Abstract:
This article presented an empirical analysis of the relationship between the portion of the “Entering Player Pool” (Rookie Cap) for each of the 32 National Football League franchises and that franchise’s draft selections. Although the formula for determining each franchise’s Rookie Cap is closely guarded by the NFL, the author hypothesized that it should be possible to model the deterministic structure used to calculate franchise spending for each rookie’s contract. The OLS-estimated models revealed statistically significant relationships between groups segmented by draft selection order and each franchise’s Rookie Cap. The model was verified in an out-of-sample test using the Rookie Cap values for the 2007 NFL season. It was found to have a mean absolute percentage error of 2.1%. The implications of these findings were contrary to language in the NFL Collective Bargaining Agreement, as the majority of rookie contracts are implicitly determined by each franchise’s Rookie Cap. The published estimates of each selection’s NFL determined cap value will provide useful bargaining information for rookie contracts.
Introduction:
Each spring, the NFL Annual Player Selection Meeting is held in New York City to “draft” the top eligible collegiate talent, swelling the rosters of the 32 NFL franchises and saturating fans with conversation topics till fall. One of these topics, rookie salaries, in particular the closely guarded formula for creating each franchise’ Rookie Cap, is the purpose of this paper.
History:
With the 1993 Collective Bargaining Agreement (CBA) between the National Football League (the owners) and the National Football League Players Association (the players), the Entering Player Pool was introduced (Levine, 1996). The Rookie Cap is the specific pool of money within each franchise’s salary cap that is reserved for the signing of recently drafted athletes and any undrafted rookie free agents. More precisely, like the League Salary cap that establishes the ceiling for the total for a given franchise in a given year, the Rookie Cap is the maximum amount that franchises can spend on rookie contracts. The sum of each franchise’s Rookie Cap comprises the league-wide Entering Player Pool.
Rookie contracts are multi-year deals that generally include bonuses ranging from a simple signing bonus for players drafted after round one to reporting bonuses and more complex incentive clauses for players drafted in the first round. To further complicate matters, agents with first round draft picks often need to contend with rigid franchise policies that may prohibit longer-term contracts or incentive bonuses (Cole, 2006). The net effect of these variations is that teams of attorneys and agents write and rewrite these contracts to maximize the amount of money for their clients, while trying to keep the player’s salary cap charge beneath a threshold essentially dictated by his portion of the Rookie Cap. Each player’s salary cap charge is computed by summing his base salary and a portion of his bonuses, determined by prorating his bonus amount over the years of his contract, not to exceed the number of years remaining under the current CBA.
Purpose:
Each year, as mandated by the CBA, the league-wide salary cap rises in accordance with increases in league revenues. The Rookie Cap rises in tandem, keeping rookie salaries from rising more quickly than their veteran peers. Created by the NFL Management Council, the formula of exactly how each team’s Rookie Cap number is determined is unknown. However, it is based on the number and round of each franchise’s draft selections. Article XVII of the amended 2006 CBA states: “The list of each Formula Allotment attributed to each draft selection shall be agreed to by the NFL and the NFLPA, and shall not be disclosed to Clubs, Players, Player Agents or the public.”
Each May, Senior ESPN writer and analyst Len Pasquarelli covers the NFL’s unveiling of the current season’s Rookie Cap. In May of 2007 he wrote, “The formula for deriving each team’s rookie pool is regarded as Byzantine even by the most astute team officials, and is basically a function of how many overall choices a franchise makes and where those picks are slotted in each round.”
Using only franchise Rookie Caps and draft information, the author hypothesized that it was possible to create a statistical model that would closely mirror the exact process that baffles even long-time sports reporters. The implications of a well-estimated model are that 1) the majority of rookie contracts are the result of negotiations in name only, and 2) the pre-determination of the majority of rookie contracts reflect, not the work of supply and demand, but rather a formula designed to limit the bargaining position of rookies.
Data:
The dataset was comprised of 6 years of Rookie Cap values and corresponding draft selections for each of the 32 franchises. These 192 observations were first used in a model validation exercise and in predicting the recently-released Rookie Cap values for 2007.
Each franchise’s draft history was obtained from drafthistory.com, a comprehensive anthology of the NFL draft grouped by year, franchise, college, and position. Rookie Cap values from 2002 – 2007 were obtained from ESPN.com. Salaries for the 2005 rookie class were obtained from the USAToday.com salaries database.
Rookie Salary Cap Values
Rookie salaries in any given year are a function of numerous parameters, the single most important of which is draft position. Rookie contracts are basically slotted by the draft round and selection number. Consequently, the total contract value of a given selection closely resembles the contract received by the same selection in the prior draft. The distributions of the resulting salary cap charges are nearly constant from year to year.
The actual 2005 salary cap expenditures by 2005 draft selection are illustrated in Table 1. A close examination of the data in rounds four through seven will yield sequentially-drafted players with significantly different salaries. This is the result of either a) split contracts, by which a player’s base salary decreases if he is moved from the active roster; or b) the player failing to make the active roster at all. Smaller differences are likely attributable to contract year differences and prorating bonus amounts over longer time horizons (Pasquarelli, 2003).
Table 1
Although the 2006 CBA states, “Nothing in this Agreement is intended to or shall be construed to mean that any Rookie’s Salary is predetermined by any Allocation or Formula Allotment,” for all practical purposes, there are very few opportunities for a drafted player’s contract value to vary significantly from those of his peers selected immediately before and after him in his draft year, or in his selection (pick #) in preceding drafts.
The league’s formula allows franchises to approach rookie contract negotiations with a strong bargaining position, because under the language of the CBA, the franchise is only allotted certain dollars with which to sign all of its rookie players. For better or worse, this also levels the playing field for many franchises, essentially publicly stating that all teams have the same financial ability to sign their draft picks. Primarily due to this Rookie Cap, and the fact that the NFLPA provides considerable contract assistance through the sharing of previous rookie contracts, rookie contracts per draft selection (pick #) rarely vary significantly from year to year. This fact is particularly pronounced for rounds two through seven, in which the majority of contracts consist solely of base salary and a signing bonus.
Modeling Rookie Cap Values with Draft Round Variables
The author has hypothesized that it is possible to create a statistical model to estimate each franchise’s Rookie Cap values in any given year, given observed draft selections. By creating seven variables corresponding to the seven rounds in the NFL draft, an initial model could be formulated and later improved upon in the next section. Each of the seven round variables was populated by the number of players a given team selected in that round. It is also important to note that all Rookie Cap values were put into their real dollar equivalents using 2005 as the base year.
To illustrate the composition of the data set, consider that in 2005 the Carolina Panthers made 10 selections in total, with one selection in rounds 1, 2, and 4; two selections in rounds 3 and 6; three selections in round 5; and no selections in round 7. The corresponding data for this observation is detailed below in Table 2.
Table 2
| Team | Year | rnd1 | rnd2 | rnd3 | rnd4 | rnd5 | rnd6 | rnd7 | Rookie_Cap |
|---|---|---|---|---|---|---|---|---|---|
| Carolina | 2005 | 1 | 1 | 2 | 1 | 3 | 2 | 0 | $4,443,290 |
The table depiction also aids in visualizing the statistical model by which we modeled the dependent variable Rookie_Cap using explanatory variables rnd1 – rnd7. All models discussed in this paper were estimated using an ordinary least squares (OLS) regression. The author estimated this model without the use of an intercept term to more accurately interpret the resulting coefficients.
Table 3 reveals that each variable is significant at the 1% level. Note that for the first five round variables, the estimated coefficients decrease substantially, as these coefficients have the interpretation of the average salary cap value for a player drafted in that particular round. A quick comparison of the coefficients in Table 3 and the player cap in Table 1 reveals that these values closely resemble the average salary cap values observed in 2005.
Table 3: Model Coefficients and Fit statisticsNote: All coefficients are significant at 1% level.
| Model I | Model II | Model III | |
|---|---|---|---|
| rnd1 | 1,374,997 | ||
| rnd2 | 596,999 | ||
| rnd3 | 420,231 | ||
| rnd4 | 336,878 | ||
| rnd5 | 213,528 | ||
| rnd6 | 327,818 | ||
| rnd7 | 362,271 | ||
| a2 | 2,493,365 | 2,481,125 | |
| a4 | 2,387,075 | 2,373,778 | |
| a6 | 2,187,145 | 2,177,540 | |
| a8 | 1,948,777 | 1,943,277 | |
| a10 | 1,702,871 | 1,695,461 | |
| a12 | 1,564,101 | 1,556,513 | |
| a15 | 1,354,384 | 1,348,879 | |
| a18 | 1,243,191 | 1,231,439 | |
| a21 | 1,170,994 | 1,160,079 | |
| a24 | 1,113,400 | 1,103,200 | |
| a27 | 1,068,810 | 1,059,178 | |
| a30 | 1,079,590 | 1,070,114 | |
| a33 | 1,006,329 | 1,001,809 | |
| a36 | 790,676 | 780,495 | |
| a40 | 703,754 | 694,743 | |
| a45 | 647,069 | 640,275 | |
| a50 | 605,217 | 599,339 | |
| a55 | 572,535 | 571,631 | |
| a60 | 478,442 | 477,501 | |
| a70 | 447,715 | 441,246 | |
| a80 | 425,390 | 417,061 | |
| a90 | 416,953 | 408,331 | |
| a100 | 370,659 | 364,277 | |
| a110 | 369,729 | 366,406 | |
| a120 | 349,568 | 349,632 | |
| a130 | 361,666 | 358,570 | |
| a140 | 322,094 | 321,281 | |
| a150 | 262,654 | 258,022 | |
| a160 | 290,968 | 281,279 | |
| a170 | 286,249 | 276,968 | |
| a180 | 255,598 | 249,709 | |
| a190 | 263,048 | 260,036 | |
| a200 | 263,584 | 259,500 | |
| a210 | 255,541 | 255,186 | |
| a220 | 278,432 | 274,878 | |
| a230 | 258,329 | 256,317 | |
| a240 | 248,462 | 244,757 | |
| a250 | 262,468 | 261,389 | |
| a260 | 237,012 | 250,752 | |
| salcap (in $M) | 2,018 | ||
| Proration_years | -21,548 | ||
| Observations | 160 | 160 | 160 |
| F Statistic | 985.49 | 8,330.05 | 10,368.27 |
| R-squared | 0.9783 | 0.9996 | 0.9997 |
| Adjusted R-Squared | 0.9773 | 0.9995 | 0.9996 |
| Root MSE | 618,821 | 91,152 | 79,689 |
| In Sample MAPE | 11.7% | 1.6% | 1.4% |
| Out of Sample MAPE | 8.9% | 3.0% | 2.1% |
Interpreting rnd6 and rnd7, however, is not as straightforward. These values are larger than several of the prior round estimates because of the variation that exists in round one. Due to the magnitude of the rnd1 variable (and the fact that selections 1 through 32 are treated equivalently in the model), there are several observations with early round one selections and multiple round six and round seven selections. Without finer groupings in the early round of the draft, the statistical model attributes some of this unexplained variation to other similarities of these observations, in effect increasing coefficients of rnd6 and rnd7. The author addressed these difficulties in Model 2.
Model 1 has an in-sample (2002-2006) Mean Absolute Percentage Error of 11.7%. Its out-of-sample (2007) MAPE is 8.9%. Model 2 will utilize explanatory variables that more precisely group similar draft selections, and the corresponding MAPEs should decrease.
Modeling Rookie Cap Values with Segmented Draft Round Variables
The coefficients of Model 1 suggest that a more detailed segmenting of the draft selections is necessary to obtain more precise coefficients and better predict in an out-of-sample exercise. The author suggested replacing the seven round variables with 39 variables, creating finer groupings within each of the rounds, with particular focus on round one. For example, the variable A2 contains the number of draft picks a franchise had in a given year for selections one and two. Variable A30 contains the number of draft picks a franchise had in a given year for selections 28, 29, and 30. Likewise, variable A170 contains the number of draft picks a franchise had in a given year for selections 161 through 170. In practice, these variables are usually dichotomous in nature, but can take values greater than one due to traded picks and compensatory selections. The parameter estimates for Model 2 are shown in Table 3.
The author again estimated Model 2 without the use of an intercept term to more accurately interpret the resulting coefficients. Each of the explanatory variables is significant at the 1% level. Again, the size of the estimated coefficients decreases substantially as the draft selection variables progress from the early rounds to the later ones. The coefficients each have straightforward interpretations. Consider the variable A30. For each draft selection between 28 and 30, the franchise’s Rookie Cap will increase by $1,079,590. Although this is merely a point estimate for a small group of draft picks (28, 29, and 30), an examination of Table 1 reveals that this estimated coefficient is remarkably similar to what players in these draft positions actually received (as a salary cap charge) in 2005. Such a confirmation reinforces the author’s contention that the vast majority of rookie contracts are, in effect, predetermined.
Model 2 has an in-sample (2002-2006) Mean Absolute Percentage Error of 1.6%, and an out-of-sample (2007) MAPE of 3.0%. The model’s R-square, adjusted R-square, and root mean square error also similarly improve. It should be mentioned that the large R-squared value (.9996) may hint at over-fitting the data and insignificant observations to support the number of explanatory variables. However, the author believed that, given the very large value of R-square in Model I (.9783), the improvement in model fit is due simply to a closer approximation of the actual Rookie Cap formula used by NFL Management Council.
Although Model 2 captures the basic deterministic structure of the Rookie Cap’s creation, the author believes that an understanding of the Rookie Cap can be further refined in Model 3 with the addition of two variables – salary cap and proration years for each of the seasons. The Salary Cap coefficient (salcap) reveals that for every million dollar increase in the salary cap, the Rookie Cap increases by about $2,000. (The salary cap has increased from $71.1 M in 2002 to $109 M in 2007, an annual increase of 7.6%). The proration years coefficient (proration_years) illustrates that for every additional year available to prorate bonuses, each franchise’s Rookie Cap decreases by about $21,500. This should be expected, as each extension of the CBA details the length over which signing bonuses can be prorated. This coefficient confirms that for drafts for which signing bonuses cannot be prorated over as many years, teams receive additional Rookie Cap dollars. The addition of these variables decreased the out-of-sample MAPE from 3.0% to 2.1%.
2007 Rookie Cap Predictions
In Table 4, the author provided the actual and Model 3 predicted franchise Rookie Cap values for 2007, and their associated percentage errors. As has happened in 4 of the last 7 years, the team with the first overall selection has the highest Rookie Cap.
It is important to note that, because the model is estimated on years 2002-2006, and this period includes a single extension of the CBA (in 2006), the model’s predictive capabilities may decline in future years. However, as additional data from future drafts is available, a simple re-estimation of the model should be sufficient for predicting each franchise’s future Rookie Cap.
Table 4
| Team | Year | Actual | Model III | PE |
|---|---|---|---|---|
| Arizona | 2007 | $ 4,186,000 | $ 4,465,853 | -6.7% |
| Atlanta | 2007 | $ 6,171,000 | $ 6,070,668 | 1.6% |
| Baltimore | 2007 | $ 3,374,000 | $ 3,297,322 | 2.3% |
| Buffalo | 2007 | $ 4,061,000 | $ 4,106,553 | -1.1% |
| Carolina | 2007 | $ 4,086,000 | $ 4,040,739 | 1.1% |
| Chicago | 2007 | $ 4,043,000 | $ 3,885,367 | 3.9% |
| Cincinnati | 2007 | $ 3,512,000 | $ 3,492,858 | 0.5% |
| Cleveland | 2007 | $ 5,674,000 | $ 5,513,377 | 2.8% |
| Dallas | 2007 | $ 3,540,000 | $ 3,519,636 | 0.6% |
| Denver | 2007 | $ 2,757,000 | $ 2,735,214 | 0.8% |
| Detroit | 2007 | $ 5,824,000 | $ 5,659,836 | 2.8% |
| Green Bay | 2007 | $ 4,907,000 | $ 4,751,741 | 3.2% |
| Houston | 2007 | $ 3,814,000 | $ 3,821,366 | -0.2% |
| Indianapolis | 2007 | $ 4,336,000 | $ 4,095,229 | 5.6% |
| Jacksonville | 2007 | $ 4,916,000 | $ 4,770,846 | 3.0% |
| Kansas City | 2007 | $ 3,432,000 | $ 3,385,453 | 1.4% |
| Miami | 2007 | $ 5,367,000 | $ 5,300,443 | 1.2% |
| Minnesota | 2007 | $ 4,840,000 | $ 4,719,324 | 2.5% |
| New England | 2007 | $ 3,683,000 | $ 3,528,865 | 4.2% |
| New Orleans | 2007 | $ 3,371,000 | $ 3,427,447 | -1.7% |
| NY Giants | >2007 | $ 3,870,000 | $ 3,829,467 | 1.0% |
| NY Jets | 2007 | $ 2,653,000 | $ 2,665,692 | -0.5% |
| Oakland | 2007 | $ 6,913,000 | $ 6,592,999 | 4.6% |
| Philadelphia | 2007 | $ 3,359,000 | $ 3,391,901 | -1.0% |
| Pittsburgh | 2007 | $ 4,256,000 | $ 4,147,304 | 2.6% |
| San Diego | 2007 | $ 3,284,000 | $ 3,233,354 | 1.5% |
| San Francisco | 2007 | $ 5,420,000 | $ 5,327,401 | 1.7% |
| Seattle | 2007 | $ 3,007,000 | $ 2,962,305 | 1.5% |
| St. Louis | 2007 | $ 3,984,000 | $ 4,003,632 | -0.5% |
| Tampa Bay | 2007 | $ 6,102,000 | $ 6,112,999 | -0.2% |
| Tennessee | 2007 | $ 4,602,000 | $ 4,507,091 | 2.1% |
| Washington | 2007 | $ 3,432,000 | $ 3,478,696 | -1.4% |
| Total | $ 136,776,000 | $ 134,840,979 | 1.2% |
Conclusion:
The author has shown that regression analysis can be used to successfully model each franchise’s Rookie Cap values, in effect emulating the NFL’s esoteric formula that determines each drafted player’s salary cap allotment. While the author conceded that this formula did not determine the actual contract value of a given draft pick, in reality, generally only big name agents with clients drafted in the first half of the first round have found much success in negotiating contracts which are significantly different from the previous year.
Despite CBA language to the contrary, the coefficients estimated in these models portray a rigid formula structure that provides the basis for rookie-year contracts. In fact, it is the very rigidity in the formula that has allowed such a strong estimation of the expected salary cap costs of different draftees and a solid, out-of-sample validation of the model.
In summation, rookie contracts are not only constrained by a franchise Rookie Cap, but in general are further constrained by an agreed upon valuation of each draft pick’s worth. This valuation is not the result of market forces, the same interplay of supply and demand that determines veteran contracts, but rather is the result of a well-protected formula that artificially depresses rookie contracts.
References:
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