Jumat, 04 November 2011

What Are They Worth? Part 1: Albert Pujols

I would like to look at the top-five free agents of the 2012 offseason and take a look at what they might a) be worth, and b) actually get; it is safe to assume that these will not be the same figures. The five free agents I will be looking at are, in order, Albert Pujols, Prince Fielder, Jose Reyes, CJ Wilson, and, because I'm a fun guy, Yu Darvish. Without further gilding the lily, and with no more ado, here we go:

Albert Pujols is a bad man. He is, without the tiniest inkling of a doubt, the player of the post-steroids era. He has a career OPS well north of 1.000, is the greatest fielding 1B of his generation, if not all-time, and had seven consecutive seasons with a WAR of at least 8.2. He is roughly halfway through his playing career and St. Louis recently unveiled a statue of the man. What I'm trying to say is, he's pretty good.

The first part of this will be analyzing solely what he should be worth in terms of sheer value, so the fact that he is a franchise player and a living legend will not come into play here, other than the obvious fact that he is those things for a reason.

How good is Albert Pujols right now? He had a pair of monster years in 2008 and 2009 (9.6 and 8.8 WAR, respectively) in what is conceivably his prime, before hitting what now appears to be a decline. In 2010 he posted a 7.1 WAR, and this year posted a 5.7 (after extrapolating a 5.4 WAR for a freak injury). Many years ago Bill James employed what he called his 'favourite toy', which weighed more recent seasons heavier, simply by putting them into a simple equation more times. So, to find what kind of value Pujols can be expected to produce, you would simply use the equation, (3(5.7)+2(7.1)+8.8)/6 = 6.7. Okay, so, for the purposes of this exercise, Pujols is a 6.7 WAR player, as he is, sitting at home playing with his kids as of this writing.

The biggest issue with Pujols is his age. There is some controversy and speculation that he may be playing under an assumed age, which I will address momentarily. The more pressing matter of his age is that he is going to turn 32 in January, which is an obvious age of decline, even for the greats -- Ruth, Williams and Gehrig all had one of their top-five seasons by WAR after age 31, but Gehrig's was his fifth-best, Ruth's was at age 32, and Ted Williams simply gave Father Time a backhand and sent him on his way, like he did with fastballs, Florida bonefish, and two wives. Pujols isn't these guys, but the point is, even legends of the game age, and even they were on the way down after passing age 30.

The Hardball Times have done some impressive work on the subject of aging, and while I don't love you all enough to cut and paste and cut and paste and paste their exact data on here, they drew up (in the link provided) several plots of player aging. I encourage you to read their article(s), but what we will be using is the data for players with at least 5000 PA (ie: good players) from 1980-2008 (ie: modern players). This gives us the following important data, which is represented in value, where 1.0 represents full, peak value, and the other numbers represent what percentage of that full value is, on average, achieved:

25: 0.92
26: 0.96
27: 0.99
28: 1.00
29: 1.00
30: 1.00
31: 0.99
32: 0.99
33: 0.98
34: 0.92
35: 0.90
36: 0.87
37: 0.83
38: 0.80
39: 0.74
40: 0.70

So, Albert is, as we decided earlier, a 6.7 WAR player. Because he is in clear decline, I do not feel that starting from his prime (something of a 9.2 WAR from 2003-2009) is prudent, but rather a 6.8 extrapolated from the above data and his current value. Using these two things, his expected aging curve for the next nine years looks something like this:

32: 6.7
33: 6.7
34: 6.3
35: 6.0
36: 5.9
37: 5.6
38: 5.4
39: 5.0
40: 4.7

This does not mean that Pujols is going to put up a Hall of Fame career over the next nine years; this is a projection of his value assuming he stays healthy, and assuming one other thing that I mentioned earlier: that he will really be turning 32 this winter.

Pujols, for various reasons, has been considered an age liar for much of his career. He's a big guy, he balded in his 20s, and, most importantly, he did things he shouldn't have been able to in his amateur career. This is not a smoking gun, but he is a Dominican, and there are concerns, and considering that he is likely to be an investment of several hundred million dollars, these are questions worth asking. But, let's continue on the path down which we were headed.

Injuries are the main concern when handing out a contract like this. Aging will obviously happen, but does anybody think that Alex Rodriguez would have gone from MVP to league-average in two years simply because of age? Probably not. However, based on a number of factors (Pujols' track record, his position, the fact that teams will have insurance against his contract), we will proceed here like he will be healthy for the duration.

Dave Cameron at FanGraphs actually just wrote an explanation of Linear Dollars Per Win, which explains the value of a win (about $5 million in 2012), and for years going forward. Applied to Pujols' expected production, this is how much value, in dollars, he can be expected to provide per year:

Year-Age-WAR($/Win) = Total Dollar Value(Value in 2012 dollars)
2012-32-6.7(5.00) = 33.5
2013-33-6.7(5.25) = 35.2 (33.5)
2014-34-6.3(5.51) = 34.7 (31.5)
2015-35-6.0(5.79) = 34.7 (30.0)
2016-36-5.9(6.08) = 35.9 (29.5)
2017-37-5.6(6.38) = 35.7 (28.0)
2018-38-5.4(6.69) = 36.1 (27.0)
2019-39-5.0(7.04) = 35.2 (25.0)
2020-40-4.7(7.39) = 34.7 (23.5)

As you can see, Pujols, in terms of actual value, will be generating roughly $35 MM of value per year. As time goes by, as in all things, that $35 MM will become less and less valuable -- Yogi Berra famously said "A nickle ain't worth a dime anymore." -- but you can see by the 2012 value approximations, that he will still be generating a ton of value by anybody's standards (keep in mind that, every year, about twice as much value is generated as is paid out, so everything is relative -- what a guy is worth is not what he is going to get paid).

So, after all of that, how much is Albert Pujols worth? You can see there how much his hypothetical contributions will be worth, but he is going to get paid in 2012 dollars, so those are the figures we will use. Length of contract is the issue here. The longer the contract goes, the better value is being provided by this version of Pujols. Of course, the longer it goes, the odds increase exponentially that Pujols will hit a sharp decline or have a severe injury; the aging curve I provided is an average -- every player is different, and no player is exempt.

Optimally, Pujols would take a seven-year deal. It is after seven years that his expected production begins decreasing more sharply. Over this time (2012-2018), by what we have discussed, he will generate some $213 MM of value, with an average annual value (AAV) of $30.4 MM. That, ladies and gentleman who have stuck with me thus far, is what Albert Pujols is worth.

But how much will he get paid? This is kind of where the analysis stops and the speculation begins. Some comparisons are Alex Rodriguez' 2007 deal ($275 MM/10 years), Joe Mauer's new contract ($184 MM/8 years), and Mark Teixeira's 2008 signing ($180 MM/8 years). In those three cases you have two free agents, one considered his generation's top talent, one franchise face, and a couple in similar age territory as Pujols.

I think Pujols' contract will resemble a mix of Teixeira's and Rodriguez'. Teixeira was like a poor man's Pujols, an offensive threat with a golden glove. While Teixeira was three years Pujols' junior when he went to free agency, Pujols is this generation's best player, which is where the A-Rod comp comes into play:

I am predicting eight years at an AAV of $27.5 MM, or $220 MM. He may go as low as 25, probably specifically with St. Louis, and there you have it. Ideally, 7 years, $213 MM, in reality, 8 years, $200-220 MM. Pujols ends up with one more year of security than he would get in a perfect (owner's) world, but makes a few million dollars less per year.

Expected length of contact: Eight years
Expected value from those years: $228 million
Expected actual salary: $220 million

In any case, the time for speculation is fast drawing to a close. Clean up, look sharp; it's the Hot Stove season, kids.

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