Albert Pujols’ Contract in NPV

A month ago, Albert Pujols agreed to terms with the Los Angeles Angels of Anaheim. It was a deal that the media and public mostly ignored due to the intense coverage of the trade that sent Nick Schmidt to the Colorado Rockies as the player-to-be-named-later in San Diego’s Huston Street acquisition. Who could  forget what a monumental day that was? Apparently desperate to get back in the limelight, Pujols and the Angels have released final terms on the contract between the two. I now will cede to their wishes and relay that information.

Pujols will be guaranteed $12 million this year, followed by $16 million in 2013 and then $23 million in 2014. That’s followed up with $1 million raises each season, concluding with a $30 million payday in 2021. There’s a bunch of other stuff in there, and that’s probably what took so long to write out and agree upon. But these are the most important figures, totaling $240 million for sure over 10 years.

I wanted to look at how many wins above replacement (WAR) Pujols needs to produce to justify his price tag, but first you have to manipulate the numbers a bit because the market price involved — the amount of money teams spend to purchase one WAR — tends to increase over time. In 10 years time, we can collectively look back and retroactively judge whether Pujols ended up over or under producing based on how the market goes, but the Angels cannot do that. The Angels have to lock in the payments now and guess at the inflation in dollars per win over time.

The evlauations we come up with rely on assumptions that we have to make regarding the inflation rate (of $/WAR) and the current amount of market dollars per WAR. I think the common way is to hold the salaries as they are and inflate the $/WAR over time at some rate so that Pujols makes $12 million this season when teams are paying X per win then $16 million next season when teams pay (likely) X+something per win and so on. However, an equivalent method is to hold that inflation rate at 0% and instead devalue the salaries using the same basic formula (a net present value or standard discount rate equation). I prefer that because I think it gives a cleaner result. Instead of a summation of salaries divided by ever-increasing market rates for wins, I can apply the inflation to the salaries and bring them all into 2012 dollars and then divide by our current amount of market dollars per WAR.

Different people have different opinions on the current and future numbers for $/WAR, so I’ll present a sampling of values for that rate.

Interest Rate ($/WAR)	0%	2%	4%	6%	8%	10%
NPV return ($M)	240.0	217.3	197.6	180.6	165.7	152.7

And you can take the one you like (I prefer 5%, for about $189 million NPV) and divide it by your current estimate of dollars per win (I prefer $4.5 million which, when adding in a 10% discount to the team for long term security, means 47 required WAR). Unexpectedly to me, the back-loading of the deal doesn’t save much money. At 5%, Pujols’ actual contract is worth $188.8 million in today’s dollars and would be worth $194.6 million if it were paid out in equal $24 million-per-year installments. At double the inflation — 10% — the gap widens to almost $10 million and levels off soon after. Even at 20% inflation, there’s only a $14 million difference.

With the figures that I’ve used to check contracts this winter, Pujols needs between 45 WAR and 50 WAR to be worth his deal — not counting his incentives that would push the WAR number higher. That doesn’t seem like a lot for a guy with almost 90 WAR in his first 11 years, but it probably won’t be a picnic to race past.

If Pujols declines at 0.5 WAR per year, then he needs to start out at 7.0 WAR next season to reach the 45-50 WAR level after 10 years (finishing up at 2.5 WAR still, which might be generous for someone of that age). He could have a higher baseline, for sure, but any of a faster decline — say, a switch to DH in the future or the switch to the AL having a negative impact — could make 45-50 WAR a struggle.

Ultimately, I think the Angels overpaid for Pujols’ production. But if a team is going to do that I, as a fan, wouldn’t have much of problem overpaying for a player like this one though it clearly carries a lot of risk.