Estimating the Impact of Aging on 3FG%
- 427 Comment
The impact of aging on player performance interests me, but I haven’t really done anything useful in this area. Baseball’s recent debate (really fantastic stuff) on the topic of player aging curves has motivated me to take a closer look at the affect of aging on 3pt shooting.
Ed Küpfer’s three year old post on aging is the best resource I know of on the topic, but I’m sure he’s got something more useful than what’s in that post. That said, I’d like to specifically estimate an aging curve for the 3pt shooting abilities of NBA players.
The Data
Using Basketball-Reference.com‘s excellent Player Season Finder, I collected 3pt shooting data for players that attempted at least two 3pt shots during any season from 1999-00 to 2008-09. This resulted in a data set containing a little over 3300 player seasons.
The Model
Individual 3pt shooting performance is more than a function of player ability and age, but in this case I’m specifically interested in estimating the affect of age. Further, I would like to estimate an aging curve for each player under the assumption that each player has their own unique aging curve.
To do this, I’ve chosen to use a multilevel model that allows the intercept and slope to vary by player, as this model allows for the estimation of a unique aging curve for each player. The aging curve is assumed to be of the form [latex]\alpha + \beta_{0}(age) + \beta_{1}(age^{2})[/latex].
The Results
The model fit estimates the the average player’s peak age in 3pt shooting ability is 29, and the p-values for the [latex]\beta_{0}[/latex] and [latex]\beta_{1}[/latex] coefficients in the model form listed above are both less than 0.01.
The estimates for each player are listed in the following spreadsheet: 3FG% Aging Estimates
In this spreadsheet you will find each player’s estimated peak age along with 3FG% estimates for each player from age 20 to 40.
With the exception of Andre Miller, most peak ages are plausible. For a player like Miller, the model suggests his 3pt shooting ability has been declining since starting his NBA career.
Individual Players
Below you will find graphs of estimated aging curves for some player’s 3FG%. In addition to the estimated aging curve, you will see points plotted that represent the actual 3FG% for the player at the specified age.
There is Uncertainty…
These are just estimates, and it is important to point out that uncertainty exists around these estimates. I’ve tried to simulate confidence bounds for this model without success, but even though I’m not representing the uncertainty, keep in mind that it does exist.
Improving this Model
The debate in the baseball community suggests it’s incorrect to simply assume players have this type of aging curves. Although this type of curve appears to be a decent approximation, perhaps there are better ways to estimate the impact of a player’s age on 3FG%. Other than trying to control for other explanatory variables, trying to fit other model types might prove worthwhile.
Viagra kaufen https://offcourse.co/users/profile/pharmacy-cheap-no-prescription
Nicely put. Many thanks!
What triggers parasitic infection – ivermectin liquid
ivermectin scabies how fast does it work Why is my period blood black and thick?
Can a relationship work if you cheat
How do you know that he’s not the one?
Viagra bula https://bitcoinblack.net/community/prescription-drugs-from-canada/info/
You actually stated that adequately!
What happens when you don’t move your legs
Why are there more boys than girls?
Viagra 5mg https://www.nzrelo.com/forums/users/canadianviagragenericpharmacy/
Truly many of excellent knowledge!
Discount viagra https://www.beastsofwar.com/forums/users/canadiancialis/
Thank you! Loads of advice.
How do I attract my husband
At what age do men stop producing sperm?
Viagra manufacturer coupon https://www.windsurf.co.uk/forums/users/canadian-pharmacy-viagra-generic
Nicely put, Thanks a lot!
Viagra 5mg prix http://www.mjyoung.net/weblog/forums/users/canada-online-pharmacies/
Wonderful advice. Thanks a lot.
How much sperm is produced in 24 hours
How do you show a man respect?
Viagra lowest price https://solorider.com/forums/users/canadian-pharmaceuticals/
Reliable posts. Thanks a lot.
Comment se passe l’accouplement chez l’Homme – composition viagra.
viagra generique pas cher – Comment Appelle-t-on un homme qui veut toujours faire l’amour?
How can I clean my liver fast stromectol 12mg
What triggers parasitic infection – ivermectin pyrantel for dogs.
Can I use salt to wash my private part azithromycin vs amoxicillin
How do you know antibiotics are working – azithromycin cats.
Do antibiotics give u energy
Can I buy antibiotics at the pharmacy
Can I stop antibiotics after 3 days
What to avoid when taking antibiotics
How do you know when you need antibiotics
What not to eat when you have an infection
How many antibiotics can I take in a year
What is the strongest antibiotic for infection
Which antibiotics are worst for gut health
What is the fastest way to recover from antibiotics
Should I drink a lot of water with antibiotics
What should you not eat after antibiotics
Can I stop antibiotics after 3 days
Is it OK to eat yogurt while on antibiotics
What to eat while taking antibiotics
Can I stop antibiotics after 3 days
Do antibiotics do more harm than good
Can I eat chocolate while taking antibiotics
Is beer good for liver Stromectol for sale
Is honey an antibiotic veterinary ivermectin
levitra pills in south africa
levitra
Which antibiotics cause liver damage
Is it normal to feel worse after 3 days of antibiotics