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Free Agent Market Tracker v. 1
By Capitol Avenue Club | December 6, 2009
As we head into the Winter Meetings, let’s take a look at how the FA market has behaved thus far. So far we’ve seen 16 contracts signed:
| Name | Yrs | Total Salary | Avg Salary |
| Chone Figgins | 4 | $36,000,000 | $9,000,000 |
| Billy Wagner | 2 | $13,500,000 | $6,750,000 |
| Takashi Saito | 1 | $4,350,000 | $4,350,000 |
| Placido Polanco | 3 | $18,000,000 | $6,000,000 |
| Gregg Zaun | 1 | $2,150,000 | $2,150,000 |
| Marco Scutaro | 3 | $14,000,000 | $4,666,667 |
| Henry Blanco | 1 | $1,500,000 | $1,500,000 |
| Alex Cora | 1 | $2,000,000 | $2,000,000 |
| Brian Schnider | 2 | $2,750,000 | $1,375,000 |
| Freddy Sanchez | 2 | $12,000,000 | $6,000,000 |
| John McDonald | 2 | $3,000,000 | $1,500,000 |
| Alex Gonzalez | 1 | $2,750,000 | $2,750,000 |
| Jack Wilson | 2 | $10,000,000 | $5,000,000 |
| Ken Griffey | 1 | $2,350,000 | $2,350,000 |
| Andruw Jones | 1 | $500,000 | $500,000 |
| Tim Hudson | 3 | $28,000,000 | $9,333,333 |
By using rough estimates of 2010 win values, we can observe how the market is behaving. I’m interested in three things 1) how win values influence contract length, 2) how win values influence total guaranteed money, and 3) how win values influence average salary. I ran the three appropriate regressions:
Using this model, we can loosely predict how long a players’ contract will be with the equation Years = 0.757*(Win Value) + 0.791 (R^2 =.703). Here goes:
| Win Value | Years |
| 0.0 | 1 |
| 0.1 | 1 |
| 0.2 | 1 |
| 0.3 | 1 |
| 0.4 | 1 |
| 0.5 | 1 |
| 0.6 | 1 |
| 0.7 | 1 |
| 0.8 | 1 |
| 0.9 | 1 |
| 1.0 | 2 |
| 1.1 | 2 |
| 1.2 | 2 |
| 1.3 | 2 |
| 1.4 | 2 |
| 1.5 | 2 |
| 1.6 | 2 |
| 1.7 | 2 |
| 1.8 | 2 |
| 1.9 | 2 |
| 2.0 | 2 |
| 2.1 | 2 |
| 2.2 | 2 |
| 2.3 | 3 |
| 2.4 | 3 |
| 2.5 | 3 |
| 2.6 | 3 |
| 2.7 | 3 |
| 2.8 | 3 |
| 2.9 | 3 |
| 3.0 | 3 |
| 3.1 | 3 |
| 3.2 | 3 |
| 3.3 | 3 |
| 3.4 | 3 |
| 3.5 | 3 |
| 3.6 | 4 |
| 3.7 | 4 |
| 3.8 | 4 |
| 3.9 | 4 |
| 4.0 | 4 |
| 4.1 | 4 |
| 4.2 | 4 |
| 4.3 | 4 |
| 4.4 | 4 |
| 4.5 | 4 |
| 4.6 | 4 |
| 4.7 | 4 |
| 4.8 | 4 |
| 4.9 | 5 |
| 5.0 | 5 |
| 5.1 | 5 |
| 5.2 | 5 |
| 5.3 | 5 |
| 5.4 | 5 |
| 5.5 | 5 |
| 5.6 | 5 |
| 5.7 | 5 |
| 5.8 | 5 |
| 5.9 | 5 |
| 6.0 | 5 |
| 6.1 | 5 |
| 6.2 | 5 |
| 6.3 | 6 |
| 6.4 | 6 |
| 6.5 | 6 |
| 6.6 | 6 |
| 6.7 | 6 |
| 6.8 | 6 |
| 6.9 | 6 |
| 7.0 | 6 |
I always talk about understanding something’s limitations. This model has plenty. 1) we only have 16 data points, so SSS applies, 2) things other than win-value are considered when decisions as to the length of a FA contract are made. This is simply a very crude model that I’m using to examine the trends, nothing more.
That said, the market is basically behaving like we’d expect it to. 1-win players get 1-year deals, 2-win players get 2-year deals, 3-win players get 3-year deals, etc…
Next task: projecting the average salary from win values:
Salary, like contract length, largely behaves linearly. The basic equation is Salary = $2.3 M*(Win Value) + $760,000 (R^2 = .795). And here’s what the model predicts:
| 0.0 | $760,000 |
| 0.1 | $991,760 |
| 0.2 | $1,223,520 |
| 0.3 | $1,455,280 |
| 0.4 | $1,687,040 |
| 0.5 | $1,918,801 |
| 0.6 | $2,150,561 |
| 0.7 | $2,382,321 |
| 0.8 | $2,614,081 |
| 0.9 | $2,845,841 |
| 1.0 | $3,077,601 |
| 1.1 | $3,309,361 |
| 1.2 | $3,541,121 |
| 1.3 | $3,772,881 |
| 1.4 | $4,004,641 |
| 1.5 | $4,236,402 |
| 1.6 | $4,468,162 |
| 1.7 | $4,699,922 |
| 1.8 | $4,931,682 |
| 1.9 | $5,163,442 |
| 2.0 | $5,395,202 |
| 2.1 | $5,626,962 |
| 2.2 | $5,858,722 |
| 2.3 | $6,090,482 |
| 2.4 | $6,322,242 |
| 2.5 | $6,554,003 |
| 2.6 | $6,785,763 |
| 2.7 | $7,017,523 |
| 2.8 | $7,249,283 |
| 2.9 | $7,481,043 |
| 3.0 | $7,712,803 |
| 3.1 | $7,944,563 |
| 3.2 | $8,176,323 |
| 3.3 | $8,408,083 |
| 3.4 | $8,639,843 |
| 3.5 | $8,871,604 |
| 3.6 | $9,103,364 |
| 3.7 | $9,335,124 |
| 3.8 | $9,566,884 |
| 3.9 | $9,798,644 |
| 4.0 | $10,030,404 |
| 4.1 | $10,262,164 |
| 4.2 | $10,493,924 |
| 4.3 | $10,725,684 |
| 4.4 | $10,957,444 |
| 4.5 | $11,189,205 |
| 4.6 | $11,420,965 |
| 4.7 | $11,652,725 |
| 4.8 | $11,884,485 |
| 4.9 | $12,116,245 |
| 5.0 | $12,348,005 |
| 5.1 | $12,579,765 |
| 5.2 | $12,811,525 |
| 5.3 | $13,043,285 |
| 5.4 | $13,275,045 |
| 5.5 | $13,506,806 |
| 5.6 | $13,738,566 |
| 5.7 | $13,970,326 |
| 5.8 | $14,202,086 |
| 5.9 | $14,433,846 |
| 6.0 | $14,665,606 |
| 6.1 | $14,897,366 |
| 6.2 | $15,129,126 |
| 6.3 | $15,360,886 |
| 6.4 | $15,592,646 |
| 6.5 | $15,824,407 |
| 6.6 | $16,056,167 |
| 6.7 | $16,287,927 |
| 6.8 | $16,519,687 |
| 6.9 | $16,751,447 |
| 7.0 | $16,983,207 |
The model sort of breaks down, but that’s because there’s inherent bias in the data. Players that sign this early usually do so for a relative discount. 5 win players make more than $12.5 million on the FA market. If we were trying to build a valid FA salary predictor, this would be a very big problem, obviously. We’re just studying trends, though.
Overall guaranteed money doesn’t behave linearly, however. This is intuitive. Total money = years * $/year. If years behave linearly and $/year behaves linearly, multiplying them together will give you something that’s anything but linear.
Here’s the visualization:
Basic equation (exponential curve): Total $ = $1.2 M * 2.816^(Win Value).
Extrapolation:
| Win Value | Total $ |
| 0.0 | $1,186,856 |
| 0.1 | $1,318,822 |
| 0.2 | $1,465,461 |
| 0.3 | $1,628,406 |
| 0.4 | $1,809,468 |
| 0.5 | $2,010,662 |
| 0.6 | $2,234,226 |
| 0.7 | $2,482,649 |
| 0.8 | $2,758,694 |
| 0.9 | $3,065,432 |
| 1.0 | $3,406,277 |
| 1.1 | $3,785,019 |
| 1.2 | $4,205,874 |
| 1.3 | $4,673,524 |
| 1.4 | $5,193,172 |
| 1.5 | $5,770,599 |
| 1.6 | $6,412,230 |
| 1.7 | $7,125,203 |
| 1.8 | $7,917,452 |
| 1.9 | $8,797,791 |
| 2.0 | $9,776,014 |
| 2.1 | $10,863,006 |
| 2.2 | $12,070,860 |
| 2.3 | $13,413,014 |
| 2.4 | $14,904,403 |
| 2.5 | $16,561,618 |
| 2.6 | $18,403,099 |
| 2.7 | $20,449,333 |
| 2.8 | $22,723,087 |
| 2.9 | $25,249,660 |
| 3.0 | $28,057,161 |
| 3.1 | $31,176,827 |
| 3.2 | $34,643,367 |
| 3.3 | $38,495,351 |
| 3.4 | $42,775,636 |
| 3.5 | $47,531,845 |
| 3.6 | $52,816,894 |
| 3.7 | $58,689,586 |
| 3.8 | $65,215,261 |
| 3.9 | $72,466,523 |
| 4.0 | $80,524,051 |
| 4.1 | $89,477,493 |
| 4.2 | $99,426,464 |
| 4.3 | $110,481,659 |
| 4.4 | $122,766,076 |
| 4.5 | $136,416,394 |
| 4.6 | $151,584,486 |
| 4.7 | $168,439,112 |
| 4.8 | $187,167,799 |
| 4.9 | $207,978,922 |
| 5.0 | $231,104,027 |
| 5.1 | $256,800,404 |
| 5.2 | $285,353,953 |
| 5.3 | $317,082,360 |
| 5.4 | $352,338,639 |
| 5.5 | $391,515,050 |
| 5.6 | $435,047,474 |
| 5.7 | $483,420,253 |
| 5.8 | $537,171,584 |
| 5.9 | $596,899,507 |
| 6.0 | $663,268,558 |
| 6.1 | $737,017,160 |
| 6.2 | $818,965,844 |
| 6.3 | $910,026,374 |
| 6.4 | $1,011,211,893 |
| 6.5 | $1,123,648,195 |
| 6.6 | $1,248,586,250 |
| 6.7 | $1,387,416,125 |
| 6.8 | $1,541,682,446 |
| 6.9 | $1,713,101,586 |
| 7.0 | $1,903,580,761 |
This model is obviously broken. Nobody gets a $2 billion contract. It seems pretty intuitive for awhile. 0-win players getting close to the league minimum 1-win players getting between $3 M and $5 M. League average players get $10 M guaranteed. 3-win players get $30 million contracts. I think the model breaks down between 4 and 5 wins. 4-win players can sometimes get $80 million guaranteed, but 5-win players don’t usually get $232 million.
I tried something different. Multiplied the salary and the years that the model projects to come up with extrapolated $. Here’s what the visualization looks like:
Basic equation (power curve): $6.1 M * (Win Value)^1.339. You can see the least squares regression line is much flatter than the data in the upper range. When some of the Hollidays, Bays, and Lackeys sign, we’ll have a better idea as to where the true value is. The corresponding table:
| Win Value | Total Extrap$ |
| 0.0 | $601,160.00 |
| 0.1 | $859,558.48 |
| 0.2 | $1,153,045.44 |
| 0.3 | $1,481,620.87 |
| 0.4 | $1,845,284.79 |
| 0.5 | $2,244,037.18 |
| 0.6 | $2,677,878.06 |
| 0.7 | $3,146,807.41 |
| 0.8 | $3,650,825.25 |
| 0.9 | $4,189,931.56 |
| 1.0 | $4,764,126.35 |
| 1.1 | $5,373,409.62 |
| 1.2 | $6,017,781.37 |
| 1.3 | $6,697,241.60 |
| 1.4 | $7,411,790.30 |
| 1.5 | $8,161,427.49 |
| 1.6 | $8,946,153.16 |
| 1.7 | $9,765,967.30 |
| 1.8 | $10,620,869.92 |
| 1.9 | $11,510,861.03 |
| 2.0 | $12,435,940.61 |
| 2.1 | $13,396,108.67 |
| 2.2 | $14,391,365.21 |
| 2.3 | $15,421,710.23 |
| 2.4 | $16,487,143.73 |
| 2.5 | $17,587,665.71 |
| 2.6 | $18,723,276.17 |
| 2.7 | $19,893,975.10 |
| 2.8 | $21,099,762.52 |
| 2.9 | $22,340,638.41 |
| 3.0 | $23,616,602.79 |
| 3.1 | $24,927,655.64 |
| 3.2 | $26,273,796.97 |
| 3.3 | $27,655,026.78 |
| 3.4 | $29,071,345.07 |
| 3.5 | $30,522,751.84 |
| 3.6 | $32,009,247.09 |
| 3.7 | $33,530,830.82 |
| 3.8 | $35,087,503.02 |
| 3.9 | $36,679,263.71 |
| 4.0 | $38,306,112.88 |
| 4.1 | $39,968,050.52 |
| 4.2 | $41,665,076.64 |
| 4.3 | $43,397,191.25 |
| 4.4 | $45,164,394.33 |
| 4.5 | $46,966,685.89 |
| 4.6 | $48,804,065.93 |
| 4.7 | $50,676,534.45 |
| 4.8 | $52,584,091.45 |
| 4.9 | $54,526,736.92 |
| 5.0 | $56,504,470.88 |
| 5.1 | $58,517,293.32 |
| 5.2 | $60,565,204.23 |
| 5.3 | $62,648,203.62 |
| 5.4 | $64,766,291.50 |
| 5.5 | $66,919,467.85 |
| 5.6 | $69,107,732.68 |
| 5.7 | $71,331,085.99 |
| 5.8 | $73,589,527.78 |
| 5.9 | $75,883,058.05 |
| 6.0 | $78,211,676.80 |
| 6.1 | $80,575,384.03 |
| 6.2 | $82,974,179.73 |
| 6.3 | $85,408,063.92 |
| 6.4 | $87,877,036.58 |
| 6.5 | $90,381,097.72 |
| 6.6 | $92,920,247.35 |
| 6.7 | $95,494,485.45 |
| 6.8 | $98,103,812.03 |
| 6.9 | $100,748,227.09 |
| 7.0 | $103,427,730.63 |
Probably a better estimator, but still has plenty of the same limitations.
Take-aways from this:
1) The market is paying less per, by quite a bit, than it has in the past. This could be a result of either a systematic bias, small sample size, or genuinely different market. I have a feeling the latter plays a minimal, if any, role.
2) The biggest overpayments in years thus far are Figgins and McDonald. The biggest underpayments are Saito and Sanchez.
3) The biggest overpayments in salary thus far are Figgins, Wagner, and Griffey. The biggest underpayments are Sanchez, Zaun, and Schnider.
4) The biggest overpayments in total guaranteed money are Hudson and Wagner. The biggest underpayments are Sanchez and Zaun.
5) All of these are subject to change as we get a more complete picture of the market.
Topics: Atlanta Braves | 8 Comments »
December 6th, 2009 at 5:46 PM
Your estimation of length of contract offer needs a downward adjustment for age that is slightly logarithmic as age is sufficiently great that the end year would project over about 35 (not sure where the real number is, but somewhere around there it should start). And the higher age would be in the end year, the greater the adjustment, by more than a lienar relationship. I realize the small sample size gives you no way to test it, but prevous years would almost certainly show a relationship like this and the factor could be “assumed” from how it has tested in the past (although before aobut 2007, the “old player market” seemed a good bit stronger and there seems to have been a “no PEDs to help old players” adjustment).
In other words, Saito might seem to deserve another year by this model, but damn, he’s 40 (and coming off injury). So, just because he projects at a level of a whatever win player, that doesn’t make year 2 a good proposition for the club offering.
December 6th, 2009 at 6:04 PM
Cliff,
I always talk about understanding something’s limitations. This model has plenty. 1) we only have 16 data points, so SSS applies, 2) things other than win-value are considered when decisions as to the length of a FA contract are made.
I’m just trying to get an idea of how the market generally behaves, not build a sophisticated predictor.
December 6th, 2009 at 6:52 PM
I think the next interesting step would be to apply this to free agents who are out there. For instance, does it look like the market for a guy like Matt Holliday is going to be more like 4y/$60m or 7y/$140m?
December 6th, 2009 at 9:49 PM
It’s best to interpolate, if anything, at this point, given the market hasn’t really set itself. When you’re talking about a guy like Matt Holliday, who the market is going to value significantly more than any of the already signed FA’s, you’re getting into extrapolation. Using the model though (and assuming he’s valued as a 4.5 win player, I value him as a 4.0 win player, the market will probably value him at closer to 5.0 wins), these models suggest he should get somewhere between 4 years, $50 million and 4 years, $136 million (depending on whether or not you’re using the exponential curve model or power curve model.
If you want to use the models I have, just estimate a player’s win value and refer to the 4 extremely long tables. That’ll give you a decent idea. Again, it’s best to stick to interpolation (~1.0-3.5 win players) at this point.
December 7th, 2009 at 3:09 AM
this is pure fantasy…
December 7th, 2009 at 4:01 AM
What do you mean? It’s far from fantasy, it’s what has actually happened.
December 7th, 2009 at 11:45 AM
When Tim Hudson signed his extension, I remember hearing the announcement was delayed because “the insurance company” wanted its own doctor to check out his arm. Since the deal got done, does that mean the Braves are protected somewhat from risk to injury?
December 7th, 2009 at 3:05 PM
Trevor,
You make a good point and bring something up a
we don’t spend enough time discussig–insurance. Most FA signings and long-term contracts come with an insurance policy. Teams like the Braves usually aren’t willing to commit without insurance.
I wish we knew more about the insurance policies. I’ll ask Keith Law about it.