Advertising Rates, Audience Composition, and Competition in the Network Television Industry
∗
Ronald Goettler Graduate School of Industrial Administration Carnegie Mellon University
[email protected]
GSIA Working Paper #1999-E28
August 8, 1999
∗
I would like to thank Mike Eisenberg, Greg Kasparian, and David Poltrack of CBS and Mark Rice of Nielsen Media Research for their help in obtaining the data for this study.
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1
Introduction
Most people think of the broadcast networks as being in the entertainment business. While the networks do play a role in the entertainment industry, their primary business is advertisements — creating audiences to be sold to companies and organizations seeking exposure to consumers. In 1997 spending on advertisements in the U.S. reached 73.2 billion dollars, including 38.1 billion dollars on television ads. The broadcast networks received 15.2 billion of these dollars, and have reaped increases in ad revenue despite the steady decline in their audience sizes as viewers migrate to cable programming and non-viewing activities such as web-surfing.1 One reason for these gains is the increase in the demand for advertising as the economy expands and companies increasingly seek to establish brand awareness. Another factor is the decrease in the supply of large audiences provided by the networks; the few shows which attract audiences exceeding 30 million viewers command a significant price premium, as evidenced by the high cost per viewer for commercials during these shows. Nearly as important as audience size is the demographic composition of the viewers. Marketers typically want to reach consumers 18 to 49 years old who have disposable income or are responsible for household purchases, and they are willing to pay a premium to advertise on shows targeting such groups. The first goal of this paper is to estimate the relationship between ad prices and audience size and composition. Since network television is broadcast free to viewers, the choice of programming content is the only mechanism for adjusting the size and composition of a network’s audience. In the short run, this strategic choice corresponds to the scheduling, or sequential positioning, of the network’s stock of shows. In the longer run, the networks can change their programming, or choice of shows available to schedule, by canceling some shows and purchasing or developing others. Previous empirical studies of the television networks, such as Rust and Eechambadi (1989) and Kelton and Schneider (1993), have focused on the short run choice and found that the networks’ average prime time ratings can be increased significantly simply by changing their schedules. This finding was confirmed in Goettler and Shachar (1999), though with more moderate gains not exceeding 16 percent. One possible explanation for the finding that the networks appear to schedule shows suboptimally is that these studies assumed a network’s objective is to maximize ratings, not profits. The second goal of this paper is to determine optimal scheduling strategies using a more realistic objective (i.e., payoff) function which accounts for the importance of audience size, demographic 1
Data from Competitive Media Reporting reported by Advertising Age on http://www.adage.com.
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composition, and costs of schedule changes. For comparison with previous studies of network scheduling, we compute optimal schedules and equilibrium schedules under the assumptions that the networks maximize average ratings and have no costs for schedule changes. Assuming the networks simply maximize average ratings is equivalent to maximizing revenue only if the relationship between show ratings and prices of commercial time during these shows is linear and demographics are unimportant.2 However, neither of these conditions hold. Using the Household & Persons Cost Per Thousand data from Nielsen Media Research, we estimate a Box-Cox model of ad prices. Our estimates reveal a convex relationship between ad prices and audience size and significant relationships between ad prices and audience age and gender measures. An implication of this model is that the value of an additional viewer (or more interestingly, an additional million viewers) differs across shows. For example, we estimate that an additional million viewers increases ad revenue by $86,974 for each half-hour of Roseanne, a popular show with desirable audience demographics, compared to an increase of only $50,649 per half-hour of Hat Squad, a less popular show with undesirable audience demographics. The finding that marginal returns for additional viewers differ across shows leads us to conjecture that a schedule which maximizes ad revenue ought to place shows with high marginal returns in time slots which are favorable (i.e., have weak competing shows) to a greater extent than a schedule which simply maximizes ratings. However, we find that for each network the schedule which maximizes ad revenue is essentially identical to the schedule which maximizes ratings. This must reflect the fact that strategies, such as counter-programming and placing strong shows at 8:00 or 9:00, which in Goettler and Shachar (1999) were found to increase ratings, are consistent with the strategies suggested by differing marginal returns. As such, we find that when analyzing competition in the short run during which a network’s stock of shows is fixed, the simpler objective of ratings maximization is consistent with revenue maximization. The predicted revenue increases are 17.7 percent for ABC, 16.8 percent for CBS, and 16.5 percent for NBC, when each network implements its best response schedule holding the other networks’ schedules fixed. In a Nash equilibrium of the static scheduling game, these revenue gains range from 6 to 16 percent. Despite the availability of such revenue gains, the networks may still be acting optimally if there exist significant costs to implementing schedule changes. After all, each 2
We are assuming that the number of commercials aired per hour is fixed. Until 1981 the National Association of Broadcasters had limited commercial time during prime time to 6 minutes per hour. However, in 1981 this was declared a violation of antitrust laws and the limit was dropped. Since then prime time commercial time has steadily increased, reaching 15.35 minutes per hour in 1996, according to the Commercial Monitoring Report.
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network is really interested in maximizing profits. In the short run expenditures on programming are fixed, so the only variable costs are the opportunity costs of using air-time to promote a new schedule. However, even when such costs are considered, we find that the networks schedule suboptimally. The paper proceeds as follows. In the next section, we discuss the market for commercial spots on network television and estimate the relationship between ratings and advertisement revenue. Then in section 3, we discuss the model of viewer choice and scheduling strategies suggested by the model. In section 4 we compute best response schedules and Nash equilibria of the scheduling game and analyze the strategic behavior of the television networks under various specifications of the payoff function. Section 5 concludes.
2
Network Ratings and Advertisement Revenue
2.1
The network advertising market and data
Typically 70 to 80 percent of network commercial time is sold in the up-front market during May for the upcoming television season commencing in early September. The remainder is sold in the scatter market during the season, occasionally hours before the show airs. Unsold time is used to promote the network’s shows or to provide public service messages. Contracts specify the prices to be paid for the commercial time and minimum guaranteed ratings, as measured by Nielsen Media Research.3 Often the guaranteed ratings correspond to particular demographic segments. For example, advertisers seeking young viewers typically receive guarantees for viewers aged 1849. Ratings particular to gender or household income are also occasionally guaranteed. When the guaranteed ratings are not attained, the networks provide make-goods to compensate their shortchanged advertisers. These make-good commercials, however, typically air on less popular shows and do not fully compensate advertisers.4 If commercial prices merely reflected guaranteed ratings, then the relationship between advertisement revenues and guaranteed ratings would be the relationship of interest. Through our 3
The accuracy of these ratings has been the subject of much debate. Nonetheless, the Nielsen ratings are the best available and serve as the industry standard. 4 Rather than specifying the total price for airing a commercial on a particular show, the contracts could specify a per viewer (or per viewer with desired demographics) rate which would then be converted into a total price after the show’s audience size is reported by Nielsen. While this alternative avoids the risk of paying for viewers who are not delivered, it introduces uncertainty regarding the total payment which complicates the coordination of an ad campaign on a fixed budget. Given the absence of such contracts, the nuisance of a variable total payment must exceed the concern that some shows will deliver fewer viewers than expected.
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discussions with network executives, we have learned that commercial prices reflect expected audiences, and the demographics of these expected audiences, more than they reflect the guaranteed ratings of the contracts, which are typically much lower than the expected audience ratings. Since we do not possess data on the expected ratings, we must estimate the relationship between realized ratings and advertisement revenues. Assuming the expected ratings to be unbiased, the difference between expected and realized ratings provides an interpretation of the error term in the econometric models presented below. The data is from the Household & Persons Cost Per Thousand monthly publications by Nielsen Media Research for September through December, 1992. These publications list for each network show the cost of airing a 30-second commercial during its broadcast and its estimated audience sizes for the following categories: Households, Total Adult Women, Women ages 18-34, Women ages 18-49, Women ages 25-54, Total Adult Men, Men ages 18-34, Men ages 18-49, Men ages 25-54, Teens (ages 12-17), and Children (ages 2-11). The data on commercial costs are provided by ABC, CBS, NBC, and Fox to the Nielsen monitoring service. The estimated audience sizes are derived from the Nielsen Television Index (NTI) sample which provides minute by minute records of viewers’ choices using the People Meter device. Since the publication is monthly, all data are averages over the month. Though the data contain observations for all network shows, we only use shows airing past 6:00 p.m. since the ratings data is often missing for earlier shows and our application involves scheduling evening shows.5 We also exclude shows which aired only once during the period. Many of these observations appear to be outliers. Furthermore, estimates based on the remaining 173 observations of shows which air only once are very different from the estimates based on shows with multiple airings. Indeed the Wald statistic testing the equality of the two sets of estimates is huge for all specifications of the model. Excluding these 173 observations leaves 437 observations which are used to estimate the models in the next subsection.
2.2
Modeling ad prices
The top plot in figure 1 reveals an essentially linear relationship between the logarithm of each show’s audience size and the logarithm of the price of 30 seconds of commercial time during that show. While this simple log-log model has a high R-squared of 0.8159 and appears to explain the 5
We considered using only shows which air during weekday prime time hours since this is the exact period for our scheduling analysis, but this resulted in too few observations.
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data extremely well, the bottom plot indicates that audience size is only able to explain a small amount (5.8 percent) of the variation in costs per viewer.6 These per viewer costs vary significantly, from .19 to 1.32 cents, and are driven primarily by viewer demographics. Much of the remaining variation, in both plots, is explained by the demographic composition of the audiences, as discussed below. While it is apparent from figure 1 that the relationship between ad prices and audience size is not linear (in levels), the degree of curvature is not obvious. Given the importance of accurately predicting ad prices, we would rather not assume that taking logs of the data is the best transformation. The Box-Cox (1964) model provides a simple method for estimating the degree of nonlinearity inherent in the relationship between costs of commercials and show ratings. In particular, one can easily test the hypotheses that the model is linear or log-log using likelihood ratio tests since both of these models are special cases of the general Box-Cox transformation. These special cases correspond respectively to λ = 1 and λ = 0 in the transformation x(λ) ≡
log(x)
(xλ −1) λ
if λ = 0
(1)
otherwise
for any variable x. We use this transformation to model ad prices as Ps(λ) = α + Xs γ + Zs(λ) β + s
(2)
where Ps is the price per 30-second commercial aired during show s, Zs is the vector of explanatory variables to be transformed, and Xs is the vector of explanatory variables which are not to be transformed. The only explanatory variable which the data reveals should be transformed is the audience size (i.e., number of viewers) for show s. Thus, we now define Zs to be audience size.7 The following variables comprise Xs : the fraction of the audience aged 12–17 years old, the fraction aged 18–34, the fraction aged 35–49, the fraction aged 50 and older, the fraction of the audience which is female, the square of the fraction which is female, and the standard deviation of the ages of the viewers comprising an audience. Table 1 presents estimates of four models: (1) the Box-Cox model using all the variables, (2) the log-log model using all the variables, (3) the Box-Cox model using only the significant variables, and (4) the log-log model using only the significant variables. First note that the log-log 6
Note that the log-log model allows costs per viewer to vary with audience size. For example, if the slope exceeds unity then costs per viewer increase with audience size. 7 Dividing Zs by the U.S. population yields the familiar Nielsen rating for the show.
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specifications are rejected using likelihood ratio tests of the restriction that λ = 0 in the BoxCox specification. The test statistics are 14.8526 and 15.3267, which have p-values of 0.00012 and 0.00009. As expected, the linear models (estimates for which are not reported) are overwhelmingly rejected with test statistics exceeding 280 for the restriction that λ = 1. While the log-log models are rejected, they are still reported since log-log models are widely used and easier to interpret. For example, the premium that advertisers place on reaching large audiences is revealed by the coefficient on audience size in models 2 and 4 being significantly greater than 1. That is, the price per viewer is increasing in the size of the audience. Another notable finding is that viewers aged 12–17 or 18–34 are apparently no more valuable to advertisers than viewers aged 2–11 (the excluded age category). Our data is from 1992, at which time the broader age category of 18–49 was considered the most desirable. Our estimates indicate that the upper end of this category was the driving force behind the value of delivering 18–49 year olds to advertisers.8 Also note the negative impact on ad price when shows target viewers 50 years of age and older. The estimates corresponding to the standard deviation of viewers’ ages and the gender variables reveal that more homogeneous audiences command higher prices. This is not surprising given the fact that most products being advertised are relevant to only a particular segment of the population. Advertisers really only care about this particular segment and are not willing to pay as much for viewers who are unlikely to be potential customers. As such, we find that ad prices are decreasing in the dispersion of viewers’ ages and are quadratic in the fraction of viewers which are female. This quadratic relationship has a minimum at 0.51 and is depicted for the show Melrose Place, as an example, in figure 2. The fraction of women in audiences ranges from 0.34 to 0.70 contributing to the significant variation in prices (and prices per viewer) for audiences of the same size. Table 2 reports estimates of two models which explicitly model prices per viewer.9 Since so much of the variation in ad prices is due to audience size, these models provide a somewhat easier way to identify the impact of audience composition on ad prices. The estimates are all in accordance with the models reported in 1. That is, the signs are all the same and the same variables are statistically significant. Also, the positive coefficient estimate for audience size (in millions of 8
Recently, the emphasis in the media has been on the younger 18–34 year olds. As such, we would expect this age group to be significant if we were to use a more recent data set. 9 Advertisers frequently report costs per thousand, denoted CPM.
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viewers) reflects the premium paid for large audiences. One explanation for the large audience premium is that two shows reaching 10 million viewers each may not reach 20 million different viewers, especially if the advertiser buys time on similar shows in order to target a specific demographic segment. Furthermore, there are few substitutes for advertising on a popular network show since such large audiences are very rare — on television or elsewhere. As such, the networks actually have some market power when selling time on these shows and, as expected, charge a higher price. When selling time on less popular shows, however, the networks face many close substitutes, both on television and in other media. In fact, an FCC study (FCC, Network Inquiry Special Staff, 1980) concluded that radio, magazine, newspaper, billboard, and alternative television advertising constrain the prices of network advertising such that prices for network ads reflect competitive forces.
2.3
Implications for scheduling strategies
Rearranging the model in equation 2, show s has an expected price of Ps = E
1/λ
1 + λ(α + Xs γ + Zs(λ) β + s )
(3)
where E[·] denotes the expectations operator. Table 3 presents expected advertisement revenue generated by three shows with different audience sizes and compositions. Monte Carlo integration using 50,000 draws of s is used to integrate over the integral implicit in equation 3. The expected gains in revenue due to an additional million viewers is presented in the lower portion of the table. The importance of viewer demographics is evident when comparing Hat Squad to Melrose Place. Advertising on Melrose Place costs (and is predicted to cost) more than 50 percent more than advertising on Hat Squad despite having 22 percent fewer viewers. This reflects the fact that Melrose Place has an audience which is 64.7 percent female and only 7.3 percent aged 50 years or older, while Hat Squad has only 58.7 percent women and a whopping 53.9 percent of viewers aged 50 and older. The result is that Melrose Place commands almost twice as much money per viewer as does Hat Squad. While the audience demographics for Roseanne are not quite as good as for Melrose Place, drawing 32.9 million viewers enables Roseanne to nearly match the per viewer price of Melrose Place. As illustrated in the last three rows of table 3, the marginal value of additional viewers differs across shows. As such, a network can potentially increase its revenues while lowering its average viewership (i.e., ratings) across shows. For each network the time slots vary in their competitiveness 8
or difficulty of attracting viewers from the other alternatives. By switching an unpopular show in a less competitive time slot with a popular show from a competitive time slot, the network can sacrifice ratings from a low marginal return show in order to increase the ratings of a high marginal return show. For example, suppose Melrose Place had a “difficult” time slot and Hat Squad had an “easy” time slot on the same network such that switching the two shows would result in a gain of a million viewers for the former show and a loss of a million for the latter. Using the predicted gains from table 3, the change in weekly revenue for the network would be 2(89, 529 − 50, 649) = $77,760 since each show is an hour long. This amounts to an annual gain of more than 4 million dollars assuming the shows aired 52 times per year. Given this substantial gain in revenue, total viewership could fall while revenue actually rises. This contrived example demonstrates how maximizing average ratings may lead to schedules which do not maximize revenue. In reality, switching two shows in a schedule effects the ratings of all the shows on the nights involved in the switch since each time slot is linked through viewer persistence, as discussed in section 3. Nonetheless, the general strategy of airing shows with high marginal returns in “easy” time slots is implied by the models in table 1. For example, this strategy suggests that the networks place their strongest shows at 9:00 p.m.—the most popular time slot for watching television during which competition from the non-viewing option is lowest. Second, the networks should avoid airing their best shows against one another in the same time slot since block-buster shows generate high prices per viewer. For instance, NBC has dominated Thursday night television for the last several years with little competition from the other networks who have instead aired their top shows on other evenings. Of course, there are many other factors influencing the networks’ scheduling strategies. The networks often avoid competing for the same types of viewers by counter-programming—airing shows with characteristics different from those of the other shows in the same time slot. Each network also tends to air similar programs in sequence in an effort to continue to serve its viewers from the previous period. This strategy is known as homogeneous programming. A third strategy is to air strong shows at 8:00 to secure a large audience which, due to viewer persistence, will likely stay tuned for most of the evening. To assess the extent to which these strategic considerations manifest themselves in the schedules, we must estimate a model which produces ratings predictions and develop an algorithm for determining optimal schedules given the objective of the network.
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3 3.1
The network’s objective function Ratings, Revenues, and Costs
To analyze competition using game theory we must specify the strategy space of each network and its payoff (or objective) function. While profit maximization is the typical firm objective, revenue maximization is consistent with the broader objective if costs do not vary over choices in the strategy space. For instance, in the short run a television network can change its show schedule but cannot easily change which shows are aired since it takes time to develop new shows. If schedule changes were cost-less then revenue maximization would be consistent with profit maximization in the short run. Since such costs are not zero, however, a revenue gain due to modifying the schedule must be interpreted as an upper bound to the profit gain. For part of the strategic analysis presented in section 4 we operate under this scenario of revenue maximization ignoring costs of schedule changes. We then analyze competition between the networks while accounting for potentially significant costs of schedule changes. Finally, we compare our findings with those obtained in Goettler and Shachar (1999) when the networks are assumed to maximize ratings. If we had data detailing the costs of purchasing (or developing) shows, then we could also analyze competition in the longer run during which the networks can change which shows they air. In the long run, assuming the networks maximize ratings may be inconsistent given the huge sums of money required to purchase hit shows, such as ER for which NBC pays Warner Brothers $13 million per episode.
3.2
Modeling viewer choice
To assess payoffs for various scheduling strategies we must predict show ratings when the schedule is hypothetically changed. Previous studies have employed a variety of models for predicting show ratings. Horen (1980) and Kelton and Schneider (1993) use linear aggregate ratings models which enable integer programming methods to be used for finding schedules that maximize weekly ratings. The drawback of these models is they do not identify the interwoven effects of switching costs, show characteristics, and viewer heterogeneity. In fact, to treat the network’s scheduling problem as an integer programming task, these studies must employ a ratings model which predicts each show’s contribution to the weekly ratings to be independent of its preceding and following shows. This directly contradicts evidence presented in Goettler and Shachar (1999) that the number of viewers 10
staying tuned to a network during a show change depends on the similarity of the two shows. The alternative to an aggregate ratings model is an individual viewer choice model in which viewers choose from among a set of shows possessing various show characteristics. A new schedule corresponds to a rearrangement of the show-specific characteristics, which are either estimated or specified a priori. Obviously, a model will accurately predict ratings only if these show characteristics effectively characterize the shows. Indeed, one of the difficult aspects of analyzing the strategic behavior of the television networks is identifying suitable show characteristics. The simplest approach is to categorize each show a priori, perhaps as a comedy, drama, or news show. Such labels, however, poorly characterize shows since shows in the same category often have striking differences and shows in different categories often have similarities. Rust and Eechambadi (1989) analyzes scheduling issues using an augmented version of the Rust and Alpert (1984) model which assigns shows a priori to one of several categories. Alternatively, show characteristics have been estimated by Gensch and Ranganathan (1974) using factor analysis and by Rust, Kamakura, and Alpert (1992) using multidimensional-scaling methods. Neither of these studies estimate show characteristics simultaneously with the other determinants of viewer behavior, such as costs of switching channels. The viewer choice model presented in Goettler and Shachar (1999), however, is a structural model which does simultaneously estimate all components of the choice model. As such, this model identifies the separate effects of switching costs and show characteristics on persistence in viewers’ choices. Furthermore, since the model estimated is the data generating process itself, it is appropriate for conducting policy experiments, such as introducing new schedules. The other models, however, are subject to the Lucas (1981) critique since their estimates of show characteristics are based on reduced form methods and would likely differ under different schedules. Thus, we employ the model of viewer choice developed in Goettler and Shachar (1999) and estimated using a panel data set from Nielsen Media Research of 3286 viewers’ choices over the week of November 9, 1992. In each period t, individual i chooses from among J=6 mutually exclusive and exhaustive options indexed by j, corresponding to (1) TV off, (2) ABC, (3) CBS, (4) NBC, (5) Fox, and (6) non-network programming, such as cable or public television. Let yi·t denote the response vector, such that for j = 1, . . . , J, yijt = 1 if i chooses j at time t and yijt = 0 otherwise. In summary, the model simultaneously estimates show characteristics in a 4-dimensional latent attribute space, the distribution of viewers’ most preferred locations in this space, the role of switching costs, the utility from not watching television, and the utility from watching non-network
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programming. The switching costs, ideal points, utility from not watching television, and utility from non-network programming all vary across demographic segments defined by age, gender, household income, and other measures. Please see Goettler and Shachar (1999) for a detailed description of the model and the parameter estimates.
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Strategic network behavior
4.1
Optimal Scheduling
The importance of program scheduling is widely acknowledged by the networks as network strategists and executives actively debate the scheduling of their shows. For the most part, these strategists currently rely on their intuition and various interpretations of the aggregate Nielsen ratings. These interpretations can vary substantially since the source of a program’s rating is difficult to discern without accurately accounting for the many factors influencing viewer behavior, such as the lead-in effect, show competition, and viewer heterogeneity.10 Disentangling the interaction of these factors is the attraction of the model presented in Goettler and Shachar (1999). For a given schedule, predicted ratings (disaggregated by demographic segments) are converted to the variables Zs and Xs and then to payoffs using equation 3.11 Each network’s bestresponse schedule maximizes its payoff holding the other networks’ schedules fixed. This bestresponse schedule is the solution to a difficult discrete optimization problem. The approximate solution which we use is described in appendix B. Table 4 presents elements of the best-response schedules for each of the big three networks using ad revenue as the payoff function. Each network is able to obtain significant revenue gains — 17.72 percent for ABC, 16.80 percent for CBS, and 16.54 percent for NBC.12 These percentage gains translate into roughly 6.1 to 7.1 million dollars per week, assuming 10 minutes of network commercial time each hour.13 Multiplying by 52 yields annual gains ranging from 317 to 369 million dollars per year. Also note that the percentage gains in ratings are roughly the same as the revenue gains. 10
The lead-in effect refers to the tendency for shows to have high ratings if the preceding (or lead-in) show had obtained a high rating. 11 Appendix A describes the method for obtaining the predicted ratings. 12 In 1992 Fox only broadcasted shows on Wednesday, Thursday, and Friday, and only from 8:00–10:00. As such, we focus on the three major networks. 13 The 15.35 minutes of commercials time reported in the introduction includes time sold by the affiliates and time used to promote the network’s programs.
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What types of scheduling strategies generate these gains in revenues and ratings? The lower half of table 4 provides measures of several typical strategies implemented by the networks. Counterprogramming (CP) is measured by the average distance from the competition in each quarter-hour. Homogeneous programming for network j is measured in two ways — by the average distance between the zjt for t corresponding to the same night (NH), and by the average distance between the zjt for sequential periods (SH). Three other strategies pertain to the placement of quality or “power” shows. Often a network airs its “power on the hour” since more viewers have just finished watching a show, and are willing to switch channels, than at the half-hour when many viewers are in the middle of an hour-long show. A network also tends to air its “power early” in an effort to build a large audience which they can retain with the help of switching costs and inertia. Both “power on the hour” and “power early” are captured by η t , the average over days of show “quality” (denoted ηjt in the model of Goettler and Shachar (1999)) in each time slot. The third power placement strategy involves not airing one’s best shows against other strong shows with (relatively) similar z characteristics. We call this strategy “power counter” (PC) and measure its implementation by the average over the week of the ratio RRjt /RRˆjt , where ˆj refers to the closest competitor (in the latent attribute space) to j at time t and RRjt is the relative rating defined as the rating for j at t divided by the average rating for j over the week. Goettler and Shachar (1999) analyze the relationship between these measures of various strategies and the predicted ratings for randomly generated schedules. Given the regression results from that analysis, best response schedules which maximize ratings are expected to have higher CP (than the actual schedule), higher PC, lower NH and NS, and higher ηt on the hours and early in the night. Indeed, the ratings maximizing schedules do exhibit these properties. Interestingly, the revenue maximizing schedules are nearly identical to the schedules which maximize ratings. In fact, for NBC the two schedules are exactly the same and for CBS the schedules are such that the values of the strategy measures are almost the same. For ABC, the only difference between the two schedules is that the revenue maximizing schedule places more “power” later in the evening, as captured by the η t measures. The reason for the strong similarity in the use of various scheduling strategies despite different objective functions is must be that the incentives related to audience size and composition (discussed at the end of section 2.3) are already provided by ratings maximization. For example, audience composition already is important under ratings maximization since ratings are higher if shows which
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target a specific demographic segment are scheduled on the same night. Also, avoiding “power wars”, which places hit shows in relatively easy slots, is important to both ratings maximization and revenue maximization. This analysis demonstrates empirically that the simpler objective of ratings maximization is consistent with revenue maximization, when analyzing competition in the short run during which a network’s stock of shows is fixed. What about costs? As mentioned in the previous section, the predicted gain in revenue serves as an upper-bound since costs to implementing the best response schedule are ignored. Such costs could be substantial since the number of schedule changes needed to move from the network’s original schedule to the best-response schedule is 26 for ABC, 20 for CBS, and 18 for NBC.14 Furthermore, mid-season schedule changes usually entail moving only a few shows or blocks of shows. To crudely account for switching costs we also computed best-response schedules in which a change in the schedule is recommended only if it results in at least a 2 percent gain in revenue. If costs are compared to annual revenue gains from modifying a schedule, then this requirement is equivalent to assuming that the cost of a schedule change for ABC is 0.02 ∗ ($124,061 per ad) ∗ (20 ads per hour) ∗ (15 hours per week) ∗ (52 weeks per year) which equals $38.7 million. Since the only cost to implementing a schedule change is the opportunity cost of commercial time used to promote the new schedule, this cost may be viewed as paying for 312 commercials to promote the new schedule. Obviously, this cost estimate is absurdly high. We want, however, to err on the side of being conservative with respect to the recommended schedule changes. Using these costs, ABC would optimally implement three changes to its schedule for a revenue gain of 10.23 percent, CBS would optimally implement two changes for a gain of 9.73 percent, and NBC would optimally implement two changes for a gain of 12.31 percent. Hence, the networks appear to be scheduling sub-optimally, even when costs of schedule changes are considered. While these gains are non-trivial, they are modest compared to the predicted gains reported in previous studies of network television scheduling. Rust and Eechambadi (1989) find a startling 78 percent improvement in NBC’s schedule using a stochastic, heuristic approach to finding the optimal schedule. Even more surprising, they find nearly as great of an improvement by choosing the best schedule of a mere 400 randomly created schedules. We suspect 14
A single schedule change is defined as a swap of one continuous block of shows with another continuous block.
14
that the source of these huge gains in average ratings is model misspecification rather than pathetic scheduling by the networks.
4.2
Nash equilibrium
A natural question is whether the gains under autarkic optimal scheduling will persist in equilibrium. A possible scenario is that strategic responses from the other networks will erase the gains. There is no guarantee that an equilibrium exists, but if one is found then it obviously exists. To search for an equilibrium we cycle through the four networks, individually implementing their best-response schedules holding the other schedules fixed. A schedule is a Nash equilibrium if no network (unilaterally) has an incentive to change. The order in which the networks hypothetically implement their best-response schedules marginally influences the equilibrium payoffs, but not in any predictable manner. Though one might expect a network to attain a higher payoff when it moves first, this is not always the case. For every specification of the viewer choice model and revenue model, the above algorithm converges to a Nash equilibrium in fewer than 4 rounds. The usefulness of analyzing the equilibrium is not in pinpointing the exact equilibrium schedule which could or should be played by the networks. In fact, the precise schedules are not determined since the best response schedules are not unique. The equilibrium found also depends on the “sequence of play” in the equilibrium search algorithm. Nonetheless, much is revealed about strategic competition by the common features of the equilibria. The most important finding is that the gains from each network unilaterally optimizing its schedule are not eroded away by strategic responses from the other networks. In each equilibria, the ratings and payoffs of the big three networks (ABC, CBS, and NBC) increase, though by less than the gains associated with the best response schedules (holding the other networks’ schedules fixed). When ABC moves first, the percentage gains in revenue are 17.6 percent for ABC, 10.9 percent for CBS, and 12.3 percent for NBC. When costs are included in the payoff function as discussed above, revenues increase by 9.1 percent for ABC, 7.0 percent for CBS, and 7.2 percent for NBC. As expected, the same strategies responsible for the gains under the autarkic scenario are at work in equilibrium. Furthermore, we again find that these strategies are the same regardless of whether ratings or revenue is maximized by each network. That is, the networks increase their revenues and ratings by increasing their use of counter-programming, homogeneous programming,
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and airing strong shows on the hours and early in the night. Inspecting the placement of shows in both the best response schedules and the equilibrium schedules, we find that the counter-programming and homogeneous programming is increased primarily by choosing to air situation comedies past 10:00. Network strategists have avoided airing any half-hour shows past 10:00. This research illustrates that this tradition may not be optimal. At a minimum, experimenting with sitcoms after 10:00 seems warranted. Obviously, since each network increases ratings and revenues, the gains are achieved by pulling viewers from the non-viewing and, to a lesser extent, non-network viewing alternatives. This reflects the benefit to all the networks of counter-programming, both along the vertical (quality) and horizontal dimensions of show attributes. Essentially, the increased use of counter-programming enables the networks to provide programming in each time slot which appeals to more viewers. Also, the increased homogeneous programming induces viewers to stay tuned to the networks longer once they start watching. One might wonder if the networks could collude to obtain higher ratings. The answer is no, regardless of the objective function. The collusive outcome results in nearly identical payoffs for the networks. This is not surprising given that the networks are obtaining their gains primarily from the non-viewing and non-network options, not by stealing from each other. Again, this reflects the strategic complementarity of counter-programming and not airing their strongest shows at the same time.
5
Conclusion
This research uses a Box-Cox model to estimate the importance of audience size and demographic composition in determining prices for commercial time on the broadcast networks. We find that for a given audience size higher prices are obtained by shows with more homogeneous viewers (as measured by age and gender) and by shows with a high percent of 35–49 year old viewers. Lower prices are obtained by shows with a high percent of viewers 50 years old and older. Furthermore, we find that the price per commercial is convex in the total number of viewers. That is, cost per viewer is increasing in the size of the audience. Interestingly, the optimal scheduling behavior of each network is the same regardless of whether the firm is modeled as maximizing ratings or ad revenue, resulting in revenue gains between 16 and 18 percent. Furthermore, substantial gains are predicted even when costs of schedule changes 16
are included in the analysis. These gains primarily reflect increased counter-programming and homogeneous programming by choosing to air some situation comedies past 10:00. If data detailing production or purchase costs for shows become available, we could extend our analysis to consider the longer run strategy space of determining which shows should be canceled and which types of shows should be adopted. We suspect that profit maximization will yield results which differ from those obtained under the assumption of ratings maximization. While shows which target homogeneous groups, particularly middle-aged viewers, generate the most revenue, they may be very expensive to develop or purchase. A 1996 change in FCC regulations has led the networks to take complete or partial ownership of many of the shows they air. While the networks claim that ownership does not impact the scheduling decisions, perhaps it should. Scheduling can make or break a show, and a show which survives for several seasons can earn millions of dollars in syndication after its network run. We would like to modify the above analysis to account for this interesting development in future work.
6
Tables and Figures
17
18 -4880.0806 14.8553 281.5602
1.7189
0.1484 13.8109 0.5443 1.7281 -0.5036 15.3507 -5.1219 -0.2434 -84.1238 82.8157
0.0404 10.9132 0.1155 4.7007 2.3926 7.2910 2.9686 0.1254 41.0696 40.0120
Standard Error
0.0668 0.8919 -4887.5083
0 -4.0589 1.1881 0.5755 -0.1594 3.0107 -0.9580 -0.0485 -15.3597 15.2010
Coefficient Estimate 1.0525 0.0227 0.9206 0.4702 0.4997 0.3596 0.0127 2.4782 2.2493
Standard Error
Model 2
6.9312 2.4701 0.1220 41.8296 40.7882
14.8117 -5.4289 -0.2495 -86.1786 84.9380
-4880.2075 15.3267 282.8470
1.7978
0.0403 10.6542 0.1138
Standard Error
0.1504 14.5982 0.5381
Coefficient Estimate
Model 3
0.0666 0.8917 -4887.8709
2.7225 -1.0243 -0.0488 -15.4026 15.2769
0 -3.9348 1.1863
Coefficient Estimate
0.3032 0.0863 0.0102 2.3992 2.1764
0.7689 0.0219
Standard Error
Model 4
Only the dependent variable (price per 30 second commercial) and audience size are transformed using equation 1. The regression of log(price) on log(AudienceSize) yields a coefficient estimate of 1.1496 and an R-squared of 0.8159. Standard errors for the Box-Cox models are computed using the Hessian matrix of the log likelihood function. The age demographic which is excluded, to avoid perfect collinearity, is the fraction of viewers aged 2–11. Using a 95 percent significance level, the critical value for the likelihood ratio tests is 3.84.
σ2 R-squared Log Likelihood χ2 for H0 : λ = 0 χ2 for H0 : λ = 1
λ Constant Audience size(λ) Fraction aged 12–17 Fraction aged 18–34 Fraction aged 35–49 Fraction aged 50+ Std. dev. of ages Fraction female (Fraction female)2
Coefficient Estimate
Model 1
Table 1: Estimates of Box-Cox and Log-Log Models of 30-second Commercial Prices
Table 2: Estimates of Models of Costs Per Viewer (in cents) Model 1 Variable Constant Millions of viewers Fraction aged 12–17 Fraction aged 18–34 Fraction aged 35–49 Fraction aged 50+ Std. dev. of ages Fraction female (Fraction female)2 σ2 R-squared
Model 2
Coefficient Estimate
Standard Error
Coefficient Estimate
Standard Error
3.3476 0.0071 0.1032 0.0527 1.3628 -0.4595 -0.0235 -10.4588 10.0878 0.0229 0.4007
0.5419 0.0012 0.5423 0.2767 0.2877 0.2131 0.0075 1.4484 1.3144
3.4341 0.0070
0.3954 0.0011
1.3271 -0.5080 -0.0246 -10.5391 10.1620 0.0228 0.4006
0.1740 0.0508 0.0059 1.4032 1.2726
19
20 $ 5,065 $ 50,649 $ 2,633,735
Gain from extra million viewers, per commercial Gain from extra million viewers, per half-hour Gain from extra million viewers, per year
$ 8,953 $ 89,529 $ 4,655,515
11,520,000 0.154 0.073 14.569 0.647 $ 90,600 $ 92,791 0.805 $ 927,912 $ 48,251,426
Melrose Place
Calculations assume 10 commercials per half-hour and 52 episodes per year.
14,770,000 0.202 0.539 18.307 0.587 $ 55,700 $ 60,707 0.411 $ 607,065 $ 31,567,387
Total viewers Fraction ages 35–49 Fraction ages 50+ Standard deviation of viewer ages Fraction women Actual price per commercial Predicted price per commercial Predicted cents per viewer per commercial Predicted revenue per half-hour Predicted revenue per year for the series
Hat Squad
$ 8,697 $ 86,974 $ 4,522,453
32,900,000 0.243 0.179 17.718 0.604 $ 254,600 $ 256,551 0.780 $ 2,565,510 $ 133,406,514
Roseanne
Table 3: Expected Revenue for Three Shows with Different Audience Sizes and Demographics
21
≡ ≡ ≡ ≡ ≡ ≡ ≡ ≡ ≡ ≡
average(|zjt − zj 0 t |) average(|zjt − zjt0 |) average(|zjt − zj,t−1 |) average(ηj,8:00 ) average(ηj,8:30 ) average(ηj,9:00 ) average(ηj,9:30 ) average(ηj,10:00 ) average(ηj,10:30 ) average(RRjt /RRˆjt ) 0.63 0.55 0.36 2.33 2.12 2.33 1.94 2.09 2.09 1.09
8.55
$124,061
0.70 0.43 0.35 2.13 2.09 2.59 2.25 2.11 1.71 1.55
9.81 1.27 14.81
$146,047 $21,986 $6,595,722 17.72
0.67 0.54 0.40 2.21 2.25 1.95 1.78 1.93 1.93 1.13
8.74
$117,080
0.71 0.37 0.33 2.10 2.08 2.02 1.93 2.01 1.90 1.24
9.78 1.03 11.80
$136,755 $19,674 $5,902,320 16.80
CBS Actual Optimal
0.59 0.59 0.52 2.12 2.06 2.11 1.95 1.90 1.90 1.27
8.32
$124,346
0.72 0.39 0.35 2.10 2.10 2.32 2.07 1.75 1.71 1.30
9.56 1.24 14.86
$144,918 $20,572 $6,171,654 16.54
NBC Actual Optimal
The first column contains the variable names: CP for Counter-Programming, NH for Nightly Homogeneity, SH for Sequential Homogeneity, η t for quality at time t, and PC for Power Counter. The variable RRjt is the Relative Rating defined as the rating for j at t divided by the average rating for j over the week. The subscript ˆj in the definition of PC refers to the closest competitor to j at time t.
CP NH SH η 8:00 η 8:30 η 9:00 η 9:30 η 10:00 η 10:30 PC
predicted weekly rating weekly ratings gain percentage gain
predicted revenue per ad revenue gain per ad weekly revenue gain (20 ads/hour) percentage revenue gain
ABC Actual Optimal
Table 4: Best Response Schedules compared to Actual Schedules
Figure 1: Commercial Prices and Audience Size
log( $ per 30−second commercial )
13 12.5 12 11.5 11 10.5 10 9.5 9 8.5
Cents per 30−second commercial per viewer
8 14
14.5
15
15.5 16 log( total number of viewers )
16.5
17
17.5
1.4 1.2 1 0.8 0.6 0.4 0.2 0
0
5
10
15 20 25 Total number of viewers (in millions)
22
30
35
40
Figure 2: Impact of Female Composition for Melrose Place 260
Predicted Price per 30−second Commercial ($1000s)
240
220
200
180
160
140
120
100
80
60 0.2
0.3
0.4 0.5 0.6 Fraction of Viewers which are Female
23
0.7
0.8
Appendix A: Predicting Show Ratings Given any candidate schedule Y , a forecast of the ratings for each show can be constructed. Conceptually, the simplest way to forecast the ratings is to simulate the structural model. This is the path chosen by Rust and Eechambadi (1989). The drawback, of course, is the additional error introduced via the stochastic nature of simulations. This error could be reduced to acceptable levels by increasing the number of simulated viewers, but such simulations take time, and the error is never eliminated. The additional time would not be such a concern if it were not for the fact that we will need to forecast ratings for many millions of candidate schedules. A more involved task, from the perspective of the researcher not the computer, is to extract the reduced forms of the expected ratings from the model’s logit structure and parameter estimates. For each viewer we randomly draw a νi from the estimated distribution of ideal points and compute the viewer’s probability of watching each show. Since the additive stochastic utility term in the model is type I extreme value, the probability of viewer i with preference vector νi choosing yijt = 1 at time t conditional on her previous choice of yi,·,t−1 is of the convenient form ˆ yi,·,t−1 , Xi , Yjt , νi ) = f (yijt = 1|θ,
ˆ yi,·,t−1 , Xi , Yjt , νi )) exp(¯ uijt (θ; J P
j 0 =1
,
(4)
ˆ yi,·,t−1 , Xi , Yj 0 t , νi )) exp(¯ uij 0 t (θ;
ˆ yi,·,t−1 , Xi , Yjt , νi ) is the non-stochastic where θˆ is the vector of estimated parameters, and u ¯ijt (θ; component of utility for viewer i watching choice j at time t with schedule Y , given having chosen yi,·,t−1 last period. Recall, the J = 6 viewing choices respectively correspond to Off, ABC, CBS, NBC, Fox, and non-network. The state dependence creates the need to express the expected rating conditional on the choice from the previous period. However, the previous choice is not known. Rather, the probability of ˆ Xi , Yjt , νi ) each previous choice is known, given the model. The marginal probability s(yijt = 1|θ, is therefore expressed as the probability weighted average of the conditional probabilities in equation (4). Explicitly, ˆ Xi , Y, νi ) = s(yijt = 1|θ,
X
h
i
ˆ Xi , Y, νi ) · f (yijt = 1|θ, ˆ yˆi,·,t−1 , Xi , Yjt , νi ) , s(ˆ yi,·,t−1 |θ,
(5)
yˆi,·,t−1 ∈Y
where the set Y contains the response vectors corresponding to each of the J possible choices at t − 1. The recursive nature of equation (5) means that in order to compute the probability of a viewer choosing network j at time t, the probabilities of having chosen each of the networks must 24
be known for all preceding periods. These viewer probabilities are then converted to expected ˆ Xi , Y, νi ) over all n viewers. network ratings for network j in period t by averaging s(yijt = 1|θ, ˆ Y ) denote the ratings for network j under schedule Y , we have Letting rt (j; θ, ˆ Y, (ν1 , . . . , νn )) = rt (j; θ,
n 1X ˆ Xi , Y, νi ) . s(yijt = 1|θ, n i=1
(6)
The dependence of rt on the particular draws of νi for each viewer implies there is some simulation error in this estimate of the network’s expected ratings. If computation time were not of concern, then we could reduce this simulation error by drawing R random νi for each viewer and compute s(yijt = 1|·) as the average of the R values from equation (5). However, ˆ Xi , Y, νi ) is an unbiased estimator of the marginal s(yijt = 1|θ, ˆ Xi , Y ). As such, each s(yijt = 1|θ, the Law of Large Numbers implies that with n = 3286 viewers the simulation error in rt will be negligible, even with R = 1.
Appendix B: Finding Best Response Schedules The strategy space available to each network is the set of feasible schedules, where a schedule is an arrangement of the network’s shows. An optimizing network will choose a schedule from this strategy space which maximizes some objective (i.e., payoff) function. Possible objective functions include profit maximization, advertisement revenue maximization, average ratings maximization, etc. Each of these payoff functions requires predicting the ratings of the candidate schedules in the strategy space. The procedure for constructing the ratings prediction of a given schedule is described in appendix 6. Each show is characterized by a set of show-specific attributes. In this study the attributes are the estimated show locations z and the unexplained popularity (η) estimates. One could also use categorical labels as in Rust and Eechambadi (1989). Each network has a stock of shows from which it can construct a schedule. In the analyses conducted in this dissertation, the stock of shows is assumed to be the prime time shows aired during the week of November 9, 1992. The algorithm presented below, however, can be applied without modification for an arbitrary number of possible shows. The number of shows of different lengths for each network are presented in table 5. The most obvious approach to finding the optimal schedule is to simply compute the payoff for each feasible schedule and select the schedule with the highest payoff. The computational demands of this approach, however, are extremely high. Each network typically airs about 20 25
Table 5: Number of Prime Time Network Shows, 11/9/92 – 11/13/92 ABC
CBS
NBC
Fox
Total Number of half hour shows Total Number of 1 hour shows Total Number of 2 hour shows
16 5 1
8 9 1
6 8 2
4 4 0
Total Number of Shows
22
18
16
8
shows during the weekday prime time hours. If each of these shows were of equal length there would be 20! ≈ 2.4 ∗ 1018 . Assuming (optimistically) that each schedule’s payoff can be computed in 1 second, this approach would require 77 billion years to find the optimal schedule for a single network. Clearly an alternative approach must be pursued.
A Computationally Feasible Best Response Algorithm We consider swapping pairs of show-blocks comprised of shows aired in sequence. A best response schedule with respect to this strategy space of sequential switches of show-block pairs may be found by cycling through the network’s schedule, executing beneficial changes, until no more payoff improving changes exist.
15
Note that this best-response schedule is not unique. If the algorithm
were to change the order in which it considers show-blocks for swapping, the terminating schedule would be different. We employ the “iterative improvements” approach of combinatoric optimization to find approximate best response schedules. Beginning with the network’s original schedule, we find and execute ratings improving swaps of continuous blocks of shows (ranging in length from 30 minutes to 3 hours) until no more ratings improving swaps exist. This process is sure to converge. There are a finite number of possible schedules; thus there exists a schedule with a (weakly) maximum payoff. If only payoff-improving changes are executed, then in finite time either the optimal schedule will be reached, or the process will terminate at a sub-optimal schedule which cannot be improved by single block swaps.16 The possibility of terminating at a sub-optimal schedule is the sense in which 15
In the literature on combinatorial optimization, simulated annealing is a common approach to finding approximate
solutions which is less suspect of finding local optima. Implementing the simulated annealing algorithm is not difficult and will be tried in the near future. 16 The algorithm typically converges in 1 to 4 hours for ABC, CBS, or NBC when the objective function is average ratings.
26
this algorithm is an approximate (or local) solution.
Expanding the strategy space An advantage of the above algorithm is that it is fast enough to compute a Nash equilibrium in the static scheduling game in 15 to 20 hours. However, its restrictive strategy space may cause the best response schedules to produce approximations which are inferior to other approximations. For comparison, we compute best response schedules using strategy spaces expanded in one of two ways. One extension is to permit the network to consider any combination of two simultaneous swaps (involving 3 or 4 continuous blocks of shows). Such an extension of the strategy space may be important if there are possible swaps which are not beneficial alone, but would be beneficial if combined with the swapping of two other blocks. This search for an optimal schedule under this strategy space takes considerably longer since the number of possible swaps has essentially been squared. Though this approach could never be used to solve for equilibrium, we can assess the impact of this extension on the quality of the approximate solution to the task of finding a best response schedule. Interestingly, we find absolutely no additional improvements to a best-response schedule obtained from the iterative improvement algorithm using single block swaps. The second extension is to obtain several candidate solutions by starting the algorithm from several randomly generated schedules. The best response schedule is then the candidate schedule with the highest payoff. Such an algorithm would be computationally feasible if, say, fewer than five random schedules were used as starting points. We assessed this extended strategy space for ABC, CBS, and NBC using the objective of maximizing average ratings. We found that of 100 randomly generated schedules (for each of the networks ), only 3 to 10 of the candidate solutions were better than the best response schedule when starting from the network’s original (i.e., current) schedule. Furthermore, the improvements were very marginal, and not statistically significant when accounting for the standard errors of the estimated z and η attributes. Thus, using the original schedule as the starting point for the algorithm instead of 5 randomly chosen starting schedules is better.
27
Restricting the strategy space It is also very easy to restrict the strategy space in various ways which a network strategist may desire. For example, a certain show could be held fixed in a particular time slot, or could be required to air on a given day or before a given hour. Also, the total number of show swaps could be limited to any desired number. For example, the network may be interested in identifying the best single schedule change which could be made.
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