Advances in sport sponsorship revenue forecasting: an event history analysis approach.

Jensen, Jonathan A. ; Turner, Brian A.

Introduction

One of the more important evolutions in the sport industry over the past decade has been the marked increase in the application of advanced data analytics. Numerous quantitative approaches are now being applied to assist sport organizations in decision-making relative to scouting (e.g., Berri & Simmons, 2009), coaching strategy (e.g., Shortridge, Goldsberry, & Adams, 2014), and the evaluation of player performance (e.g., Baumer, Jensen, & Matthews, 2015). These approaches have helped ensure that these important decisions, once made by the gut and in the absence of any methodological rigor, are now informed by data. Slowly, over the past several years, analytics have increasingly also been applied to better inform decisions made off of the field, on the business side of sport organizations. In one example, many decisions relative to the pricing of tickets were once made in the absence of any empirical data. Changes in ticket prices can now be largely made in real time, with the benefit of dynamic, sophisticated pricing models (Shapiro & Drayer, 2012; Shapiro & Drayer, 2014). Another example involves the utilization of customer analytics to better understand consumer motivation for purchasing tickets or potentially upgrading to a season ticket plan (Zurier, 2014). Now that most tickets are purchased online, the data collected from each sale can be analyzed to ascertain buying patterns and isolate variables that predict purchases or upgrades. The implications of such efforts are that sport organizations are able to maximize revenue, while at the same time improving the organization's response to ever-changing consumer demand.

However, one area that has yet to be impacted by this trend in the application of data analytics is revenue projections and forecasting. Revenue forecasts for many sport organizations still largely depend on an aggregated measure of central tendency, the renewal rate. The renewal rate reflects the average percentage of buyers who choose to repurchase (Brown, 2002). The renewal rate is still the prevailing measure in use by sport organizations for sponsorship revenue projections, who forecast future revenue based simply on the historical percentage of sponsors who choose to renew their sponsorships of the organization (Irwin, Zwick, & Sutton, 1999). For example, former IOC marketing director Michael Payne noted that the TOP (i.e., The Olympic Partners) sponsorship program historically has enjoyed a renewal rate of greater than 90%, "virtually unheard of within the industry" (Payne, 2012, p. 100).

Many sport organizations rely on sponsorship as an increasingly important means for survival. Conversely, 70% of all sponsorship expenditures by brand marketers are allocated towards sport organizations (IEG, 2015). For example, in the global, ultra-competitive world of Formula One Racing, its teams rely on sponsorship for upwards of 70% of their entire operating budget (Jensen & Cobbs, 2014). Such revenue is also crucial for non-profit organizations, such as the International Olympic Committee (IOC) and the Federation Internationale de Football Association (FIFA). For example, more than 34% of the revenue generated by the Olympic movement during the most recently completed quadrennial (2009-2012) resulted from sponsorship (IOC, 2015). This included $950 million in revenue from the IOC's TOP program and $1.83 billion in revenue from domestic Organizing Committees for the Olympic Games (OCOG) sponsorship programs (IOC, 2015). For FIFA's most recently completed 2011-14 event cycle, sponsorship revenue totaled $1.63 billion, comprising 31.7% of total event-related revenue ($5.14 billion). Sponsorship revenue can be even more critical for smaller, amateur sport organizations (Maxwell & Lough, 2009).

However, despite its importance in the financing of sport organizations' continuing operations, the accurate forecasting of future sponsorship revenue is still reliant on a decades-old methodology, and there are several limitations to this oft-utilized approach. As an aggregated measure, the renewal rate simply tells the organization, on average, what percentage of sponsors renew. This data do not provide any indication when sponsorships may be most susceptible to dissolution (i.e., early, mid-term, or later in the lifetime of a sponsorship). Second, it tells the organization nothing about the actual duration of the partnerships, nor predicts how long they should be expected to last. Finally, as a measure of central tendency, the renewal rate does not properly account for censored observations or the durations of sponsorships that are currently ongoing.

Thus, an argument can be made that historical sponsorship data has yet to be empirically investigated utilizing appropriate statistical methods. Singer and Willett (2003) explained: "Traditional statistical methods provide no ready way of simultaneously analyzing observed and censored event times. Survival methods do" (p. 325). Therefore, the purpose of this study is to undertake the first application of survival-based methodological approaches to the empirical study of sport sponsorships. The goal of these efforts is to assist sport organizations in ongoing sponsorship revenue forecasting activities by providing a variety of data related to the duration of sponsorships. Rather than simply providing information on how many sponsors typically renew, this approach will provide a variety of additional information, including how many sponsorships have historically continued during each discrete time period, the conditional probability of a sponsor renewing during each period, and how long sponsorships have historically lasted.

Exchange Theory

The relationship between the buyer and seller in any sponsorship relationship is undergirded by exchange theory. Exchange theory is based on the concept that a successful exchange between parties is dependent on both agreeing that the price paid for their goods or services is at least equal to what has been offered in exchange (Crompton, 2004). In other words, both sides of the exchange must feel confident that the relationship is beneficial and meeting its stated objectives. In the sport context, exchange theory has been previously utilized to better understand the commitment of athletes (Schmidt & Stein, 1991), motivation and attrition among coaches (Weiss & Stevens, 1993), and the development of a sport league (Southall, Nagel, & LeGrande, 2005). Exchange theory is a useful lens in which to examine the sponsorship relationship, which consists of a sponsoring brand (the buyer) and the sponsored sport, arts, music/entertainment, or non-profit organization (the seller).

McCarville and Copeland (1994) first applied exchange theory to understand the motivations of each side of a sponsorship relationship, proposing that the principles of rationality, marginal utility, and fairness guide sponsorship-related decision-making. This paper builds upon the prior work of McCarville and Copeland by embarking on the first empirical investigation of the duration of sponsorship relationships, paving the way for future work that can utilize the lens of exchange theory to determine which factors empirically impact the duration of the relationship. Viewing sponsorship through the lens of exchange theory informs the perspective that only when both sides are satisfied with the resources provided by each via the relationship will it continue. Thus, this empirical investigation is a useful first step towards a more nuanced understanding of the importance of various types of resources for both sides of the sponsorship relationship.

Based on exchange theory, it is expected that the relationship between a sponsoring brand and sponsored organization would be most tenuous, and therefore most likely to fail, in the partnership's initial stages. During this time, both sides of the relationship are provided with the opportunity to understand each other's capabilities and objectives (Palmatier, Dant, Grewal, & Evans, 2006). Once an understanding of the resources that may be brought to bear by both partners is established, then a decision will likely be made by one or both partners whether to continue or end the relationship. As explained by Doney and Cannon (1997), longer-term relationships allow both sides to further understand each other's motives and expectations, which reduces the risk of the partnership failing. The longer the partnership continues, the better the chance that the relationship will be enhanced by both partners leveraging each other's capabilities.

Literature Review

In initial work on the importance of duration to sponsorships, Armstrong (1988) found that sponsorships of longer durations were more likely to assist the firm in moving beyond the initial objectives of brand awareness to influencing brand image, consistent with Keller's (1993) conceptualization of brand equity. A multi-year study of season ticket holders found that sponsorship length was predictive of both recall and decay rates of residual recall even after the sponsorship had ended (McDonald & Karg, 2014). Similar research on the length of outdoor (Bhargava, Donthu, & Caron, 1994) and television advertising campaigns (Dunlop, Cotter, Perez, & Wakefield, 2013) found that longer-running campaigns were predictive of higher rates of brand recall and behavioral change.

Olson and Thjomoe (2011) found that the announcement of a continuation of an existing sponsorship was perceived by consumers to enhance the fit of the sponsorship, compared to the announcement of a new sponsorship. Research by Kruger, Goldman, and Ward (2014) also found that the announcements of the continuation of sponsorship agreements were met with an increase in shareholder value of more than 4% in the short-term period after the announcement. The researchers reasoned that the continuance of the agreement may be seen by shareholders as a tacit endorsement by the marketers in their decision-making, given that the partnerships were worthy of renewal.

As explained by Cornwell, Roy, and Steinard (2001), a longer-term sponsorship relationship also increases the potential that the sponsorship may become a source of competitive advantage, based on its ability to better influence unique consumer-based outcomes. For example, the longer the duration of the sponsorship, the higher the potential is for a stronger association between the brand and property in a consumer's memory (Cornwell & Humphreys, 2013; Johar & Pham, 1999). According to Cornwell et al. (2001), "Seeing a sponsor's name associated with the same sporting event, year after year, gives the consumer multiple opportunities to elaborate about the significance of the product-sponsorship relationship, thus creating stronger associations in memory" (p. 42). As stated, the ability to more accurately forecast the ultimate duration of sponsorships is crucial for sport organizations that depend on such revenue for survival. These approaches provide managers with the ability to better understand partner retention from a historical standpoint, which can be utilized to predict future revenue from sponsorship moving forward. However, an empirical investigation of the duration of sponsorships has yet to be attempted, with this study filling an important gap in the sport marketing literature.

Methodology

This study utilizes event history analysis (EHA) approaches (i.e., survival analysis) to empirically examine the duration of sponsorships. To begin, the study utilizes what Box-Steffensmeier and Jones (1997) termed a "life-table analysis" to construct life tables for sponsorships. The life table can then be utilized to calculate the survival and hazard functions for sponsorships over discrete time periods. Together, these tools can then be used to determine the median lifetime for a sponsorship of a particular organization. Information will be provided to support the superiority of these approaches in allowing sport organizations to predict future revenues from sponsorships much more accurately than using measures of central tendency, such as the traditional renewal rate.

EHA has been previously utilized to analyze time-to-event duration data ranging from United Nations peacekeeping missions, military interventions, the careers of members of Congress, and marriages (Box-Steffensmeier & Jones, 2004). In other examples, Cooney, Kadden, Litt, and Getter (1991) utilized the methodology to examine the duration of after-care programs for alcoholics (with the event in question being a relapse to alcohol use), Bolger, Downey, Walker, and Steininger (1989) examined the duration of time before an undergraduate student ideates about suicide, while Furby, Weinrott, and Blackshaw (1989) investigated recidivism (return to prison) among sex offenders. However, despite its widespread use across several diverse academic fields, EHA has scarcely been utilized to study time-to-event durations in the sport industry. One prior application is an analysis of factors impacting a player's career, finding that both draft order (Staw & Hoang, 1995) and race (Hoang & Rascher, 1999) were significant predictors of the career longevity of basketball players.

Contexts

In order to invite comparisons across two different illustrative contexts, EHA will be applied in this study to two of the more recognized and influential sponsorship programs, the TOP Olympic sponsorship program and Partners/Sponsors of the FIFA World Cup. This study's data spans the entire history of the TOP program, which began in 1985 and continues to this day (Davis, 2012). A TOP sponsorship of the Olympic Games provides, among other assets and rights, the ability for a brand to associate itself with one of the most recognized and admired symbols in the world, the Olympic rings (Davis, 2012; Preuss, 2004). The second dataset is comprised of the complete history of FIFA Global Partners and Men's World Cup Sponsors dating back to 1979 (FIFA, 2016). These two events are indisputably the most popular and most-watched sporting events in the world. Davis (2012) noted: "Only two sports events command a truly global audience, the FIFA World Cup and the Olympics" (p. 206). A global audience of more than 1 billion watched the 2014 Men's World Cup Final (Philipson, 2014). The Summer Olympic Games in 2012 were watched by more than 219.4 million Americans, making it the most-watched event in U.S. television history (Crupi, 2012). On a global scale, a total of 220 countries broadcasted the Games to an audience of more than 3.6 billion (IOC, 2015). In addition, Olympic and World Cup sponsorships begin and end in a discrete time period of four years, or a quadrennial (Jensen & Hsu, 2011). Though the EHA methodology is robust to the inclusion of different durations across observations, the four-year periods utilized for both sponsorships are useful for facilitating meaningful comparisons between the two contexts.

Data Compilation Overview

The first step in the EHA methodology is to compile a complete history of all TOP and FIFA sponsorships dating back to the initiation of the programs. This analysis reveals that the TOP program has encompassed 29 different sponsorships over eight total quadrennials through 2015 (Ferrand et al., 2012; Hill, 1996; IOC, 2015; Payne, 2012; Preuss, 2004). A history of each corporation that has participated in the TOP program, including the duration of each sponsorship and years of participation, is detailed in Table 1. The same approach is then utilized to reconstruct the history of FIFA sponsorships, dating back to 1979. The FIFA World Cup sponsorship program has included a total of 42 sponsorships over the past nine World Cup events (FIFA, 2016). A history of each corporation that has served as either a FIFA Partner or Men's World Cup Sponsor is included in Table 2.

The next step in data compilation for EHA is to construct the censoring indicator, by indicating both if and when each firm experienced the target event (the end of the sponsorship). A dichotomous variable (0 = Not Ended, 1 = Ended) indicating whether the sponsorship ended or is censored (i.e., still ongoing) by the end of each four-year period was compiled. For example, there are 12 corporations who are currently still active in the TOP sponsorship program, which results in a total of 17 of the 88 observations indicating that the sponsorship has ended. For the FIFA World Cup sponsorship program, a total of seven sponsorships continue today, including five FIFA Partners (Adidas, Coca-Cola, Hyundai-Kia Motors, Gazprom, and Visa) and two FIFA World Cup sponsors (Anheuser-Busch and McDonald's). This results in 35 of the 119 total observations reflecting that those sponsorships have ended.

Data Analysis Overview

There are three key concepts that are essential to data analysis via EHA, and will be used as recommended alternatives to the utilization of an aggregated measure of central tendency in forecasting future sponsorship revenues. To begin, the Kaplan-Meier (1958) survivor function estimate, S([t.sub.ij]), is defined by Singer and Willett (2003) as the 'probability that individual i will survive past time period j" (p. 334). For this to occur, the individual i cannot experience the event occurrence in the jth time interval, and survives to the end of time period j. In other words, the random variable for time ([T.sub.i]) for individual i exceeds j. The survivor function is defined by the formula below:

S([t.sub.ij]) = Pr[[T.sub.i]>j]

Of arguably more utility than the survivor function in EHA is the hazard function, or hazard rate. The hazard rate is defined as the rate in which the duration or event ends (i.e., the event has been experienced), given that the target event or the duration has not ended prior to that particular time interval (Box-Steffensmeier & Jones, 1997). One can easily see why furthering an understanding of the conditional probability of a sponsorship ending during a particular time period would be very appealing for sport organizations. Given that [T.sub.i] represents the time period T for individual i, according to Singer and Willett (2003) the discrete-time hazard function can be represented as follows:

h([t.sub.ij]) = Pr[[T.sub.i=j]|[T.sub.i] [greater than or equal to] j]

The median lifetime is de fined by Singer and Willett (2003, p. 337) as "that value of T for which the value of the estimated survivor function is .5." In the example of this study, the median lifetime is the point in which exactly half of the sponsorships have ended and half have survived. To determine the exact median lifetime, the formula provided by Miller (1981) can be utilized to linearly interpolate the exact median lifetime when a survivor function of 0.5 falls between two values of S(tj). Miller's (1981) formula involves letting m represent the last time interval in which the survivor function is above 0.5, letting [??]([t.sub.m]) equal the survivor function in that particular interval and letting [??]([t.sub.m+1]) equal the survivor function for the next interval.

The formula is as follows:

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Results

The first data analysis step in EHA is the construction of a life table, which was developed for the TOP and FIFA World Cup sponsorship programs and is depicted in Tables 3 and 4. Singer and Willett (2003) recommended the construction of life tables as the first step in any event history analysis in which the duration of time before the event in question is of interest. The life table includes a compilation of how many of the observations enter each time interval and how many experienced the target event during each interval, in this case how many of the sponsorships ended. The life table also includes the previously defined survivor and hazard functions for each period, and is necessary to compute the median lifetime of the sponsorships.

Survivor Functions

As indicated in Table 3, there have been a total of 29 different sponsors to participate in the TOP program, with a total of seven ending after the first quadrennial. Therefore, a total of 20 TOP sponsorships "survived" past the first time interval, while two (Bridgestone and Toyota) are still currently in their first quadrennial (i.e., censored). The TOP sponsorships that only lasted one quadrennial were held by Acer, FedEx, Johnson & Johnson, Lenovo, Mars, Ricoh, and the U.S. Postal Service. Per Table 3, the survivor function for the first interval for TOP sponsorships is 0.7586 (SE = .0795). This function can be interpreted as the conditional probability that a TOP sponsorship will continue past the first quadrennial is 75.86%. Conversely, the failure function, or the probability that the sponsorship will end, can also be computed. In this example, it is 0.2414, or 24.14%. As indicated in Table 3, after another four years, 12 of the 29 TOP sponsorships have survived, equating to a survivor rate of 0.5310 (i.e., the conditional probability of surviving past the second quadrennial is 53.10%). The standard error for the second survivor function for TOP sponsorships is 0.0956. A total of six additional sponsorships ended after two quadrennials, while two (Dow and Procter & Gamble) were censored.

A total of 10 TOP sponsorships survived past the third quadrennial, with only one (Xerox) ending at this juncture, a pattern which will continue. There is one current sponsor whose sponsorship currently has a duration of three quadrennials (General Electric), which consequently adjusts the survivor function to 0.4868 (SE = .0973). Once again, only one sponsorship ended at the conclusion of the fourth quadrennial (John Hancock/Manulife), while two (Omega and Atos) were censored. This equates to an updated survivor function of 0.4381 (SE = .0990). Of the seven sponsorships that survived into five quadrennials, again only one ended during that interval (Time, Inc.), while there are two current sponsorships with a duration of five quadrennials (McDonald's and Samsung). This equates to a survivor function of 0.3755 (SE = .1028) after five intervals. Only one of the four sponsorships to have survived into the sixth interval ended at this point (Kodak), adjusting the survivor function down to 0.2816 after six quadrennials. As stated previously, there are three TOP sponsorships that were initiated at the program's inception, have continued into the seventh and eighth quadrennial, and remain active to this day (Coca-Cola, Panasonic and Visa). Thus, the final survivor function remains at 0.2816. Given the smaller sample size, the standard error for the final survivor function for TOP sponsorships increased to 0.1120 (up from 0.0795).

A similar analysis can be performed for FIFA World Cup sponsorships. As indicated in Table 4, a total of 15 of the 42 historical sponsorships ended after their first World Cup, while one (Gazprom) is considered censored. This equates to a survivor function of 0.6429 (SE = 0.0739), more than 10% greater than that of the TOP program. After two World Cups, a total of 26 of the original sponsorships have survived, for a 0.3709 survivor function (SE = 0.0755), compared to 0.5310 for the TOP program. This pattern continues until the seventh iteration, where the survivor function decreases to 0.0910 (SE = 0.0554), indicating that a total of only one of the original 42 sponsorships (Coca-Cola) have continued through seven World Cups.

The results above are also reflected in the graph of the survivor functions for both sponsorship programs (Figure 1). The graph indicates a fairly steep drop through the first two time intervals for both sponsorship programs. However, the FIFA World Cup program's drop is steeper, as a larger percentage of the sponsorships have ended. The function for both then flattens out with much smaller drops through the next several intervals, as fewer and fewer of the surviving sponsorships end.

Hazard Functions

The life table for TOP sponsorships (Table 3) also includes the hazard function during each individual time interval. Recall that the hazard function is defined as the rate in which the duration or event ends, given that the target event or duration has not ended prior to that particular time interval (Box-Steffensmeier & Jones, 1997). The hazard function for the TOP sponsorship program's first quadrennial is 0.2414, given that seven of 29 TOP sponsorships ended after one quadrennial. The hazard function for the second quadrennial increases to .3000, given that six of the 20 sponsorships that survived the first time interval ended at this point. The hazard function drops to 0.0833 in the third quadrennial as only one of the 12 sponsorships that had survived ended during the interval. The hazard function in the fourth quadrennial is .1000, given that in the history of the TOP sponsorship program only one ended after this interval. The function increases to 0.1429 over the next interval (with one of seven sponsorships ending) and 0.2500 for quadrennial six (one of four sponsorships ending). Similarly, the hazard function for the FIFA World Cup sponsorship program (Table 4) begins at 0.3571, given that 15 of the 42 sponsorships ended after one World Cup. The hazard function increases to 0.4231, given that an additional 11 sponsorships ended after just two World Cups. The function then continues to decrease, from 0.2000 after three World Cups, to 0.0909 after four and 0.1000 after five.

It is also possible to graphically depict the hazard rate of a sponsorship ending over time. For both Olympic TOP and FIFA World Cup sponsorships (Figure 2), the hazard rate of a TOP sponsorship ending decreases as a function of time in a fairly linear fashion. For TOP, there is a slight increase in the hazard between the third and fourth time interval (between 12-16 years), and another slight increase between 16-20 years. For FIFA sponsorships, the slope also decreases continuously over time. The overall shape of both graphs can be interpreted that the longer a sponsorship continues, the probability that the sponsorship will end also decreases.

Of interest is the overall, cumulative hazard function for the entire history of both sponsorship programs. As an aggregated measure, the inverse of these functions are precisely equivalent to the previously defined renewal rate. As indicated in Tables 3 and 4, they are 0.1932 for TOP and 0.2941 for FIFA (reflecting renewal rates of 80.68% and 70.59%, respectively). These functions can be interpreted as the cumulative probability that a sponsorship ends during the entire history of both programs. As indicated, on average FIFA World Cup sponsorships are more than 10% more likely to end in any particular time period, compared to TOP sponsorships.

Median Lifetimes

After a life table for both sponsorship programs have been constructed, it is possible to then compute the median lifetime for each sponsorship program. As stated, the median lifetime is the point in time where exactly half of the observations have experienced the event, while half have not. It is also the point in time at which the survivor function is exactly 0.5 (Singer & Willett, 2003). The process starts by examining the survivor functions in Tables 3 and 4. For TOP sponsorships, the survivor function for the second time interval is above .5 (0.5310), while the function for the third interval is below .5 (.4868). This indicates that half of TOP sponsorships end somewhere between the second and third time interval, or between eight and 12 years. Plugging these values into the aforementioned equation from Miller (1981) results in a median lifetime of 2.70 time periods (or 10.81 years) for TOP Olympic sponsorships. For FIFA World Cup sponsorships, as indicated in Table 4 the survivor function for the second time interval is under 0.5 (0.3709). This indicates that the median lifetime is less than two intervals. Utilizing Miller's (1981) formula, we find that the median lifetime for FIFA World Cup sponsorships is 1.53 (6.12 years), more than one full quadrennial less than TOP sponsorships.

Discussion

Managerial and Theoretical Implications

The preceding analysis of hazard rates, survivor functions, and median lifetimes yields several interesting insights for managers tasked with selling and managing corporate sponsorships. The analysis also demonstrates the superiority of applying such advanced methodological approaches compared to the use of standard measures of central tendency. The aggregated renewal rates for both sponsorship programs tell us that given the rate for TOP sponsorships (80.68%), managers should budget and prepare for the possibility in any given quadrennial (four-year period) that roughly 20% of its partners will end the relationship. As the TOP sponsorship program for the current quadrennial (2012-16) includes 12 sponsors, based on this analysis the IOC should be prepared for at least two of these current sponsors not renewing beyond the 2016 Summer Olympic Games. For the World Cup program, its renewal rate of 70.59% indicates that on average nearly one-third of its sponsorships will end after each event. This trend was recently borne out following the 2014 World Cup, when several World Cup Partners failed to renew, including multinational brands Castrol, Continental, Emirates, Johnson & Johnson, and Sony. The loss of these sponsors left the organization with a total of only seven sponsors (as reflected in Table 2).

While helpful, this analysis is the totality of what is available when applying traditional measures of central tendency to sponsorships. Several additional managerial insights are evident when applying EHA methods to examine trends related to each individual time period, and describing the duration of sponsorships utilizing the median lifetime approach. These insights are helpful to managers in better understanding the nature of partner retention, such as when sponsorships are historically most susceptible to dissolution, and assisting managers in decision-making relative to the allocation of resources towards ensuring such partnerships continue. First, graphing the survivor functions of both sponsorship programs (Figure 1) allows one to clearly see that the vast majority of sponsorships end during the first two time periods. This is the case for both of these sponsorship programs. From a managerial standpoint, these results suggest that all resources available to managers of sponsorship programs should be allocated during the first two renewal periods to ensure the sponsorship survives beyond this crucial span of time. This analysis also demonstrates that if a sponsor can be convinced to continue on after two renewal periods it is highly likely that they will remain a sponsor for at least another eight years.

Meanwhile, hazard rates during specific time periods indicate that the probability of a TOP sponsorship ending is highest during the second quadrennial (.3000). After the second quadrennial, the hazard rate is reduced considerably, to .0833 during the third, .1 during the fourth, and .1429 during the fifth. Results were similar for the FIFA World Cup program, which saw higher hazard rates (.3571 and .4231) during the first two periods. After that timeframe the hazard of the sponsorship ending dropped considerably, to .2000 (20%) during the third period and .0909 (less than 10%) during the fourth. Results were similar during the fifth period, exactly 10% (hazard function of .1000). These results also indicate that sport organization managers should devote considerably greater resources towards ensuring sponsors are reaching their stated objectives during the early years of a sponsorship, if they hope to increase the probability of the relationship continuing for years to come.

These results are consistent with the principles of exchange theory, and prior research that has applied it to understand buyer-seller relationships (e.g., McCarville & Copeland, 1994). Only after understanding each side's objectives and capabilities can partners determine whether to engage in a longer-term relationship. The results provide evidence that such partners utilize these crucial first two time periods (in this context, first four to eight years) to educate one another on their capabilities and the resources that each side can contribute to the relationship, prior to ultimately deciding whether to continue for the long term.

However, while many partnerships did only last for 48 years, there are several instances across both programs (including Adidas, Coca-Cola, McDonald's, and Visa) where both sides developed a mutually beneficial partnership that has proven to stand the test of time. Thus, in this context exchange theory is helpful in explaining and confirming the forces that led to the study's results, an important consideration in quantitative research (Zhang, Kim, & Pifer, 2015).

Finally, the median lifetime for Olympic TOP sponsorships was 10.81 years, compared to 6.12 years for World Cup sponsors. Given this finding, the result of analyzing the durations of more than 70 different sponsorships dating back more than 30 years, it would be unwise for managers with the responsibility over similar sponsorship programs to expect, and more importantly budget and forecast for, many sponsorships to last beyond eight to twelve years. Consistent with exchange theory, the obvious precipitous drop that occurs during these crucial periods demonstrates the importance of focusing on best servicing and placing resources towards sponsors early on in the relationship.

Methodological Implications

In order to properly analyze the methodological implications of these approaches to the duration of sponsorships, it is helpful to review results utilizing less sophisticated approaches and compare the results. For example, if EHA was not utilized to investigate the historical duration of sponsorships, standard estimates of central tendency would be utilized. However, how would the sponsorships whose durations were not finalized be handled? In one approach, since the final duration of censored observations is yet unknown, these sponsorships of unknown duration would simply be omitted from the analysis. Any current sponsorships would be removed from the sample. As indicated in Table 1, if this approach were utilized to examine the duration of sponsorships for the TOP program, there would be a loss of 12 of the 29 TOP historical sponsorships. This would also result in the omission of some of the longest-running sponsorships, including those of Coca-Cola, Panasonic and Visa. As depicted in Figure 3, calculating the mean lifetime of TOP sponsorships omitting the censored observations results in a duration of 2.11 time intervals (8.44 years) for the TOP program and 2.25 intervals (9.0 years) for the FIFA World Cup program. Given that it is unwise to omit observations from a sample, a more widely-used approach is to simply truncate the duration of censored observations at a point in time, such as the present day. For sponsorships, this approach would involve assigning a duration for the sponsorships that are currently ongoing equal to the time they possess at the end of data collection. The application of this approach yields a mean lifetime of 3.03 (12.14 years) for TOP sponsorships and 2.81 (11.24 years) for FIFA sponsorships (Figure 3).

In the end, the calculation of sponsorship durations utilizing two different approaches results in significantly different measures. For the TOP program, the first approach (omitting observations) yields a duration of 8.44 years, while the second (truncating) results in a duration of 12.14 years. A difference of nearly one time interval may not seem like much. However, consider that in the most recently completed Olympic quadrennial (2009-2012), 11 TOP sponsors yielded a total of $950 million in revenue for the IOC. This results in an average revenue of $86 million per sponsor (IOC, 2015). Therefore, this difference of just 3.7 years in the two durations, for just one sponsor, equates to a difference in revenue of $79.89 million. For five sponsors, which is less than half of the current total of 12, the difference would equate to $400 million in revenue for the IOC.

For FIFA sponsorships, the result using EHA approaches is actually the shortest of the three. The EHA estimate is only 6.12 years, compared to 9.00 and 11.24, respectively (Figure 3). The most recently available public records for the 2014 FIFA World Cup reflect a total of $1.63 billion in revenue from sponsorship (FIFA, 2015), which for the 2014 event was collected from a total of 14 different sponsors, including six Global Partners and eight Sponsors. This equates to an average revenue of $116.5 million per sponsor over the four-year period. Therefore, revenue projections on an annual basis for just one sponsor, based on the popular approach to truncate sponsorship durations in the present day (11.24 years) compared to the total based on the median lifetime achieved via the EHA approach (6.12 years), would result in a total revenue projection differential of $149.7 million. These figures illustrate the implications of determining the most accurate method for computing the historical lifetime for corporate sponsorships, as revenue forecasts using these divergent methods would result in differentials of hundreds of millions of dollars. Thus, it is evident that the utilization of more advanced quantitative methodologies such as EHA can aid managers in these efforts.

Limitations

It is important to understand some inherent limitations of studies utilizing event history analysis. Singer and Willett (2003) identified several limitations to median lifetimes that researchers utilizing the EHA methodology must acknowledge. First, given that it is a median value, it is fairly insensitive to extreme values. It is also important to keep in mind that the median lifetime does not reveal much about the distribution of the risk of event occurrence over time. Examining survivor and hazard functions is a much more effective way to examine changes in risk over the lifetime of the sponsorship's duration. This fact illustrates the importance of graphing both hazard and survivor functions (Figures 1 and 2) in order to visually depict how the functions change over time.

Perhaps most importantly, one must understand that the median lifetime does not inherently indicate when the risk of experiencing the event is highest. For example, in their study of the durations of careers of female Congresswomen, Singer and Willett (2003) utilized this approach to determine a median lifetime of exactly 3.5 terms. However, the researchers found that the risk for event occurrence (i.e., in this context the end of the Congressional career) was not particularly strong during the fourth term. In the example of the Olympic sponsorship program, we also found differing results. As noted in Table 3, the hazard rate for TOP sponsorships was highest during the second time interval (.3000). This means that TOP sponsorships have the highest probability of ending during the second term of the sponsorship. However, the median lifetime for TOP sponsorships indicated that the time period during which half of the sponsorships survived and half failed was nearly halfway between the second and third time intervals (given the median lifetime of 2.70 quadrennials, or 10.81 years). Further, the time interval when TOP sponsorships have one of the lowest hazards for ending was during the third quadrennial (.0833), or years 12-16. Based on this analysis, it is evident that to view a clear picture of the history of durations, researchers must analyze not just the median lifetime, but all of the various metrics in their totality, an approach advocated in this paper.

Future Research

While this paper's results support that applying EHA approaches to time-to-event durations is a more accurate representation than typical measures of central tendency, it is important to acknowledge that this paper focuses solely on describing the duration of corporate sponsorships utilizing such approaches. The results included within provide no information about what factors actually influence these metrics. The next recommended step in the application of EHA modeling approaches in this context is to determine the influence of independent variables, or covariates, on the hazard functions (i.e., the probability of event occurrence). This approach would help determine not just the nature of the time-to-event durations in question, but answer additional questions related to which factors might either increase or decrease the hazard of event occurrence (i.e., the conditional probability that the sponsorships ends). Once a dataset is constructed for EHA utilizing the procedures outlined in this study, it is relatively simple to take the next step of modeling the hazard rate based on a variety of different covariates. In the context of sponsorships, these may include factors related to the sponsoring brand, such as the sponsor's brand equity, where the sponsoring firm is located, and whether it is a public or private corporation. From the perspective of the sponsored property, locations of current or future event locations or the number of sponsors (i.e., clutter) could play a role. Finally, there may be external factors, such as economic conditions within the sponsor's home country, which may serve as a time-varying covariate that can influence whether a sponsorship continues or is dissolved.

In addition, there are many other potential applications of EHA approaches in sport marketing, including relationships beyond that of the sponsorship buyer and seller. As stated, data are now available to assist managers who are tasked with convincing consumers to make an investment in or upgrade to season ticket plans. As noted by Zurier (2014), some Major League Baseball (MLB) teams have season ticket holders dating as far back as 1975. Given the longitudinal nature of the relationship between a season ticket holder and sport organizations, EHA can be applied to understand when such relationships are most susceptible to dissolution, and appropriately assess their ultimate duration. In addition, covariates such as the actual use of tickets (which using today's technology can be tracked in real time) and demographic information about the ticket holder (i.e., age, gender, education, employment, and geography) can be utilized to determine whether these variables are statistically significant predictors of the dissolution of the relationship between the consumer and the organization.

Another potential application could involve the analysis of the relationship between donors and intercollegiate athletic departments (i.e., Gladden, Mahony, & Apostolopoulou, 2005). In addition to determining when the relationship is most likely to end, covariates such as the distance of the donor from campus, whether or not the donor was a student-athlete, employment information, years since graduating, and the number of times contacted by the athletic department can be inserted into the model in an attempt to isolate factors that may predict the end of the donor's relationship with a university.

Conclusion

Given the advancement in the use of analytics across the sport industry over the past decade, this paper suggests the application of such approaches in the forecasting of revenue from an increasingly important source for sport organizations, corporate sponsorship. Rather than a reliance on an aggregated measure of central tendency, the renewal rate (Irwin et al., 1999), this study applied event history analysis in order to better understand not only how many sponsors currently renew, but when sponsorships are most susceptible to dissolution. Results not only suggest a more accurate approach to determining their ultimate duration, but also properly take into account sponsorships that are still ongoing. An analysis was undertaken of the survivor and hazard functions, as well as median lifetimes, of the complete history of two influential global sponsorship programs, that of the Olympic Games and the FIFA World Cup. Consistent with exchange theory, which would suggest that the initial stages of the relationship between the seller and buyer in any sponsorship is crucial for both sides to understand each other's capabilities and resources, results found that sponsorships were less likely to survive and most susceptible to dissolution in the first two renewal periods. Results also demonstrated that the final duration of these sponsorships differed considerably based on the traditional approaches of either omitting or truncating the durations of sponsorships that were still ongoing, compared to the computation of the median lifetime. Revenue forecasts based on the various durations resulted in differentials of nearly $100 million, based on the renewal or end of just one Olympic or World Cup sponsorship. These results suggest that rather than allocating resources towards longer-running sponsor partners, managers tasked with ensuring such sponsorships continue should focus their efforts on the first two crucial sponsorship renewal periods. From a managerial standpoint, this study provides empirical evidence that if the relationship between sport organizations and their partners can be shepherded through this critical time, it is much more likely that sponsors will continue their partnerships for many years to come.

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Jonathan A. Jensen, PhD, is an assistant professor of sport administration at the University of North Carolina at Chapel Hill. His research interests include sport marketing, sponsorship, and consumer behavior.

Brian A. Turner, PhD, is an associate professor and coordinator of the sport management program in the College of Education and Human Ecology at Ohio State University. His research interests include organizational behavior and sport marketing.

Caption: Figure 1. Graph of survivor functions for both TOP and FIFA World Cup sponsorships.

Caption: Figure 2. Graph of smoothed hazard functions for both TOP and FIFA World Cup sponsorships. Table 1 History of Olympic (TOP) Sponsors (1985-2016) Corporation Years Duration 3M 1985-1992 2 Acer 2009-2012 1 Atos * 2001-2016 4 Bausch & Lomb 1989-1996 2 Bridgestone * 2015-2024 1 Brother 1985-1992 2 Coca-Cola * 1985-2016 8 Dow * 2009-2016 2 FedEx 1985-1988 1 GE * 2005-2016 3 IBM 1993-2000 2 John Hancock 1993-2008 4 Johnson & Johnson 2005-2008 1 Kodak 1985-2008 6 Lenovo 2005-2008 1 Mars 1989-1992 1 McDonald's * 1997-2016 5 Omega * 2001-2016 4 Panasonic * 1985-2016 8 Philips 1985-1992 2 Procter & Gamble * 2009-2016 2 Ricoh 1989-1992 1 Samsung * 1997-2016 5 T ime, Inc. 1985-2004 5 T o yota * 2015-2024 1 UPS 1993-2000 2 U .S. Postal Service 1989-1992 1 Visa * 1985-2016 8 Xerox 1993-2004 3 Corporation Product Category 3M Office Material Acer Computer Atos * Information Technology Bausch & Lomb Optical Products Bridgestone * Tires, Seismic Isolation Bearings & Bicycles Brother Typewriters Coca-Cola * Non-Alcoholic Beverages Dow * Official Chemistry Company FedEx Express Mail/Package Delivery GE * See Below IBM Information Technology John Hancock Life Insurance Johnson & Johnson H ealth Care Kodak Film/Imaging Lenovo Computer Mars Snacks McDonald's * Retail Food Services Omega * Timing, Scoring & Venue Results Services Panasonic * TV/Audio/V ideo Equipment Philips Li ghting Procter & Gamble * Personal Care/Household Products Ricoh Docum ent Proce s sing Samsung * Wireless Communication Equipment T ime, Inc. Pu blicat io n s T o yota * Mo bility UPS Expre ss Mail/Package Delivery U .S. Postal Service Express Mail/Package Delivery Visa * Payment Services Xerox Docum ent Processing * Denotes sponsorships currently ongoing (i.e., censored) Sources: Ferrand et al. (2012), Hill (1996), Preuss (2004), & IOC (2015) Note: GE's exclusive product or service categories are Energy Generation Systems, Energy Distribution Systems, Healthcare: Diagnostic Imaging, Monitoring and Electronic Medical Records Technology, Lighting Fixtures & Systems, Aircraft Engines, Rail Transportation, Water Treatment Facilities & Services, Equipment & Transportation Management (IOC, 2015) Table 2 History of FIFA Partners-Men's World Cup Sponsors (1979-2016) Corporation Years Duration Adidas * 1995-2016 6 Alfa Romeo 1987-1990 1 Anheuser-Busch 1983-1990 2 Anheuser-Busch * 1995-2016 6 Avaya 1999-2006 2 Bata 1983-1986 1 Canon 1979-1998 5 Castrol 2007-2014 2 Cinzano 1983-1986 1 Coca-Cola * 1979-2016 10 Continental 2003-2014 3 Deutsche Telecom 2003-2006 1 Emirates 2003-2014 3 Energizer 1991-1994 1 Fuji Xerox 1999-2002 1 Fujifilm 1979-2006 7 Gazprom * 2015-2016 1 Gillette 1979-2006 7 Hyundai-Kia * 1999-2016 5 Iveco 1979-1982 1 Johnson & Johnson 2011-2014 1 JVC 1979-2002 6 Korea Telecom/NTT 1999-2002 1 Mars 1987-1998 3 MasterCard 1991-2006 4 McDonald's * 1991-2016 7 Metaxa 1979-1982 1 MTN 2007-2010 1 Oi 2011-2014 1 Opel 1983-1986 1 Opel 1991-98 2 Philips 1983-2006 6 RJReynolds 1983-1986 1 Satyam 2007-2010 1 Seara 2010-2014 2 Seiko 1979-1986 2 Sony 2007-2014 2 Toshiba 1999-2006 2 Vini d'ltalia 1987-1990 1 Visa * 2007-2016 3 Yahoo! 1999-2006 2 Yingli Solar 2010-2016 2 Corporation Product Category Adidas * Athletic Apparel Alfa Romeo Automobile Anheuser-Busch Malt Beverages Anheuser-Busch * Malt Beverages Avaya Information Technology Bata Footwear Canon Photographic/Photocopying Castrol Lubricants Cinzano Alcoholic Beverages Coca-Cola * Non-Alcoholic Beverages Continental Tires Deutsche Telecom Telecommunications Emirates Airlines Energizer Batteries Fuji Xerox Document Services Fujifilm Photographic Film Gazprom * Oil and Gas Gillette Personal Care Hyundai-Kia * Automobiles Iveco Manufacturing Johnson & Johnson Healthcare JVC Consumer Electronics Korea Telecom/NTT Telecommunications Mars Confections MasterCard Payment Systems McDonald's * Restaurant Metaxa Alcoholic Beverages MTN Telecommunications Oi Telecommunications Opel Automobile Opel Automobile Philips Consumer Electronics RJReynolds Tobacco Satyam Information Technology Seara Uncooked Meat & Frozen Food Seiko Timekeeping Sony Consumer Electronics Toshiba Consumer Electronics Vini d'ltalia Publishing Visa * Payment Services Yahoo! Information Technology Yingli Solar Renewable Energy * Denotes sponsorships currently ongoing (i.e., censored); Source: FIFA (2016) Table 3 Life Table Describing Durations of TOP Sponsorships Ended Time Beginning during Period interval total period 0 [0, 1) 29 -- 1 [1, 2) 29 7 2 [2, 3) 20 6 3 [3, 4) 12 1 4 [4, 5) 10 1 5 [5, 6) 7 1 6 [6, 7) 4 1 7 [7, 8) 3 0 8 [8, 9) 3 0 Overall hazard rate Censored at end Hazard Survivor Period of period function function 0 -- -- 1.0000 1 2 0.2414 0.7586 2 2 0.3000 0.5310 3 1 0.0833 0.4868 4 2 0.1000 0.4381 5 2 0.1429 0.3755 6 0 0.2500 0.2816 7 0 0.0000 0.2816 8 3 0.0000 0.2816 Overall hazard rate 0.1932 Note: Survivor function is calculated over full data and evaluated at indicated times; it is not calculated from aggregates shown at left. Table 4 Life Table Describing Durations of FIFA World Cup Sponsorships Ended Time Beginning during Period interval total period 0 [0, 1) 42 --- 1 [1, 2) 42 15 2 [2, 3) 26 11 3 [3, 4) 15 3 4 [4, 5) 11 1 5 [5, 6) 10 1 6 [6, 7) 8 2 7 [7, 8) 4 2 8 [8, 9) 1 0 9 [9, 10) 1 0 10 [10, 11) 1 0 Overall hazard rate Censored at end Hazard Survivor Period of period function function 0 -- -- 1.0000 1 1 0.3571 0.6429 2 0 0.4231 0.3709 3 1 0.2000 0.2967 4 0 0.0909 0.2967 5 1 0.1000 0.2428 6 2 0.2500 0.1821 7 1 0.5000 0.0910 8 0 0.0000 0.0910 9 0 0.0000 0.0910 10 1 0.0000 0.0910 Overall hazard rate 0.2941 Note: Survivor function is calculated over full data and evaluated at indicated times; it is not calculated from aggregates shown at left. Figure 3. Graph comparing differences in sponsorship durations based on EHA vs. alternate approaches. TOP Olympic FIFA World Cup Sponsorships Sponsorships Omitting Observations 8.44 9.0 Median Lifetime via EHA 10.61 6.12 Truncating @ Present Day 12.14 11.24 Note: Table made from bar graph.