﻿ Measuring the Dollar Value of a Player: Part 2 | The Hardball Times

# Measuring the Dollar Value of a Player: Part 2

In Part 1, I defined the process, the thinking and some of the math behind my approach to player valuation. In this part of the series, I’ll focus on the team-to-team differences in the value of a win and discuss how the attendance and revenue curve estimates impact the value of players. There are four key drivers affecting a player’s value:

• The player’s on-field performance
• The responsiveness of his team’s fans to changes in winning percentage
• The relative success of his team—generally, improving an 85-win team is more lucrative than improving a 72-win team
• The strength of the revenue streams his team has established—the level of ticket prices, concessions, parking, advertising and sponsorships

The attendance curves below show changes in per game attendance for selected teams at various win levels. For example, the Angels would draw about 10,000 more fans per game during an 87-win season vs. a 70-win season. At the same 87-win level, the Twins would draw an incremental 8,400, the White Sox +7,600, The A’s +5,600 and the Yanks +4,400. (While these numbers are an estimate of how attendance responds to winning, the baseline attendance levels—attendance for a 70-win season—of these teams are very different. The Yanks baseline level of attendance is over 40,000 per game and is more than double that of Oakland, Minnesota and the White Sox.) Even though the Yankees appear to gain less incremental attendance from winning, this graph tells only one piece of the story. Don’t feel sorry for the Yanks yet, as later I’ll show how higher ticket prices, stronger revenue streams and enormous broadcast revenues ultimately place the Bronx Bombers in a dramatically advantaged position in terms of player value.

Incremental or marginal attendance is only one piece of the “value” story. Dissecting these estimates further, we can look at the portion of the curve a player affects. In valuing a player who improves his team by 5 wins, it is important to consider the team’s win total. Below is a bar chart of the models’ estimates of attendance gains that result from 5-win improvements. Each bar represents the increase in per game attendance from the specific 5-win improvement.

Of the five teams selected, the Yankees and Angels have the steepest curves—the change in attendance increases (or decreases) at a greater rate as the win level increases (or decreases). It is also interesting to note that the Yanks have the lowest gain in attendance when “improving” from 77 to 82 wins. While most teams’ fans consider this improvement worthy of additional support, Yankee fans’ lofty expectations cause them to make little distinction between 77 or 82 wins, reflecting their “post-season or bust” attitude. Oakland has the flattest attendance curve—there is no more than a 400 fans-per-game difference across all 5-win increments. At the other extreme, the Yanks nearly triple their attendance increase by being in the “sweet spot” (92 to 97 wins) on their attendance curve.

From Attendance Gains to Marginal Revenue

Translating the per game attendance gains into revenue yields a different picture. The Yankees emerge as the team that converts playoff contention win totals (87+ wins) into the highest revenue gains. The chart below also shows the White Sox generating marginal revenue at a greater rate than the Twins and A’s. The efficient conversion of attendance gains into revenue gains for the Yanks and White Sox is partly attributable to ticket prices approximately 50% higher than the other three teams listed.

The Yanks also benefit from the highest value broadcast arrangement of any MLB team. In order to quantify teams broadcast revenue, I had to account for teams which have created their own regional sports network, or teams owned by a media entity that may leave a portion of the “fair value” of their broadcast rights on the income statement of the media company, rather than the ballclub. The Yankees’ YES network, the Red Sox’ affiliation with NESN, among others, can be considered to fall into this category of teams that have “related party transactions”. (I relied heavily on the detailed treatment of this topic in Zimbalist, “May the Best Team Win”). Where teams have a relationship with a media entity, the model assumes a somewhat higher portion of broadcast revenues are variable. If a team improves and attracts more viewers and commands more advertising dollars, the model reflects a more efficient pass-through to the ballclub, instead of the upside being “pocketed” by the broadcast entity. The end result is that teams strong enough to start their own regional network, get the added benefit of also profiting from an upside in revenues from improvement in the team— boosting their marginal revenue per win. This is consistent with the perception that the Mets are prepared to aggressively invest in payroll to improve the team on the eve of the launch of their own network.

Finally, to convert the model’s attendance results into total local revenue (attendance + broadcast + all other), I also had to make assumptions regarding the amounts of broadcast and “all other” that would vary with attendance—the classic fixed vs. variable dilemma. From speaking to several experts, the general conclusion is that broadcast revenues are largely fixed (90%+ fixed and up to 10% variable) and therefore, less dependent on a team’s performance in any given year. Categories like parking and concessions, however, move in tandem with attendance.

The Value of a Win

So how much is a win worth? While I will explore this more in Part 3 of this series, there is a wide range from highest to lowest team. Since not all wins are created equal, I’ll use the 88-win level as a point of comparison. The highest marginal revenue team (after the revenue sharing tax is deducted, which I will discuss in more detail in Part 3) is the Braves at over \$1.3 million for the 88th win, with the lowest being the Orioles at less than \$300,000 for their 88th win.

Another way to look at the marginal revenue estimates is to calculate the value of each team’s last win. For 2005, that means the Yankees’, Angels’, and Red Sox’ 95th win, the Mets’, Marlins’, and Twins’ 83rd win. After the revenue sharing tax is taken from the gross revenue estimates, we’re left with the following marginal value of a win for the above mentioned teams for 2005:

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It is important to note that the model defines “value”—the value of a win and the value of a player—as marginal value. Each team also has a baseline level of revenue which does not fluctuate based on the team’s on-field performance. These baseline revenues, defined as the amount of revenue a team is likely to generate in a season even if it wins 70 or less games, reflect the value of the team as a “brand”, or the popularity of baseball in their respective market. (In the short-run, a poor performing season or two should not affect the baseline revenue estimates. However, over the long-term, a team’s baseline revenues are not a “given”. A string of poor performing seasons can erode a team’s equity with its fans and lower its baseline revenues.) Baseline revenues vary widely from team-to-team with the Yankees, Red Sox and Cubs at the top end of the scale, with baseline revenues of \$200 million or more. At the other end of the scale are the Devil Rays, Royals, Twins and A’s with baseline revenues (excluding any payments they would receive from the revenue sharing or luxury tax pool) equivalent to about 25% of the top tier.

Translating Team Revenue into Player Value

Using Vladimir Guerrero as an example, let’s look at his value to the Angels for the 2005 season. Guerrero’s WARP1 value (from Baseball Prospectus) is listed at 7.8 for the 2005 season&mdahs;implying that Guerrero’s offense and defensive skills were responsible for 7.8 of the Angels’ 95 wins. In other words, if the Angels gave his 594 plate appearances and innings in right field to a replacement player, they would have won only 87 games. By referencing a table of revenue estimates, derived from my regression model, I can calculate the amount of additional revenue attributable to Guerrero. This estimate includes attendance revenue and other revenues at the ballpark (parking, concessions, etc) and a small percentage of broadcast revenue, all of which is adjusted for an estimate of the revenue sharing tax. The dollar value of the player also takes into account the increasing value of each win—the 95th win is worth more revenue than the 90th win.

Working backwards from the Angels’ 95th win, Guerrero’s WARP1 of 7.8 earns him credit for wins 89 through 95 and partial credit for the 88th win. Taking all of these factors into consideration, the estimate of Vlad’s value to the 2005 Angels is \$9,169,549. If we look at the 2004 season, Guerrero’s first year with the Angels, WARP1 credits him with 9.1 of the Angels 92 wins. Using 2004 ticket prices and making all the necessary adjustments, the model says that Vlad was worth \$10,298,351 to the Angels for his 2004 AL MVP season. In both instances, these numbers do not account for any additional revenue form reaching the post-season, something that Guerrero was instrumental in helping the Angels achieve in his first two years in Anaheim.

In Part 3, the final part of this series on player valuation, I will show a ranking of the top value players of 2005 and discuss the degree to which the Yankees and other well endowed teams maintain an advantage in signing and justifying high priced talent.

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