Measuring the Dollar Value of a Player: Part 3

In Part 1, I defined the process, the thinking and some of the math behind my approach to player valuation. In Part 2, I focused on the win-attendance-revenue relationship for various teams. In this final part, I’ll shift my attention to showing the dollar values for selected players for the 2005 season and drawing some conclusions about the results. I define player value as the amount of revenue a player generates for his team. I quantify the dollar value of a player to his team by converting a player’s on-field performance into its impact on the team’s wins, and then translating those wins into attendance and revenue.

The model includes six factors that affect a player’s value to his team:

The player’s on-field performance – I’m using WARP1 from Baseball Prospectus as the measure to convert a player’s offense, defense and pitching performance into wins for his team, although alternative measures could be used.

The effect of wins on attendance for his team – Each team has a unique wins-attendance relationship driven by market size, fan loyalty and fan expectations about the team’s performance.

The number of games the team wins – My analysis shows that the more games a team wins (up to 98 wins), the higher the “value” of the win. More additional fans attend games when the team reaches contention for the post-season. If a player is responsible for taking his team from 85 to 90 wins, he’s more valuable than if he takes his team from 70 to 75 wins.

Ticket prices – An extra 5,000 fans per game at the Mets’ average ticket price is worth nearly $400,000 more than the same 5,000 incremental fans at the Royals’ average ticket price.

The mix of broadcast and “all other” revenue – Teams that supplement their in-stadium attendance with strong broadcast revenues and all other (advertising, sponsorships, parking, concessions, etc) revenue, get a “bigger bang for the buck” when they improve their team. The Yanks have about 70% of their total local revenues in broadcast and all other, compared to less than 50% for the A’s.

The team’s revenue sharing tax – The marginal tax on a team’s revenues range from the low of 39% to over 45%+, based on how the team is classified in the 2002 Collective Bargaining Agreement. (See Andrew Zimbalist’s book , May the Best Team Win) Even a tax rate difference of 10 or 15 percentage points can have a significant impact on a player’s value. Each team pays a marginal tax, even if they separately receive a revenue sharing check from the from MLB office.

Each of these factors was included in the calculation of a player’s dollar value. It is important to note that each player’s dollar value is defined as marginal value. The model calculates the revenues of the team with- vs. without the player. In the Top 10 table below, Alex Rodriguez and his 10.2 WARP1 get credit for taking the Yankees from an 85-win to a 95-win team. If a replacement player was installed at 3B instead of A-Rod, the 2005 Yanks would have 10.2 less wins, and according to the model, $14.2 million less in revenue.

Consequently, the Mariano Rivera valuation places A-Rod back on the Yankee roster and calculates the Yankees’ marginal revenue with- and without Rivera. This means that the same portion of the revenue curve is being utilized to measure each player, reflecting the approach of truly measuring the impact of one player in isolation. I will discuss the merits of this approach, but first let’s get to the results.

The following is the Top 10 list of the MO$T Valuable Players of 2005:

Rank     Player            WARP1   Team         Value
1.       Alex Rodriguez     10.2    NYY   $14,226,561
2.       Mariano Rivera      9.1    NYY    13,018,862
3.       Derek Jeter         8.8    NYY    12,671,245
4.       Derek Lee          12.3    CHC    12,478,310
5.       Rafael Furcal       8.2    ATL    10,527,742
6.       Roger Clemens      10.4    HOU    10,392,508
7. Tie   Randy Johnson       6.8    NYY    10,205,675
7. Tie   Gary Sheffield      6.8    NYY    10,205,675
9.       Andruw Jones        7.9    ATL    10,184,500
10.      Hideki Matsui       6.7    NYY    10,073,079

It’s no surprise that six of the Top 10 are Yankees. Combine talent laden, high performing players, with one of the highest marginal revenue per win teams, and the result is a domination of the Top 10 of player value. The key to high value is the combination of the team, its win-level, and the high performance of a star player. A-Rod hit the trifecta—an economic juggernaut team, a 95-win playoff bound team and an MVP season—resulting in the highest value player for 2005.


Derrek Lee is the only member of the Top 10 whose team did not reach the post-season—a tribute to his extraordinary season and the strong economics underlying the Cubs. If Lee were a Yankee, and performed identically, he would be valued at over $17 million. By contrast, if A-Rod were a Cub, he would be valued at less than $11 million, ranking him 7th in the Top 10.

The approach of valuing each player using the same portion of his team’s marginal revenue curve could raise some concerns among those who would prefer to allocate players’ value across a broader spectrum of wins, particularly when valuing multiple players at the same time. While I have a preference of valuing each player on a truly marginal basis, I recognize the legitimacy of the debate. Some may think that the sum of the marginal values of an entire team, using my marginal approach, would lead to some unwieldy, unexplainable results.

As a quick test, I summed the marginal value of every player from four teams (with a positive WARP1 and ignored the negative WARP1 values) and compared it with the team payroll for 2005—not that payroll is necessarily any indication of “reasonableness”. Of the four teams I sampled, comparing the sum of marginal values vs. their payroll, two are greater and two are less. While this does not definitively answer the question, it may indicate that major league teams do not value players consistently higher or consistently lower than this approach.

A Hardball Times Update
Goodbye for now.


If we expand our list to include the Top 25 MO$T Valuable Players of 2005:

Rank     Player            WARP1   Team         Value
11.      Marcus Giles        8.2    ATL   $ 9,831,649
12.      John Smoltz         7.6    ATL     9,714,032
13.      Roy Oswalt          9.5    HOU     9,537,398
14.      Andy Pettitte       9.4    HOU     9,441,447
15.      David Ortiz         8.0    BOS     9,434,126
16.      Vladimir Guerrero   7.8    LAA     9,169,549
17.      Jason Giambi        5.9    NYY     9,005,143
18.      Bartolo Colon       7.4    LAA     8,725,807
19.      Morgn Ensberg       8.4    HOU     8,470,288
20.      Albert Pujols      10.7    STL     8,410,461
21.      Pedro Martinez      7.9    NYM     8,285,276
22.      Cliff Floyd         7.8    NYM     8,186,194
23.      Jhonny Peralta      9.2    CLE     8,146,908
24.      Tim Hudson          6.1    ATL     8,025,858
25.      Carlos Zambrano     8.0    CHC     8,008,808

While only four teams are represented in the Top 10, nine teams are represented in the Top 25 MO$T Valuable Players. Only five of the Top 25 did not appear in this year’s post-season—The Cubs’ Lee and Zambrano, the Mets’ Martinez and Floyd and the Indians’ Peralta. The values for Giambi and Hudson benefit the most from the strong economics of their teams, as many players from smaller market clubs have stronger on-field performance for 2005.

One factor that I would like to address is the current revenue sharing system. In its present form it has a dramatic negative impact on player value and very little positive impact, if any, on competitive balance. Since each team pays a marginal tax (and the poorest teams at a higher marginal rate), its primary function is to depress the marginal value of players to a team. Just examining the top end of the player market, the above analysis shows that 10 players have a value greater than $10 million in 2005. Without a marginal revenue sharing tax, A-Rod would have generated $23.5 million in value for the Yanks, and 56 players would have generated value in excess of $10 million for their teams.

The downward pressure on salaries is not a necessary consequence of any revenue sharing system. It is a design flaw in the current system—or possibly intentional if you believe the owners’ motivation in implementing revenue sharing is to reduce players’ salaries. The current system reduces the marginal value of a win to all teams, but reduces it more to the poorest teams.

An alternative to the current system would be to tax teams a fixed dollar amount each year based on their revenue opportunity—their market size or other relevant variables—rather than actual revenues. Such a program would be more efficient at moving dollars from the high resource base teams to the low resource base teams, without sapping the economic motivation to grow revenues. The ideal program would also provide a bonus for “wins” by the disadvantaged teams. This would provide a further incentive to invest in payroll, scouting and development, by increasing the marginal value of a win to the poorest teams and help them compete more effectively in the free agent market.

Let’s look at the Top 10 performers (as measured by WARP1) who were not on the Top 25 MO$T Valuable Player list:

Rank     Player            WARP1   Team        Value*
 -       Dontrelle Willis   11.4    FLA    $4,791,947
 -       Jason Bay          10.0    PIT     2,708,296
 -       Todd Helton         9.6    COL     5,274,055
 -       Johann Santana      9.3    MIN     4,136,380
 -       Mark Teixeira       9.3    TEX     2,639,471
 -       Brian Roberts       8.9    BAL     1,517,396
 -       Jim Edmonds         8.9    STL     6,944,696
 -       Miguel Cabrera      8.7    FLA     4,306,355
 -       Brian Giles         8.4    SDP     3,615,201
 -       Kenny Rogers        8.1    TEX     2,344,811

* For players whose teams had low win totals, a modification was necessary to establish a value for the player. Since my model does not impute marginal value below 70 wins, for low win teams, I credited a player with the lowest value wins equal to his WARP1.

The dramatic effect of the team on a player’s value is evident when comparing Brian Roberts and Edmonds. With the equivalent on-field performance, there is a difference of more than $5 million in their marginal value. The Edmonds-Roberts differential is attributable to two factors: St. Louis’ league leading 100 wins vs. a ho-hum 74 wins for the Orioles; and much higher marginal revenue per win for the Cardinals. The bar chart below shows the marginal value of the last win for the four teams represented in the Top 10 MO$T Valuable and four teams that had high WARP1 players, which did not qualify for the Top 25 MO$T Valuable.


An interesting and topical case study is Rafael Furcal, who is currently testing the free agent market. If Furcal can perform at or near his 2005 performance over the next four years (which could be asking too much), his value to the Braves would be in the neighborhood of $45 to $50 million. (This assumes modest increases in ticket prices and other revenues over the next four years). The only other teams that 1) have a space for a starting shortstop and 2) could compete financially with the Braves are the Marlins and potentially the Cubs.

The Marlins have a steep sloping revenue curve (similar to the Yankees), meaning that they need to be in contention for the post-season to drive significant revenue growth. If the Marlins replace Burnett and assemble enough talent to have a legitimate chance at 90+ wins, they could justify a value comparable to the Braves’ value for Furcal. Conversely, the Cubs have a relatively flat revenue curve due to their limited capacity and strong base of loyal fans, even in poor performing seasons. Furcal’s value to the Cubs would be several million dollars per year less than his value to Atlanta or Florida, but this gap could be mitigated if Furcal proved to be the missing link to carry Chicago into the post-season.

In my latest attempt to measure a player’s dollar value, I have been able to quantify many of the relevant variables that attribute a team’s marginal revenues to a player. Clearly there are some unanswered questions, such as the “bonus value” or carry-over effect of reaching the post-season or winning a World Series, or the value of a star player who creates a special bond with local fans, creating revenue beyond his playing performance. While not part of the base model, these effects can be customized to the analysis of a specific player or team.

At a time when sabermetric tools can diagnose a player’s performance better than an MRI can detect a rotator cuff tear, it is reasonable to think that player dollar valuation is a void that needs to be filled. This comprehensive, analytical approach to estimating the dollar value of a player to his team could arm GMs with additional information to help manage the largest component of their cost structure—player salaries. In today’s game, information and insight can be the difference between winning and losing.

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