What’s the Price of a Replacement Player?

In a thread on the Raul Mondesi signing at Baseball Primer the other day several posters commented that Mondesi projected to be a “replacement-level” player. Using Keith Woolner’s definition this means, that he projects to produce the output equal to “the expected level of performance the average team can obtain if it needs to replace a starting player at minimal cost.” In the minds of most, the viable replacements are in the minors. Maybe they’re not playing because they’re blocked on the big club and the GM wants him to gets some at-bats, I don’t know. These guys are cheap and provide the base-level of talent for MLB. From this benchmark we can value the contribution of individual players based on the contribution above a replacement player. The rule-of-thumb offensive measure of replacement level is 70 points of OPS below the league average at that defensive position. The statistic known as VORP measures the Value Over Replacement Level that any player provides.

But back to Raul Mondesi. For now, I’ll grant that this is an accurate prediction; let’s assume he possesses “replacement-level” talent. However, the next logical step in the argument in this thread goes a little too far, although it makes sense. Mondesi basically signed a \$1 million 1-year deal. The minimum salary for a baseball player is \$300K, which is the salary a team would be paying to player on the margin between the majors and minors. Therefore, the Braves are paying Mondesi about \$700K too much.

But wait, who makes \$300K? Largely, it’s players who are reserved by teams. For the first three years of Major League service, players make what teams tell them they make. This doesn’t mean team’s actually value these players equal to their salaries. In fact, in his classic study estimating the marginal revenue product (MRP) of baseball players (the amount a player’s performance contributes to team revenues) Gerald Scully estimates that monopsony extraction by teams was about 7/8ths of a player’s value that he contributes to the team. 7/8ths! This means that the value to the team of a reserved player is, on average, 8-times larger than the salary of the player. So, the actual price of a replacement player is actually \$2.4 million? Well, not exactly. Scully’s paper was published in 1974 when the economic structure of the game was much different. All players were reserved by teams, and I’m not sure what the minimum salary was. I suspect that if not for the league-minimum salary requirement that the reserved players would be making less than \$300K.

Regardless of exact magnitude of the exploitation, certainly we can say the that teams receive more in value from reserved players than the wage they pay out to these players. To acquire a replacement-level player from another team will require compensating the team with reserve rights for the value lost. Therefore, it is incorrect to say that the purchase price of a replacement-level player is equal to the league minimum. Raul Mondesi is not reserved, and therefore does not suffer from the monopsonistic exploitation of a particular team. He is going to receive more compensation for his services than a reserved player. The question is, with the exploitation removed, how much should he be paid for the services (MRP) he will provide? While I don’t have an answer, I have some ideas of where to start looking but have not thought it through. I would like to ask readers to lend me your suggestions in the comments section on a way to estimate the actual price of a replacement-level player.

Addendum: In addition to the comments below, there is now a thread on Baseball Primer with some very good stuff.

2 Responses “What’s the Price of a Replacement Player?”

1. Anonymous says:

Very interesting idea…I was hoping to study something like this myself in the future. At the moment I have no suggestions as I would have to research more into the topic. If I were studying this at the moment (I’m currently working on DIPS) I would probably us the best run producing stat (OPS, etc.)as my main measure of player contribution (I’m pretty sure you have thought of this, though). Good luck in your work and I can’t wait to see the results and analyze your procedure for any help to my future market value study(ies).

2. Anonymous says:

Well, let’s update the study (though I never read the original). For each Win Share last year, Free Agents received \$451K, arbitration-eligible players received \$344K and non-arbitration players received \$110K, for an average of \$329K per WS across all players.

For 234 WS, non-arbitration players received \$25.8M. At a market rate of \$329K, they would have received \$77K. That’s a ratio of 26/77, or 30%. So owners are keeping 70% of a “reserved” player’s value (if my numbers are correct).

I guess you could compare reserved players to free agents, but that seems to me to be flawed, because free agents would be paid less if everyone was a free agent.

I must say that I consider Win Shares to be a better stat than OPS or whatever you want to use for this kind of study. As a stat, it is directly related to wins, and it allows you to compare different types of players. And it includes all skills, including fielding.

If you’re not comfortable with Win Shares, I would understand that. But, in the end, it seems to me that win-based systems are the best for this kind of analysis, because wins=value. But, of course, you knew I’d say that. ðŸ™‚

This is a great line of thinking, JC. It’s very much worth kicking around.