The Relationship Between Age, Usage, and 3FG%
- 673 Comment
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:
[latex]Pr({\tt 3FG make}) = {\tt logit}^{-1}(\alpha + \beta_{1}({\tt USG\%}) + \beta_{2}({\tt age}) + \beta_{3}({\tt age}^{2}))[/latex]
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: [latex]\alpha = -1.62[/latex], [latex]\beta_{1} = -0.0061[/latex], [latex]\beta_{2} = 0.081[/latex], [latex]\beta_{3} = -0.00136[/latex]. 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, [latex]\beta_{1} = -0.0061[/latex], 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, [latex]\beta_{2} = 0.081[/latex] and [latex]\beta_{3} = -0.00136[/latex], 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)
Maillot de football
[…]Here are a number of the web pages we advise for our visitors[…]
Maillot de football
[…]that will be the end of this report. Here youll discover some websites that we assume youll enjoy, just click the hyperlinks over[…]
Maillot de football
[…]we prefer to honor a lot of other net websites on the web, even if they arent linked to us, by linking to them. Underneath are some webpages really worth checking out[…]
Maillot de football
[…]Here are a number of the internet sites we suggest for our visitors[…]
Maillot de football
[…]Sites of interest we have a link to[…]
Maillot de football
[…]check beneath, are some totally unrelated sites to ours, however, they may be most trustworthy sources that we use[…]
Maillot de football
[…]usually posts some quite interesting stuff like this. If you are new to this site[…]
What happens when you drink alcohol everyday??
What is parasitic anxiety?
The Relationship Between Age, Usage, and 3FG%
https://fragapisos.com.br/how-outsourcing-your-logistic-needs-to-us-can-prove-to-be-cost-effective-for-you/
izmir escort
izmir escort sitesi gururlar sunar.
child porn
best porn web site click and go watch porn.
SEOSolutionVIP Fiverr
[…]Wonderful story, reckoned we could combine a handful of unrelated information, nonetheless definitely worth taking a appear, whoa did one master about Mid East has got far more problerms at the same time […]
SEOSolutionVIP Fiverr
[…]we came across a cool site that you simply might take pleasure in. Take a look if you want[…]
SEOSolutionVIP Fiverr
[…]we like to honor a lot of other world-wide-web web-sites around the internet, even if they arent linked to us, by linking to them. Under are some webpages really worth checking out[…]
SEOSolutionVIP Fiverr
[…]just beneath, are quite a few entirely not associated internet sites to ours, even so, they may be certainly really worth going over[…]
The Relationship Between Age, Usage, and 3FG%
https://investissement-immobilier-ancien.fr/comment-trouver-un-appartement-renover/
Viagra dosage https://buyviagraonlinet.com/
Seriously loads of amazing material.
luci led camera
[…]The information and facts mentioned inside the report are several of the most effective out there […]
strisce led corridoio
[…]The info talked about within the post are some of the best accessible […]
structure de callisthénie
[…]just beneath, are a lot of completely not associated sites to ours, even so, they’re certainly really worth going over[…]
structure ninja warrior
[…]check below, are some completely unrelated websites to ours, however, they are most trustworthy sources that we use[…]
arm extension
[…]Here are a few of the web sites we advocate for our visitors[…]
symbole art martiaux
[…]Here is a superb Blog You might Find Exciting that we Encourage You[…]