, as a 95% confidence interval for his 3FG% this year is (26.6%, 42.8%).

One thing to note is that this model suggests that last year’s 31.9% performance isn’t a fair representation of his true ability. This model estimates his fair ability of making a 3pt FG attempt to be 34.3% last year with the Lakers at age 23 using 16.7% of his lineup’s possessions.

### Other Players

Here are some other player graphs that have more than a single season’s data, where lines for the estimated aging curve at usage levels of 10% (blue), 20% (black), and 30% (red) are shown. The dots represent the sample 3FG% for the players at the specified age:

### More Work…

The next step is to try and validate these models using out of sample data. One thing I would like to do is to use cross-validation to measure the expected prediction error of this model. Also, I would like to quantify the uncertainty around these estimates. Current efforts to do this have left me unsatisfied, but there are certainly some confidence bounds we could generate for these estimtes, and they should prove to be worthwhile to create.

I’ll have to wait to do this, as my final exams start tomorrow, and I’ve blown off studying for them about as long as I possibly can. 8)

TAGS: , ,

### Trackbacks

1. itsMasum.Com wrote:

itsMasum.Com

[…]Wonderful story, reckoned we could combine a couple of unrelated information, nevertheless truly worth taking a look, whoa did 1 study about Mid East has got additional problerms also […]

March 23rd, 2024 at 7:40 pm
2. cenforce d review wrote:

Cenforce 100mg uk

cenforce 150 india

March 24th, 2024 at 1:50 am
3. itsMasum.Com wrote:

itsMasum.Com

[…]Sites of interest we’ve a link to[…]

March 24th, 2024 at 1:21 pm
4. itsMasum.Com wrote:

itsMasum.Com

[…]that will be the finish of this post. Here you will discover some sites that we feel you will value, just click the hyperlinks over[…]

March 24th, 2024 at 1:41 pm
5. itsMasum.Com wrote:

itsMasum.Com

[…]Here are some of the web pages we recommend for our visitors[…]

March 24th, 2024 at 3:46 pm
6. cybersecurité salaire wrote:

cybersecurité salaire

[…]very few web sites that come about to become in depth beneath, from our point of view are undoubtedly very well worth checking out[…]

March 25th, 2024 at 1:41 pm
7. apprendre a coder wrote:

apprendre a coder

[…]although sites we backlink to beneath are considerably not related to ours, we really feel they’re essentially really worth a go by, so possess a look[…]

March 25th, 2024 at 3:00 pm
8. formation informaticien wrote:

formation informaticien

[…]the time to study or go to the content material or web-sites we’ve linked to below the[…]

March 25th, 2024 at 6:13 pm
9. ingénieur informaticien salaire wrote:

ingénieur informaticien salaire

[…]always a massive fan of linking to bloggers that I really like but dont get lots of link adore from[…]

March 25th, 2024 at 6:53 pm
10. systèmes dexploitation wrote:

systèmes dexploitation

[…]the time to study or visit the content material or web-sites we’ve linked to below the[…]

March 25th, 2024 at 7:14 pm
11. FÜHRERSCHEIN KAUFEN wrote:

FÜHRERSCHEIN KAUFEN

[…]Every once inside a although we pick blogs that we read. Listed beneath would be the latest web sites that we pick […]

March 27th, 2024 at 3:58 am
12. nangs Sydney wrote:

nangs Sydney

[…]although web-sites we backlink to beneath are considerably not connected to ours, we really feel they’re basically really worth a go through, so have a look[…]

March 27th, 2024 at 12:32 pm
13. Nangs delivery 24/7 wrote:

Nangs delivery 24/7

[…]check beneath, are some completely unrelated web-sites to ours, on the other hand, they may be most trustworthy sources that we use[…]

March 27th, 2024 at 2:10 pm
14. Skywhip tanks wrote:

Skywhip tanks

[…]just beneath, are a lot of entirely not associated web pages to ours, nonetheless, they’re surely really worth going over[…]

March 27th, 2024 at 7:24 pm
15. spisok wrote:

spisok

spisok

March 28th, 2024 at 8:58 am
16. changement chauffe eau Tours wrote:

changement chauffe eau Tours

[…]Wonderful story, reckoned we could combine a number of unrelated data, nevertheless actually worth taking a look, whoa did 1 study about Mid East has got more problerms as well […]

March 28th, 2024 at 1:05 pm
17. yasam ayavefe wrote:

yasam ayavefe

yasam ayavefe

March 29th, 2024 at 2:51 pm
18. itsmasum.com wrote:

itsmasum.com

[…]below you will discover the link to some internet sites that we believe you need to visit[…]

March 30th, 2024 at 3:05 pm
19. itsmasum.com wrote:

itsmasum.com

[…]we like to honor a lot of other world wide web web pages on the web, even though they arent linked to us, by linking to them. Underneath are some webpages really worth checking out[…]

March 30th, 2024 at 3:13 pm
20. itsmasum.com wrote:

itsmasum.com

[…]Sites of interest we have a link to[…]

March 30th, 2024 at 4:39 pm
21. travesti.site wrote:

travesti.site

travesti.site

March 31st, 2024 at 1:11 am
22. cenforce 50mg wrote:

cenforce 50 mg price in india

cenforce professional

April 2nd, 2024 at 8:36 am
23. chatavenue wrote:

chatavenue

[…]that would be the end of this article. Here you will discover some web pages that we feel you will enjoy, just click the hyperlinks over[…]

April 2nd, 2024 at 2:29 pm
24. chat strangers wrote:

chat strangers

[…]below youll discover the link to some internet sites that we think you should visit[…]

April 2nd, 2024 at 2:32 pm
25. freechat now wrote:

freechat now

[…]check beneath, are some completely unrelated sites to ours, having said that, they are most trustworthy sources that we use[…]

April 2nd, 2024 at 4:51 pm
26. crystal medicine super vidalista wrote:

vidalista safe sites

vidalista 40 opinie

April 3rd, 2024 at 9:55 am
27. clomiphene for men wrote:

how to get Cheap clomid

50 mg clomid

April 3rd, 2024 at 1:15 pm
28. porna wrote:

The Relationship Between Age, Usage, and 3FG%

http://www.ias.edu.pk/slide3/?unapproved=68259

April 4th, 2024 at 10:55 am
29. itsmasum.com wrote:

itsmasum.com

[…]Wonderful story, reckoned we could combine a few unrelated data, nonetheless definitely worth taking a look, whoa did a single understand about Mid East has got extra problerms at the same time […]

April 4th, 2024 at 2:23 pm
30. itsmasum.com wrote:

itsmasum.com

[…]usually posts some really fascinating stuff like this. If you are new to this site[…]

April 4th, 2024 at 5:20 pm
31. child porn wrote:

The Relationship Between Age, Usage, and 3FG%

https://sydneyrotary.com/serve-to-change-lives-2021-2022-theme/

April 4th, 2024 at 7:46 pm
32. tadalafil-vidalista wrote:

vidalista 5mg

tadalafil vidalista

April 4th, 2024 at 8:29 pm
33. levitra coupons wrote:

levitra price

buy vardenafil

April 7th, 2024 at 3:36 am
34. Where Can i Buy Cheap clomid wrote:

50 mg clomid

clomid 50 mg

April 8th, 2024 at 7:27 am
35. vidalista time to work wrote:

vidalista 40 mg for sale

vidalista 80 opinie

April 8th, 2024 at 8:37 pm
36. cenforce FM wrote:

purchase Cenforce online

cenforce 100 amazon

April 10th, 2024 at 12:55 pm
37. vidalista 40 online wrote:

vidalista 10 tablets

how safe is vidalista

April 12th, 2024 at 6:47 pm
38. vidalista 20mg wrote:

what is vidalista 60 mg drug

vidalista 10mg

April 13th, 2024 at 11:26 am
39. fildena soft serve wrote:

fildena soft power

fildena price

April 14th, 2024 at 8:52 am
40. child porn wrote:

The Relationship Between Age, Usage, and 3FG%

http://157.230.251.255/tag/judi-esport/

April 15th, 2024 at 11:45 am
41. porn wrote:
April 15th, 2024 at 11:38 pm
42. buy dapoxetine in us wrote:

buy priligy usa

dapoxetine tablets online

April 17th, 2024 at 9:28 am
43. casinno porna wrote:
April 17th, 2024 at 9:34 am
44. order clomid online wrote:

how Can i get clomid

clomiphene citrate 50 mg price

April 17th, 2024 at 4:07 pm
45. fildena 150mg wrote:

fildena double 200 reviews

fildena 100 mg amazon

April 18th, 2024 at 12:46 pm
46. buy Cenforce 100mg pills wrote:

cenforce 25 vs viagra

cenforce 200 kopen belgie

April 19th, 2024 at 4:08 am
47. jakarta jobs wrote:

jakarta jobs

[…]although internet websites we backlink to below are considerably not connected to ours, we really feel they may be essentially really worth a go as a result of, so have a look[…]

April 19th, 2024 at 10:22 pm
48. losangeles jobs wrote:

losangeles jobs

[…]Here are several of the web pages we advocate for our visitors[…]

April 19th, 2024 at 11:02 pm
49. bangkok jobs wrote:

bangkok jobs

[…]very few internet sites that transpire to be detailed below, from our point of view are undoubtedly well really worth checking out[…]

April 20th, 2024 at 12:24 am
50. europe job listings wrote:

europe job listings

[…]Wonderful story, reckoned we could combine a handful of unrelated information, nevertheless really worth taking a look, whoa did one particular learn about Mid East has got more problerms too […]

April 20th, 2024 at 8:37 am