Defining Player Value
With the development of dozens of insightful and innovative statistical measures, baseball’s forward thinking general managers and managers are working to create an edge for their ballclubs and get the most from the talent they put on the field. The weakest link in the analytical chain is the ability to place an objective dollar value on an individual player’s performance, measured by his contribution to his team’s revenues.
While others may define value based on relative salaries of players at the same position, or free agent contract values or arbitration settlement figures, I am defining player value as the amount of revenue a player generates for his team. By converting a player’s on-field performance into his impact on his team’s wins and then translating those wins into attendance and revenue, I quantify the dollar value of a player to his team.
My model answers the question, “How much more revenue do the Angels earn because Vladimir Guerrero is their right fielder (and sometimes designated hitter)?” The model estimates the Angels’ revenue with Guerrero’s 594 plate appearances vs. what the Angels’ revenue would have been without Guerrero and with a “replacement player” playing right field and taking his 594 plate appearances.
The first half of the player valuation equation—measuring player performance in terms of its impact on team wins—has been the subject of much debate in the sabermetric world. As a result, numerous measures have been developed by innovative statisticians to convert a player’s offensive, defensive, and pitching stats into team wins.
The second half of the player valuation equation—converting a team’s wins into a team’s dollar revenue—has received far less attention by the math experts. While there has been much academic research to determine the impact of winning on attendance, I am unaware of any comprehensive, team-specific analyses which quantify the value of a player to his team.
How could a player valuation analysis help a major league team? Just as a manager can adjust his on-the-field strategy by using statistical tools like the expected runs matrix, general managers and owners (and player agents) could now determine if a player’s “price is right” by using the output of a comprehensive player valuation model. It provides one more tool in the arsenal of the general manager to play the “what if” game before making an irreversible decision. The model can convert the results of innovative sabermetric decision tools into the bottom line common denominator of dollar value to the team.
Process of Assigning a Dollar Value to a Player
The objective is to add numbers to the thought process that a general manager intuitively follows when determining how to assemble and compensate talent. By quantifying the process, a general manager can divide a complicated thought process into tiny, digestible components which reduce the risk of overlooking any factor that would ultimately make a difference in a free-agent signing, a trade decision, an arbitration submission, or a waiver claim. This is how the process works:
WARP1 attempts to measure a player’s offensive, defensive and pitching contributions to his team’s wins. By anchoring the baseline to “replacement level,” it simplifies the valuation process. Replacement level is considered to be a widely available commodity, such as a journeyman Triple-A player, and has an objective dollar cost—the major league minimum salary.
Much of the past statistical work in this area has merged the data across all teams and tried to define the relationship between attendance and wins based on market size. That method ignores the fact that even teams in the same market have different fan loyalties and responses to its team’s success. Another important nuance of my analytical framework is its focus on capturing the non-linear relationship between wins and attendance—not every incremental win is of equal value. This is discussed in more detail below.
If you wonder why some small market teams are reluctant to reinvest their revenue sharing windfall into players’ salaries, look no further than the revenue sharing tax. A team with a 47% tax needs to grow gross revenues by nearly $19 million for every $10 million it spends, just to break even. To make matters worse, the current CBA calls for the small market teams to pay the highest marginal tax rate. This ill-conceived revenue sharing program and its tax have the dramatic effect of directly reducing the marginal value of players, by reducing a team’s dollar value of a win by 39% to 47%.
Another factor influencing a player’s value that is not presently included in the model is the carryover effect of reaching the post-season, or winning the World Series. When a team reaches the post-season (particularly for several consecutive years) there seems to be a carryover effect that raises the profile of the team in its city and serves as a boost to attendance. The Royals experienced this in the early ‘80s, the Blue Jays in the early ‘90s, and the Indians in the late ‘90s. In these instances wins alone do not fully explain the surge in attendance. Despite this premise, the data and modeling have yet to provide a consistent confirmation of the value of reaching the post-season.
One effect of reaching the postseason that can be quantified is the impact on ticket prices. Dating back to 1990, teams reaching the postseason raised their ticket prices the following year by an average of 10.1%, compared to 5.9% for teams that did not reach the post-season. World Champions averaged a 10.4% ticket price increase in the year after they earned their rings. I continue to work on a method to quantify the postseason carryover effect, as it can have a large effect on player valuation, particularly if the player in question puts a team over the threshold (i.e., takes a team from 88 to 95 wins and puts his team into the playoffs).
Also, the model does not explicitly include the rare situation where a star player has “gate appeal” and the capacity to attract fans to the ballpark beyond his impact on team performance. This effect is easier to measure for a starting pitcher rather than an everyday player, as his appearances are isolated. The gate appeal factor is not part of the base calculation of the player valuation model.
By building a player valuation model for each team, and factoring in the impact of the revenue sharing tax, I can convert the playing performance of any player into the marginal dollar value to his team – in a sense, the ceiling of what the player is worth to the team for that season. Alternatively, a general manager can use the model by plugging in his performance expectations for future years and thereby generating a marginal dollar value for any player.
The Relationship Between Winning and Attendance
The key missing link in the chain to place a dollar value on individual playing performance is quantifying the relationship between a team’s on-the-field success and their attendance. I used multiple regressions to quantify this key relationship for each team. Five key hypotheses were confirmed (sometimes through trial and error) by the results of my modeling.
1) Winning affects attendance and a team’s revenue.
The data verifies that fans respond to winning. For every team, the model shows that fans are inspired and motivated to attend their team’s games based on the success of the team—the more a team wins, the higher the attendance. However, this relationship does not hold up on the low end of the win range. I validated the assumption that an improvement in wins, below 70 wins, did not generally have a statistically significant impact on attendance. We can think of the 70-win threshold as representing a baseline level of attendance for each major league club.
2) The effects differ not only by market, but also by team.
Different income levels, entertainment options and competing sports in each MLB market, affect the attendance-win relationship. Even within a market, Cubs and White Sox fans respond differently to their team’s on-the-field success, as do Yankees and Mets fans, Giants and A’s fans and Dodgers and Angels fans. Each team is a “regional brand,” with unique brand equities and fan loyalties. It was important to develop individual models for each ballclub, to quantify the relationship for each team and its fans, but equally important to maintain a consistent framework across all the models.
3) Current year attendance is impacted by both current year and previous year winning percentage.
Fan interest in the team and demand for season tickets and advance ticket sales can be greatly influenced by the previous year’s performance. However, as the season evolves and fans form perceptions regarding the quality of the team, current performance will become a primary driver of attendance. To capture this effect, my models include the combination (equally weighted) of previous and current year wins.
4) The attendance-wins relationship is non-linear … improving from 85 to 90 wins, will benefit attendance more than improving from 70 to 75 wins.
When a team is in contention for a postseason spot, fan interest and attendance rise disproportionately. The hardcore fan is more likely to attend more games and more casual fans are jumping on the bandwagon. While an improvement from 70 to 75 wins still has a positive impact, it is less than when a team approaches contention. To capture this non-linear effect for each team, I estimated the attendance-win relationship by converting wins to an exponential power based on which exponent yielded the best fit.
5) Wins in the “sweet spot” have the highest “value” to a team.
Wins beyond the high end of the sweet spot diminish in value. This sweet spot is approximately 85-98 wins. Any improvement in the team within this range generally has the highest impact on attendance. The bottom end of this range begins to legitimize the club as a post-season contender. Beyond the top of the range (beyond 98 wins) a team generally decreases the suspense of their appearance in the postseason and while they may attract more fans, they do so at a lesser rate.
The Yankees in 2004 and 2005 help illustrate this point. In 2004, the Yanks won 101 games and earned a post-season spot by nine games (92 wins would still have won the Wild Card). As a result, post-Labor Day attendance, when their fate was already decided, declined significantly, averaging 7,000 fewer fans for the last 12 home games. By contrast in 2005, when the Yanks did not clinch a playoff birth until October 1, their post-Labor Day attendance increased 1,500 fans per game over their pre-Labor Day average. In this specific case, the Yankees actually generated more attendance revenue by winning 95 vs. 101 games the previous season.
The graph below is an example the model’s estimate of the attendance-wins relationship for the Yankees. The attendance gains from 70 to 80 wins are modest, but accelerate as the season win total reaches the mid-80’s and through 98 wins. Beyond 98 wins the shape of the curve changes and attendance increases, but at a lesser rate.
Examining five-win increments we see the shape of the curve reflected in the model’s estimates:
Improving from 77 to 82 wins +1,453 fans per game Improving from 82 to 87 wins +2,219 fans per game Improving from 87 to 92 wins +2,983 fans per game Improving from 92 to 97 wins +3,749 fans per game Improving from 97 to 102 wins +2,096 fans per game
Other Factors Influencing Attendance
In order to quantify the relationship between winning and attendance, a number of other factors had to be included in my models. The variables included the impact of new stadiums, the effects of the various work stoppages, a “new franchise effect” to account for the attendance levels in the early years of an expansion club, when fans are excited about the new game in town and have little expectation of winning.
It was also important to account for unique, team-specific events such as the record setting home run chase of Mark McGwire in 1998, which attracted fans for reasons other than the quality of the ballclub. The most unexpected result of my modeling efforts was the absence of ticket price as a determinant of attendance. I am not suggesting there is no impact, as fans clearly have some degree of price sensitivity, but it consistently failed to be a statistically significant variable in my attendance models.
Part 1 was intended to be an introduction to the concept of player valuation and an overview of my conceptual and statistical approach. In Part 2, I will focus on team-to-team differences in the value of a win and discuss the estimated revenue curves for selected teams. In Part 3, I will show specific player valuations and a ranking of the highest value players in 2005—including the MO$T Valuable Player in each league.