Baseball Statistical Fallacy – Value Over Replacement Player

There’s frequently-cited baseball statistic, “value over replacement player”. It’s misleading and incorrect.

A player’s statistics can be approximately converted into wins and losses. A “replacement player” is someone earning the minimum salary. The idea is to compare the player’s performance to a “replacement player”. It’s frequently cited as cost per win.

Suppose a player’s “value over replacement player” is 5 wins. The team won 5 more games with that player, compared to what a minimum salary player would have produced. If the player is paid $10M, then the team paid $2M per win.

One fallacy is that this statistic can be unfair to superstar players. One year, Derek Jeter was the highest paid player and one of the statistically best players. However, according to “cost per win”, the Yankees weren’t getting a bargain. I already wrote about this.

The fallacy is that “replacement player” isn’t a minimum salary player. For a small-market team, the replacement is a minimum salary player. For the Yankees or another big-market team, the “replacement” would be one of the top free agents. If the Yankees didn’t have Derek Jeter, they wouldn’t have a minimum salary shortstop; they would get the top free agent. Derek Jeter’s value shouldn’t be compared to a replacement player. He should be compared to one of the top 15 players the Yankees would otherwise have.

For example, Alex Rodriguez is out for a few months with surgery. They Yankees didn’t pick up a minimum salary replacement. The Yankees signed Kevin Youkilis for $12M.

Also, the “value over replacement player” analysis indirectly converts statistics to wins and losses. Using modern sabermetrics, it’s possible to evaluate the win/loss effect of each play. Getting a homerun when the game is tied is worth a lot more than getting a homerun when the game isn’t close. Instead of indirectly converting statistics to wins and losses, this could be directly calculated. After each play, evaluate whether the team’s chance of winning increased or decreased. Then, you can figure out how many wins each player produced.

There are serious flaws with the “value over replacement player” analysis. Instead of converting statistics into wins and losses, a play-by-play analysis would be more accurate. On big market teams, the “replacement player” is not a minimum salary player, but rather one of the top free agents.

10 Responses to Baseball Statistical Fallacy – Value Over Replacement Player

  1. Hey again agorist!

    I’m wondering what do you think about companies who use proprietary APIs.

    Just kidding! I want to know what you think about companies who use such APIs and harass people who reverse/implement/include their support.

    There’s this company called NaturalPoint that does head pose tracking and harassed FreeTrack developers. But the cycle will once again repeat in the upcoming days.

    Here’s the full implementation:

    Here’s a dude who competently documents their ongoing abuse:

    Please, help us with it ’cause there’s so much indifference.

    PS Wonder how’s mixie. Haven’t seen her on my latest visit to onionnet. The server has been delinked as well.


    • Do you mean onionnet = Tor? I stopped using tor because it was ridiculously slow. Also, most of the Tor nodes are run by the NSA.

      I briefly used Tor because I wanted to get some documents on the Zyprexa lawsuit, which were forbidden for distribution in the USA. It was easier to get the documents from a BitTorrent tracker located outside the USA.

      I already wrote a post on a related subject. The short answer is “Don’t build a business that is based on someone else’s API, because they can cut you off at any time.”

      According to that post, he wrote an open source product that implements the same interface as the proprietary product. The company’s legal customer agreements forbid that. They are putting technical changes in their product to frustrate people who try to use the open source interface.

      Actually, this isn’t what would happen in a free market. In a free market, the people would develop their own hardware instead of relying on this corporation. They would make their own software interface, so that they couldn’t be sued.

      If there’s enough demand for it, they could make their own hardware. The GCW Zero made their own game hardware, with only a couple thousand people funding it through preorders and kickstarter.

      If enough people are angry at this corporation, they probably could raise money to develop a competing product. That’s more productive than raising money for a legal fight. If their business is incorporated with almost no assets, they might have nothing to lose even if their is a patent lawsuit, although they still could get sued directly as individuals. If sued as an individual, you should consider representing yourself instead of wasting money on a lawyer. The judge won’t like it, but it might earn you some sympathy with a jury.

  2. Hey again FSK. I didn’t sign any EULA/NDA. Never owned the device. There might be problems with ‘copyrighted strings’ and the lookup table falling under ‘anti-circumvention’ laws.

    We already have software that works without specialized hardware. Either a regular webcam capable of removing the infrared filter, or even a regular webcam.

    The issue is software support. They refuse to deal with people who implement other protocols. So without implementing it there’s little market penetration.


  3. Our software is mixed MIT/X11 and GPL3, forgot to add. There are some blobs running in separate address space. It’s distributed free of charge.

    And TOR got new handshake code that builds a circuit faster. :)


    • Due to the way copyright law has been interpreted, implementing someone else’s proprietary API could be considered infringement. If you’re successful enough, the large corporation will try to use its legal muscle against you.

      For software support, you’d have to target people who write flight simulator games and not the people who have the monopoly. If they explicitly refuse to deal with vendors who support competitors, that could be a violation of antitrust law, but you don’t have the millions of dollars to waste on legal fees. If you want to build a legal case, start a flight simulator software business, and try to implement both their protocol and the open source one.

  4. There’s already some support, people seem to have begun violating the NDA. There’s the DCS series on and ArmA II on

    But there are some titles that require memory modification in a running process, which give issues with regard to copy protection and ‘anti-cheating’ measures.

    Damn rigid body dynamics is hard :P Due to the “education” system being broken where I live, doubt ever will write a flight sim :(

    Wrote some image processing software that gives rotation and translation of a face, though. Even learned how to multiply a matrix by hand – ‘first horizontal, second vertical’. Never learned of its significance with regard to linear equations, though.

    • You could try the Kahn academy, if you want to learn linear algebra.

      If you’re solving a system of linear equations, it has a shorthand representation as a matrix operation.

  5. I feel like the argument here is that VORP has little application within the Yankees organization. I don’t know that one could extrapolate from this that the metric is inaccurate. Few of the everyday concerns of even other large market teams are relevant inside Ft. Steinbrenner. For most MLB teams who would replace even a top 15 player with a low to minimum cost player, VORP is legit or at least worth consideration. The Yankees don’t live in the baseball world with the rest of the league when it comes to acquiring players, setting ticket prices, or (coincidentally) calculating the value of a player in dollars. Or at least not in dollar figures that don’t rival the cost of the Iraq War.

    • This analysis applies to other big-market teams and not just the Yankees (Dodgers, Red Sox, any team with a $100M+ payroll). If a team has a $100M payroll and a starter gets injured or lost to free agency, the replacement isn’t going to be a minimum-salary player; it’s going to be an average or better player.

  6. Sorry, but whoever wrote this is an idiot and has no understanding of value over replacement.
    A replacement player is always a minimum salary player because even if you’re the Yankees you still could start that player. If what a replacement was depended on how much your team made the value of it wouldn’t be consistent at all and would thus be a worthless stat.

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