This is my preferred history of Brady and the Expos

First, the link in #1 is really funny,

Second, I really don't get why anybody who would be getting a full ride to play QB at Michigan (or Alabama, or Ohio State, etc.) would choose baseball unless they were a multi-million dollar first round draft pick.

Think about the difference in your life from ages 18-23.

You get a free college degree from one of the options.
You are the literal Big Man On Campus.
You have a pretty good chance of at least getting invited as a rookie free agent to attend an NFL training camp upon graduation.
If you can make an NFL roster as a backup, there is a good chance you'll stick around for five years in the NFL making at least several hundred grand a year, largely to hold a clipboard.

In the other option, you are riding busses for months at a time, in front of 500-2500 fans, typically in small towns, where if things go really well, you could be in AA in your 3rd year.
You probably got a signing bonus of less than $250K - and potentially a lot less than that - and then made zilcho for money while playing in Auburn, New York, riding a bus to Utica, New York.
You did not get free college, and if this doesn't work out (which it probably won't, by the numbers), you will then have to go to college as a 20-something year old freshman.
If you were a catcher, it isn't like you weren't getting beat up physically compared to most other sports besides football.

I think a lot of this comes down to three things:
1) How much the 18-year-old values the full ride scholarship;
2) What college you would be attending.
3) What position you play in college.

I still like to think that Drew Henson left MLB for the NFL because he saw the success of Tom Brady - a player he might have foolishly thought of as his football equal - and figured being an NFL MVP-level quarterback can't be that hard if Brady is that good.

I think people are underestimating a key factor for an 18 year in this position: women.

you will then have to go to college as a 20-something year old freshman.

It's been a while since I was in undergrad, but being a freshman who can buy alcohol and is also a former professional athlete would seem to be able to have his pick of sorority girls and be a not-terrible fallback option in case the whole baseball thing doesn't work out.

I think most athletes good enough to get drafted by baseball or given a football scholarship really care about getting a free college education.

I think the decision usually comes down to how much will a baseball team pay you to sign, how good you think your chances are in baseball and football, and will my college teams let me play both sports.

how much will a baseball team pay you to sign

The bonus/bagman that comes from playing college football at a top D1 school might be higher than the MLB draft bonus.

Not too long ago, Kyler Murray had a baseball/football decision. His play this year was uneven, but it appears he made the correct long-term choice.

Rickey Henderson was a dominant high school tailback. According to his SABR bio, he received "dozens" of D1 scholarship offers; however, his mom and stepdad convinced him to choose baseball because of the greater risk of catastrophic injury in football.

The bonus/bagman that comes from playing college football at a top D1 school might be higher than the MLB draft bonus.

I haven't been keeping up on the NIL market, but for the talented ones at a top school, that might well outweigh mediocre bonus + piddling MIL salary.

Think about the difference in your life from ages 18-23.

You get a free college degree from one of the options.
You are the literal Big Man On Campus.
You have a pretty good chance of at least getting invited as a rookie free agent to attend an NFL training camp upon graduation.
If you can make an NFL roster as a backup, there is a good chance you'll stick around for five years in the NFL making at least several hundred grand a year, largely to hold a clipboard.

It seems like you've got some mixed reasoning here. For example, to choose football, you need to have that 18-year-old sense of invincibility to choose football, with no guaranteed money and the physical damage you do to your body/mind. But that same outlook would mean you probably aren't worried about getting a college degree, you're confident you'll make the majors, and you're not thinking about being a backup in the NFL.

With the benefit of being slightly (ahem) older than 18, baseball looks like the far safer choice. Maybe $200K bonus guaranteed, perhaps the promise of your team paying for college (often the case, right?). That's a big head start financially for an 18-year-old.

On the other side, I don't see the "free" degree as very attractive since a) you're probably not graduating, and b) in most cases you're really a student in name only. The question here, of course, how much money you can make under the table, and I have no idea about that.

I haven't been keeping up on the NIL market, but for the talented ones at a top school, that might well outweigh mediocre bonus + piddling MIL salary.

And that's only the money that's changed hands above the table.

Investing an 18th round pick in a righthanded high school catcher is not exactly a vote of confidence.

At that level of the draft, you're hoping for one significant MLBer every round or two, which means a 2 or 3 percent chance for any given player.

As a Michigan recruit, Brady would be seen as a tough sign, so maybe put him down as a 5% chance who fell in the draft.

A starting QB coming out of a powerhouse school has a much better chance of catching on. Heck, even as a famous draft miss, Brady was taken in the sixth round, got guaranteed money, and started the year as a backup.