How Much is Albert Pujols Getting Overpaid?

By Chris Bruce

Big news hit the baseball world yesterday as the Los Angeles Angels announced a $254 million, 10-year contract for 31-year-old Albert Pujols, a strikingly large contract for such an old player, even if Pujols is still a perennial all star and MVP-candidate. It’s pretty clear that the contract is long and a lot of money for a player so late in his career, but just how much is he getting overpaid? Let’s take a look.

To get a sense of what the rest of Pujols’ career will look like we can examine how other top players’ performance typically drops off at the end of their career. Looking at other top first basemen from the past, we can map out a typical trajectory for a player in Pujols’ position, and then make a reasonable estimate of what will happen for him. We use Wins Above Replacement as a proxy for overall production (not a perfect proxy, but a good estimation of each player’s value to the team – FYI, we use Baseball Reference‘s version of WAR). On average, top first basemen start to decline precipitously after age 32. Using this trajectory, we can expect Pujols to contribute approximately 47 WAR over the rest of his 10-year contract. (Here we are generous in assuming that he won’t have any wrist, or other, issues and will be able to bounce back to a high level this year like his counterparts from the past instead of continuing his decline from the past few years. There is a bit of sample bias here in Pujols’ favor because we have used as comparables other Hall of Fame / MVP / All Star caliber players who played out their career and did not see it cut short by injury. We also assume he’s actually 31-years-old… unlike some people)

(Note: it’s strikingly difficult to find a large sample of first basemen who ended their career recently, performed at a near-MVP level and haven’t been suspected of steroid use. I used the group consisting of Jeff Bagwell, Frank Thomas, Mark Grace, John Olerud, Jim Thome, and Will Clark – not all perfect comparables to Pujols, but they still should provide a good sample of how performance degrades over time, including some players that transitioned to DH to extend their productivity)

So how much is 47 WAR worth? Many writers cite a value of $5 million for a marginal win on the free agent market today, implying that Pujols’ remaining years should be worth approximately $235 million to over $254 million depending on salary inflation – right around his contract with the Angels. However, looking at the 2011 salaries and performance of all non-pitchers in the league (excluding those who did not play), teams will pay, on average, $600,000 for a replacement level player (WAR = 0) and $3 million for each incremental win above replacement (including players on pre-arbitration salaries). Given these market values and annual salary increases of about 2.7%, the Angels should theoretically be able to find the performance that Pujols is bringing to the team over the next 10 years with $159 million – overpaying by a whopping $95 million. [Additional note: this does not include the fact that having Pujols would free up talent coming up through their farm system to be traded, so the net overpayment would be somewhat lower.]

This has also just looked at the baseball side of things. It’s also possible that the Angels expect to garner significantly more ticket sales or merchandise revenue from Pujols’ arrival besides just what he is adding on the field. To look at Pujols like the Angels’ front office, additional revenue would need to be considered, not just WAR. But a gap of up to $95 million is a large gap to fill, especially if you only expect another 3-4 quality years from him. (Additionally, the market rates we’ve used to calculate the market value of a WAR should already take into account teams “overpaying” to get additional off-the-field revenues).

Albert Pujols is an extraordinary player, and it’s certainly possible that he could extend his career and play at a high level longer than others have in the past, but if using history as a guide and being a little less rosy about how his career will progress, the Angels could end up being stuck with a $100 million mistake.

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12 Responses to How Much is Albert Pujols Getting Overpaid?

  1. erik says:

    I’ve always seen analysis of FA contracts use marginal win price taking only what’s paid for FAs, not the league as a whole. The cost of a marginal win on the FA market is about $5-6MM, no? 47 wins times $5MM is $235MM, so this deal isn’t really overpaying relative to the market value of a FA win.

    Here’s an argument for basing $/win only on FA contracts: http://www.fangraphs.com/blogs/index.php/win-values-explained-part-six/

  2. David Pinto says:

    You seem to be using a different method for determining the price of a win than is normally used. The value of a player is what a team is willing to pay on the free agent market, which is where the $5 million figure comes from. Given that other teams were willing to pay him close to the $235 million mark, that’s probably the right price.

  3. Chris Bruce says:

    David and Erik – you are correct that the $5M figure that’s usually cited is for a “marginal win on the free agent market”. I think the issue here is that the Angels won’t be restricted to finding wins on the free agent market, they can also trade and rely on younger players coming up through the system. In this case, since Pujols will likely fall off to a much more average level of performance after a few years, you would expect that he could be replaced by someone with a smaller contract not necessarily coming through the free agent market.

    You bring up good points though. In reality, the real answer is probably a combination of both – in the next few years Pujols is definitely a marquee free agent and will command a high price for the marginal wins that he adds, but in later years the price that he garnered on the free agent market won’t really be applicable. All that said, since multiple teams were willing to overpay with a lengthy contract to get his next few years of prime production, “the market” is obviously valuing those marginal wins at a higher price (either because they are actually worth more, or because the buyers are not behaving rationally).

    • erik says:

      “I think the issue here is that the Angels won’t be restricted to finding wins on the free agent market, they can also trade and rely on younger players coming up through the system.”

      Both of these strategies “cost” more than simply the salary. To acquire players via trade, you must trade away some assets, so the cost of the player is his salary plus what it takes to acquire him. Young, pre-FA players cost money to scout, sign, and develop. These costs are not factored into the salary numbers from which you derived your calculation of the price of a marginal win. You also have to assume the sunk cost of failed prospects if you’re going to assign the performance surplus to those who make the majors.

      There’s a reason why the cost of a marginal win on the FA market costs $5MM. You’re welcome to argue against it, but it’ll be an uphill battle that’ll take a lot more accounting that you’ve got room for in this article or the comments. Convince Tango and I’m in.

      • Chris Bruce says:

        It is true that scouting and developing adds cost to supporting a player in addition to his salary, but the issue with your logic is that the Angels aren’t going to reduce their scouting, coaching and other spending just because they’ve locked down one (read: one) free agent for 10 years. These items are largely sunk costs (and won’t go away – no one will ever create a team from year to year with just free agents), so when evaluating an incremental contract you must evaluate the incremental spending over these sunk costs, which is the salaries of the players. (And of course, for trades you do have to give up some assets and the value of the trade will depend on the terms, I definitely wouldn’t argue that GMs tend to get better deals via trades all the time)

        Certainly there is value in having a “proven” free agent now versus the expectation of finding production somewhere within your system in the future, but I would still argue that teams overvalue free agents in general.

        And in response to “Tango”, I fully agree. It’s all about the assumptions, and free agents on the whole are probably overvalued, not just Pujols.

  4. Nick says:

    Young players with team-friendly contracts drive the league-wide price per win down. The market for them is basically completely separate from the free agent market. Read Tango.

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  6. rynev says:

    As someone who is currently a grad student in statistics, I appreciate all of these attempts to quantify how much a player is worth to his team, but it seems like they ignore important information. The Angels signed a $3 billion 20-year TV contract shortly after signing Pujols. If his signing had even the smallest impact on that deal, it seems to me that he is more than “worth” the money paid regardless of what the average dollar per win is on the free agent market.

  7. Adam says:

    If there are any termination or buyout clauses in the contract, that will complicate the analysis but on margin make the deal more attractive for the angels and reduce the amount of overpayment.

    It would appear that even this analysis suggests the Angels are getting a “fair” deal for the first 4-5 years. It’s the 2H of the contract that is a risk.

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