|Valuing Professional Sports Franchises: An Econometric Approach|
|Valuing Professional Sports Franchises: An Econometric Approach
by Kelly Smith
Kelly Smith for The 2004 Moffatt Prize in EconomicsSports franchises often boast values of striking magnitudes. The Yankees, for example, are nearing the $1 billion mark. Football teams have an average value of $530 million and even the less popular and less prosperous NHL teams exceed $150 million on average. I find these numbers astonishing, but at the same time, ambiguous. What exactly determines the value of a professional sports team? What assets, qualities, and accomplishments account for the differences between the values of teams? How big of an impact do the venue, ticket price, concession sales, broadcasting revenue, and performance make in terms of overall value? Furthermore, do these variables interact with value differently among leagues? Can revenue sharing schemes, payroll limits, and unique features of the sport account for these differences? In this paper, I use econometric analysis to model team values for four leagues: the NFL, NBA, MLB, and NHL.
Approaches to Valuation
The value of any business is based on its potential for future earnings. There are three common approaches to valuation. First is the cost or asset-based approach, centering on the principle that an investor will be unwilling to pay more for an asset than it would cost to obtain another asset that produce the same future cash flows. Common measures of cost are replacement cost and reproduction cost-both indicating the amount an owner is willing to pay to obtain the same cash flow from the asset. For professional sports franchises, the cost approach is not as helpful or reliable as the other two valuation methods. The prevalence of intangible assets in these franchises makes the replacement and reproduction cost approaches inadequate for future cash flow or value predictions.
The market/sales comparison uses principles of competition in a free market and relies on the assumption that, in an equilibrium, the price of an investment will apply to similar investments, with some modification. Looking at actual data from sales and other transactions, an analyst can make comparisons by noting the differences between the franchise to be valued and other recently traded franchises. Important for consideration are market size, location, demographics, venue ownership or lease terms, venue revenue, and local television agreements. This approach to valuation is made more difficult because of a lack of available data on comparable franchises and variability in value adjustments.
With the income approach, the value of the team is based directly on the present value of the expected net cash flow earned for the duration of the enterprise. The most common estimate of value based on future cash flow uses the discounted cash flow method. By making assumptions about how different value drivers might contribute to future earnings, an analyst can work backward and make a calculation of present value. Both the income approach and the market/sales comparison often are used to make calculations about the value of sports franchises. In addition, both of these approaches employ the several different factors I identified as possible contributors to value, such as stadium attributes, ticket sales, and team performance.
Developing a Model
Forbes Magazine publishes independently-determined valuations of all franchises in the NFL, NBA, MLB, and NHL each year. I started my analysis of value with these data for the 2001-2002 seasons. From that point I collected data quantifying the various factors I thought might affect value such as the revenue of the team, the payroll, the age of the team's home stadium, home attendance, ticket price, and the number of television-owning households in the major metropolitan area, among other variables. I collected these data for every team in all four of the major leagues. I applied simple regression analysis and developed a model to explain differences in value within a league, with one model for each league. From that point I sought to work out explanations for the coefficients in each league model and explain what varied between models.
I collected data for 19 different variables for the 2001-2002 seasons of professional football, basketball, baseball, and hockey. The variables, the short-hand references I used in my tables and the data sources are listed on page A of the appendix. The full data tables are located at the end of this paper on appendix pages B to E.
Taking a quick glance at the data gathered, I immediately noticed a few characteristics. The average NFL franchise is significantly more valuable than franchises in the other three leagues; NHL teams tend to be on the low end. Average revenue follows the same pattern, with NFL teams the highest, then Major League Baseball, followed by the NBA, with NHL at the end with average yearly revenue of $69 million. For the most part, ticket prices in all leagues have a common average between $40 and $50 dollars. However, MLB games are much cheaper at $18 for a ticket, but average yearly attendance is quite a bit higher at 2,264,707. The next highest yearly attendance average is for NBA franchises at 695,620. It is important to note that baseball teams play many more games than teams in other sports, in particular football with a regular-season schedule of 16 games, which would give its franchises the highest per-game attendance average. A summary of some of the variables and their average values is listed in the table at the side.
Construction of the League Models
The first thing I noticed when I began to develop league models was that revenue and value are very highly correlated. The correlations follow a close linear relationship and the coefficients in regressions of value on revenue produce estimates of revenue multiples. I performed regressions of value on revenue, and the log of value on the log of revenue. These regressions are available in full form on appendix pages F and G. When I attempted to include other independent variables in a regression of value, the high correlation between value and revenue was overwhelmingly significant, whereas when they were included, no other independent variables had statistically significant coefficients. These regressions are available on appendix page H. Furthermore, there was multicollinearity between revenue and most other independent variables.
One explanation of why my regression analysis produced near-perfect correlation between revenue and value is that my value and revenue data is from Forbes Magazine, and Forbes uses a multiple to convert revenue to value. This method explains the correlation, but also indicates that revenue and value have a sufficiently strong linear relationship to allow Forbes to use a multiple to make accurate value predictions from revenue. Nonetheless, it is safe to assume that I cannot put perfect faith in the level of correlation between value and
revenue that my analysis predicts.
Another challenge I faced was the regression results for the NFL. As demonstrated by the graph on the previous page, the scatter points for football are less clustered around a linear trend-there is a lot of room for variation in an expression of the relationship. Yet, this lack of linearity is not surprising and may be driven by a couple of factors. First, the NFL teams play a short season, and the room for variability in revenue may be due to the high stake of each game played. If a team plays 16 games, all revenue derived from one game (broadcasting, gate receipts, concession sales, performance effects, etc.) determines nearly 1/16th of the team's total revenue-increasing the probability of randomness. Second, there is a higher level of revenue sharing in the NFL than there is in other leagues. The variation among teams should be more even when the value of the team has less to do with revenue factors. I did try to include other independent variables in my regression of the log of value on the log of revenue (see table above), but was unable to come up with any models with statistically significant coefficients for anything but ln(revenue). In the long run, the variability should smooth. If I were to use several years' worth of data, I expect that the relationship between revenue and value should be more pronounced. With time-series data, random outcomes would become less significant, allowing consistent trends to become apparent.
Revenue as the Dependant Variable
Because it was difficult to determine any predictors of value other than revenue, I decided to use the data I had collected to model determinants of revenue. The original model I came up with worked fairly well for all four leagues. I regressed the log of revenue on championship wins (wins), the log of the team's age (TeamAge), the log of attendance (Attend), the log of the number of television households (TVs), the stadium age, ticket price, and the fan cost index less the price of tickets (FCI-tickets). An example of this model, using the data for the NBA, is at the right; the rest of these initial models are in the upper left-hand corners on pages I through L of the appendix.
From the beginning, each model I developed had a fairly significant adjusted R-squared value and at least two statistically significant coefficients. I discuss each league model in detail shortly.
One piece that the initial model was lacking, however, was a variable that might determine whether or not franchises receive a return to investments in players, how significant this return is, and what, if any,
differences there are between leagues for player investment. I added the franchises' payrolls as an additional variable in the regressions. The regressions with payroll included are located on the upper left-hand corners of appendix pages I through L. With the addition of the payroll variable, some aspects of the original model changed. In all cases the adjusted R squared value increased. Nothing exceptionally notable changed in the model for the NFL and the coefficient on ln(payroll) was not significant. The coefficients on payroll were significant at a 10 percent level in the NBA and NHL and at a five-percent level for MLB. What was striking is a jump in the coefficient on stadium age in the NBA between the model without payroll and the one with it (see table to the left). The coefficient, approximately zero in the no-payroll model, became .010 in the model with payroll, and the p-values changed from .895 to .000. This change seemed to indicate that stadium age actually has a positive effect on revenue-a one-year increase in the age of the stadium would lead to a 10 percent rise in revenue. However, this result strikes me as unlikely; I think what it indicates is a high correlation between the stadium age and payroll, which may have been caused by a few strange outliers that the model seeks to explain. The same behavior occurs in the NHL and NBA models, but to a lesser extent.
Additional Team Dummy Variable
I was also concerned that the model I chose would not accurately represent the effect of TV households or attendance on value in cities with more than one team. I added a dummy variable to all four league models (Another team in city =1) to control for these situations. All of these models are located on the lower left-hand corners of appendix pages B through E. The coefficient on this dummy variable was not significant for the NHL or MLB, and it was barely significant at the 10 percent level for the NBA. However, the results for the NFL were interesting. The dummy variable had a coefficient of -.177 and a p-value of .016. This result indicates that, with a two-percent chance that the coefficient was randomly generated, a team's revenue in the NFL will decrease by 17.7 percent if the city has
an additional team. This outcome is especially striking because of the considerable level of revenue sharing in the NFL. The adjusted R squared value for the NFL regression also increased noticeably from .475 to .585. However, the addition of the dummy variable did not have a dramatic effect on the coefficients for TV households or attendance. The TV households coefficient changed from negative to positive (which makes more sense), but it was not statistically significant before and it became even less so after the addition of the dummy variable. The coefficient for attendance became more significant, nearing a 10 percent level, but the coefficient did not change dramatically. What I think is evident between the two regressions is that there were small changes in the model after the addition of the dummy, which made the model more explanatory of revenue among NFL teams.
Nevertheless, a problem arises when I add the dummy variable for an additional team. A large city is more likely to have more than one team of the same sport. Thus, the dummy variable should tend to be highly correlated with the TV households variable, which is proportional to a population. On page M of the appendix there are several correlation matrices. The level of correlation between TV households and the dummy is substantial and this multicollinarity biases the coefficients.
The last adjustment I made to the league models was removing the FCI-tickets variable (FCI-tickets is the fan cost index less the cost of tickets). I noticed that the variable had some degree of correlation with most of the other dependant variables and did not behave predictably. My hypothesis is that the variable is endogenous: it is determined by the factors that determine revenue. The final models that I settled on are located in the lower right-hand corners of appendix pages I through L.
As I discussed earlier, the NFL model gives me the most trouble because the correlation between revenue and value is not as close as it is for the other leagues. In addition, there is a high degree of variability in the NFL in terms of season performance from year to year as well as widespread revenue sharing. These features make it difficult to determine from one year's data if there are any factors that make a significant impact on the value of a single NFL franchise.
In this regression there are four coefficients that are statistically significant at a five-percent level: the coefficients for Wins, ln(Attend), Stadium Age, and the dummy for an additional team. The coefficient for Wins is .046, which means that an additional championship win in the history of the team increases the revenue of the team by 4.6 percent. A one-percent increase in the home game attendance for the year increases revenue by .28 percent. An additional year in a stadium decreases revenue by a marginal .2 percent, and if another football team resides it the city a franchise should experience a 19.7 percent decrease in revenue. In the NFL, franchises share almost 70 percent of their revenue including gate receipts, national television contracts, and merchandising and licensing revenue, so it is somewhat surprising that the dummy variable for an additional team should have as much of an impact as it does.
On the other hand, much of the day-of-game revenue is split between the home and visiting teams, and not redistributed among all teams. If one or both of those teams can manage to draw a large crowd then each team should realize a gain, even if it is only half of the total revenue generated. Day-of-game revenue splitting would allow variables like wins, stadium age, attendance, and the additional team dummy, to have an impact. If a team has more championship wins, that team might be more of a crowd-drawer both at home and away. The age of the stadium and the presence of another team will interact negatively with attendance and thus, gate receipts. Similarly, the attendance is positively correlated with game-day revenue, even if the team only receives a portion.
In addition, there is multicollinearity between stadium age and the dummy variable, which would bias the coefficients. Given that the stadium age is making a small, negative impact, it is probably the case that the coefficient for the dummy variable is overstating the effect of an additional team.
The payroll variable does not have a statistically significant coefficient, but this result is not surprising. Due to the revenue redistribution, the benefits that a team would accrue by playing a winning season are significantly mitigated. Thus, there isn't much of a revenue return to investments in players. In addition, the hard salary cap of the NFL does maintain a fairly uniform expenditure among franchises on players. An investments made on an individual player require reshuffling of account ledgers more than it poses an additional expense, and shouldn't lead to a noticeable increase in the aggregate players' salaries value.
The NBA model seems to explain the determinants of revenue quite well. The adjusted R squared value is high, .829, and four of the coefficients are statistically significant. Basketball and hockey teams keep their own home gate receipts, which should explain why several of the coefficients are meaningful. The coefficient for the log of attendance, .439, is significant. A one percent increase in the attendance at home games increases revenue by .439 percent. The coefficient for ln(TVs) is also positive and significant; a one percent increase in the number of television households will increase franchise revenue for the year by .142 percent. This relationship may have a number of causes. First, as the number of TV households
increases there are more people available to attend games in person. Second, the more populous the city is, the more local television revenue the team will generate. Third, a large local fan base can have a positive effect on merchandising and licensing revenue. The presence of another team sharing the city will attenuate the impact that population factors can have on revenue. The coefficient for the additional team dummy is -.147, and is significant at a 10 percent level. This coefficient indicates that when a team shares a city, its yearly revenue decreases by 14.7 percent.
The ticket price is significant as well, and likely interacts with the attendance according to a demand function. Nonetheless, the model suggests that if the average ticket price increases by a dollar, the NBA franchise's revenue will increase by 1.1 percent. Although championship wins are not significant, there are positive returns to basketball teams for investing in players-which makes sense given the large salaries for players in the NBA. The coefficient on the log of the payroll, with a p-value of .090, is .211; a one percent increase in the team's payroll will increase revenue by .21 percent. What is also interesting is that how storied the franchise is does not seem to be making a difference in terms of revenue. Both the team age and number of championship wins are not statistically significant.
In the MLB model, attendance and ticket price are statistically significant at the five-percent level. Both factors contribute to gate receipts and other revenue sources. The coefficient for ln(Attend) means that if the attendance for the year increases by 10 percent, the franchise's revenue will increase by .298 percent. A one-dollar rise in the average ticket price raises revenue by 1.7 percent. Although these coefficients are small and suggest a minimal impact on revenue, they do indicate that there is some benefit to a team for continuing its season as long as possible to keep attendance revenue flowing. Like the NBA and the NHL, the lack of NFL-style revenue sharing makes playoff participation important. However, there is a nominal level of revenue sharing in baseball, 10 to 20 percent of game-day revenue goes to the away team. According to estimates from Kane Reece Associates, Inc., printed in "Chapter 19: Sports Team Valuation and Venue Feasibility" of The Handbook for Advanced Business Valuation, published in 2000, playoff revenue constitutes two percent of revenue in the MLB. It is four percent in the NBA and NHL, but 0 percent for NFL teams. If going to the playoffs will increase a team's revenue, then franchises should have more incentive to invest in players and such investments should have a positive affect on revenue streams. This is the case for the NBA, MLB, and the NHL according to my models (I will discuss the NHL momentarily). In each model the coefficient for the player salary variable was statistically significant. For baseball, the coefficient is .177 and is significant at a 10 percent level. According to the estimates from Kane Reece, the importance of playoff performance is greater in the NBA and NHL than it is in MLB. The coefficients that I have for payroll for the NBA and NHL, .211 and
.375 respectively, support this distinction-they are both greater than the payroll coefficient for MLB.
The payroll variable is problematic. Although payroll investments seem to have a positive impact on revenue streams for the NBA, NHL and MLB, there is more happening beneath the surface. What the value numbers might pick up, and revenue numbers will miss, is the tax benefits a franchise owner reaps from player contracts. An owner is allowed to count player contracts as 50 percent of a team's value and then amortize that value, count the loss with his personal income, and significantly reduce his income tax liability. The revenue/payroll relationship would show none of this value, but it is reasonable to assume that tax benefits of expensive player contracts will augment what someone is willing to pay for a franchise-which is also true for the other three models.
The NHL model follows the same pattern as the models for the NBA and MLB, although the adjusted R squared value is a little lower at .715. Like the previous two models, ticket price (.009), ln(attend) (.632), and ln(payroll) (.375) are significant; the first two coefficients are significant at a 10 percent level, the last at five percent. It is not surprising that the NHL, NBA, and MLB are similar to each other where the NFL stands alone. I believe that the fundamental difference lies with revenue sharing. Where any home-ice game day can make a large contribution to a NHL team's revenue, the NFL franchises are dependant on the success of the league as a whole. This has important implications for player salaries and competitive balance. Non-NFL franchises spend more on their players and reap direct benefits from doing so. Teams that are successful can afford better players and, in turn, increase their probability of success.
The variability in NFL outcomes indicates that the revenue sharing system, among other things, preserves competitive balance within the league.
Venue attributes, specifically, the terms of the lease, operating costs, and economy of scale benefits, are not well-described by this model. I did include in the model a variable for stadium age, which generally showed a negligible or insignificant impact. While I do suspect that the age of the stadium should have some impact of revenue due to its ability to draw a crowd, there are other roles that the stadium plays in franchise finance. If the franchise owner benefits from a favorable lease agreement or owns the venue outright, the value of the franchise should increase. Even in cases where a venue is owned publicly, the degree of public financing affects the value of the franchise. Stadiums that are constructed with more luxury seating and that facilitate consumption should boost revenue as well. Finally, as is the case with most NHL and NBA franchises, shared stadiums are more financially efficient due to economy-of-scale savings such as a skilled and affordable in-house staff, and a year-round revenue streams from marketing and attendance. However, in instances where there are different owners for a NHL and NBA team sharing the same stadium-these benefits will be split, often in the favor of the NBA franchise.
Due to the high correlation of revenue and value, I feel fairly comfortable using a model for revenue to draw conclusions about determinants of value for professional sports franchises. The most notable trend among the league models for revenue is the difference between the NFL and the other three leagues. The significant coefficients in the NHL model are championship wins, the stadium age, attendance, and the presence of another team in the city. In addition the NFL model is not as robust in explaining revenue generation based on the variables I used, as demonstrated by the unimpressive adjusted R squared statistic. I believe the NFL stands out because of broad revenue sharing throughout the league for nearly all revenue generators like television contracts, gate receipts, and merchandising. However, the gate receipt and other day-of-game revenue is split between opposing teams and allows each team to generate or loose some revenue based on performance, quality of venue, and in-city competition from another football franchise.
The modes for the NBA, MLB, and NHL have higher adjusted R squared statistics and similar sets of significant coefficients. In each model, the attendance, ticket price, and payroll are the variables with significant coefficients. This uniformity, and difference from the NFL, suggests that when revenue sharing is low, franchises depend on their abilities to draw crowds. Furthermore, drawing a crowd has a lot to do with how well a team performs. There are two reasons fro this attendance-performance relationship. First, high-performing team may be more popular. Second, going into the championship playoffs increases the number of games played and increases game-day revenue.
I encountered several problems in developing and analyzing the league models of revenue. Most importantly, I struggled with the NFL model. The correlation between revenue and value was not as tight as it was for the other leagues. The reason the NFL lacks a close revenue/value relationship may be due to a high level of competitive balance and short seasons, both of which make the year-to-year performance of a NFL franchise quite variable. A more thorough analysis would include time-series data. With additional data, I believe that I would see average revenue more closely correlated with value than it is in a single year. In addition, revenue sharing makes it difficult to find detectable variables that affect revenue generation. NFL franchise values seem to be determined by more intangible assets.
Intangible assets pose a problem in all of the leagues' revenue models. Relying on the revenue/value relationship, I used models with revenue as the dependant variable to make assumptions about value. Intangibles like tax breaks and favorable venue leases should affect value, but are not considered in my statistical analysis. Given more time and resources, I think my results could be significantly improved by considerations of these intangibles and their impact on value. More in-depth considerations of merchandising, licensing, and local broadcasting revenue would also improve my study.
Finally, troubles with multicolinarity and endogeneity made reaching firm conclusions difficult. Many of the variables that I included, or wanted to include, in my models are highly correlated with one another. In particular, stadium age and the dummy variable for additional teams may have resulted in biased coefficients. I suspect that much of my research could be improved by more sophisticated econometric analysis of these and other interactions.
Eric A. Thornton, "How to Value Professional Sports Franchise Intangible Assets," Insights: Willamette Management Associates Willamette Capital (Special Issue 2002): 10.
 Chapter 19 page 384.
 Ibid, 386.
 Ibid, 375.
 Chapter 19, 375.
 Chapter 19 page 375.
 Lee and Chun 2.
 Thornton 12.
 Chapter 19, page 380.This was an entry for The 2004 Moffatt Prize in Economics. See the contest rules for more information.
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