Would MLB salaries drop if all players were free agents?

If every player became a free agent, would player salaries drop? Here's an argument that suggests that, yes, they *must* drop. I'm not sure if it's right, but I can't find a flaw ... maybe you guys can.

Assumptions: all teams are rational, and all teams know the expected value of the future performance of every player.

Here goes.

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Suppose that right now, at equilibrium, a marginal win in the major leagues is worth about $X million.

That means that the last win every team buys (in free agency) must give them $X million in extra revenues. If it gave less, they wouldn't have signed the guy. If it resulted in more than a $X million increase, the team could probably increase profits by signing even more free agents.

OK, now the hypothetical: what if EVERY player were a free agent? That is, what if there were no "arbs" or "slaves", so that every player cost the same price per WAR?

I don't know the exact breakdown of free agents vs. arbs vs. slaves. But, for the sake of argument, let's suppose that, right now, free agents contribute 1/2 the overall WAR, arbs contribute 1/4, and slaves contribute the other 1/4.

Also, let's assume that arbs make half of what free agents do, and that slaves make $0. Then, the average WAR costs major league teams exactly $0.625X -- that is, 5/8 of what a free agent WAR costs.

The fraction 5/8 works out to 62.5%. That's not too far from the fraction of revenues that go to player salaries. So, if every player were a free agent at $4.5 million per WAR, the 62.5% would go to 100%, and it would turn out that ALL of MLB's revenues would go to payroll.

That can't happen, can it? If payroll is higher than revenue for the league, it must be the case that payroll is higher than revenue for at least one team. For that team, it would be better to cut payroll. The only way it wouldn't be better to cut payroll would be if that team would lose even MORE money with EVERY possible payroll cut.

But ... minimum payroll is only about $13 million. It's hard to imagine that even a small-market team wouldn't get $13 million in revenue, even with a replacement level team expected to go 60-102. (And, in any case, the team could fold, and avoid losing money that way.)

So, no team would ever spend more on payroll than it got in revenues. Therefore, payroll can't be more than 100% of revenues. Therefore, at least one of the assumptions in our model must be false. The most likely candidate is the assumption that wins would still cost $4.5 million.

So it must be the case that the cost per free-agent WAR would drop, from $4.5 million to something lower, to allow the league to still turn a profit.

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Does that argument work? I think it does. But I have another one if that one doesn't.