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That's not the reality for most youth sports anymore. It's gotten much more competitive. Participating in school sports isn't enough. They generally can't develop the level of skill necessary to gain advantage in college admissions without paying a lot to participate in travel club teams and for private coaching. And I'm not talking just about NCAA recruited athletic scholarships but even for the sort of regular extracurricular sports activities that might give someone an advantage in college admissions.
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My kids were able to take some SAT test prep course through their school (partially funded by the PTA) and it helped a lot. They wrote a bunch of practice exams and each time their scores went up. Also, test taking itself is a skill and the more you practice it the better you get at it. If you’ve written the SAT 15 times over the past 2 years, then the 16th time won’t be as stressful and you will know strategies that work and the questions will be familiar.

If you are in a school that doesn’t have a well funded PTA, you are at a disadvantage.

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You can, as of about a year ago, take official SAT practice exams for free in Google Gemini.
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SAT prep is much more than just taking practice exams.
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The person to whom I responded seemed to imply that it consists chiefly or entirely of taking practice exams. I merely wish to point out that if you want your kid to take SAT practice exams every month you can do it for free at home.
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Such a "SAT test prep course" is going to involve more than just self-guided practice exams. It'll include feedback and coaching to address deficits revealed by those practice exams.
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This is exactly right. Writing each practice exam only takes a few hours and this course last months. The reset of the time is filled with all the things you talked about.

Plus, for some kids writing a practice exam at home isn’t the same thing as a simulated seating with kids all around and a proctor in the room.

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You seem to be arguing with someone else.
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No; I'm saying "just take practice exams" isn't what we're really talking about. They are merely a part of high-end test prep offerings.
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Sports is the most expensive way to get into college. Tennis is close to $1 million to get your kid into an Ivy league through tennis. Malcom Gladwell wrote about sports and colleges in his book "revenge of the tipping point". Sports is used by the wealthy to get their less academically inclined children in to top schools and some school are expanding it.
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Your analogy works against you, given that tons of professional athletes come from poverty.
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Professional athletes are like people who get 1600s on the SAT; a bit of an outlier.
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That's exactly the point. Top schools are looking for outlier intellectual talent, but the egalitarian approach (high school grade inflation plus weakening of standardized testing) smooths the differences and makes it harder for them to admit the right people.

The visible result has been the weakening of these institutions. Do also observe that this is recursive — as these institutions have lowered their standards over decades, the people who go through them and end up leading them are weaker, too.

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We're talking about the California state education system here. They do not have the option to restrict the provision of their services to a tiny elite. The concerns of "top schools" absorbs altogether too much oxygen.
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IMHO, California state higher education is setup to be tiered. UC > CSU > Community Colleges. If UC is getting a lot of STEM students that need remedial math, I think something has gone wrong. Those students might be better served by getting their math needs met at a community college and transfering to UC later.

For one, why pay UC prices for remedial math? For two, community college has a lot more sections of remedial math and more experience teaching it.

If you're in a degree that doesn't need much math, taking remedial math at UC is probably fine; but all the STEM degrees want at least the full calculus series (afaik).

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> Top schools are looking for outlier intellectual talent…

Eh, somewhat. They want some of those outliers hobnobbing with the legacies.

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> tons of professional athletes come from poverty

Is that actually the case?

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Depends on the sport. I don’t think the Olympic equestrian competitors would be dirt poor.
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Read up on Kobe Bryant or Bronny James.
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Sure, those are some good counterexamples: both sons of professional athletes. And there are plenty of others.

On the other hand, we have: Allen Iverson, Larry Bird, Shaquille O'Neal, Carmelo Anthony, Michael Vick, Bo Jackson, Jackie Robinson, Babe Ruth, Mickey Mantle, Fernando Valenzuela, Albert Pujols, Jim Thorpe, ...

Oh, and LeBron James himself!

So my view is that people of both rich and poor upbringings have a good chance in the sports world these days, at least for those sports where the necessary gear is relatively cheap.

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Times have changed. Due to the rise of expensive youth travel club sports leagues I suspect we will see fewer poor children turn professional. There will always be a few outliers but if you don't have access to top coaching and extra competitive playing time prior to college then you're really at a disadvantage.
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According to IA this is mostly a myth though.
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Whatever gates you put up, the wealthy can fire cannons of cash at them. You just have to pick the ones least vulnerable to cash barrages.

What is the marginal gain of expensive SAT prep? Versus just doing hundreds of mock tests out of some prep book, like SWEs grinding LeetCode?

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It feels like the problem are the SAT prep courses' existence then
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