Introduction

MLB’s biggest free agent prize this offseason is, of course, Albert Pujols.  Pujols is a sure-fire hall-of-famer and arguably the best hitter of his generation.  Some have even argued that Pujols is the best hitter of any generation.

So what is the value of such an elite player, as he enters his age 32 season?

To answer this question, we must begin by assessing how Pujols’ production is likely to look as we go forward.  Everyone knows players decline with age, so it’s very likely that over the next decade, Pujols will not be the same, incredibly productive player he been over the last decade.  So how much decline can we expect, and how quickly will it happen?

Core Methodology and Baseline Results

To tackle this question, we will rely on an empirical analysis of the players Baseball-Reference lists as most similar to Pujols.  We will dig into the data to see how these similar star players have performed in their 30s.

Our list of comparable players includes 4 active players, and 15 retired players.  The following table shows the Wins Above Replacement (WAR) that these comparable players generated during their careers, beginning with their age 32 season.

As we can see, these players averaged around 4.5 wins in their age 32 and 33 seasons, dipped to 3.8 wins in their age 34 and 35 seasons, and then gradually declined into the range of fringe starter as they reached age 36 and beyond.  For what it’s worth, a player following this aging pattern exactly would provide 22.8 wins.  If we value each of these wins at $5M, our hypothetical aging star would yield $114.1M of total value over the 9-year window of his age 32-40 seasons.

While interesting on its surface, this data is not directly applicable to the question at hand regarding Mr. Pujols and his future.  Not yet, anyway.  The reason is fairly obvious – Pujols is a markedly better player overall than many of the guys on this list.  Fortunately, what we’re really interested in garnering from this sample is a more general view of the aging pattern players similar to Pujols have exhibited.  Thus, our next step is to normalize the data.  We will do this by dividing each of the datapoints in the above table by the player’s average WAR in the three seasons prior to turning 32.  Again, what we really seek to understand is how Pujols’ production going forward will compare with what it has been to date.  This normalization process helps get us there, by illustrating in real terms what has already happened to the sample of comparable players.

Now our typical aging curve is represented not as absolute WAR values, but as percentages of age 29-31 WAR values.  Naturally, we know what Pujols did from age 29-31 – he averaged 7.2 WAR over those three seasons.  So, we can multiply each annual average in the last row of the table above by 7.2 to convert back to a Pujols-specific WAR value.  Lastly, we apply our assumed value of $5M/win to give us this initial estimate of Pujols’ value over the coming 9 seasons.

What we see here is that our initial expectation is that in 2012, at age 32, Pujols will generate 74% as many wins as the 7.2 he provided, on average, between ages 29 and 31.  That gives us 5.4 wins, and a value of $26.9M.  Cumulatively over the 9-year period, Pujols pumps out 25.8 wins, worth $128.9M.

Our first impression of Pujols’ value moving forward is surely not a very favorable one, relative to the much larger contract demands we’ve heard rumors of.  So let’s next investigate how sensitive our findings are to changes in the sample we’re using.

Sensitivity Analysis

First, we’ll see how restricting the sample based on how long players ended up lasting in the bigleagues impacts our results.  This seems at least defensible on the grounds that Pujols takes great care of his body, and therefore might be expected to last a bit longer than his comp average.  The next two tables do just this.

Note that in the first pass, we drop all players that retired at or before age 36.  In the second pass, we drop all players that retired at or before age 38.  So, if we feel 100% certain that Pujols will play at least another 6 seasons, then we should boost his value up to $138.2M; if we think he’s a lock for 8 more seasons, then we can go all the way up to $174.5M.

Of note, taking it a step further, and restricting the sample to players that lasted to age 40, does not offer any further improvement:

As a second sensitivity check, we will restrict the sample based on how close to Pujols players performed in their age 29-31 seasons.  In doing so, we will discard the Carlos Delgados and Juan Gonzalez’s of the world, as well as Ken Griffey Jr. who, while certainly comparable to as Pujols in his prime, had already begun to decline before age 32.  Again, we will develop two subsamples from the data.

Now we really are focusing on the legitimate all-time greats.  Yet, the bottom-line values don’t change too dramatically from our last sensitivity exercise – the first filter helped more ($147.5 vs $138.2); the second filter helped less ($163.2 vs $174.5).

In his article on this subject, Tim argued for a comparable sample comprised just of Aaron, Robinson, Mays and Ramirez.  These are guys that combine the best of both worlds – all-time great talents, that managed to stay healthy and productive for a long time.  Here’s what we get using these four guys only.

Having a career arc that mirrors the composite of these four players would make Pujols worth just over $200M on our anticipated 9-year contract.

Alternative View

Let’s take a slightly different look at the problem.  For this, we will go back to our full sample (retired players only).  Reading the first row of the table below, what we see is that if Pujols’ career arc mirrors Larry Walker’s exactly (and applying the 7.2 average WAR Pujols generated from ages 29-31), Pujols will end up generating 41.4 WAR and $207.1M in value over the next 9 years.

The frequency distribution we see emerge here is particularly troublesome.  Applying these 15 career arcs to Pujols yields a 40% chance (6 in 15) of value less than $100M going forward; a 53% chance of value less than $150M; and an 80% chance of value less than $200M.  Only 3 of the 15 career arcs, or 20% of Pujols’ comparables, yield more than $200M in value over the coming 9 years.

Digging Deeper

So far we’ve shuffled our sample of Pujols’ comparable players into 6 distinct groups – the full sample; the two samples restricted based on career length; the two samples restricted based on age 29-31 production; and Tim’s sample.  The pattern we see fairly consistently across these groups is that Pujols remains an elite, highly productive player for the next 4 seasons, then a marked decline occurs at age 36, and in the final four years of the contract Pujols’ production is fairly pedestrian.  This result is evident in the following table, illustrating Pujols’ annual average value in these three phases of the contract for each of our 6 scenarios.

This pattern is also seen in the following graph.

Conclusion

There can be no question that Albert Pujols is an elite, once-in-a-generation player.  The best evidence we can gather indicates that he will likely remain highly productive for the next 4 or 5 seasons.  However except in a small number of cases, the decline his historical comparables have suffered in their mid-30s has been dramatic.  In light of this reality, a reasonable expectation is that Pujols will be worth between 1 and 3 wins per year for roughly half of a 9-year contract.

If I had to boil all of this analysis down to a single, expected value for Pujols’ production over the coming 9 years, I would use the average of the 5 sensitivity cases.  This number is $165.3M.

In order to justify a $200+M commitment to Pujols, a team would have to have two things going for it:

• A current roster that is just one impact player away from being a World Series frontrunner.  Anything short of that, and the risk is too great that one or more of Pujols’ remaining elite years are wasted on a non-playoff team.  Given the enormous downside risk on the back half of the contract, the team absolutely has to be poised to be a strong contender in each of the first 4 to 5 years they have Pujols.
• The financial strength to endure the back half of a contract, in which the team will be dramatically overpaying for the production Pujols will provide… if he is on the field at all.

The Cubs may meet the second criterion, but they clearly fall short of meeting the first criterion.  Neither the Cubs nor any other team (save, perhaps the Yankees or Red Sox) have the luxury of spending a year or two to build a World Series-caliber team around Pujols.  With the present state of their roster, this is indeed the outlook they are faced with.   Therefore, a $200+M commitment to Pujols is unwise.