When is a win worth more?

In Commentary And Analysis, theory by myles13 Comments

I was thinking about Michael Bourn this morning, because I need psychiatric help. It kind of struck me that the Cubs could use Bourn more than most other teams… but taking a common approach to free agency, we shouldn’t be offering him more money than any other team (Bourn’s worth is more or less a constant), especially because we are so far away from contending. That’s obviously not true, but it is the assumption we essentially rely on when trying to compute a free agent’s worth. For instance:


Age-29 : 6.0 WAR

Age-30: 3.5 WAR (projected)

Age-31: 3.2 WAR (projected)

Age-32: 2.8 WAR (projected)

Age-33: 2.2 WAR (projected)

Age-34: 1.4 WAR (projected)

This is a back-of-the-napkin estimate, where I took Age-30 to be 3.5 and depreciated by 10/10/20/40 percent. If a free agent is “worth” 4.5 million in free agency, then this table becomes

3.5 * 4.5 = 15.75 million

3.2 * 4.5 * 1.05 (inflation) = 15.12 million

2.8 * 4.5 * 1.05^2 = 13.89 million

2.2 * 4.5 * 1.05^3 = 11.46 million

1.4 * 4.5 * 1.05^4 = 7.66 million

So, a 3-year pact would look like 44.76, a 4-year deal worth 50.60 (10% decrease for 4th-year premium- otherwise 56.22), and a 5-year deal worth 63.88/57.49)

Let’s simplify that to 3/45, 4/56, and 5/64, as those seem reasonable.

This is the inherent problem with “fair market value”, though: is Bourn worth that much to the Angels, who already have a loaded outfield? Of course not. We aren’t trying to buy wins above replacement, we are trying to buy wins above replacing our guy.

Last year, the Cubs trotted out a .230/.303/.337 line at CF. Using this WAR calculator, we can see that the Cubs got 0.4 WAR from their CF last year. Bourn would provide 3.5 WAR, but only 3.1 Wins Above Alternative. The Angels, on the other hand, put up a .292/.365/.470 line, for a WAR of 7.3; Bourn is worth -3.8 WAA for the Angels (which, of course, is one reason they aren’t bidding for him). Of course, the Angels could move Bourn to RF or LF, but that diminishes with WAR, so his WAA will certainly improve but not by much.

If we think of players as providing Wins Above Alternative instead of Wins Above Replacement, we can get a much clearer picture of who teams are targeting and why they should be targeting them. You could even sort of predict who should offer a player more (I haven’t done the research, but it’d be very impressive if a team had a greater need for Bourn than the Cubs do).

The value of a WAA is certainly higher than 4.5 million (the average FA is not replacing a 0 WAR player, but obviously they are paid the same in my formula), but we actually don’t need that precise value to compute who should offer the most (all else similar- obviously, team payrolls and where they are in the contention cycle matters also). It is simply the team with the greatest potential WAA.

Of course, FA is way, way more complicated then just coming up with this number; I just thought it would be interesting to note. This will be much, much more useful when the Cubs are only a player or two away from being really competitive.

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  1. dmick89

    Nicely done. I’m coming up with slightly different numbers than you, but that’s just how projections work (not all the same).

    CAIRO projects 2.5 offensive WAR and +7 fielding. That would be 3.2 WAR (680 plate appearances). Add in the 5 baserunning runs the fans project (Fangraphs) and you’ve got 3.7 WAR in 2013.

    Personally, I’d go something like this over the next 4+ years:

    2013: 3.7
    2014: 3.2
    2015: 2.7
    2016: 2.2
    2017: 1.7
    Total: 13.5 WAR

    The win vale was about $5 to $5.5 million last year. Using a win value of $5.5 million in 2013 and increasing by half a million per year, you get an average win value over 5 years of $6.5 million. So that’s about $87.75 million in value over those years. Add in the 10% bonus teams get for multi-year contracts and I’m coming up with a value over 5 years of $79 million.

    If we use a 5% rate of inflation, we’d get an average win value of $6.1 million, total value of $83 million and a contract value of $74 million.

    I think he’s more valuable than you, but also less valuable to the Cubs as a result of that. By the time the Cubs are contending he’s likely to be an averageish player or so. Not to mention you have a guy who relies heavily on speed and we’ve seen what a leg injury can do to the values of players like that (Soriano, Crawford).

    I’d hate to offer something in the $70 million range for a talent like Bourn. While I think he’s more valuable than you and I think he’ll get more than you do, I probably wouldn’t spend any more than you’re suggesting.

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  2. Urk

    As probably the least statistically-driven fan here, my opinion doesn’t mean diddley. but, that said, this seems to make a lot of sense and it seems to get at soemthing that’s intuitively there about a particular player’s value to a particular team. cool.

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  3. Urk

    So, I have a totally off-topic question. Maybe it should be a forum post, but I couldn’t figure out how to do that. (edit: I jsut saw the button below, but this post is already written and I’m lazy).

    We’re getting ready to cut the cable and go internet only, but, living it Iowa City it looks like MLBTV will be totally useless for watching Cubs games because of blackouts. Assuming I want to watch some bad baseball, and the Cubs are the bad team I want to watch, do I have any options?

    thanks dudes.

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  4. dmick89

    @ Urk:
    I’ve never had blackout issues where I’m living or in Iowa when I lived there. In iowa I got Fox Sports and WGN and then later CSN and still had WGN. Here in Kansas I’ve always gotten MLB Extra Innings, which has the same blackout restrictions that MLB.TV does. I don’t watch the Royals much, but am blacked out from many of their games.

    Unfortunately, I don’t think there’s a whole lot you can do. I’ve read that the entire state of Iowa is blacked out for Cubs games on MLB.TV. I don’t know if that’s true or not, but if it is, you’re probably shit out of luck.

    There are some streaming services online, which are often hard to find. I know Pinetar and Mercurial Outfielder have linked to such places in the past. As far as I know, that would be your only alternative.

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  5. Author

    You could also use a proxy to appear to be from a different part of the country, but I don’t know how to do that and how legal it may or may not be.

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  6. WaLi

    @ Urk:
    We cut cable but our cable company has a package that has like local broadcast tv + turbo internet for almost the same price as just internet (maybe $5 more). I think we get WGN and we live in NC. That way you could get the WGN games.

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  7. EnricoPallazzo

    SVB wrote:

    This is progress. Real progress. Not just Hope Monsterism.


    @ Urk:
    i believe that at one point mlb.tv would just black you out of games depending on the address that you gave them. so you could just give an address for some state whose games you don’t give a shit about and then you would just get blacked out of those games. not sure if this is still true though. (it might be, though, because it doesn’t seem that mlb.tv has any particular incentive to make sure that blackout restrictions are properly enforced?)

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  8. Myles

    EnricoPallazzo wrote:

    has mcnutt been pretty much written off as a bust?

    He’s got a chance to be an impact late-inning reliever, but his days as a real prospect are essentially over.

    On the other hand, he’s still entering his age-23 season. I think there’s a really low chance he regains his 2010 form, but it’s definitely not 0%

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