Calculating Wins Above Replacement

Dave · February 6, 2008 at 2:50 pm · Filed Under Mariners 

If you’ve read the blog for a while, you’ve seen us refer to players as +/- so many wins. For instance, I’ll often call Adam Jones a “two win player” and Erik Bedard a “five win player” when talking about their 2008 value.

If you’ve ever wondered where those numbers come from, Tango has the post for you. In it, he breaks down the basics for calculating a player’s win values yourself. It’s actually easier than you might think, assuming math doesn’t make your head explode.

On a job application for running a major league franchise, this should be question #1. If you can’t grasp this concept, you don’t get to make decisions.


54 Responses to “Calculating Wins Above Replacement”

  1. Broadcast James on February 7th, 2008 10:37 am

    I’m having a really hard time grasping the argument for using average players as the baseline player over using the baseline player as the baseline…

    Bullet point one: How are you defining average? Mean? Median? Mode? I don’t see how any of those are of particular value. So what if all the batting averages equal out to .280, what does that have to do with the players that are actually available? I just think the entire concept of there being some non-mythical average players out there is flawed to begin with. (As a side note, if you’re using mode, replacement level might actually be the definition of an average ball player.)

    Bullet point two: Using the true baseline of talent makes intrinsic sense. In music theory it’s the bottom note of the triad that gives the chord it’s name, not some bizarre average. That’s just the way it works in nature, even tough it might seem counter intuitive at first.

    Bullet point three: If you’re going to be making business decisions you need your data to be practical. Replacement level players will always be a practical option, while, finding a “league average player (again, whatever that means)” might not be realistic.

    Maybe this just comes down to people looking at the world through different lenses, but again I just don’t get what the argument is here. Replacement level sets a realistic and authentic baseline… From a scientific perspective, that’s what you want.

    BTW: Can we figure out Wins Over “Dude of the Street” (WODotS) next? If we figure the average MLB team wins 81 games, and the dude off the street wins 1 due to a “Bad News Bears” type scenario, we can figure 80/25 is 3.2 wins per player… or 8 wins per starter (80/10)… So is Eric Bedard really only worth 13 wins over me?? 🙂 I kid… most ridiculous analysis ever.

  2. smb on February 7th, 2008 10:55 am

    I think the best advantage is that it is geared toward payroll efficiency. This type of analysis is exactly why the A’s are able to consistently win more games than us without spending nearly as much money. What more proof of the value of these statistical constructs could be needed? If you compare the apparent analytical methodologies of two teams like the A’s and M’s, it’s like a freestyle swim race in which one competitor (M’s) is wearing lead socks. Either work the system to your advantage or get worked by it, right?

  3. gwangung on February 7th, 2008 11:03 am


    Gooooood points I like that.

    And to repeat some things….there are more replacement level players out there. Easier to get a hold of…AND you’re less likely to be distracted by the noise of individual players and easier to get a true picture.

  4. tangotiger on February 7th, 2008 1:21 pm

    The hard part of replacement level is deciding what that level is.

    The easy part of average is that we know exactly what that level is: 4.8 runs per game in the recent past.

    As I said, you can stick with average and ignore replacement completely. Consider that the average payroll is 90MM of which around 12MM is required minimum payroll, leaving you with 78MM to play with for an average team (.500). Presuming you allocate around 57% of your payroll to nonpitchers, that gives them 45MM to allocate for 9 full-time nonpitchers.

    That means the average player will get 5MM per 162 games played. Presume for the moment that each win (free agent, arbitration, pre-arb, on average) is worth $2.2MM per win. (Plus of course every player gets his 400K minimum.)

    So, this is what you get for a guy who plays 162 games:
    $7.6MM +1 win above average (WAA)
    $5.4MM +0 WAA
    $3.2MM -1 WAA
    $1.0MM -2 WAA
    $0.4MM -2.27 WAA

    And if he plays 81 games:
    $5.1MM +1 win above average per 81 games (WAA)
    $2.9MM +0 WAA
    $0.7MM -1 WAA
    $0.4MM -1.135 WAA

    So, roughly speaking, a guy who is an average player for 162 games is equal to a guy who is +1 wins above average over 81 games. How do you equate those two with 1 number, rather than necessitating carrying two numbers (his WAA, and his games played)?

    Well, if you add .014 wins per game to each player, this is what you get:
    First player: 0 wins above average + .014 * 162 = 2.27 wins
    Second player: 1 wins above average + .014 * 81 = 2.13

    As you can see, both roughly equal. If you multiply the above numbers by $2.2MM per win, and then add $400K, you get:
    2.27 * 2.2 + 0.400 = $5.4MM
    2.13 * 2.2 + 0.400 = $5.1MM

    And those are the numbers we got when we ONLY talked about average and never brought up replacement level.

    So, both sides can go ahead and do what they want to do: use only average or use only replacement. You end up at the exact same spot.

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