If you read my article on How Much Should Each Baseball Team Spend? I reference a lot of ideas about how profitable winning is.  For the sake of repetition, I won’t go over them again now, but the general conclusion is that winning creates significant revenues in extra ticket sales, extra merchandise sales, decreases in job difficulty (selling transaction costs), increases in ticket prices, increased fan loyalty, intangibles, etc.  But how exactly do these teams decide how much they should spend on a pending free agent?  Well, you can actually think about this in a logical way.  As with anything, it’s most easily done with simplified examples, so bear with me as we create a central point.

Economics 101: Spend To Where Your Returns Meet Your Investment (Accounting For Risk)

You’ll often learn in your entry-level economics class that the price is set where supply meets demand in a perfectly competitive environment.  You’ll also learn that, in their examples, it is assumed that individuals will compete up to the point where their marginal benefit meets their marginal costs.  If you are unfamiliar with these ideas, here’s a quick example:

Say you’re in a town and you are the seller of bananas and the only one.  Assume that there is a fixed cost of selling these bananas in order to do so (say, a selling permit that you bought one time that you cannot resell).  Assume then that there is also a variable cost of every banana you sell – the cost of the banana itself as well as the cost of your time, etc.  This is dependent purely on how much you sell.  On the other hand, there is a marginal benefit that you gain from selling each banana – say in the money you receive in the transaction.  Simple economics says that you will continue to sell bananas as long as your marginal benefit is larger than your marginal cost.  That is, if you say, sell your bananas for $4 and it costs you $3 per banana in marginal cost, you’d sell.

You would continue to sell if you could only sell your bananas for say, $3.01 because there would still be a marginal benefit associated with your marginal cost.  Theoretically, marginal costs should take into consideration the idea of your next best alternatives (say, you could be making a larger profit selling apples) as well (as a note).  Hardcore economics will even tell you that sellers will sell when marginal benefit equals marginal cost (if you were only selling them for $3, you’d still sell.  I think this is mostly for simplicity’s sake, but the point is really unimportant.)

An important note here is the fixed sunk cost: it is ignored.  That is because this falls into the category of “sunk cost”, something that cannot be recuperated no matter what and should not be considered.  Now of course, in the real world, there are very few examples of legal things that can not be sold on the open market, but as far as things go, a baseball stadium is up there.  We can imagine that it would be very difficult to sell the stadium itself and take the money and invest in something else – there are extremely high exit barriers to such a task and the stadium is rarely owned by a single entity.  Thus, when we are thinking in economic terms here, we will assume that the stadium itself is a sunk cost that should not be considered.

Besides that, the ultimate conclusion I want you to come to here is that, just like bananas, teams should theoretically spend to the point where their marginal cost meets their marginal benefit according to economic theory.

What are those Marginal Costs and Marginal Benefits in Baseball?

It would be ridiculous to try to list all the different potential costs for an MLB team.  There are the lights that they turn on for every night game, there’s the baseballs they have to buy, there’s the radio announcers they have to pay, and there is the racing sausages that come out in the 7th inning.  There’s just too many.  But we could all agree that, on a relative basis, there are many costs that are about equal across all major league teams: they all need staff, they all need concessions, they all need a website, etc.  We can even come to the conclusion that in many ways these are, at the basis, close to competitive parity.  Now, as a person that wants to work in the front office in the future in perhaps ticket sales or marketing (though we all know the dream job), I do not dare diminish the roles that these individuals play.  A good pricing strategy has very serious benefits that should not be ignored.  Perhaps I will write a post on this idea in the future as well.

But if we assume that all those costs are relatively minor and average out amongst most teams to a relatively identical number (sure, one team may have more scouts, one team may have more money spent on advertising) we can come to the realization that the majority of the money is spent on the product on the field.  This is where we come to the idea of Major League payrolls.  These are the things that largely differ between teams.

So Those Payrolls…

We are going to use one very simplified theory here: that the amount spent is a large component in the competitiveness/quality of a team.  We both know this is not  an absolute (see the Tampa Bay Rays) but I think we can all agree that at the very least it’s relatively highly correlated (see the Yankees postseason appearances from 1995-2012).  But if say we actually were able to believe that every General Manager was rational in their decisions (and money spending) and also knew it was only .60 correlation between money spent and odds of competitiveness, my conclusions would still be the same.  This is just a simplified approach.

As I mentioned, I intend to use simplified examples here.  Let’s assume there are only two teams in MLB and they have exactly identical teams in every single metric and make-up.  For all argument’s sake, they are a mirror of one another.  If the season was to be played out, they would constantly end in a virtual tie.

Now let’s say that there is exactly one free agent on the market that each team can bid on.  Let’s say that, using whatever metrics you want, this player that plays right field is superior to the team’s current right fielder.  How much should they spend on this free agent?

Well the answer is extremely simple if you truly think about it: each team will spend to where their marginal benefit equals their marginal cost.  If we are to believe my previous post that winning gives you significant revenues, then the teams should spend significant costs trying to outbid each other.  If this player causes the team that buys him to win all the games and reach the postseason and reap all those benefits, he is worth the equivalence of that revenue stream.  Realize this reality: this is why the best player is not necessarily the one who is paid the most.

We could see this easily: say the two teams have the best player at each position except for right field.  That is, they both have the Mike Trouts, Robinson Cano’s, and Mariano Rivera’s of the world and they are identical (whatever your personal preferences are) and they are all already signed at the same prices.  However, in right field, they have me, Steve, a guy who had ten hits in his Freshman year of high school baseball as an above average defensive first baseman (real valuable huh?).  Now let’s assume that Reed Johnson is out on the market, 4th outfielder journeyman who holds a special place in the heart of some (he made a miraculous catch against my Brewers in one game I attended robbing a game winning home run).  Similar to what I was previously mentioning, Reed Johnson is the only player on the free agent market (for whatever reason) and there are no other options available.

Thus, how much do you think either team should pay Reed Johnson to play over me?  Yes, they should pay him the amount that is equal to the amount of revenue he would create by their team winning all the games.  As such, Reed Johnson may actually become the highest paid player on the team because of the marginal benefit he provides.

This is why I often scratch my head when people try to do data outputs for “valuing” a player relative to his contract.  Sure, player X may be overpaid in comparison to the output he provides relative to player Y, but that was not the circumstances in which he was given the contract.  He was given the contract because the team decided that the marginal revenue he created was greater than the marginal cost.  This isn’t to say I don’t see value in these metrics of course, I just think we overestimate their inherent limitations on free-market realities.

Now you may be saying this is an oversimplification and of course I understand that, but that wasn’t the point of this.  The point of this was to show you that free agents can and probably will receive money that isn’t entirely dependent on their actual production relative to others because they should be tied to the marginal revenue they create.

Of course, these two features do intertwine somewhat.  Often the players with the best statistics are the players that receive the highest paychecks as the chances of them increasing the likelihood of victory for any team is larger than any other player (and thus they have a strong chance of increasing marginal revenue).  But very often the amount of money they receive is relative to the situations that surround them – Zack Greinke may have easily received two very different contract offers from this year to next year (assuming the player himself somehow stayed the same including in age) just based on what needs were at the time that dictated possibility of competing and thus the marginal revenue potentials created.

So in the end how much should each free agent get paid?  As much as the marginal revenue they are going to create.  An important thing to note is that there is more than one way to skin a cat; if a team can create the same marginal revenue at a lower marginal cost with a different player or combination of players, this essentially creates a higher profit.  Because of differences in how players are perceived in terms of “skill”, as well as different approaches general managers are using to “get to the ends”, this is why all the attention isn’t focused on one single player at a time.

Hopefully you followed some of my logic here.  I must point out that there isn’t any perfect valuing system just yet and we all know that spending money doesn’t necessarily translate into victories (it just often increases the likelihood given some rationality).  If you have any comments, feel free to leave them below.

Baseball Rethought.

-Steve