April 18, 2008

Lies, Damned Lies

Adding Birthdays

by Nate Silver

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My first thought after I learned that Miguel Tejada was two years older than his listed birth date was that I wasn't really all that surprised by the news. My second thought was that he just threw away his shot at the Hall of Fame. One of these two thoughts is valid; the other is a little out of place. Let's take care of the obvious part first. Below is a comparison of Miguel Tejada's original PECOTA forecast with a new one that we've generated by aging him exactly two years and leaving everything else alone:

If you own Miguel Tejada in a fantasy league this year, you can breathe easy-PECOTA had already registered a fairly pessimistic forecast for Tejada, and it only got just the slightest bit more pessimistic as a result of aging him by two seasons. We actually have him drawing a few more walks; it's not uncommon for players to draw more walks as they age, as they tend to work the count harder once their bat speed declines. However, those walks come at the expense of a handful of extra-base hits. Overall, we have him losing just a couple of points of VORP, and about $1.0 million in MORP-not anything that should cause Ed Wade to break into night sweats.

Were you expecting to see something more dramatic? Keep in mind that there is a little bit of luck involved in PECOTA, since we're running the player's forecast based on the performance of actual comparables, rather than some theoretical aging curve. Fundamentally, I would argue that we shouldn't be that surprised. The reason gets into sort of Bayesian math. We just aged Tejada by two years, but we also aged his previous performances by two years, so it's not like we're comparing a 32-year-old who was a good major leaguer at age 31 to a 34-year-old who was a good major leaguer at age 31. We're comparing a 32-year-old who was a good major leaguer at age 31 to a 34-year-old who was a good major leaguer at age 33-and it's more difficult to be a good major leaguer at age 33 than at age 31. So, while the circumstances are now less favorable to Tejada, in a sense he has also accomplished a little bit more. It also happens to be the case that age-32 seasons tend to be a particularly accursed point in the careers of certain major leaguers; that's when Dale Murphy's career imploded. The fact that we now know that Tejada survived that year works somewhat to his favor.

However, there is a little more drama if we look further down the line. That's when the immediate fact of his recent performances becomes less important in his forecasts, and the fundamental facts about Mother Nature a lot more so. In 2009, we have him losing about eight points of EqA; perhaps more importantly, his attrition rate is much higher, 30 percent versus just 14 percent before. These two factors conspire to wipe about $3.2 million off his MORP. Fortunately for the Astros, 2009 will be the last year of Tejada's present contract, as his decline tends to get steeper from there:

(A stray methodological note: the MORP factors I'm working with in this article will differ slightly from the versions you see on the PECOTA cards. Specifically, I have backed out both the inflationary factor that we apply to future seasons and the minimum salary, in order to give you a truer sense of Tejada's value at the margins.)

Overall, aging Miguel Tejada by two years removes about 40 percent of his remaining lifetime value. In the context of the decline that he has already experienced-see the purple line above-this is not all that significant. Nevertheless, it could be quite important from the standpoint of Tejada's chances of reaching the Hall of Fame. Tejada came into this season with a lifetime WARP-3 of 78.5, and his MVP, his RBI title, and consecutive games streak will probably allow him to do well enough on the Keltner List type of questions to warrant a serious discussion. But he needs to finish well; a good general rule of thumb is that a player is as likely as not to make the Hall of Fame once he hits 100 WARP. Tejada's original PECOTA had him picking up 17.9 wins through age 38, and perhaps just a little bit of residual value thereafter, putting him right on the brink of that 100-WARP threshold. His new, age-34 PECOTA robs him of at least 6-7 wins. Those are wins that his Cooperstown dossier can't afford to lose, especially given the bit of ignominy that this latest incident has brought upon him.

So the second of my two initial thoughts was right. But what about the first: should we have seen this coming? My response was conditioned by the fact that I'd heard a relatively credible rumor about this particular scenario from a front office executive many years ago. Contrary to my first impression, I don't think this is something you could have guessed from looking at Tejada's stat lines alone. Below is a graph of Tejada's EqA performance, going all the way back to his minor league days. I've also drawn in a generic aging curve, "forcing" the generic player to have a peak at about a .290 EqA (slightly lower than Tejada's):

There are a couple of obvious conclusions that come from this. Firstly, that no matter what age he is, Tejada has been an overachiever. A generic player can expect to see about 25 points of improvement in his EqA from the age of 21 to age 26. Whichever age you start Tejada at, he improved by around 80 points during this period. Of course, this is likely to be true for many players who turn out to be as good as Miguel Tejada; if you look at the universe of major league All-Stars, there are probably as many of them who at some point in their careers were undifferentiated from the unwashed prospect masses as those Justin Upton types who looked like they came out of the womb ready to play. The irony, of course, is that Tejada was a highly-regarded prospect, probably even an overrated prospect.

Secondly, it's important to note that Tejada's "new" career path is no better a fit for the generic aging curve than the one we would have drawn up 24 hours ago. In fact, it's actually a bit worse. Tejada's peak lasted for roughly five seasons, from 2002 through 2006 (interrupted slightly by a merely good year in 2003). Before, that peak would have come from age-26 through age-30 seasons, a very, very, normal career path. Now it spans his age-28 through age-32 seasons, and while I would not call that abnormal-I think that people generally underrate the stochasticity inherent in baseball player-aging patterns-it's a little less normal. In fact, Tejada's career path would be a better fit for the generic aging curve if you made him two years younger, rather than two years older.

Ultimately, the more interesting question might not be what happens to Tejada's PECOTA forecast, but why he felt compelled to misrepresent his age in the first place. It's true that there is a fair amount of difference in the valuation of a player, say, who hits for a .220 EqA in his age-18 season and one who does the same thing when he's 20. At the same time talent is talent, and, particularly for Latin American players, major league organizations are going to have an awfully tough time evaluating exactly how much talent a player has until they see him perform against professional competition.

Put a bit differently, when you're considering signing an amateur in the Dominican Republic, the uncertainty term regarding exactly how much talent the player has is of a greater magnitude than any differences related to a year or two's worth of aging. Think about the mistake the A's would have made, for instance, if they hadn't signed Tejada. The optimal strategy, therefore, probably involves throwing a bunch of players into your minor league complex and seeing who sticks. However, the shadowy economics of the Latin American player development system do not really offer incentives that align with this strategy; players feel compelled to lie about their age because they figure that getting a signing bonus from a major league organization might be one of the only chances they'll ever encounter to make the kind of money that can lift them out of poverty. A system that placed less emphasis on signing bonuses and more on remunerating players on an ongoing basis might do more to resolve this dilemma, especially if it came with additional benefits like vocational training for the young men who didn't make it as baseball players. Given the abject poverty that he grew up in, Tejada would have been stupid not to lie about his age, if it made the difference between getting a signing bonus and an opportunity with a major league club and not.

Nate Silver is an author of Baseball Prospectus. 
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