tag:blogger.com,1999:blog-31545676.post5798372511472167172..comments2021-06-19T03:12:04.657-04:00Comments on Sabermetric Research: Why you can't calculate aging trajectories with a standard regressionPhil Birnbaumhttp://www.blogger.com/profile/03800617749001032996noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-31545676.post-41581230623901124682019-12-08T20:56:25.347-05:002019-12-08T20:56:25.347-05:00Phil - I tried out some random effects regression ...Phil - I tried out some random effects regression stuff and it worked relatively well. I sent you an email about it, not sure if it's still an address you use.Alexnoreply@blogger.comtag:blogger.com,1999:blog-31545676.post-35563932429966419292019-11-24T14:11:21.948-05:002019-11-24T14:11:21.948-05:00Correct. A random effects regression in theory ca...Correct. A random effects regression in theory can help solve a few different problems presented by an aging curve: (1) players are always tracked relative to themselves; (2) players of any career length still borrow strength from the other players in the sample, including those with longer careers; (3) because the random effects automatically shrink the values toward their probable mean for all players for all years, you are working with more accurate underlying estimates which helps everything. You may still need an additional control for survivorship but this an approach worth looking at. You could model the aging effect itself as a spline or an additional random effect but the values I suspect would be fairly similar.Jonathan Judgehttps://www.blogger.com/profile/10070517889418724003noreply@blogger.comtag:blogger.com,1999:blog-31545676.post-54598466193067450352019-11-23T13:45:11.096-05:002019-11-23T13:45:11.096-05:00Hi, Alex,
Sorry for the delay getting back to thi...Hi, Alex,<br /><br />Sorry for the delay getting back to this.<br /><br />Not sure what a random effects regression is. <br /><br />The biggest difference is the delta compares 25s only to 26s, rather than comparing 25s to 35s (and all other ages). By doing it that way, it lessens the effects of attrition of the lesser players. <br /><br />What you want is to compare a player to himself. If you compare all 25s to all 35s, the pool has shrunk from (say) 200 players to 40 (better) players, so you're comparing the better 40 players to themselves, but also comparing the worse 160 players to the better 40 players.<br /><br />By doing only 25 to 26, the pools might be 200 players to 190 players, so you're mostly comparing players to themselves.<br /><br />Then you compare 26 to 27, 27 to 28, and so on, and combine all the results.<br /><br />PhilPhil Birnbaumhttps://www.blogger.com/profile/03800617749001032996noreply@blogger.comtag:blogger.com,1999:blog-31545676.post-27695127053306904002019-11-23T13:41:41.150-05:002019-11-23T13:41:41.150-05:00Hi, Rod,
Sorry so delayed getting back to you!
...Hi, Rod,<br /><br />Sorry so delayed getting back to you! <br /><br />I think experience and age are different issues ... it's a good point that experience can "contaminate" age if what you're really looking for is just age-related performance changes without the effects of experience or coaching.<br /><br />I was getting at something else, that when you mix different careers, the regression is unable to combine trajectories and it just smooths the average at each age, so what you get is the effects of the population change rather than the age changes.<br /><br />Phil<br /><br />Phil Birnbaumhttps://www.blogger.com/profile/03800617749001032996noreply@blogger.comtag:blogger.com,1999:blog-31545676.post-30634587351731830862019-11-23T13:38:18.907-05:002019-11-23T13:38:18.907-05:00Jonas,
Hmmm ... I don't think that's nece...Jonas,<br /><br />Hmmm ... I don't think that's necessarily the case. Suppose ALL 27 year olds were better than ALL 26 year olds. If there aren't enough 27s to fill a whole league, teams will also have 26s, but the average performance of 27s will be higher than the average performance of 26s.<br /><br />Sorry for the late response!<br />Phil Birnbaumhttps://www.blogger.com/profile/03800617749001032996noreply@blogger.comtag:blogger.com,1999:blog-31545676.post-61230569966762860182019-11-22T18:07:34.062-05:002019-11-22T18:07:34.062-05:00I'm not familiar with baseball research, but h...I'm not familiar with baseball research, but has anyone done a random effects regression to calculate aging curves? I imagine someone must have. From reading through the link you have on the delta method it seems like the key difference is that the delta method compares each player to himself, whereas the standard regression just throws everyone together. A random effects regression would be more similar in that it compares individual players to themselves.Alexnoreply@blogger.comtag:blogger.com,1999:blog-31545676.post-46000257279837349882019-11-19T08:13:38.776-05:002019-11-19T08:13:38.776-05:00Hi Phil.
The question seems to be the impact of a...Hi Phil.<br /><br />The question seems to be the impact of aging on performance. And it seems you find that the relationship is “contaminated” by experience varying across ages. I’ve used the following to untangle age and experience when thinking about player value (and salary, too).<br /><br />Just put in age and its square, and experience and its square. Then, the regression gives you the non-linear impact of age on performance, holding experience constant. It’s also fair to include other impacts by player (injury for example).<br /><br />Or, in work with Roger Noll, we regressed age and its square on experience and used the residual of experience and its square. A bit less intuitive interpretation since now it is “more experienced than age would suggest” or “less experienced than age would suggest”.<br /><br />Or it’s entirely possible I’ve missed the point (you know that I sometimes do). Cheers. Rod FortRodney Forthttps://www.blogger.com/profile/06906706552463504573noreply@blogger.comtag:blogger.com,1999:blog-31545676.post-13133091638616332732019-11-19T02:15:43.706-05:002019-11-19T02:15:43.706-05:00Correct me if I'm wrong, but if teams are pick...Correct me if I'm wrong, but if teams are picking players optimally, without any age bias, then given sufficiently large sample, the average performance for each age should be the same, i.e., league average. Right?Jonasnoreply@blogger.comtag:blogger.com,1999:blog-31545676.post-9249663410690149202019-11-18T22:33:01.821-05:002019-11-18T22:33:01.821-05:00I've thought about this a bit myself over the ...I've thought about this a bit myself over the years, and I think it's likely that players who put up (say) 2 WAR at age 20 have differently *shaped* careers than players who put up 5 WAR, particularly on the back end.<br />I haven't made the effort to get the data to try to examine that, but I really should.Mikehttps://www.blogger.com/profile/12506620740117742071noreply@blogger.comtag:blogger.com,1999:blog-31545676.post-72875800798097063692019-11-18T18:51:15.837-05:002019-11-18T18:51:15.837-05:00You're not old! You're a student of baseb...You're not old! You're a student of baseball history. :)Phil Birnbaumhttps://www.blogger.com/profile/03800617749001032996noreply@blogger.comtag:blogger.com,1999:blog-31545676.post-15949302960540677422019-11-18T18:24:53.631-05:002019-11-18T18:24:53.631-05:00I'm building a probabilistic age estimator bas...I'm building a probabilistic age estimator based on understanding references to Damaso Griffin and Alfredo Garcia in 2019. It, uh, thinks I'm pretty old. ;)<br /><br />Friend of the site Tyler D.Anonymousnoreply@blogger.com