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First the basics. It is the Rule 4 Draft (Rules 1-3 stipulate that you don't talk about fight club. Actually they deal with player eligibility and other issues) and it does have a limit. In years past the Rule 4 draft went on until teams got sick of picking and gave up (that's not an exagerration, the 1990 draft went 101 "rounds" with several "Rounds" consisting of just the Houston Astros saying "We'll take this guy.". In the mid-90's a rule change limited the draft to no more than 50 rounds, but teams could still quit drafting whenever they wanted to). Currently rules stipulate that the draft is 40 rounds.
Eligibility:
Any player who has finished his high school eligibility is eligible for the MLB draft. Junior College players are mostly eligible (this part of the rule is like the tax code with lots of caveats, but it's easy enough just to say most. This is how Bryce Harper kind of skirted the High School Eligibility rule.). For players at regular Colleges they need to be Juniors, or 21 years of age or older. A player can be drafted after High School, consult with an agent (can't officially hire one, but you can be represented by Scott Boras), negotiate a contract, fall short and simply go to College if they don't like the offer. Same is true for College Juniors (weirdly though as Bo Jackson found out a few decades ago, contact with a footbal agent or NFL team and you lose baseball eligibility. Weird ass arcane NCAA rules and whatnot) who can return for Senior seasons if the money isn't what they want (Mark Appel did this last year and as such cannot be drafted by the Pirates, who were unable to sign him last year). College Seniors can do what many recall JD Drew doing 15 years ago and play Independent baseball for a year and reenter the draft, so you have some extra leverage in signing a College Senior, but if Mark Appel gets a lowball offer, he can refuse to sign and go again.
Draft slot/money
There is a slotting system for draft picks, which makes things quite easy, for the most part, for pro teams. We're slotted at about $2,000,000 with the 16th pick, so whoever we select we can simply offer a number and go no higher than that amount. Kinda. Every pick in the first 10 rounds has a slot value. This adds up to a total for that part of the draft. You can spend up to that total. You can spend over that total, but with penalties. Go less than 5% over that threshhold and you pay a luxury tax equal to 75% of the amount exceeding the pool. Go 10% over and you pay a 100% luxury tax and lose your next First Round pick. Go 15% over? 100% tax and lose your next two first round picks. I assume at 20% Selig sells your team to Jeff Loria as punishment.
Here's a way you can kind of game the system though (h/t to Joecatz for suggesting this example, kind of). The Astros have the #1 overall pick, which has a slot value of ~$7mm. They could draft Colin Moran #1 overall. Moran will likely be a perfectly fine, roughly league average player getting something around 2.0-3.0 WAR per year. He should be picked somewhere between 5 and 10 and probably is well aware of that. Next year's draft looks much stronger and he'd be a likely 10-20 pick in that draft, were he to return to UNC. All this means you can probably sign Moran for $3-4mm, saving ~$3mm to use on later picks. So let's say, with the First Pick in the Second Round the Astros find falling into their lap a big signability risk. For example, we'll say Rob Kaminsky dropped because of his UNC commitment. The Astros can offer Kaminsky $3mm they saved on Colin Moran, and just like that the Astros got the equivalent of 2 First Round picks. Now, back in the days prior to the 2012 CBA teams could offer a 38th round selection $750K to forego a college commitment, but that's much, much harder now, as you'd have to overdraft a bunch of guys early and take those gambles late, but fail at that and your left with an underwhelming draft full of marginal talents.
Here's where it gets really funky though. There's a breaking point in the 10th round. Let's say the Bonus Pool (slotting system) is set at $10mm based on your pick, but you fail to sign 2 players in the Top 10, worth $500K total. Your pool goes down that $500K. Now let's say you draft Jared Cosart now in the 38th round, the most you can offer him is $100K. Anything offered to a pick after the 10th round in excess of $100K is counted against the pool for Top 10 rounds. In other words, if the Astros do what I said above with Moran and Kaminsky and still manage to come in $500k under the cap for the first 10 rounds with no unsigned picks reducing their money, they could draft a Jared Cosart in the 38th and offer him $600K to sign. Half a million of that total would go against their Top 10 round money, bringing them to the max.
When do players need to be signed by?
It depends. For High Schoolers with College Commitments and College players with eligibility remaining the deadline in July 15, 2013 at 5:00 PM EDT. For College players with no remaining eligibilty, they can be negotiated with until 7 days prior to the next year's Rule 4 Draft. If a team fails to sign a Top 10 pick, they get an equivalent pick in the next year's draft (hence the reason the Pirates have the #9 overall pick this year, as compensation for not signing Appel last Summer). If a team is unable to sign a First or Second round pick, they get a compensatory pick in the next Rule 4 Draft. Next year's draft should be stellar compared to this one, so a team in the no man's land of the middle of the first round may be wise to gamble on a signing risk in the First or Second round. If you get him, you got talent above your draft slot. If you don't, you may get a much better crop to choose from in 2014 and have 2 First or Second round picks to do it with.
Trades
MLB has a lot of stupid rules (the whole All Star Game deciding Home Field in the World Series crap. The whole point of the All Star Game is that it is meaningless. That's kind of the point.). The rules surrounding trading of Draft picks is and isn't stupid. To be more accurate, it's arcane. The rule is there to prevent wealthy teams like, well, us, from taking the First overall pick from the Astros for John Mayberry. The concern was basically that draft picks help build clubs, but some clubs wanted to trade high picks to avoid paying enormous bonuses to kids who may never get beyond Low-A. With the new Bonus Pool rules, this is mostly now diminished in impact. Besides if the Astros want to trade the top pick to the Pirates for picks 9 and 14, why shouldn't they be allowed to? It's sound strategy and a club with a barren wasteland of a Minor League System would be greatly benefitted by trading down and acquiring more picks (the Astros system is not close to barren, but you get the point). At present the only tradeable picks are the competitve balance picks between the First and Second and Second and Third Rounds. A few of these picks have been traded the last few years. They need to be traded during the season (no Winter Meeting deals or Spring Training swaps) and cannot be traded for cash.
In another arcane bit of weirdness a team cannot trade a player until one year after he was drafted. This rule always seemed weird to me. Let's say the Rangers contact Amaro and says "We love Mitch Gueller and we'll send you Jurickson Profar, Mike Olt and Yu Darvish for him." Anyone who is not insane would make that trade in a heartbeat, but you can't due to a weird rule. We don't limit crazy trades in other situations, why here? If there are concerns about a young player changing instruction so early, then allow such trades through the end of the signing period or something.
I'm sure there are additional questions and I'm sure I left out some interesting or weird nugget, so if you catch anything leave a comment. The 2013 Rule 4 MLB Draft occurs Thursday, 6 June 2013 starting at 7 PM you can watch rounds 1 and 2 on MLB Network. Rounds 3-10 will occur Friday 7 June 2013 starting at 1 PM and rounds 11 -40 take place Saturday 8 June from 1 PM until... The picks happen really fast and furious on Saturday, less so on Thursday and Friday. I would expect the Phillies to pick sometime around 7:30 - 8 PM and again around 10:30 - 11:00 PM on Thursday. We'll have coverage of all the picks and analysis, poems, tribute songs, etc. Throughout the Draft.