A Basic Cost Projection For a Dozen 2015 Free Agents

Yesterday, I created a model of agent pricing using projected 2014 WAR as the only variable. As I noted in the post, I would classify this model as more of a toy than a rigorous attempt at analyzing the market, as we know there are plenty of factors beyond next season’s performance that influence the size of a free agent contract. Ignoring age and health are obvious flaws, as both are significant factors in contract size, especially when forecasting how many years a player might sign for. And we know that the market pays a different price for offense than it does for defense, reflecting some of the uncertainty that the defensive evaluations have relative to our ability to measure offensive production.

So, before I say any more about this model, let’s remember that this was essentially designed as something like the Marcel projections for salaries. Tom Tango built the Marcel projections as something of a baseline forecast, using very simplistic adjustments and ignoring things like park factors in order to show the bare minimum that a projection system should be able to accomplish. Likewise, I’d say that any serious attempt at evaluating the free agent market should be able to do better than what this basic model can do. This system is as simple as it gets — without being completely wrong, anyway — and we can almost certainly do better, but doing better comes with added complexity, and it’s still nice to have a simple, easily explained baseline to measure other forecasts against.

That said, let’s see what this basic pricing model — naming suggestions welcome, by the way — spits out for a dozen of the more notable 2015 free agents. For now, let’s ignore the future and pretend that these 12 players were free agents this past off-season, and see what the model would have forecast for them as 2014 free agents. As a reminder, we’re using a hybrid ZIPS/Steamer WAR forecasts, and the model multiplies projected WAR by five to estimate annual average value and projected WAR by 2.0 (for 3+ WAR players), 1.5 (for +2.0 to +2.9 WAR players), or 1.1 (for 1.0-1.9 WAR players) to estimate the number of years a player will sign for.

Because I selected 12 of the more notable pending free agents, we’re only looking at players with either a 2.0 or 1.5 multiple, as they’re all projected as above average performers for 2014. On to the forecasts:


Player 2014 WAR ProjYears ProjAmount ProjAAV
Max Scherzer 4.8 10 240 24
James Shields 4.1 8 164 21
Jon Lester 3.9 8 156 20
Pablo Sandoval 3.8 8 152 19
Hanley Ramirez 3.7 7 130 19
Chase Headley 3.5 7 123 18
Justin Masterson 3.2 6 96 16
JJ Hardy 3.1 6 93 16
Jake Peavy 3.0 6 90 15
Colby Rasmus 2.7 4 54 14
Asdrubal Cabrera 2.1 3 32 11
Jed Lowrie 2.1 3 32 11

I think we can see right away that the model probably has problems with over-projecting years for free agent pitchers. We know that MLB teams are comfortable going to 10 years for position players, so that length got built into the model, but because we’re not separating out pitchers and hitters, the model is overestimating a team’s willingness to pay Scherzer the same as the Mariners paid Robinson Cano, because it sees them as equally valuable free agents. I don’t see any scenario under which Scherzer would land a 10 year contract as a free agent, and my initial reaction to all of these numbers is that they’re just way too high. No one would really give Pablo Sandoval $152 million coming off a +2.3 WAR season, right?

Probably not, no. But it’s worth keeping in mind that Sandoval’s career averages put him at +3.7 WAR per 600 PA, and he’s entering his age-27 season. If a team thought they could keep Kung Fu Panda in shape and healthy, betting on him wouldn’t be all that different than betting on Jacoby Ellsbury, whose price is heavily influencing this projection for Sandoval. We live in a world where Hunter Pence got $90 million for his mid-30s, so maybe pricing Sandoval’s peak years — with the expectation that he’ll be healthy, as these forecasts do — at $150 million isn’t entirely insane.

And, to be honest, I’d probably take the over on the Hanley Ramirez forecast. Like Sandoval and Ellsbury, the questions about him revolve around health more than performance, and I think Hanley would appeal to a wider base of teams than Shin-Soo Choo did. And I think both Asdrubal Cabrera and Jed Lowrie could have done better than the 3/$32M that the model is suggesting, especially given how badly it missed on Jhonny Peralta. So it’s not like the model is just overstating the value of all 12 players.

It just seems systematically high on the numbers of years for high-end pitchers, because it doesn’t know that teams don’t really go beyond seven year deals for hurlers. That’s why it projected nine years for Tanaka too. It’s a flaw that stems from the simplicity of the model, but it’s also a pretty easy one to fix. For instance, if we just cap the pitcher multiplier at 1.7 instead of 2.0, Scherzer goes from 10/240 to 8/$192M, a believable figure given his pedigree and the recent contracts signed by guys like Zack Greinke and Masahiro Tanaka. Instead of 8/$164M and 8/$156M for Shields and Lester respectively, they come in at 7/$144M and 7/$137M, putting them in the same range as Cole Hamels, which seems about right. And Justin Masterson goes from 6/$96M down to 5/$80M, which seems a little bit more reasonable given the deals signed by the Garza/Jimenez/Nolasco trio this winter.

Whether you want the model to make positional differentiations is a question of trading simplicity for accuracy. The more you break down specific players into different buckets, the less the model can work as a catch-all baseline that is easy to explain in English, but of course, I already flagged catchers as being an exception to the rule, so maybe it’s better to flag pitchers too. I’m not married to the uniform multiplier model, and since this is mostly a toy, I’m happy to hear feedback on which model would be preferable.

But at the same time, let’s also keep in mind that these players weren’t free agents this winter, and we don’t want to use their 2014 WAR estimates to calculate expected 2015 prices. For one thing, players generally get worse as they get older, and these players were selected as the “most notable upcoming free agents” because they generally have a track record of success, so we’d expect some regression to the mean just because of how I picked the dozen players for the list. Odds are pretty good that these 12 players will be forecast for a lower 2015 WAR than they are for 2014, and that’s the projection that the model would use to actually determine what they’d get as free agents. So, let’s age everyone by one year and assume that their 2015 forecast will be 90% of their 2014 WAR forecast, and re-run the calculations based on that number instead.

Player 2015 WAR ProjYears ProjAmount ProjAAV
Max Scherzer 4.3 9 194 22
James Shields 3.7 7 129 18
Jon Lester 3.5 7 123 18
Pablo Sandoval 3.4 7 120 17
Hanley Ramirez 3.3 7 117 17
Chase Headley 3.2 6 95 16
Justin Masterson 2.9 4 58 14
JJ Hardy 2.8 4 56 14
Jake Peavy 2.7 4 54 14
Colby Rasmus 2.4 4 49 12
Asdrubal Cabrera 1.9 2 19 9
Jed Lowrie 1.9 2 19 9

Now, these numbers look more reasonable, right? Free agents are almost always going to look a little rosier before they actually get to free agency, since age often chips away at their skills and health, and applying some expected decline to this group gives us a set of projections that look pretty solid at first glance. Scherzer gets the same forecast as Tanaka did this year, with Shields, Lester, Sandoval, and Ramirez landing in the same range as Choo’s deal. And remember, this is with the 2.0 multiplier for pitchers, which is pretty clearly wrong. What if we re-ran the numbers with the the 1.7 multiplier for 3+ WAR pitchers? Then the table would look like this.

Player 2015 WAR ProjYears ProjAmount ProjAAV
Max Scherzer 4.3 7 151 22
James Shields 3.7 6 111 18
Jon Lester 3.5 6 105 18
Pablo Sandoval 3.4 7 120 17
Hanley Ramirez 3.3 7 117 17
Chase Headley 3.2 6 95 16
Justin Masterson 2.9 4 58 14
JJ Hardy 2.8 4 56 14
Jake Peavy 2.7 4 54 14
Colby Rasmus 2.4 4 49 12
Asdrubal Cabrera 1.9 2 19 9
Jed Lowrie 1.9 2 19 9

These “feel” like the best estimates yet — with the exception of the Scherzer forecast, which seems entirely too low — for whatever my gut feelings are worth. In general, though, tweaking a model to make the output match your initial expectation does more harm than good; what’s the point of modeling something if you’re just going to force it to conform to what you already believe? We could keep manipulating the numbers all day until we got a set of projections that we all agreed seemed reasonable, but then the model wouldn’t add anything beyond basic crowdsourcing.

Because this is a toy in progress, I’m certainly open to suggestions on tweaks or improvements that retain the simplicity that was the original goal. Since we already have the more complex models of free agent pricing that include aging curves and the like, I think the value in this tool is that it can be calculated using a minimalistic number of variables and done without the aid of a calculator or spreadsheet. If there’s a way to make the model better while retaining that strength, then I’m all for it.

But that last table does feel pretty close to a decent forecast, and gun to my head, I’d probably be okay using those as a barometer of what kinds of deals the impending free agents should set as baseline expectations if they decide to test the market. Scherzer, Cabrera, and Lowrie could easily land bigger deals, while maybe Sandoval’s health and weight problems mean he’d have to settle for less, but I think the numbers listed in that final table are fairly okay estimates of what these players should be looking for in an extension if they want to bypass free agency and sign in the next couple of weeks. Maybe they’ll raise their stock in 2014, and maybe inflation — another important variable we didn’t include — will render these forecasts obsolete, but if any of these 12 sign extensions in the next few weeks, I won’t be shocked if the numbers look pretty similar to the ones listed in that last table.




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Dave is a co-founder of USSMariner.com and contributes to the Wall Street Journal.


48 Responses to “A Basic Cost Projection For a Dozen 2015 Free Agents”

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  1. gator32301 says:

    Shouldn’t the $ multiplier be bumped a bit? IIRC, going rate this past offseason was in the range of $7/WAR

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  2. Nifty says:

    Just when I was about to forgive you for saying Peter Bourjous was a “far more valuable asset than David Wright (http://www.fangraphs.com/blogs/the-angels-would-be-nuts-to-trade-peter-bourjos/), you go and project Pablo Sandoval will make more money per year than Hanley Ramirez.

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    • LaLoosh says:

      yeah, this projection looks way off.

      Scherzer: 7/168M 24 aav
      Shields: 5/100M 20 aav
      Lester: 6/111M 18.5aav
      Hanley: 6/126M 21 aav
      Sandoval: 5/90M 18 aav
      Masterson: 4/68M 17 aav
      Hardy: 4/68M 17 aav
      Lowrie: 4/56M 14 aav
      the other four: 3/36M

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    • Simon says:

      Quality analysis that you provided there – obviously your random perceptions are more valuable than any sort of statistical stuff at all. Anyway, he said that he thinks the model suggests more than the market will bear for Sandoval, and that it’s probably light for Hanley.

      Also, do you really spend your time collecting all the things Dave says so you can make posts like this?

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    • Dave Cameron says:

      It really shouldn’t be that hard to understand why five years of Peter Bourjos was more valuable than one year of David Wright.

      And no, I’m not “projecting” anything. Your issue is with the fact that ZIPS and Steamer like Sandoval more than Hanley Ramirez. I’ll take their forecasts over your gut feeling, personally.

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      • M Scarne says:

        Also this:

        BOOM! Roasted.

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      • LaLoosh says:

        that’s not acknowledging that lots of potential inconsistencies exist with “Zips” or “Steamer” or other projections. Can’t be that much a slave to the computer generated projections, imo.

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        • Dave Cameron says:

          Yes, much better to be a slave to gut feel and human guessing, which we all know is infallible.

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        • not-Cistulli says:

          Dave called this a “toy”.

          The intended use for this is for questions like “Is Ervin Santana worth closer to $10M, $25M, $50M, or $100M of guaranteed money in the free agent market?” It was never intended to fine-tune ranking between players in the same or even adjacent “tiers” like Ramirez and Sandoval.

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        • M Scarne says:

          Damn, son. We’re about to open a whole chain of Kenny Rogers’ Roasters here.

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        • Bip says:

          It’s true you don’t want to be a slave to projections. There are things that they just don’t know, especially when it comes to playing time. However, it’s relatively easy to spot the bias in a projection system and adjust for it. It’s quite a bit harder to know your own biases. Better to be as objective as possible as much as possible and make tweaks where it is obviously necessary.

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    • Baltar says:

      I’d certainly take the under on Sandoval, but Dave can’t just adjust every number he doesn’t like. What, then, would be the point of the model?
      I think Dave should just keep the last iteration of this model and not tinker anymore. It’s good enough for a rough guess most of the time and that’s all it’s designed for.

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  3. vivalajeter says:

    I think the last chart looks the most reasonable, although I also think that fans, in general, look towards the lower end of projected salaries.

    I’d be a little surprised if Sandoval got 7 years from anyone. It seems pretty risky to give 7 years to someone who’s usually fat. Obviously, a formula can’t know that though.

    The two SS look a little low, but who knows what to make of the SS market? A few months ago Drew looked like the top free agent SS, and Peralta looked like a good potential bargain. Oops.

    Just about everybody else looks pretty accurate to me though. Hanley’s AAV seems light, but at 31 he might not get the full 7 years.

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    • olethros says:

      The Drew/Peralta disconnect is probably primarily the result of two factors: the QO hamstringing Drew, and the Cardinals being way more willing to spend FA dollars than to trade top-tier pitching for a shortstop.

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  4. Jays fan says:

    I’d imagine the Jays would happily lock up Rasmus at between $12 and $14 million per year for 4 years.

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    • Muck Bartinez says:

      I agree, considering he’s the best OF FA available. If there were some other big OF names (Choo, Ellsbury, etc.) hitting the market at the same time, then I could see him getting the projected amount, but obviously the model doesn’t take that into account.

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    • jdbolick says:

      It obviously depends on what type of year he has. Normally you’d say that a batter who hits as many fly-balls and swings at as many pitches out of the zone as Rasmus has absolutely no chance of repeating that .356 BABIP and yet it’s basically what he did in 2010. The odds are still pretty heavily against him, though. The projections are hedging between that high and the ’11-’12 low, but I’ll still take the under.

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  5. jerry60555 says:

    Will Masterson seek for a 100M deal??
    And,will teams give him that much money??

    It is a six year deal………

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  6. TK says:

    I think you should name this model after Catfish Hunter, the first MLB free agent. Calling it Catfish would also have allusions to online dating and fraud, and after all when you buy a free agent you never get exactly what you expect.

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  7. Jack says:

    Based on some of the really high year and $ numbers coming out, I suggest you call it Basic Objective Remuneration Anticipation System, or BORAS

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  8. Jeb says:

    Any chance you’d be willing to plug in Gardner for the hell of it?

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    • King Buzzo says:

      Welcome to math class. Prof Cameron laid out the blueprint to run these numbers yourself and I hear its easy

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  9. Fabian says:

    I just had to point out that this system thinks that Mike Trout should get something like an 18yr contract at $45 mil per year for a total of $810 million if he were a free agent. This goes to show that he is out yo break all the models!

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    • nd says:

      That’s because most baseball analysis assumes linearity, so errors for outliers can be quite absurd.

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    • jruby says:

      As someone said on the first article’s comment thread, if you take into account the fact that you’re getting some cost-controlled years, and cap it at, say, 15, it gives you something like 15/510, which isn’t all that ridiculous for Trout. At least, we’ve thrown around numbers like that on FG like they’re a bit higher than we’d think someone would pay in real life but not necessarily higher than he’s worth…

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  10. Boris Chinchilla says:

    I love me some Jake Peavy, but a 4 year deal?

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  11. tz says:

    Dave, if you wanted to use this toy to ballpark what past FA markets paid, what do you think would be a good proxy for “projected” WAR? (being simple to keep with the spirit of this exercise)

    Maybe using a 5/4/3 weighted average of the previous seasons’ WAR totals (like Tango did), with say a 25-50% mean reversion back to 2.0 WAR per 600 PA?

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    • Baltar says:

      Too complicated. Dave wants to keep it simple.

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      • Eric R says:

        That said, using the average 2014 Steamer/ZiPS is “not too complicated” because someone else did the math on those projections already.

        If you didn’t have the numbers calculated for you, I imagine that ZiPS and Steamer are each far more complicated than a regressed weighted average…

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  12. The Ancient Mariner says:

    To go with Marcel, maybe you should call it Marceau.

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  13. jpg says:

    I’m going with the name Liberty in honor of Dave’s shoe stealing pup.

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  14. pft says:

    So Jake Peavy coming off a 3 WAR season at age 33 is projected to make 6/90 or 4/54 while Erwin Santanna coming off the same at age 30 settles for 1/14?

    I actually agree with the model but reality suggests something else is up.

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    • Catoblepas says:

      i think what reality is suggesting is that ervin santana had -1 WAR in 2012, where jake peavy had 4.4. the model doesn’t consider that, but it makes me think peavy’s line might not be all that wrong.

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  15. Chris says:

    Since the first post was inspired by Ervin Santana, how about ERV, for Expected Remuneration Value?

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  16. Jason Powers says:

    Cameron, name suggestions:
    Player Asset Value Equation: (PAVE)

    Player Asset Performance Pricing Algorithmic Sort 1.0: (PAPPAS 1.0) in honor of Doug Pappas. As you refine, you can upgrade to a 2.0!

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  17. jesse says:

    You say the sherzer deal looks low, but that seemss a bit of recency bias beacause forecasts are looking back further than last year’s 6 war season, before last year those numbers would not look so low.

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  18. Bip says:

    It seems the main complaint everyone has is related to the fact that the commenters, and Dave himself, are weighing recent performance (particularly last season’s performance) more heavily than the model is. People seem to think Rasmus and Scherzer would get more than projected, while Sandoval would get less. I believe this is because Scherzer and Rasmus had unusually good years last year, relative to their recent career track records, while Sandoval had the opposite. I’m inclined to agree with everyone’s assessment as well.

    However, the model is just using projected WAR as an input, so really it’s that the projections systems don’t weigh last season’s WAR as heavily as we do. The projections think Sandoval will likely be more like his old self than his sad, 2013 self. On the other hand, they are not reading too much into Hanley’s incredible 2013, and they certainly haven’t forgotten 2012-2011. It’s interesting that people don’t generally complain more about the fact that projection systems don’t put too much weight on last-season’s performance. Why is it that we’re generally ok with the projections, but find a contract estimator based on those projections to be too dismissive of a player’s most recent stats?

    Maybe that is because that is how contracts actually work? I don’t know if it is a weakness of the market or what, but I’d be willing to bet the market actually does weigh more recent performance a bit too heavily. That’s where the concept of “but low” comes from. If an otherwise good player has a down year, people will overreact and his value will plummet, even though an objective projection would tell you that he’ll probably be more or less back to normal the next season. Teams who understand this often can get good bargains on players like this.

    If my hypothesis is correct, then that means that Dave shouldn’t have used projected WAR alone for this model. Maybe just an average of projected WAR and last season’s WAR, to increase the influence last year’s WAR has on the calculation? That would keep the calculation quite simple, and may yield more accurate results.

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