Monday, December 12, 2011

What’s the Best Player in Baseball Worth?

In a twist reminiscent of last year’s Cliff Lee negotiations, what appeared to be a two-team race for the services of Albert Pujols between the Cardinals and Marlins was upset by the entrance of a third “Mystery Team.” Though many believed the Mystery Team was simply a tactic Pujols’ agent, Dan Lozano, was using to squeeze every possible dollar out of Pujols’ suitors, buzz around the mystery team rumor continued to grow. In the course of roughly 12 hours on Wednesday night and Thursday morning of the Winter Meetings, headlines such as “Pujols Deciding Between Cardinals, Marlins” and statements such as “Angels are definitely not in on Pujols” gave way to news that Pujols’ pact with the Angels was confirmed. Pujols will receive $254M over the next ten years, with his contract expiring in his age 41 season.

Signing a once-in-a-generation player to a Free Agent deal is always a difficult proposition because, almost by definition, there are very few players who can be invoked as comparables to the 31 year old Pujols and used to determine his long-term value. In analyzing Pujols’ contract, I will look at the aging curves of players approaching Pujols’ caliber to estimate a reasonable expectation for Pujols’ future production and determine whether he is likely to produce enough value to be worth the value of his massive contract.

I used Baseball-Reference’s Play Index (a nifty tool, if you haven’t played around with it) to find all expansion-era (post-1961) players who produced >50 WAR in their first 11 seasons while playing an offense-heavy position (1B, 3B, LF, RF). In his first 11 seasons, Pujols has put up an incredible 89.1 WAR, but looking at players in this group who eclipsed that mammoth total would leave you with… well, Pujols. Though he’s an outlier among outliers, the rest of this group is populated with Hall of Famers and all-time greats, and I believe the aging curve established by these players will provide some insight into how Pujols may age. Overall, this group included 20 players, but I removed Pujols and Ichiro Suzuki, as both have just completed their 11th season in the Majors. I then looked at the average production among the players for each subsequent year after their 11th. Comparing this average production to the players’ three-year weighted (standard 5-4-3 weighting) average from their 9th to 11th seasons, we can determine how quickly a player’s contributions diminish as they age. Then, using Pujols’ 3-year averages as a starting point, we can depreciate his value based on these ratios and estimate his production in each year of his contract. Multiplying these values by $/WAR, with a 5%/year inflation rate added, gives us Pujols’ total expected value over the length of the contract. Got all that? Let’s dive in.

The 18 players included in the data set are: Barry Bonds, Mike Schmidt, Wade Boggs, Ricky Henderson, Jeff Bagwell, Carl Yastrzemski, Frank Thomas, Reggie Jackson, Ron Santo, Dick Allen, George Brett, Bobby Bonds, Todd Helton, Eddie Murray, Sal Bando, Pete Rose, Scott Rolen, and Chipper Jones. Most of these players, unsurprisingly, were not able to finish their 21st seasons in the Majors, so players are not included in the average for any year after their retirement. This may understate the likelihood that Pujols retires before the end of his contract, but I don’t see this as a major risk, especially considering Pujols’ incredible durability. Pujols has played 1705 games in his first 11 seasons, the best total for any player included in this data. Several active players also have not completed their 21st seasons, which was treated similarly to players who retired. Regardless, it’s difficult to project much production as Pujols nears and passes age 40, so these data aren’t as important as trying to estimate production for the first few years of Pujols’ contract.

Overall, the players averaged almost exactly 5 WAR in their 9th through 11th MLB seasons. After this point, their production dropped off by an average of 15% per year until the end of their careers. In total, taking the average production from each year produces an expected 27 WAR for players’ 12th to 21st seasons, or 5.44 times the players’ three-year average baseline.

Click to see data from comparables

Pujols’ three-year weighted average is 6.9 WAR, so we’ll use that as our starting point. The projected first six years of Pujols’ contract, through the 2017 campaign, seem to be something like what the Angels have in mind in signing Pujols, as this model suggests he will be in the 4-6 WAR range each season. After 2017, however, Pujols’ expected value drops precipitously, as the model projects less than 10 WAR total over the final four seasons of Pujols’ deal. After multiplying these WAR values by the $/WAR inflation rates, Pujols’ total expected value over the course of the deal comes out to $222M, $32M short of the total value of his contract. Although this is a fairly rough calculation, it offers a clear indication that Pujols could have trouble living up to the total dollar value of his massive deal.

Click to see the model's predictions for Pujols' production

So, if that’s the case, what’s the reasoning behind the Angels’ huge bid? Well, first of all, there are a ton of ways to calculate Pujols’ expected future value, and each one results in a slightly different evaluation. Additionally, since more recent data are weighted more heavily to improve the accuracy of our projections, Pujols' "down" (5.1 WAR) year has a large effect on Pujols' initial value and every subsequent value. If Pujols can prove 2011 was a fluke and return to producing 7+ WAR per year, as he did in nine of his first ten Big League seasons, his projected value will see a big jump throughout the life of the contract. However, even if Pujols doesn’t produce a full $254M worth of value over the course of his stay in Los Angeles, there are still reasons to believe this contract could be a win for the Angels.

Pujols’ value off the field, especially to the Angels, is huge. Since purchasing the Angels in 2003, owner Arte Moreno has positioned the team as a representative of the city’s massive Latino population, to fantastic results in attendance and revenue. If there’s any player that can be leveraged to market to that population, it’s Pujols. The team just signed a 20-year, $3 Billion TV contract with FOX Sports. While the deal was signed before the Winter Meetings, it certainly provides the funds needed to make big Free Agency splashes, as the Angels did with Pujols and CJ Wilson. It’s also not outside of the realm of possibility that the Angels and FOX had an understanding that, once their deal was agreed upon, some of the Angels’ new revenue would be infused into their future Major League payroll to increase TV viewership and fan interest. Additionally, Pujols will contribute as a veteran presence and respected leader, assisting with the development of the team’s young players both during his contract and afterward, as his contract includes the stipulation that he will serve as a consultant to Moreno for a decade after his retirement.

Although Pujols is unlikely to produce at a high enough level to justify his contract based on his on-field value alone, he provides so much added value in his other attributes that it’s easy to see why the Angels felt comfortable offering this huge deal despite his advanced age. Pujols is a franchise-changing talent, and the Angels hope that his total value to the franchise will far exceed the dollars he’ll be paid over the next decade.

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