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August 25, 2005

Lies, Damned Lies

Valuing Draft Picks

by Nate Silver

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Three weeks ago, I prepared an analysis of the ill-fated Manny Ramirez-to-the-Mets deal. The workup applied some standard valuation techniques in an attempt to put a price on something that is notoriously difficult to quantify: the value achieved by dumping a big, backloaded contract. That article triggered about as much response as anything I've written in the past year. Most of the responses focused on complementary applications of the framework--those other difficult economic questions that both sabermetrics and traditional analysis have largely avoided.

For example: what is the value of a first-round draft pick? This is an essential thing for a baseball club to have a handle on. Under baseball's compensation rules, a team signing a Type A free agent must sacrifice its first-round draft pick (or its second-round pick, if it picks in the top half of the first round), while a team losing the same free agent acquires that first-round pick, as well as a sandwich pick between the first and second rounds. If the value of these picks is material--above and beyond the signing bonus that would typically be paid to a draft pick--that ought to have a corresponding impact on a team's behavior in the free-agent market.

The economic value of a prospect or a draft pick is in his potential to provide on-field value to his club before he accumulates six years of service time. This period incorporates both his first two years of service--when he has little to no negotiating leverage--and his subsequent four years of service time, when he is subject to arbitration, a process through which teams generally get to pay desirable players well below market price.

After I published my previous article, BP up-and-comer Tom Gorman was kind enough to forward me a paper written by John D. Burger and Stephen J.K. Walters, from Loyola College in Maryland, which quantifies the arbitration discount more precisely. Burger and Walters concluded that:

  • A typical, arbitration-eligible player entering his third year of service time is priced at about 31% of his market value;
  • An arbitration-eligible player entering his fourth year of service time is priced at 44% of his market value;
  • An arbitration-eligible player entering his fifth year of service time is priced at 61% of his market value;
  • An arbitration-eligible player entering his sixth year of service time is priced at 64% of his market value.

These figures imply a somewhat larger discount relative to market than the guesstimates I had made before. But my figures weren't based on any evidence, and since a player has limited flexibility under the arbitration system--a player who doesn't like his arbitration result can hold out, but can't sign with another team--it makes sense that the discount is substantial.

What about a player's first and second years of service time? For purposes of this article, I am going to assign a marginal cost of $500,000 for a player's first major-league service year, and $750,000 for his second major-league service year. These figures are intended to represent a player's marginal salary above the major-league minimum in his first two service years, as well as some attendant costs, such as his salaries and benefits in the minor leagues, the allocation of developmental resources toward that player, and the possibility that he will be subject to arbitration early if he is a "Super 2" player (16.7% of players with between two and three years of service time can go to arbitration). It is not meant to incorporate his signing bonus, which we will discuss later.

We also, of course, need to have an estimate of a draft pick's value. In the spirit of Rany Jazayerli's recent series of articles, I looked at each of the six major-league drafts from 1989-1994 and attempted to evaluate a typical first-round draft pick's WARP score for each of his first six years of service time. Since precise records of service time are hard to come by, I instead applied a quick-and-dirty estimate of service time years using the following criteria:

  • A player's first year of service time consists of all seasons up to and including the first in which the player accumulates 200 career at-bats or 50 career innings pitched.

  • Subsequent years of service time accumulate after each season, or set of seasons, in which a player has at least 150 AB or 35 IP (e.g., if a player has 121 AB in 1996 and 85 AB in 1997, this counts as one service-time year rather than two).

  • A player ceases to accumulate value in the 11th season after his draft class. For example, a player drafted in 1991 can accumulate value in the years 1991-2001, but not in 2002 or any year thereafter. This is meant to account for players who become subject to minor-league free agency before their arbitration eligibility expires, accumulate unaccounted-for service time while sitting on the major-league bench or the major-league disabled list, or take so long to develop that their original owners find it suitable to dispose of them to clear a spot on the roster.

This is not a perfect set of rules--it gives Alex Rodriguez one too many years of arbitration time, for example--but should provide a good approximation in the vast majority of cases.

I broke down the first-round draft picks into four sub-classes: Tier 1 (picks 1-7), Tier 2 (picks 8-15), Tier 3 (picks 16-25) and Tier 4 (26 and higher, including first-round sandwich picks). The divisions among the tiers are necessarily somewhat arbitrary, although Tiers 3 and 4 are intended to represent the typical draft picks that a team gives up when it signs a free agent. I excluded those players I identified as not having signed with the clubs that drafted them.

Applying that method, here are the average WARP scores for 1st Tier draft picks (selections 1-7 overall):

Service Time Year 1: 2.11 WARP
Service Time Year 2: 2.37 WARP
Service Time Year 3: 2.44 WARP
Service Time Year 4: 2.99 WARP
Service Time Year 5: 2.56 WARP
Service Time Year 6: 1.94 WARP

There are a couple of things to keep in mind. First, these figures are averages from draft picks who achieve all sorts of different outcomes. Many prominent draft picks never reach the majors, and many more never make a significant contribution at the big-league level. On the other hand, we have folks like Rodriguez and Chipper Jones, and one A-Rod makes up for an awful lot of Antone Williamsons.

Second, a considerable majority of draft picks, including many who make some contribution in the major leagues, never reach six years of service time. Indeed, it is quite a feat to accumulate six years of service time; there are many more fringe players than there are major-league regulars. This is why the WARP scores tail off in years five and six: there are more zeroes to average in. One upshot of this is that some players who are widely perceived as disappointments may nevertheless give their clubs a reasonable return on their money. Willie Greene, for example, contributed about 14 wins to his clubs, far less than what was expected of him, but decent value for a player who never achieved his free-agent payday.

With these considerations in mind, we can plug in our estimates of a draft pick's cost and value into our net present value framework. As before, I'm using a figure of $2.14 million for the marginal cost of a win in the free-agent market, as derived from this study. These are the results for the Tier 1 draft picks:


Tier 1 (1-7)                Y1     Y2     Y3     Y4     Y5     Y6     Total
WARP                      2.11   2.37   2.42   2.99   2.56   1.94     14.38
Market Value ($M)        $4.51  $5.08  $5.17  $6.39  $5.48  $4.14    $30.78
Marginal Cost ($M)       $0.50  $0.75  $1.60  $2.81  $3.34  $2.65    $11.66
Net Value ($M)           $4.01  $4.33  $3.57  $3.58  $2.14  $1.49    $19.12
Gross Present Value ($M) $3.55  $3.65  $2.87  $2.74  $1.56  $1.03    $15.39
Signing Bonus                                                         $3.00
Net Present Value ($M)                                               $12.39
I've described this methodology in some detail before, so I'll discuss it just briefly now. Market Value is a player's WARP score translated into dollars, using the $2.14 million/win estimate. Marginal Cost represents the salary and related costs to be paid to that player, which we estimate as a fixed sum of $500,000 in his first service year, $750,000 in his second, 31% of his Market Value in Year Three, 44% of his Market Value in Year Four, and 61 and 64% of his Market Value in Years Five and Six, respectively.

Net Value is simply the player's Market Value less his Marginal Cost. The next row, Gross Present Value, takes his Net Value and discounts it at a rate of 5% a year, assuming that his first year of service time begins 2 1/2 years after he is drafted.

The "Total" column at the right is the key. We figure that the Gross Present Value of a Tier 1 draft pick--a player who goes between first and seventh overall in the amateur draft--is about $15.4 million. Keep in mind that, even though this analysis is derived from the results of players who were selected from 1989-1994, it is calibrated to present-day market rates, and so would represent the value of a player selected in the 2005 draft.

Let's pause for a moment and consider that number. MLB bigwigs are fond of complaining about the escalating cost of signing bonuses paid to amateur draft picks (and have done a remarkably good job of controlling them), but a typical top-tier draft pick can be expected to contribute about $15 million worth of value to his club above and beyond what comparable production would cost in the free-agent market. That is a large margin of error to cover for the Williamsons and Brien Taylors of the world, and a team that punts on a first-round pick for the sake of saving a few bucks of signing bonus is almost certainly making a large mistake.

We can, of course, consider the signing bonus if we want to do so. Over the past year or two, a typical signing bonus for a Tier 1 draft pick has run at about $3 million. If we subtract that number to come up with the Net Present Value associated with a top draft pick, we are left with about $12.4 million of profit for the club. If amateur draft picks were tradable, this is about what they ought to be worth in the market.

Here are the results for the Tier 2 picks:


Tier 2 (8-15)               Y1     Y2     Y3     Y4     Y5     Y6     Total
WARP                      1.53   1.94   2.44   1.94   2.73   1.80     12.37
Market Value ($M)        $3.28  $4.15  $5.22  $4.15  $5.83  $3.85    $26.48
Marginal Cost ($M)       $0.50  $0.75  $1.62  $1.82  $3.56  $2.46    $10.71
Net Value ($M)           $2.78  $3.40  $3.60  $2.32  $2.28  $1.39    $15.77
Gross Present Value ($M) $2.46  $2.87  $2.89  $1.77  $1.66  $0.96    $12.61
Signing Bonus                                                         $1.90
Net Present Value ($M)                                               $10.71
The years 1989-1994 were a fruitful time in this range of the amateur draft, as players like Nomar Garciaparra, Manny Ramirez and Billy Wagner were nabbed between picks eight and 15. The drop-off might have been slightly larger if we'd considered a wider range of years; nevertheless it's clear that these picks are plenty valuable too.

Tier 3 (16-25)              Y1     Y2     Y3     Y4     Y5     Y6     Total
WARP                      1.37   1.92   1.85   1.67   1.70   1.32      9.84
Market Value ($M)        $2.93  $4.10  $3.96  $3.58  $3.64  $2.83    $21.05
Marginal Cost ($M)       $0.50  $0.75  $1.23  $1.58  $2.22  $1.81     $8.09
Net Value ($M)           $2.43  $3.35  $2.74  $2.01  $1.42  $1.02    $12.96
Gross Present Value ($M) $2.15  $2.82  $2.20  $1.53  $1.03  $0.71    $10.45
Signing Bonus                                                         $1.50
Net Present Value ($M)                                                $8.95
Tier 3 is significant since it represents the draft pick that an upper-division club would sacrifice when signing a Type A free agent. That sacrifice amounts to about $9 million--the chance to pick up a player like Mike Mussina, Chuck Knoblauch or Jason Kendall, all of whom were selected in this phase.

Tier 4 (26+)                Y1     Y2     Y3     Y4     Y5     Y6     Total
WARP                      0.87   0.90   0.80   0.63   0.53   0.35      4.08
Market Value ($M)        $1.87  $1.93  $1.72  $1.34  $1.13  $0.74     $8.73
Marginal Cost ($M)       $0.50  $0.75  $0.53  $0.59  $0.69  $0.47     $3.54
Net Value ($M)           $1.37  $1.18  $1.19  $0.75  $0.44  $0.27     $5.19
Gross Present Value ($M) $1.21  $0.99  $0.95  $0.57  $0.32  $0.19     $4.24
Signing Bonus                                                         $1.00
Net Present Value ($M)                                                $3.24
There do appear to be some diminishing returns once we reach the sandwich pick stage. Still, we figure that a team losing a Type A free agent is compensated with about $12 million in draft picks ($9 million for the Tier 3 pick and $3 million for the Tier 4 pick); it's well worth it to offer arbitration to your veterans if there's any material chance that they'll sign somewhere else.

It's also worth considering very briefly the perverse incentives that the draft compensation system creates. A team seeking to sign a Type A free agent from another club starts off about $9 million in the hole, the cost of the first-round draft pick it would give up by signing that player. But the team seeking to re-sign its player has an even bigger disincentive--it is giving up the opportunity to acquire both a first-round pick and the sandwich pick, total value about $12 million. Thus, the compensation system is ill-designed as a way to keep potential free agents at home; it's no surprise that someone like Billy Beane wasn't willing to go the last dollar with stars like Jason Giambi and Miguel Tejada.

Of course, the real intention of the draft compensation system isn't to balance incentives, but to hold the salaries paid to premium free agents down, by acting as a tax on whichever club winds up with the player. The mechanism ought to work in that regard--sacrificing a draft pick worth $9 million is significant. My guess, however, is that the compensation system fails here as well, because I doubt that major-league teams are adequately accounting for the value of their draft picks. Certainly, Major League Baseball is within its rights to act as a cartel in an effort to hold singing bonuses down. Nevertheless, a significant and increasing number of draft picks have gone unsigned each year, even when a rational analysis reveals that draft picks provide very good value on the money. It's possible that teams like the Cincinnati Reds are taking one for the team in steadfastly refusing to pay a draft pick above his slot value, but it's more likely that these teams are behaving in both a self-interested and a short-sighted manner.

NBA and NFL teams intuitively recognize the value of high draft picks, probably because players take less time to develop in those sports, making the gratification more instantaneous. But high draft picks are very probably just as valuable in MLB. If baseball draft picks are a little bit more difficult to project, the sport's economic structure more than makes up for this by allowing a club to hold a player essentially free of charge in the minor leagues until he's ready, and then providing him at a deep discount for six full seasons of performance.

Nate Silver is an author of Baseball Prospectus. 
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