Thursday, October 06, 2011

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.


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.


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

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At Thursday, October 06, 2011 8:21:00 PM, Blogger JD Mathewson said...

While I'm not certain that actual salaries would go down, I agree that you've identified a mechanism that would put downward pressure on player salaries. The question becomes what are the other price-setting mechanisms, what effect do they have, and how do they interact with each other?

Here's another thought. The free agent market in the MLB more resembles an auction rather than a standard market, in that in any given bidding cycle the relationship between the number of bidders to the availability of products is relatively high.

This is even more true when it comes to the occasional foreign superstar or the Japanese posting system.

As such, the price-setting mechanism resembles that of an auction rather than a supermarket. It's well-established that in an auction system, prices tend to be set by not the most rational buyers but the most optimistic buyers. IOW, the purchase price of any free agent contract is likely higher than the consensus on said contract's return.

Now let's take away the draft and limit all contracts to one year. All of a sudden the ratio of products to purchasers in any bidding cycle looks less like that of an auction and more like that of a supermarket. Technically, the player becomes less a specific good and more a commodity.

In such a system, while there will always be some overpaying, teams will have more alternatives at similar prices, some of which will be better values than others.

The resulting price point for contracts should then shift from where it is now towards the point at which return and price are equal.

At Thursday, October 06, 2011 8:57:00 PM, Blogger zjelveh said...

Isn't this just supply and demand? Making everyone free-agent eligible increases the supply of talent available each year. If revenues stay the same and teams don't ever decide to go in the red, then price per unit talent goes down. Which is the same thing as saying price of the marginal win declines.

At Tuesday, October 11, 2011 3:49:00 PM, Blogger Johnmeister said...

At least the Yankees have disagreed with your analysis a few times.


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