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August 20, 2007

Lies, Damned Lies

Slotto Madness, Part 3

by Nate Silver

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Picking up from where we left off yesterday, let's take a more detailed look at the subset of players selected between 1998 and 2001, which represents 32 names in all. These are players who have already exhausted their arbitration clocks, or are close enough to doing so that we can form some reasonable estimate of their likely return.

You'll see several unfamiliar columns in the table below:

  • Actual is a player's WARP3 over his first six years of major league service time. If the player has not yet exhausted his service time, we use his PECOTA projection to make up the difference. The exception is players like Borchard and Stokes who are not presently on major league rosters; these players are credited with one-third of the balance of their PECOTA forecasts to account for the fact that they may opt for minor league free agency or retirement.

  • Slot is the expected WARP3 for a player selected with that draft pick, based on an extrapolation of Rany's research. Rany's original numbers covered the first 15 seasons after a player had been drafted; we assume that two-thirds of this amount is realized before a player becomes eligible for free agency. This is perhaps a conservative estimate, but keep in mind that most major leaguers never reach six years of major league service time at all, and many of the others are past their peak once they do.

  • Excess Wins is a player's Actual WARP less his Slot WARP.

  • Excess Cost is the amount that a player's bonus went above slot, included any guaranteed major league money that he received. If the player managed to play substantially in the major leagues while still under the terms of his draft-day contract, I have subtracted $250,000 for each such season to represent the team's down payment toward the minimum salary.

  • Earn is calculated by treating each Excess Win as worth $800,000, and subtracting out the Excess Cost. The way we arrive at $800,000 is as follows: the linear estimate of a marginal value of a win as determined in Baseball Between the Numbers was $1.2 million. However, teams are not done paying for a player's service once they give him his draft bonus; they also have to settle with him in arbitration. Generally speaking, these costs pare off about one-third of a player's market value over the course of his first six years of service time. Therefore, we subtract one-third of our estimated value of a win, leaving us at $800,000.

Return on Above-Slot Draft Picks, 1998-2001


Player    Draft    Actual  Slot  ExcessWins ExcessCost($000) Earn($000)
Sizemore  2000/75   50.6    2.0    +48.6      1525             +37355
Crawford  1999/52   41.1    4.0    +37.1       610             +29070
C.Young   2000/89   26.7    1.1    +25.6      1225             +19255
Teixeira  2001/5    40.6   16.6    +24.0      6250             +12950
Sheets    1999/10   27.6   12.8    +14.8       550             +11290
Mauer     2001/1    46.0   31.3    +14.7      1150             +10583
Drew      1998/5    34.4   16.6    +17.8      4000             +10240
Nady      2000/49   16.7    4.3    +12.4      1900              +8020
Beckett   1999/2    31.5   21.4    +10.1      3430              +4650
Belisle   1999/52    9.6    4.0     +5.6      1150              +3330
Burrell   1998/1    38.0   31.3     +6.7      3650              +1710
Patterson 1999/3    21.1   19.3     +1.8      1000               +440
Gosling   2001/66    3.6    2.7     +0.9      1440               -720
Jenkins   1999/87    0.0    1.2     -1.2       500              -1460
Hill      2000/43    3.7    5.0     -1.3       638              -1678
Henson    1998/97   -0.1    0.7     -0.8      1640              -2280
Freeman   2000/36    3.5    6.0     -2.5       550              -2550
Stokes    2000/41    3.5    5.9     -2.4      1202              -3122
Prior     2001/2    22.3   21.4     +0.9      4000              -3280
Espinosa  2000/23    5.8    8.4     -2.6      1550              -3630
Crosby    2001/53    0.0    3.9     -3.9      1090              -4210
Sardinha  2000/46    0.0    4.6     -4.6      1150              -4830
Stocks    1999/36    0.0    6.0     -6.0       510              -5310
M.G'parra 2001/36    0.1    6.0     -5.9      1050              -5770
J.Young   2000/47   -0.4    4.5     -4.9      2020              -5940
H'chinson 1999/48   -0.4    4.4     -4.8      2750              -6590
Diggins   2000/17   -0.5   10.0    -10.5       625              -9025
Hale      2000/14    0.1   11.0    -10.9       550              -9270
Borchard  2000/12    3.5   11.9     -8.4      3500             -10220
Floyd     2001/4     4.6   16.0    -11.4      1450             -10538
Munson    1999/3     7.4   19.3    -11.9      3900             -13420
Brazelton 2001/3     0.8   19.3    -18.5      1600             -16400
Total              441.4  332.9   +108.5     58155             +28651
Average             13.8   10.4     +3.4      1817               +895

There are several points of interest in this table. As we had guessed during our more subjective version of this exercise, the majority of players who make extra bonus money do not provide enough extra return to warrant it. However, as we had also anticipated, the upside of a win has much larger magnitude than the downside of a loss. The five best players in this study have produced an average return of about $22 million dollars. But the five worst players have cost their teams "only" an average of about $12 million dollars.

Next, the extra bonus money is not all that important at the macro level. Only two of the 32 players go from producing a positive return to a negative one on the basis of their extra slot money. This should not imply, however, that teams should go about giving extra bonus money to just anyone. The whole question is whether teams are discerning enough in their scouting judgments to justify going over slot. It's not how much Player A is worth in the abstract, but how much better Player A is than Player B.

On that front, the answer seems to be yes, teams know what they're doing, although the evidence is not overwhelming. The players in this study have produced, on average, an excess return of $895,000 on an excess investment of about $1.8 million. That implies a return on investment of 49 percent. For every dollar that teams have spent in going above slot, they've received about a dollar and fifty cents back in return. However, this is not a particularly robust result given our sample size. If you take Grady Sizemore out of the study, for example, the average return dips into the negative. What I feel most comfortable saying is that the extra bonus money has at least paid for itself. Probably, but not certainly, teams are making a little extra on top of that.

The logical follow-up is whether there is any way to differentiate the good uses of extra slot money from the bad. While the sample size prohibits us from reaching any definitive conclusions, we can run a few "splits" on the data. First, high school versus college:


Class        Count  Actual  Slot  ExcessWins  ExcessCost($000)  Earn($000)  ROI
HighSchool    15     14.5    9.0     5.5         1269.8           3135.9    247%
College       17     13.2   11.7     1.5         2300.4          -1081.6    -47%

Excess money spent on prep players has produced a substantially better return than that spent on college players, although as indicated previously, none of these splits are statistically significant. Note that the high school players haven't been paid as much above slot as the college guys, probably because fewer high school players have been given guaranteed MLB contracts. In fact, we can examine this phenomenon directly:


Class       Count  Actual   Slot  ExcessWins  ExcessCost($000) Earn($000)   ROI
No MLB $     21     11.6     7.9     3.8         1141.6          1868.1     164%
MLB $        11     17.9    15.2     2.7         3107.3          -961.8     -31%

Those players who received guaranteed major league contracts have produced a worse return on balance, even though they have also been better players:


Class       Count  Actual   Slot  ExcessWins  ExcessCost($000) Earn($000)   ROI
Hitter       17     16.1     9.6     6.6         1703.2          3551.7     209%
Pitcher      15     11.2    11.4    -0.2         1946.7         -2115.2    -109%

The hitter versus pitcher split is one of the stronger ones in the data; the average hitter has produced an excess return of about $3.5 million, while the average pitcher has cost his team $2.1 million. Hitters are easier to differentiate than pitchers, and it may be that the level of resolution isn't high enough to justify spending above-slot money on a pitcher based on his amateur track record. However, this result could also be a reflection of the high school versus college phenomenon-most players who go above slot tend to be either high school hitters, who generally have the highest upside, or college pitchers, who may have more leverage because they require little development time and teams have an insatiable need for near-term pitching talent.


Class       Count  Actual   Slot  ExcessWins  ExcessCost($000) Earn($000)   ROI
Early        11     24.9    20.5     4.5         2816.4           747.8      27%
Late         21      8.0     5.1     2.8         1294.0           972.6      75%

Another distinction is between those players selected early-within the first 10 picks of the draft-and those who went later on. Both groups have produced a favorable return on investment, although the late picks have done slightly better. One last way to permute the data:


Class        Count  Actual   Slot  ExcessWins  ExcessCost($000) Earn($000)   ROI
OtherSports    9     19.0     7.3    11.7         1560.0          7823.7     502%
NoOtherSports 23     11.8    11.6     0.1         1918.0         -1815.8     -95%

Surprisingly, those players who had scholarship or professional offers to play another sport have done better than those that didn't. This may be a sample-size fluke, or it may be because ability in another sport is a good proxy for athleticism. This somewhat calls into question the notion that football players receive better signing bonuses because they're football players. You can probably draw a distinction between those players like Drew Henson that needed to be bought away from football, and those like Sizemore or Joe Mauer who were baseball players first, and whose football pedigrees perhaps gave their teams a good excuse to go over slot money.

So, if you're looking to splurge, the perfect combination of attributes would seem to be a high school position player who also plays football, is available after the first ten picks of the draft, and does not require a guaranteed MLB contract. Sizemore and Carl Crawford both fit that description perfectly; on the other hand, so did Drew Henson and Choo Freeman. There is plenty of evidence that going over slot money can be a wise investment when the circumstances warrant it, but figuring out just when those cases come up is still up to the scouting department.

Nate Silver is an author of Baseball Prospectus. 
Click here to see Nate's other articles. You can contact Nate by clicking here

Related Content:  The Who,  3-0 Count,  Money

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