PRODUCTION AND OPERATIONS MANAGEMENT POMS · 2019. 12. 12. · Measuring Seat Value in Stadiums and...

Measuring Seat Value in Stadiums and Theaters

Senthil VeeraraghavanOPIM Department, Wharton School, Philadelphia, Pennslyvania 19104, USA, [email protected]

Ramnath VaidyanathanDesautels Faculty of Management, Montreal, Quebec H3A 1G5, Canada, [email protected]

We study how the seat value perceived by consumers attending an event in a theater/stadium depends on the location oftheir seat relative to the stage/field. We develop a measure of seat value, called the Seat Value Index, and relate it toseat location and consumer characteristics. We implement our analysis on a proprietary data set that a professional baseballfranchise in Japan collected from its customers, and provide recommendations. For instance, we find that customers seated insymmetric seats on left and right fields might derive very different valuations from the seats. We also find that the morefrequent visitors to the stadium report extreme seat value less often when compared with first-time visitors. Our findings andinsights remain robust to the effects of price and game-related factors. Thus, our research quantifies the significant influenceof seat location on the ex-post seat value perceived by customers. Utilizing the heterogeneity in seat values at different seatlocations, we provide segment-specific pricing recommendations based on a service-level objective that would limit thefraction of customers experiencing low seat value to a desired threshold.

Key words: seat value; empirical research; revenue management applications; customer behavior; ordinal logit modelsHistory: Received: May 2009; Accepted: November 2010 by Michael Lapre, after 3 revisions.

1. IntroductionTheaters and sports stadiums have several character-istics that are well suited to Revenue Management(RM) methods. There are many different customersegments (e.g., season ticket holders, families, students)each with varying usage patterns and willingness topay. The value experienced by a consumer attendingan event depends on several factors, such as the loca-tion of his seat, the popularity of the event, and otherconsumer-related attributes (see Talluri and van Ryzin2004 for more details). However, there has been lim-ited research on how the value experienced byconsumers in such settings is influenced by the afore-mentioned factors.

According to Talluri and van Ryzin (2004), ‘‘fear ofnegative customer reactions and consequent loss ofcustomer goodwill are the main reasons firms seem tobe avoiding bolder demand management strategies.’’This fear is not unfounded; Anderson et al. (2004) finda positive association between customer satisfactionand long-run financial performance of firms in retailsettings. Hence, it is imperative to develop a system-atic understanding of seat value experienced byconsumers in order to be able to improve ticket sell-ing strategies. This is the main research objective ofour paper.

The value of a seat in a stadium/theater is a func-tion of the experience they offer consumers, and couldbe driven significantly by the location of the seat rel-ative to the stage or playing field. For instance, front

row seats in a theater are valued higher as they offer abetter view of the performance. This is in stark con-trast to airline seats, where seat value in the sametravel class is less sensitive to seat location,1 as airlineseats primarily serve as a conduit for transporting aperson from an origin to a destination. Consequently,for the most part, the price of a ticket in economy classindicates how much a person values the trip, morethan how much he values the seat itself. However,theater/stadium seats might be thought of as experi-ence goods. It is unclear how consumer valuations aredistributed across different attributes. Moreover, thedependence of seat value on the location of the seatcan be fairly complex. For example, in theaters,seats in the middle of a row might be preferred overseats toward the end of a row further forward, andseats at the front of second-level sections are some-times preferred to seats at the back of first-levelsections (Leslie 2004). This ordering of seat value bylocation is only understood subjectively by theatersand stadiums. However, there has been little researchon developing a measure of seat value in these set-tings. Measuring seat value and developing a betterunderstanding of how it is driven by seat locationwould assist theaters and stadiums in formulatingtheir ticket selling strategies.

The relationship between seat value and seat loca-tion is not well understood. This has been a focus ofsubjective discussions recently. We briefly discuss onesuch case. In 2006, the Oakland Athletics decided toreduce the capacity of McAfee Coliseum (where their

PRODUCTION AND OPERATIONS MANAGEMENT POMS

49

Vol. 21, No. 1, January–February 2012, pp. 49–68 DOI 10.1111/j.1937-5956.2011.01249.xISSN 1059-1478|EISSN 1937-5956|12|2101|0049 © 2011 Production and Operations Management Society

home games are played) by covering several of theirupper deck seats with tarpaulin sheets, thus reducingthe stadium capacity from 44,000 seats to about 34,077seats (Urban 2005). The Oakland A’s announced thatthe decision was made in order to provide an ‘‘inti-mate’’ experience to those in attendance, in a smallerfield. In fact, when the team moves to a newer field forthe 2012 season, they plan to play in a stadium thathas lesser capacity (32,000) than the currently usedtarpaulin-covered stadium. Bnet.com quoted ‘‘. . . thefans who are feeling slighted most are the lower-income brackets who feel the third deck was their lastaffordable large-scale refuge for a seat behind homeplate, even one so high.’’ The team management con-tended that people liked the upper deck mostlybecause of availability, and perhaps not so much be-cause of the view (Steward 2006). One article in SlateMagazine criticized the move, stating ‘‘some of uswant to sit far away’’ (Craggs 2006). Thus, the seatvalue perceived by consumers seated at the upperdeck was not only unclear, but also varied amongdifferent fans. So is it true that the consumers seatedin the upper deck valued those seats highly? Werethe upper deck seats being underpriced? How did theseat value perceived by consumers attending thegame differ across seat locations? These are some ofthe questions that will be addressed by our research.

In addition to seat location, there are a number ofother factors that might affect the seat value perceivedby a customer. For instance, in the case of a sportsstadium, the nature of the opposing team, the age ofthe customer, or whether the customer is a regular oran infrequent visitor, might affect her valuation of theseat. For most theaters and stadiums, understandingheterogeneity in customer valuations is the key to in-creasing revenues. A clear understanding of the seatvaluations would lead to the creation of better‘‘fences’’ that would provide theaters and stadiumswith an opportunity to manage their revenues andcustomer base better. Our paper sheds more light onthe key factors influencing seat value in these settings.

Our research on nontraditional industries (theaterand sports) complements current RM literature by (1)developing a measure of seat value (Seat Value Index[SVI]), (2) establishing the critical relationship be-tween the SVI and seat locations, and (3) providingsegment-specific recommendations that would help thefirm achieve a service-level objective such as a ‘‘de-sired level of seat value.’’2 We apply this researchmethodology to a proprietary data set collected by aprofessional baseball franchise in Japan, from a sur-vey of its customers. Based on the findings fromthe data set, we provide various measures by whichstadiums/theaters can improve customer satisfac-tion through better handling of ticket pricing, seatrationing, and seating layout decisions. Because RM

practices are not employed on a large scale in theseareas of interest, our research fills a gap, both in the-ory and practice.

To our knowledge, ours is the first paper to studythe distribution of consumer seat value and its depen-dence on seat location in theater/stadium environ-ments. RM practice hinges on the ability to pricediscriminate, which is possible only if there is hetero-geneity in seat value. Based on service-level objectives,we provide pricing recommendations that a firm mayuse to improve positive experience from the repeatedconsumption of the good. We apply our model to adata set collected by a Japanese baseball franchise andfind evidence for heterogeneity in seat value at thestadium. Using our model, we quantify this heteroge-neity in terms of customer attributes and their seatlocations. Pursuant to the results from applying ourmethod, we provide some segment-specific pricingrecommendations.

In the following section 2, we position our paperwith respect to the existing literature. In section 3, wediscuss our research design, methodology and its ap-plication to a proprietary data set. In section 4, we testthe robustness of our results to game effects, prices,and seat location. In section 5, we provide segment-specific pricing recommendations and discuss in-sights from our analysis. We conclude the paper bysummarizing the key ideas of our methodology andcharting future research directions.

2. Literature PositioningWe analyze seat value perceived by consumers, andthe key implications it has for pricing in sports sta-diums and theaters. Most of the literature in the sportsand entertainment industry has been about secondarymarkets and ticket pricing in scalping markets (seeCourty 2000 for a comprehensive survey). The onlypaper related to ours is Leslie (2004), which studiesthe profit implications of price discrimination basedon exogenously defined seat quality and consumers’income levels for a Broadway theater. In contrast toLeslie (2004), we measure seat value based on con-sumer perceptions.

Our paper also contributes to an evolving literatureon consumer behavior and empirical modeling in RM.Shugan and Xie (2000) show that advanced sellingmechanisms can be used effectively to improve firmprofits as long as (a) consumers have to purchase aproduct ahead of their consumption, and (b) theirpostconsumption valuation is uncertain. Xie andShugan (2001) provide guidelines for when and howsellers should advance sell in markets with capacityconstraints. Dana (1998) shows that advance-purchasediscounts can be employed effectively in competitivemarkets, if consumers’ uncertain demand for a good

Veeraraghavan and Vaidyanathan: Measuring Seat Value in Stadiums and Theaters50 Production and Operations Management 21(1), pp. 49–68, © 2011 Production and Operations Management Society

is not resolved before the purchase of the good. Su(2007) finds that heterogeneity in consumer valua-tions, along with waiting time behavior, influencespricing policies of a monopolist. Gaur and Park (2007)consider consumer learning in competitive environ-ments. While most of this literature is analytical, wetake an empirical approach to analyze seat values asperceived by customers, and study its implications forRM decisions in the sports/theater business.

There has been recent interest in modeling RMdecisions in nontraditional settings. Roels and Frid-geirsdottir (2009) consider a web publisher who canmanage online display advertising revenues by se-lecting and delivering requests dynamically. Popescuand Rudi (2008) study RM in stadiums where expe-rience is often dictated by the collective experience ofothers around a patron.

Methodologically, our paper is related to the liter-ature employing ordinal models to study theantecedents and drivers of customer satisfaction.Kekre et al. (1995) study the drivers of customer sat-isfaction for software products by employing anordinal probit model to analyze a survey of customerresponses. Bradlow and Zaslavsky (1999) use a Bayes-ian ordinal model to analyze a customer satisfactionsurvey with ‘‘no answer’’ responses. Rossi et al. (2001)propose a hierarchical approach to model customersatisfaction survey data that overcomes reporting het-erogeneity across consumers. We use an ordinal logitmodel similar to the aforementioned papers, takinginto account heterogeneity in reporting (across cus-tomers) and heterogeneity in the distribution of seatvalues (across seat locations).

Anderson and Sullivan (1993) note that relativelyfew studies investigate the antecedents of satisfaction,though the issue of postsatisfaction behavior is treatedextensively. They note that disconfirmation of ex-pected valuation causes lower satisfaction and affectsfuture consumption. While previous considerationsabout a product might affect how consumers valuethe experience, we mainly focus on how productattributes such as seat location, and personal attri-butes such as gender, age and frequency of visitsaffect customer valuations.

Homburg et al. (2005) show that customer satisfac-tion has a strong impact on willingness to pay. Ittnerand Larcker (1998) provide empirical evidence thatfinancial performance of a firm is positively associatedwith customer satisfaction and customer value per-ception. We use seat value measures reported byconsumers in a survey to recommend changes thatwould help the firm (a baseball franchise in our con-text) achieve a chosen service objective on seat value.Hence we believe that this objective would improvecustomer goodwill, which in turn would lead to betterlong-run performance.

3. Research Issues and Methodology

3.1. Research IssuesThe focus of our research is to understand how theseat value perceived by a customer in a stadium/the-ater varies based on the location of her seat relative tothe stage/field. Because we are interested in post-consumption seat value perceived by customers inattendance, we do not consider the underlying trade-offs made while arriving at the purchase and seatchoice decisions. Therefore, we only model the ex-post net valuations realized by consumers, in order tounderstand how they differ based on seat location.

To derive sharper insights, we assume that con-sumers are forward-looking and have rationalexpectations, i.e., that they do not make systematicforecasting errors about what valuations they mightreceive from attending a game or seeing a show. Therational expectations assumption is widely employedin empirical research in economics (Hansen and Sar-gent 1991, Lucas and Sargent 1981, Muth 1961) andmarketing literature (e.g., Sun et al. 2003). Accord-ingly, we assume that every consumer has some beliefon the distribution of possible valuations that shecould realize, conditional on her covariates. Further-more, the ex-ante distribution of valuations for arational consumer is identical to the ex-post distri-bution of valuations realized by the consumer popu-lation with identical covariates. Note that rationalexpectations does not imply that consumers are per-fectly informed about their true valuations.

3.2. Methodology

3.2.1. Seat Value. We define the value perceived bya consumer as the valuation realized from her eventexperience net of the price paid (consistent withZeithaml 1988). We note that the exact valuationrealized from the experience cannot be easilyquantified, and therefore the value perceived islatent. However, the consumer would be able totranslate her latent value perceived on some gradedscale. In other words, although she cannot describethe exact worth of the show she attended, she canusually confirm if the value she perceived was low,medium, or high. We define SVI as an ordinalmeasure that captures the postconsumption latentvalue perceived by a consumer. Let Vi denote the SVIreported by a respondent i. It takes values inf1, 2, . . . , Jg J 2 N, where Vi 5 1 corresponds to thelowest SVI (low net value), and Vi 5 J represents thehighest SVI (high net value).

3.2.2. Service Objective. In many operationalcontexts, firms that seek to improve customerservice adopt a service level measure such as fill rateor in-stock probability (Cachon and Terwiesch 2008).

Veeraraghavan and Vaidyanathan: Measuring Seat Value in Stadiums and TheatersProduction and Operations Management 21(1), pp. 49–68, © 2011 Production and Operations Management Society 51

Such decisions are based on the belief that improvingavailability of products reduces the incidence of coststhat might be associated with stockouts, and theresultant loss of goodwill. For instance, firms wouldhope to set prices such that it keeps the fraction ofcustomers experiencing low seat value to an acceptablelevel at each seat location. Such service level measuresthat focus on limiting the fraction of customers facinginferior service experience are commonly applied inseveral industries. Call centers choose staffing levelaccording to an 80/20 rule (or some variation thereof)that focuses on limiting the fraction of customers thatface waiting times exceeding a certain threshold.

While a newsvendor can adjust quantities of goodsproduced based on the chosen service level objec-tive, in many RM scenarios, the quantities areunchangeable (e.g., the number of seats in a theatercannot be adjusted easily). In such cases, prices arethe main lever by which RM firms can attain theirservice objective. However, in many RM scenarios,especially in stadiums/theaters, the value of theproduct is intrinsically linked to the experience. Forexample, it is possible that customers who experi-ence low value might switch to other services, orbalk from visiting again. Firms would hope to setprices such that the fraction of customers experienc-ing low seat value could be limited to acceptablelevels. Such an objective would be consistent withthe models of customer behavior linked to service/stockout experiences considered in previous Opera-tions Management settings (e.g., see Gans 2003, Gaurand Park 2007, Hall and Porteus 2000).

Several RM firms desire to limit the fraction ofcustomers experiencing low seat value in order tomitigate the loss of goodwill or to reduce switching.Hence, we consider a service-level objective thataims to set prices to maximize revenues while keep-ing the probability of a customer reporting low SVIto a maximum threshold level, al, at some seat lo-cation l. For expositional ease, we shall assume thatal 5 a across all seat locations. This clearly need notbe the typical case. A theater might be willing toimpose more stringent constraints on certain sectionsof the arena compared with other sections. There-fore, under our service level objective for a particularseat category l, the firm would like to set some pricep�l under the constraint

Pr½SVI � jjp�l � � al ð1Þ

The choice of al and j are flexible, and could bebased on the long-term objective of the firm.

We only consider static price adjustments inour setting, since such schemes are consistent withindustry practice where we apply our model. It isvery common that theaters and sports stadiums

announce prices for the entire season; the number ofprice changes are extremely limited within the sell-ing horizon.

3.2.3. Modeling SVI. Utilizing the service levelobjective we elaborated, the firm can increase ordecrease prices suitably to achieve a desired level ofseat value. We describe our model of SVI in thecontext of our data set.

3.3. Description of Baseball Data setWe now illustrate our research issue based on the datafrom a professional league baseball franchise (equiv-alent of Major League Baseball) in Japan. Thefranchise is located in a mid-small city, and hencecould not rely on conventional streams of revenuesuch as broadcasting, merchandising, and advertising.The franchise management decided to focus on ticketsales as it saw an upside potential in considering im-provements in pricing and seating layouts.

As the team was a recently established franchise,the management conducted a survey to better under-stand the traction for the team among its fans. Thesurvey discussed in the paper was designed by theteam based on inputs from various departments andteam executives in the franchise. The survey was ad-ministered to a random sample of consumers at thefranchise’s stadium on a weeknight game. Only oneresponse was obtained from each consumer.

In the survey, respondents were asked to report thenet worth of the seats they sat in as low, medium, orhigh. This corresponds to the SVI measure that wasdefined before as a quantification of a respondent’srealized net value. In addition, customers were askedto report their age,3 gender, hometown, seat, fre-quency of visits to the stadium, and preference forvisiting teams. Table 1 provides more details on thesevariables and how we treat them in our models.

The experience and the resulting value perceivedare highly dependent on the location of the seat fromwhich a respondent watched the game. However, thisinformation is not clearly captured by the explanatory

Table 1 Description of Variables in the Data Set

Variable name Values Treatment

SVI Low, medium, high Ordinal (1–3)

Age 0–9, 10–19, 20–29, 30–39, 40–49, 50–59, 601 Continuous

(1–7)

Gender Male, female Categorical

Hometown City, prefecture, outside Categorical

Seat 1–12 (see Figure 1) Categorical

Frequency First time, once, thrice, five times, all games Continuous

(1–5)

Visiting team Team 1, Team 2, Team 3, Team 4, Team 5 Categorical


variable Seat. For example, customers seated in loca-tions 2 and 7 have almost identical views, but thislinkage is not apparent in the current coding of the Seatvariable. Hence, we represented each seat in terms ofthree location attributes given by Side 5 fFirst Base,Third Base, Backnet, Field, Grassg, InOut 5 fInfield,Outfieldg and Deck 5 fUpper, Lowerg.

3.4. Preliminary AnalysisFrom a total of 1397 respondents, 259 responses weredropped due to missing information, resulting inN 5 1138 responses. A preliminary analysis revealedthat the frequency distribution of SVIs was skewedtoward the right, as shown in Figure 2. This impliesthat a higher proportion of consumers reported a lowSVI, which underlines the further need for studyingseat value.

Figure 2 also reveals some cursory insights. The SVIreported by older respondents seems to be more ho-mogeneous. Customers seated in Grass seats reporthigher SVI, while respondents seated at Backnet seemto have a lower SVI. Infield and Lower Deck seatsseem to have a higher proportion of respondents re-porting low SVI as compared with Outfield andUpper Deck seats. Finally, the season regulars attend-ing all games seem to have more homogeneous SVIsas compared with the first-timers. We now discuss theregression methodology adopted and the estimationof model parameters.

3.5. Estimation of ParametersLet Vi denote the SVI reported by respondent i,i 5 1, 2, . . . , N. Note that Vi can take the rank-orderedvalues j 5 1, 2, 3 corresponding to low, medium, andhigh, respectively. Given that our response variable isordinal, we follow McCullagh (1980) and use ordinalregression to model our data. The reader is directed toLiu (2005) for a detailed overview and survey ofordinal data analysis.

Low Medium High

Seat Value Index

0

200

400

600

800

216

843

79

0−9 30−39 50−59

Age

0.0

0.2

0.4

0.6

0.8

1.071119137 324 235 150102

Female Male

Gender

0.0

0.2

0.4

0.6

0.8

1.0479 659

Outside City

Hometown

0.0

0.2

0.4

0.6

0.8

1.0124 313 701

1st 3rd Backnet

Side

0.0

0.2

0.4

0.6

0.8

1.0257 483 198 92108

Infield Outfield0.0

0.2

0.4

0.6

0.8

1.0653 485

Lower Upper

Deck

0.0

0.2

0.4

0.6

0.8

1.0623 515

First Time Three Times

Frequency

0.0

0.2

0.4

0.6

0.8

1.0221 326 306 166 119

Field

Figure 2 The Distribution of Seat Value Indices Reported by the Respondents for Each Covariate. The Width of the Histogram Denotes the Number ofResponses (Which is Also Indicated on Top for Each Value of the Covariate)

Figure 1 Stadium Seating Layout. Side = f1st Base, Third Base, Backnet,Field, Grassg, InOut = fInfield, Outfieldg and Deck = fUpper, Lowerg


Following the specification of the ordinal regressionmodel, we assume that a respondent i derives her SVI,ViAf1, 2, 3g, by categorizing her post-consumptionlatent net value realized (valuation of the experiencenet of the price paid), V�i , into buckets defined by thethresholds ft 0i ; t 1i ; t 2i ; t 3i g, where it is understood thatt 0i ¼ �1 and t 3i ¼ þ1. Hence, respondent i reportsher SVI as Vi 5 j, if and only if t

j�1i oV�i � t

ji, for

j 5 1, 2, 3.The net value experienced by the customer can

be expressed as V�i ¼ xTi bþ ei, where the vector ofcovariates xi consists of Age, Gender, Hometown, Side,InOut, Deck, Frequency, and Team 1. b is the associatedvector of parameters, and ei is a stochastic term thatcaptures the idiosyncratic value derived from theexperience, which is assumed to follow a standardlogistic distribution (L). Following McCullagh (1980),we assume that t ji ¼ t j for all consumers i. We cannow write down the cumulative probability distribu-tion of Vi as

PrðVi � jjxiÞ ¼ Lðt j � xTi bÞ 8j ¼ 1; 2; ð2Þ

where

xTi b ¼ b1Agei þ b2Malei þ b3Cityiþ b4Prefecturei þ b5ThirdBasei þ b6Backnetiþ b7Fieldi þ b8Grassi þ b9Outfieldiþ b10UpperDecki þ b11Frequencyi þ b12Team1i:

4

Before running the regression model, we first testedfor the usual symptoms of multicollinearity (Greene2003): (1) high-standard errors, (2) incorrect sign orimplausible magnitude of parameter estimates, and(3) sensitivity of estimates to marginal changes indata. We found no evidence of these symptoms in ourdata set. We computed the Variance Inflation Factors(VIF) for every covariate and found all of them to beo2 (i.e., max(VIF)o2), which again suggests thatmulticollinearity is not an issue. In addition, weadded random perturbations to the independent vari-ables and re-estimated the model (Belsley 1991). Wedetermined the changes to the coefficients of thosevariables to be insignificant on repeated trials, thusfurther supporting that multicollinearity might not bea significant concern.We use the OLOGIT routine inSTATA 10.0 to estimate the parameters of the modelusing the maximum likelihood approach. The resultsare summarized in Table 2. The standard ordinalmodel implicitly assumes proportional odds.5 To val-idate this assumption, we applied a likelihood ratiotest and found that the standard ordinal logit model isstrongly rejected in favor of an expanded model thatallows for the slope coefficients to differ across thresh-old levels (w2ð12Þ ¼ 46:74, po0.0001). Consequently, weconducted a test proposed by Brant (1990), to find thatthe proportional-odds property is violated for the

coefficients b1 (Age), b2 (Side), and b10 (Deck).6 To rule

out the possibility of a misspecified link, we appliedthe Brant test to ordinal models with differentlink functions (probit, log–log, and complementarylog–log), but still found the same violations of the pro-portional-odds property.Violation of the proportional-odds property suggests that the standard ordinal logitmodel might be inadequate to explain the variations inSVI. It also suggests the presence of heterogeneityacross consumers and seat locations. Hence, we con-sider two different modifications to the standardordinal logit model that account for this heterogeneity.

1. First, we consider a generalized threshold modelthat addresses the possibility of customers usingdifferent thresholds in reporting their responses,by relaxing the assumption that the thresholds, t ji,are identical for all respondents.

2. Second, we consider a heteroskedastic modelthat addresses the inherent differences in thedistribution of net value across seat locations, byallowing the variance of the idiosyncratic valueterm, ei, to systematically vary across respondentgroups.

We now discuss these two sources of heterogeneityand the modeling strategies that can account for them.

3.5.1. Heterogeneity in Response Thresholds:Generalized Threshold Model (Peterson and Harrell1990). It is not uncommon for people to use differentthresholds in reporting their ordinal responses.7 Thegeneralized threshold ordinal logit model retains theidea that consumers realize their net value from acommon distribution, V�i � LðxTi b; p

2

3 Þ, but assumes thatthey use systematically different thresholds, t ji, whilereporting their net value. A common approach tomodel generalized thresholds is to make the thresholdparameters linear (Maddala 1983, Peterson and Harrell1990) or polynomial functions of the covariates. Wechoose the linear specification and accordingly lett ji ¼ ~t j þ xTi d j, where xi is the set of covariates and d

j,j 5 1, 2, are vectors of the associated parameters thatcapture the effect of the covariates in shifting thethresholds. Substituting the expression for t ji in place oftj in Equation (2), we can write the defining set ofequations for the generalized ordinal logit model as

PrðVi � jjxiÞ ¼ Lð~t j � xTi b jÞ;b j ¼ b� d j 8j ¼ 1; 2: ð3Þ

According to the generalized threshold ordinallogit model, the net effect of any covariate k, b jk onSVI is a combination of two effects (a) the real effect(bk) and (b) the threshold-shifting effect ðd jkÞ. It is thethreshold-shifting effect ðd jkÞ that leads to the man-ifestation of unequal slopes detected by the Branttest. Thus, two groups of customers might have


identical distributions of net value, but the distribu-tions of their reported SVIs might differ because ofdifferent reporting thresholds. Figure 3 illustratesthis case for two customers, A and B, seated at iden-tical locations.

3.5.2. Generalized Threshold Model

3.5.2.1. Heteroskedastic Ordinal Regression. Fromthe results of the Brant test, we infer that the covari-ates Age, Third Base, and Upper Deck could be driving

Net Value(Vi*)

Pro

babi

lity

Den

sity

Net Value(Vi*)

Pro

babi

lity

Den

sity

(a) (b)

Figure 3 (a) Generalized Threshold Model. (a) The figure on the left compares Seat Value Indices (SVIs) at the same seat location for two differentcustomers, A and B. Although the distribution of net value is identical for both customers, the difference in reporting thresholds causes them toreport different SVI for the same realization of net value. (b) Heteroskedastic Ordinal Logit Model. (b) The figure on the right compares SVIs for thesame customer at two different seat locations, A and B. Although the mean realization of net value and the response thresholds are identical atboth seat locations, the difference in variances causes the customer to report a particular SVI with different probabilities across the two locations

Table 2 Parameter Estimates for All Models

Variable

Standard ordinal logit Generalized ordinal logit Heteroskedastic ordinal logit

j 5 1, 2 j 5 1 j 5 2 j 5 1, 2

Threshold: low–medium t1 � 1.215�� 0.761�� 0.748��

Threshold: medium–high t2 3.387�� 2.071�� 2.067��

Age bj1 0.048 0.127�� 0.172�� 0.034

Male bj2 � 0.019 � 0.026 � 0.034City (vs. outside) bj3 0.083 0.029 0.011

Prefecture (vs. outside) bj4 0.192 0.166 0.102

Third Base (vs. First Base) bj5 0.428�� 0.873�� 0.727�� 0.145

Backnet (vs. First Base) bj6 � 0.730�� 0.678�� 0.678�� 0.440��

Field (vs. First Base) bj7 � 0.893�� 0.824�� 0.509��

Grass (vs. First Base) bj8 1.816�� 1.206�� 0.919��

Outfield bj9 0.215 0.211 0.171

Upper Deck bj10 0.246 0.066 0.947�� 0.263��

Frequency bj11 � 0.126�� 0.093 � 0.234�� 0.081��

Team 1 bj12 0.249� 0.250� 0.185��

Age g1 NA � 0.075��

Third Base (vs. First Base) g5 NA � 0.324��

Upper Deck g10 NA 0.208��

Frequency g11 NA � 0.057�

Log likelihood LL � 748.12 � 727.18 � 726.27Likelihood ratio (w2) LR 149.02 190.90 192.72

No. of parameters 14 18 18

McFadden pseudo-R2 (%) 9.06 11.60 11.71

��po0.01; ��po0.05; �po0.1.


the shift in thresholds. In addition, we believe thatrepeated visits help respondents learn the true valueof the game experience and would induce them to usedifferent thresholds. Accordingly, we let the thresh-olds depend on the subset of covariates zi 5 fAge,Third Base, Upper Deck, Frequencyg, and set d jk ¼ 0;j ¼ 1; 2 for kezi.

We estimate the parameters of this generalizedthreshold model using the GOLOGIT2 routine(Williams 2006a) in STATA 10.0. The results are sum-marized in Table 2. We observe that in addition toSide and Frequency, Age also becomes a significantpredictor now. A standard measure of fit for ordinalregression models is the McFadden pseudo-R2,

which is defined as 1� LLModelLLNull , where LLModel refersto the model log-likelihood. It indicates the improve-ment in likelihood due to the explanatory variablesover the intercepts-only (null) model. We find thepseudo-R2 for the generalized threshold model to be11.60%.8

3.5.3. Heterogeneity in Net Value Distribution:Hetetoskedastic Ordinal Logit (McCullagh andNelder 1989). In the previous subsection, weconsidered customers using different thresholds toreport different levels for the same realized experi-ence. However, it is also possible that the distributionof values, ei, realized by different consumer groupsmight, themselves, be different. Consumers seated indifferent locations could have different variabilities intheir experience depending on their seat location.Such occurrences are very likely in several RMsettings. It is likely that consumers seated in somesections such as dress circles may have smaller differ-ences in the value experienced than those consumersseated at farther sections of the same theater.Therefore, we believe that it is important for firms toaccount for such systematic differences in the varianceof the distribution of idiosyncratic value, to obtainmeaningful parameter estimates.9

We capture the dependence of the error varianceon the covariates using a skedastic function h( � ) thatscales the iid eis in the standard ordinal logit model.Mathematically, we write V�i ¼ xTi bþ hðziÞei, wherezi is the vector of covariates upon which the residualvariance depends. Following Harvey (1976), we pa-rametrize h( � ) as an exponential skedastic functiongiven by hðziÞ ¼ expðzTi gÞ. We can now rewrite Equa-tion (2) to obtain the defining set of equations for theheteroskedastic ordinal logit model as

PrðVi � jjxiÞ ¼ Lt j � xTi bexpðzTi gÞ

� �8j ¼ 1; 2: ð4Þ

The heteroskedastic ordinal logit model belongs toa larger class of models known as location-scale

models, and the reader is directed to McCullagh andNelder (1989) for more details.10

Because the explanatory variables Age, Third Base,and Upper Deck violated the Brant test, we includethese covariates in the expression for variance of id-iosyncratic value. In addition, we also include thecovariate Frequency in the variance expression, as webelieve that repeated visits should help respondentslearn the ‘‘true value’’ of the game experience, andconsequently reduce the residual variation in theirnet value perceived. We estimate the parameters ofthe heteroskedastic ordinal logit model using theOGLM routine (Williams 2006b) in STATA 10.0.

From the results summarized in Table 2, we ob-serve that the covariates Frequency, Side (except ThirdBase), and Upper Deck have significant b coefficients.All the g coefficients included in the variance equa-tion are significant. We can draw several interestinginferences from these results.

Controlling for heteroskedasticity, we find that re-spondents at the third base have the same averagenet value as respondents at the first base, as b̂5 is notsignificant. However, the respondents seated on thethird base side have significantly less variance in thenet value realized (standard deviation is 1� expðĝ5Þ¼ 28% lower) as compared with those seated onthe first base side. This could be due to the locationof the home team dugout and/or the relative inci-dence of foul balls/home runs on the left field.Figure 3 details a comparison of reported SVIs for acustomer located on the first base side and the thirdbase side.

We find that the net value experienced by respon-dents seated at the upper deck has a higher mean(b̂10 ¼ 0:263, p 5 0.04), as well as a higher variance(ĝ10 ¼ 0:208, p 5 0.0408), when compared with thenet value experienced by respondents seated at thelower deck. The net value experienced by customersvisiting more frequently has a lower mean(b̂11 ¼ �0:081, p 5 0.028) and a lower variance(ĝ11 ¼ �0:058, p 5 0.074). Age of a respondent doesnot affect the mean of net value experienced, butolder respondents tend to have lower variance in thenet value experienced.

The current data set has only one response for eachconsumer. Hence, it is not possible to econometri-cally distinguish between the Generalized ThresholdModel and the Heteroskedastic Model. The observeddeviation from proportional-odds could be a mani-festation of consumers using different thresholds, orof the value distribution being heteroskedastic acrossseat locations. Hence, the applicability of eithermodel must depend on the appropriate interpreta-tion. For example, it is more likely that heterogeneityacross consumers is explained by thresholds,while heterogeneity across seat locations is better


explained by differences in the idiosyncratic valuedistribution. We interpret our results accordingly.

3.6. Achieving the Service ObjectiveLet us now consider the aforementioned service-levelobjective that we discussed before, where the firmaims to set prices such that the probability of a cus-tomer reporting low SVI is limited to a maximumthreshold level, a, at all seat locations l. In Lemma 1,we derive an expression for the price change at eachseat location that would help the firm achieve thisobjective, using the heteroskedastic ordinal logitmodel specification.

LEMMA 1. Let xl denote the vector of covariates for a cus-tomer seated at location l. Let a,b, g and zl be defined as inthe heteroskedastic ordinal logit model, and y denote theprice elasticity of V�l . To limit the probability of this cus-tomer reporting SVI 5 1 at seat location l to a threshold a,the required price change Dpl is given by

Dpl ¼1

y�t 1 þ xTl bþ L

�1ðaÞexpðzTl gÞ� �

: ð5Þ

PROOF: At current prices, the probability of a typicalcustomer reporting SVI as low is given by

PrðV�l � t 1Þ ¼ Lt 1 � xTl bexpðzTl gÞ

!: ð6Þ

Increasing the ticket price for seat location l by Dplwould change this probability to

PrðV�l � yDpl � t 1Þ ¼ Lt 1 þ yDpl � xTl b

expðzTl gÞ

!:

Equating this to a, we can calculate the desiredprice change Dpl shown in Equation (5).

We apply the results of this lemma in section 3.8to derive price changes for a baseball franchise. Notethat we could allow the service-level thresholdsto differ across seat locations by specifying differ-ent as.

3.7. Calculating Marginal ProbabilitiesThe main purpose of our model is to predict theprobability that a consumer seated at a particular seatlocation reports a certain SVI. In order to manage SVI,it is crucial to understand how these probabilities of aconsumer reporting a certain SVI change with seatlocation and other covariates. Regression coefficientsonly explain the mean effects. In contrast, marginalprobabilities measure how a change in a covariateimpacts the distribution of the response variable.11

Hence we calculated the marginal probabilities of theimpact of different covariates on SVI. While measur-

ing the marginal probability effects of any covariate,we define a typical customer for every covariate by fix-ing the rest of the covariates at their mean (or theirmode for categorical covariates).

We use the MFX2 routine in STATA 10.0 to estimatethe marginal probability effects and the results aresummarized in Table 3, and interpreted in section 5.Note that both the generalized threshold andheteroskedastic models provide comparable marginalprobability estimates. Therefore, irrespective of thenonproportional odds model considered, we obtainthe same qualitative insights. As indicated before, weemploy the threshold interpretation for consumerattributes (such as age, gender, frequency of visit,etc.), and the heterogeneity interpretation for all seatattributes.

In addition to the calculation of marginal probabil-ities for a typical customer, we also calculate themarginal probabilities for different customer seg-ments (Age, Geography, Frequency of Visits). Wediscuss these results and their implications for seg-ment-specific pricing in section 5.1.

Table 3 Marginal Probability Effects of Ordinal Logit Models for SelectCovariatesa

SVI Variable Standard Generalized Heteroskedastic

Low Age � 0.006 � 0.017�� 0.024��

Third Base � 0.056�� 0.114�� 0.102��

Backnet 0.114�� 0.107�� 0.116��

Field 0.151�� 0.139�� 0.143��

Grass � 0.149�� 0.118�� 0.136��

Upper Deck � 0.033 � 0.009 � 0.013Frequency 0.017�� 0.013 0.006

Team 1 � 0.034� � 0.035� � 0.043��

Medium Age 0.004 0.024�� 0.030

Third Base 0.035�� 0.143�� 0.131��

Backnet � 0.086�� 0.084�� 0.090��

Field � 0.120�� 0.114�� 0.120��

Grass � 0.023 0.039�� 0.011�

Upper Deck 0.021 � 0.032 � 0.036Frequency � 0.011�� 0.003 0.008

Team 1 0.022� 0.025 0.030��

High Age 0.002 � 0.007�� 0.0087��

Third Base 0.021�� 0.029�� 0.031��

Backnet � 0.029�� 0.023�� 0.026��

Field � 0.031�� 0.025�� 0.027��

Grass 0.172�� 0.079�� 0.120��

Upper Deck 0.012 0.041�� 0.048��

Frequency � 0.006�� 0.010�� 0.013��

Team 1 0.012� 0.010� 0.013��

aGender, Hometown, and In–Out did not have significant effects.�po0.1; ��po0.05; ��po0.01.


3.8. Calculating Price Adjustments to Achieve theService ObjectiveSuppose that the franchise wants to keep the proba-bility of a specific customer reporting SVI 5 low to athreshold a at all seats. The current probability of aspecific customer seated at location l reportingSVI 5 low, can be calculated using Equation (6). Wecan then use Equation (5) to calculate the price changerequired at each seat location that would equate theprobability of this customer reporting SVI 5 low, tothe threshold value a. The parameters (b, g) are knownfrom the regression estimates, while the price elastic-ity of SVI (y) can be estimated using the pricevariation observed across seat locations.

We now illustrate this calculation for a typical cus-tomer of the franchise (Age 5 4.22, Gender 5 Male,Hometown 5 City, Frequency 5 2.68) and a thresholdof a5 15%. Table 4 summarizes the current service

levels and the price changes (Dpl) that achieve thethreshold service level of a5 15% for a typicalcustomer. Note that the franchise might be interestedin achieving this service objective for different con-sumer segments. We discuss this in section 5.1.

4. Validation: Effects of Game, SeatLocation, and Prices

In this section, we validate our empirical results usingvarious robustness checks. Specifically, we studygame-related effects with an additional data set andthe effects of price on seat value. In addition, wecompare the effect of seat-specific attributes (such asseat location) vs. customer-specific attributes (such asage) on SVI.

4.1. Model ValidationThe standard approach to validate regression modelsis to estimate the model parameters on a calibrationsample and validate those results on a hold-out sam-ple. Accordingly, we constructed a calibration sampleand a validation sample by randomly splitting ourdata-set into two equal parts. We measured the pre-dictive accuracy of our model using an R2 measure(see Equation 7), and find that R2H ¼ 57:1%, whichimplies that the model significantly improves predic-tion accuracy over a naive model. Figure 4 shows acomparison of the actual number of respondents ateach seat location reporting a particular SVI, with theexpected numbers predicted by the model for thehold-out sample. These predictions generally matchthe distribution of the SVI for various seat locations.

Table 4 Calculation of Price Increase that Keeps the Probability of aTypical Customer Reporting a Low SVI, to a = 15%

Seat location/frequency of visits Pr ðV �l � t 1Þ (%) yDpl Dpl (Yen)

First Base, Lower Deck, Infield/Outfield 20.8 � 0.249 � 259Third Base, Lower Deck, Infield/Outfield 10.3 0.197 205

Backnet, Lower Deck, Infield 34.7 � 0.689 � 718Field, Lower Deck, Infield/Outfield 37.2 � 0.758 � 790First Base, Upper Deck, Infield/Outfield 19.3 � 0.236 � 246Third Base, Upper Deck, Outfield 9.7 0.278 290

Grass, Upper Deck, Outfield 6.8 0.683 711

One Additional Visit 20.8 � 0.269 � 280

Actual No. of Respondents

Pre

dict

ed N

umbe

r of

Res

pond

ents

20

40

60

80

100

First Dataset

100

Combined Dataset

40 100

SVI123

Seat.Location12345789

101112200 060 80 4020 60 80

Figure 4 Comparison of the Actual Number of Respondents at a Given Seat Location Reporting a Particular SVI With Those Predicted by the Model for aHold-Out Sample

The graph on the left shows the comparison for the first data set, while the graph on the right shows the comparison for the combineddataset


While the R2 is an indirect measure of predictiveaccuracy computed at a highly disaggregated level, amore direct measure is the accuracy of the predictedservice level, Pr(SVI 5 1). Computing the predictedservice level for the hold-out sample, we find thatwhile the actual service level is 19.6%, our model pre-dicts a service level of 19.2%, thereby providing furtherconfidence on the predictive power of our model.

We now briefly describe how we calculate our R2

measure of predictive accuracy.

Calculating R2: To calculate a measure of predictiveaccuracy, we ran the heteroskedastic ordinal logitmodel (M) on the calibration sample (C) to obtain es-timates of the parameters b, g, and tj, j 5 1, 2. We thencomputed the expected number of respondents re-porting SVI 5 jA1, 2, 3 at each seat location l, for thehold-out sample (H), using the following expressions:

EMlH½SVI ¼ j� ¼X

i2H;Location¼lPrðSVIi ¼ jjxiÞ:

A naive model (N) would estimate this probabilityof reporting SVI 5 j as 1jCj

Pi2C IðSVIi ¼ jÞ, which

would predict the expected number of respondentsreporting SVI 5 j at seat location l as

ENlH½SVI ¼ j� ¼nlHjCjXi2C

IðSVIi ¼ jÞ;

where nlH is the number of respondents in the hold-out sample, seated at location l.

If we let njlHbe the number of respondents in the hold-

out sample seated at location l reporting SVI 5 j, then we

can calculate the squared error of predicting njlH using

the ordinal logit model (M) as eMH ¼P

l2AllLocationsPj21;2;3 n

jlH � EMlH½SVI ¼ j�

� �2. We can compute an R2

measure of predictive accuracy by comparing the ratio

of eMH to the squared errors of the naive model

eNH ¼P

l2AllLocationsP

j21;2;3 njlH � ENlH½SVI ¼ j�

� �2, which

gives us

R2H ¼ 1� eMH =eNH: ð7Þ

4.2. Game EffectsClearly, SVI is influenced by the actual game/eventand hence it is important to consider the robustness ofour results to variations across games. For instance,the outcome of the game, the composition of theplaying teams, or the weather could have affected theseat value distribution customers reported. However,this limitation could be easily overcome by surveyingconsumers from multiple games and employing thesame methodology to analyze the collected data andexplore specific recommendations.

While the ideal way to test this would be to conductthe same survey across multiple games, record keygame-related attributes (result, attendance, visitingteam, etc.) and use them as control variables in theregression equation, for reasons beyond our control,the franchise chose to vary some aspects of the surveyacross multiple games. For instance, a survey con-ducted during a different game included many of thesame questions as before (Age, Gender, and Seat Lo-cation), but did not capture a few variables likeHometown and Frequency. We decided to combinethe data from these two surveys to check the robust-ness of our results, especially the relationship betweenSVI and Seat Location, to inter-game variations.

We modify our regression equation for the HOLMby including only the common covariates across thetwo surveys and adding a fixed effects parameter tocontrol for difference in valuations across games. Themodified regression equation can be written as

V�i ¼b1 Agei þ b2Malei þ b5ThirdBasei þ b6Backnetiþ b7Fieldi þ b8Grassi þ b9Outfieldiþ b10UpperDecki þ b13Gamei þ siei;

where ei is a standard logistic random variable, and siis a heteroskedastic variance scaling factor given by

si ¼ expðg1Agei þ g5ThirdBasei þ g10UpperDeckiþ g13GameiÞ:

Note that the parameter g13 captures differences inthe variance of the distribution of seat values across thegames. Table 5 shows a comparison of the parameterestimates obtained using the combined data set withthose obtained from the single game. Note that all ourverifiable conclusions hold even after we control forvariations across games. Customers seated on the ThirdBase continue to experience lower variance in the seatvalue perceived (g5 5� 0.319, po0.001), while themeans show no statistically significant differences. Sim-ilarly, customers seated on the Upper Deck continue tohave higher mean valuations (b10 5 0.303, po0.001) aswell as higher variance (g10 5 0.140, po0.05). This sug-gests that our findings might be robust across games.

It is interesting to note that while the mean valu-ations across games are not significantly different(b13 5 0.055, po0.64), the variances are significantlydifferent (g13 5 0.854, po0.001). In other words, theshape of the distribution of seat values is significantlyinfluenced by the game. For instance, the first surveywas conducted during a game that the home teamlost, while the second survey was conducted during agame that the home team won. The result of the gamecould explain a portion of the difference in variances.Nevertheless, even after controlling for differencesacross the games, our seat value results remain largelyunchanged.


Repeating the validation analysis discussed in sec-tion 4.1, we find that even for the combined data set,the model significantly improves the predictive powerover the naive model (R2H ¼ 56:1%, see Table 6 for asummary of the results).

4.3. Seat Location EffectsThe experience in such entertainment settings isclearly a function of the product (the game in thecontext of our paper), the consumer, and her seat

location. Hence it is important to investigate howmuch of SVI is accounted for by each of these factors(game attributes, consumer attributes, and seat loca-tion attributes). We study the relative impact of eachof these three factors in influencing SVI, by followinga three-step approach:

1. First, we ran several heteroskedastic ordinal regres-sions using a combination of these three factors asexplanatory variables, both on the original data setas well as the combined data set.

2. Second, we measured the ability of each of thesemodels to predict the number of consumers re-porting a particular SVI at each seat location,using the R2 defined in Equation (7).

3. Third, we compared the computed R2 across thedifferent models to understand the contributionof each of the three factors in predicting SVI.

Applying this analysis to the original data set, wefind that while the model consisting of both consumerand seat-location factors had an R2H of 57.1%, a majorportion of SVI is accounted for by seat location attributes(with an R2 of 56.1%), while consumer attributes havealmost insignificant predictive power (R2 5 6%).

To investigate how seat location factors influenceSVI once we control for game-related attributes, weapplied the same analysis to the combined data set.We find that while all three factors combined togetherhave an R2H of 56.1%, seat location attributes still accountfor a major portion of the SVI, with an R2H of 38.5%, evenafter controlling for game-related factors (See Table 6).

The analysis summarized in Table 6 emphasizesthat seat location factors explain a significant portionof SVI. Game and Consumer attributes do matter, butexplain a smaller portion. This finding underscoresthe importance of seat location factors in influencingseat value. It also strengthens the case for the need forstudies like ours that shed more light on the drivers ofseat value. Finally, firms have reasonable control overseat location factors, and hence can take advantage ofthese findings to manage SVI.

4.4. Seat Price EffectsIn order to properly estimate the relationship betweenseat value and seat location, we need to further isolatethe effect of the location-dependent price variable. Weaddress this issue by studying the relationship be-tween SVI and Seat Location, controlling for the pricevariable. To achieve this, we consider three versions ofthe Heteroskedastic Ordinal Logit Model.

1. The original model described in section 3 thatdoes not include ticket price.

2. A model that included the ticket price for eachseat section in addition to all the other covariates.

Table 6 Predictive Accuracy of Consumer Attributes, Seat LocationAttributes, and Game Attributes

Explanatory variables

First data

set R2H (%)

Combined data

set R2H (%)

Consumer attributes 6.0 9.1

Seat location attributes 56.1 38.5

Game attributes 17.3

Consumer1seat location

attributes

57.1 51.1

Consumer1game attributes 17.7

Seat location1game attributes 55.6

All attributes 56.1

Note that sub-models that include seat location attributes have higher predictive

accuracy than those models that do not include them.

Table 5 Comparison of Parameter Estimates for the Single Data Set vs. theCombined Data Set

Variable Single game Combined

Age b1 0.034 � 0.007Male b2 � 0.034 � 0.146City (vs. Outside) b3 0.011

Prefecture (vs. Outside) b4 0.102

Third Base (vs. First Base) b5 0.145 0.080

Backnet (vs. First Base) b6 � 0.440�� 0.126Field (vs. First Base) b7 � 0.509�� 0.449��

Grass (vs. First Base) b8 0.919�� 1.055��

Outfield b9 0.171 � 0.153Upper Deck b10 0.263

�� 0.303��

Frequency b11 � 0.081��

Team 1 b12 0.185��

Game b13 0.055

Age g1 � 0.075�� 0.062��

Third Base (vs. First Base) g5 � 0.324�� 0.319��

Upper Deck g10 0.208�� 0.140��

Frequency g11 � 0.057�

Game g13 0.854��

Log likelihood LL � 726.27 � 2043.87Likelihood ratio (w2) LR 192.72 364.82

No. of parameters 16 18

McFadden Pseudo-R2 (%) 11.71 8.19

Bold indicates coefficients corresponding to variables of interest.��po0.01; ��po0.05; �po0.1.


3. A model that includes ticket price for eachseat section, but excludes all the seat locationattributes.

The motivating question behind this analysis is todetermine the extent to which the introduction ofticket prices impact our results. From Table 7, we ob-serve that seat location attributes continue to explain asignificant portion of SVI even after controllingfor ticket price, as can be seen by comparing theMcFadden Pseudo-R2 of Models (b) and (c). In fact,adding seat location attributes to Model (c), whichuses only ticket price, increases the pseudo-R2 from5.5% to 12.4%. Finally, we find that most of our resultsand inferences made in section 3.5 continue to hold.

1. The effect of Age on SVI remains almost un-changed, as seen by the b and g coefficients inModels (a) and (b).

2. Frequency of Visits have almost the same effecton SVI as before. The estimates for both the meaneffect and the variance effect remain almost un-changed.

3. The asymmetry that we identified in the paperstill holds, as can be seen from the g coefficientfor the Third Base. The mean effect still stays in-significant.

4. Consumers still find Grass seats very valuable, asseen from the b coefficient.

5. The mean effect of Backnet has changed signifi-cantly (b is now positive). This might be becauseprice affects SVI nonlinearly, or that Backnetcustomers are significantly different. The vari-ance effect that we identified, on the other hand,remains almost unchanged.

6. The b parameter corresponding to the UpperDeck is no longer significant. However, the het-erogeneity effects still persist. In fact, theparameter estimates show no significant changeðga10 ¼ 0:208; gb10 ¼ 0:223Þ.

The surveys did not ask consumers for the actualprice that they paid, as the franchise felt that con-sumers might be more biased in their responses ifprice-related information was asked. Hence, we onlyhad seat prices at each section. The absence of vari-ation in price across consumers seated at the samelocation renders any regression involving location andseat prices susceptible to the effects of multicollinear-ity. This also makes it difficult to isolate the effects ofprice from seat location. Hence, we study the impactof different prices paid by consumers, by adding arandom noise term to perturb the ticket price specifiedfor each seat section. Accordingly, the price paid byconsumer i for a seat in section l was modeled aspil ¼ pl � ð1� ciÞ, where pl is the ticket price specifiedfor section l and ci is the noise term distributed uni-formly over [0, m]. Based on conversations with the

Table 7 Parameter Estimates

Variable HOLMa HOLM with priceb HOLM with price and no seat attributesc

Threshold: low–medium t1 � 0.748�� 2.71�� 1.34��

Threshold: medium–high t2 2.067�� 0.09 1.24��

Age bj1 0.034 0.03 � 0.02Male bj2 � 0.034 � 0.03 � 0.02City (vs. Outside) bj3 0.011 0.009 0.010

Prefecture (vs. Outside) bj4 0.102 � 0.101 � 0.100Third Base (vs. First Base) bj5 0.145 0.110

Backnet (vs. First Base) bj6 � 0.440�� 4.642��

Field (vs. First Base) bj7 � 0.509�� 0.311

Grass (vs. First Base) bj8 0.919�� 0.722��

Outfield bj9 0.171 � 0.221Upper Deck bj10 0.263

�� 0.042Frequency bj11 � 0.081

�� 0.071�� 0.053Team 1 bj12 0.185

�� 0.184�� 0.224��

Price bj13 � 0.01�� 0.001��

Age g1 � 0.075�� 0.080�� 0.071��

Third Base (vs. First Base) g5 � 0.324�� 0.367��

Upper deck g10 0.208�� 0.223��

Frequency g11 � 0.057� � 0.062�� 0.072��

McFadden Pseudo-R2 (%) 11.71 12.4 5.5

a, b, c are superscripts used to reference model coefficients.��po0.01; ��po0.05; �po0.1.


franchise management on the range of discounts pro-vided to consumers, we varied m from 5% to 20%. Werepeated the analysis discussed above with theseprices, and find that our results remain unchanged.

5. Findings and PricingRecommendations

Based on robustness checks in section 4, we are able tounderline the importance of seat location in influenc-ing consumer experience. Hence it is appropriate toconsider seat-location-specific prices for each con-sumer segment.

5.1. Segment-Specific PricingIn sections 3.7 and 3.8, we discussed the calculation ofmarginal probability effects for a typical consumerand the price changes across seat locations required toachieve a service-level objective of a5 15%. However,the firm could engage in more targeted pricingschemes based on how the marginal probabilitiesvaried across consumer segments. We now calculatethe marginal probability effects for different seat lo-cations for each consumer segment based on agegroups (Table 8) and visiting frequencies (Table 9).

From the marginal probability tables, we infer thatcustomers in the age group 40–49 years and 50–59years tend to have the highest probabilities of report-ing low SVI for the Backnet and Field seats, ascompared with a similar seat on the First Base side.Hence, the franchise could offer reduced prices forthese customers for the Backnet and Field seats.

We also infer that the regulars to the games have amuch higher propensity to report a low SVI for thepricier Backnet and Field seats. Given that it is im-portant for the franchise to manage the satisfactionlevels of its most loyal customers, the franchise couldoffer discounts for multigame tickets for selected sta-dium seats on the Backnet and Field, and set pricessuch that the dissatisfaction levels are below an ap-propriate threshold.

It is also interesting to note that for the Grass andThird Base seats, the first-timers are more likely toreport a low SVI. Hence the franchise can encourage

people to start watching games in the stadium byoffering special discounts to newcomers, on the Grassand Third Base seats, or reserving a portion of theseseats at lower prices for the first-timers.

The recommended segment-specific price changesfor each seat section are summarized in Table 10 (forconsumer segments based on age) and Table 11 (forconsumer segments based on frequency of visits).

5.2. Actionable Pricing RecommendationsWe now develop more concrete and actionable pricingrecommendations that would help a franchise achievea specified threshold service level on any given set ofseat products that they might make available. For thisanalysis, we ignore substitution effects associatedwith the price changes. In Lemma 1 in the paper, wederived an expression for the price change at each seatlocation that would help the firm achieve its servicelevel objective of keeping PrðSVIl � 1jp�l Þ to a thresh-old a. If we let pl denote the current seat price, then wecan use Lemma 1 to calculate the new price p�l to becharged at each seat location as:

p�l ¼ pl þ1

yxTl b� t 1 þ ln

a1� a� �

expðzTl gÞn o

:

This equation prices each seat location for a specificconsumer whose characteristics are known. However,we can use this equation to price any set of seatproducts that a baseball firm could make available.For example, a firm is interested in setting a singleprice for each seat location such that the service levelconstraint is met. We can derive the new price p�l tocharge consumers by taking a weighted average of the

Table 8 Marginal Probability of SVI = Low by Age (Reference: First Base,Infield, Lower Deck)

Age Third Base (%) Backnet (%) Field (%) Grass (%)

0–9 � 10.6 12.4 14.6 � 17.410–19 � 10.8 13.0 15.2 � 17.020–29 � 10.8 13.5 15.8 � 16.330–39 � 10.6 13.8 16.3 � 15.340–49 � 10.2 14.0 16.6 � 14.250–59 � 9.6 14.0 16.7 � 12.8601 � 8.7 13.8 16.6 � 11.2

Table 9 Marginal Probability of SVI = Low by Frequency of Visits(Reference: First Base, Infield, Lower Deck)

Frequency Third Base (%) Backnet (%) Field (%) Grass (%)

First time � 10.0 12.0 14.2 � 13.6Once � 10.3 13.1 15.5 � 14.4Thrice � 10.7 14.3 16.9 � 15.4Five times � 11.1 15.6 18.5 � 16.6All games � 11.5 17.2 20.2 � 18.0

Table 10 Price Change Percentage to Set Pr(SVI = Low) to a = 15%

Age Third Base (%) Backnet (%) Field (%) Grass (%)

0–9 � 6.0 � 14.8 � 52.7 25.110–19 � 1.0 � 13.0 � 46.6 37.720–29 3.8 � 11.3 � 40.9 49.730–39 8.3 � 9.7 � 35.5 61.140–49 12.7 � 8.1 � 30.3 71.850–59 16.8 � 6.7 � 25.4 82.1601 20.8 � 5.3 � 20.8 91.8


new prices derived using Lemma 1 over the distribu-tion of consumer characteristics. Alternately, if thefirm wants to provide targeted prices for specificconsumer segments (e.g., Age, Frequency, Age–Frequency combination), then the new price to chargeeach segment can be derived by taking a weightedaverage of the new price over the distribution of theremaining consumer characteristics.

We now illustrate the application of this method incalculating seat prices. First, we calculate the location-specific seat prices that the firm should set in order toachieve the service level objective for each seat loca-tion. The results are summarized in Table 12. From theseat location-specific prices calculated in Table 12, weobserve that the seat prices across Third base and Firstbase are asymmetric. In fact, the seats located on theThird base command a 33% premium on average ascompared with those on the First base. Moreover, asone would expect, seats on the lower deck continue tobe priced higher than those on the upper deck.

Now, the firm can do better by setting targetedprices for specific consumer segments. For instance,the firm can target specific age groups such as stu-dents, regulars, and retirees. The price to charge eachgroup for a particular seat location is calculated as inTable 12. Note that, as expected, student tickets areheavily discounted across seat locations, while retireesare made to pay a premium.12

In addition, the firm might also consider targetingconsumers based on their frequency of visits by set-ting different prices for five game packs and seasonpasses. From the seat prices based on frequency, assummarized in Table 12, we observe that seasonpasses are discounted, compared with single gametickets. An interesting thing to note is that the max-imum discount for season passes occurs for Thirdbase tickets, which suggests that the firm stands togain by exploiting the asymmetry in more than oneway.

While we have illustrated price calculations forsome specific instances of variable pricing, ourmethod is general enough to accommodate morecomplex forms. For example, the firm might want tooffer price bundles based on combination of age andfrequency of visits. In this case, we can integrate theconsumer-specific seat prices across the distributionof remaining consumer characteristics (Gender, City,Team1, etc.) to derive the best price for each bundlethat achieves a given service level.

The ideal way to test the impact of our recommen-dations would have been to offer the new prices toconsumers and observe the resulting distribution ofSVIs. However, that approach was not feasible, in ourcase, as it required the franchise to implement pricechanges across the board, and conduct the survey postimplementation. Hence, we used the demographicprofile of consumers in our validation sample to cal-culate the achieved service levels, assuming thatconsumers had paid these set prices. From Table 13,we clearly observe that the new prices achieve a ser-vice level very close to the threshold of a5 15% thatwe set out to achieve.

5.3. Insights and RecommendationsBased on the results obtained, we gather several in-teresting insights on the net value perceived by

Table 11 Price Change Percentage to Set Pr (SVI = Low) to a = 15%

Frequency Third Base (%) Backnet (%) Field (%) Grass (%)

First time 12.0 � 8.9 � 33.1 66.1Once 10.5 � 9.1 � 33.8 64.6Thrice 8.8 � 9.4 � 34.6 62.9Five times 6.9 � 9.7 � 35.6 60.8All games 5.0 � 10.0 � 36.7 58.4

Table 12 Seat Prices by Consumer Segment to Achieve Service Level Objective of a = 15%

Seat Location Section Row

Price (Yen)

Seat Price Student Regular Retirees Five Game Seasons

1 Backnet Infield Lower 6980 6670 6930 7270 6940 6920

2 Third Infield Lower 2420 2160 2360 2630 2380 2340

3 Third Outfield Lower 1650 1470 1670 1940 1620 1580/

4 Third Infield Upper 1740 1480 1710 2030 1700 1670

5 Third Outfield Upper 1850 1660 1890 2200 1820 1790

7 First Infield Lower 1980 1660 1920 2260 1950 1920

8 First Outfield Lower 1260 970 1230 1570 1230 1200

9 First Infield Upper 1230 870 1170 1570 1220 1200

10 First Outfield Upper 1270 1030 1330 1720 1270 1260

11 Field Infield Lower 1490 1190 1450 1790 1450 1430

12 Grass Outfield Upper 2000 1670 1970 2350 2000 1980


consumers who attended the game. Our results helpquantify seat value in terms of seat location charac-teristics and consumer attributes. Furthermore, wealso characterize the distribution of SVIs that helps usdetermine the probability of customers reporting lowSVI. We make several recommendations based on ourempirical results and the service objective considered,and these are being implemented by the franchise.

1. Seats are Asymmetric: We find that consumersseated on opposite sides of the ball park report asym-metric SVIs. Thus, the distribution of SVIs reported bycustomers seated on the third base side is significantlydifferent from that of customers seated on the firstbase side. In fact, any customer located on the thirdbase side has a lower probability of reporting low SVIas compared with an identical customer seated in asymmetric location on the first base side. This asym-metry is intriguing. Although every professionalbaseball team prices its tickets identically for left fieldand right fields, there are several underlying asym-metries in the game/ballpark that could possiblyexplain this difference in perceived value. First, theincidence of foul balls is generally higher in right field,which could influence how customers respond to theirexperience of the game. Second, for the stadium of thefranchise we study, the location of the home-team dug-out was on the third base side, which possibly providedhigher value for some of the fans. Third, weather re-lated factors like sunlight, wind, etc., can affect theviewing experience across seat locations. Finally, inmany professional ball parks, although the prices arealways symmetric, the views from the seats are not. Infact, to many players and baseball fans, the fundamen-tal asymmetries in the design of a ballpark add to theidiosyncratic charm of the game (Maske 1992).

Asymmetric seat values provide the franchise withan opportunity to price tickets differently while main-

taining identical probabilities of experiencing low seatvalue on both sides of the stadium. Our recommen-dations would initiate differential pricing acrosssymmetric locations and achieve two goals. First, theyeliminate the inherent asymmetry in net value per-ceived (and SVIs). Secondly, they also help thefranchise achieve a certain desired level of customerservice. The franchise is currently implementing ourrecommendation of pricing the single-game ticketsasymmetrically for the upcoming season.

2. Value of Seat Locations for Consumer Segments (Basedon Age): Conventional wisdom provides some guide-lines on valuable seat locations in a baseball stadium.For example, Backnet seats are considered quite valu-able to customers. In the introduction, we raised thequestion: ‘‘Do the customers seated at the upper deckvalue those seats highly?’’ Equipped with our analy-sis, we can now summarize the value perceived bycustomers at those seats, and compare our findingswith common notions of seat value. Moreover, we cando this analysis across each consumer segment.

Upper Deck Seats: First, we consider upper deck seatsthat are generally inexpensive, and located further awayfrom the playing field. Our results suggest higher meanSVI for customers seated at the upper deck. Whilehigher mean seat values are interesting in their ownright, our analysis of marginal probabilities reveals asubtler insight. For example, considering a customer inthe age group 30–39, we find that he has the sameprobability of reporting his SVI as low (or medium)whether he is seated at the lower deck or the upperdeck. However, the probability of reporting SVI ashigh increases as he moves from a lower deck seat to asimilar upper deck seat. In other words, the highervalue perceived at the upper deck is almost entirelydriven by a significantly higher proportion of customersreporting their seat value as high. Thus, our results

Table 13 Service Levels Achieved in the Validation Sample for Each Segment Based on New Prices

Seat Location Section Row

Pr ðSVI ¼ 1jValidation sampleÞ

Seat Price Student Regular Retirees Five Game Seasons

1 Backnet Infield Lower 0.143 0.146 0.150 0.163 0.152 0.127

2 Third Infield Lower 0.162 0.162 0.155 0.155 0.161 0.141

3 Third Outfield Lower 0.150 0.150 0.144 0.146 0.131 0.127

4 Third Infield Upper 0.140 0.137 0.155 0.166 0.152 0.115

5 Third Outfield Upper 0.151 0.144 0.143 0.121 0.129 0.124

7 First Infield Lower 0.151 0.151 0.155 0.144 0.161 0.132

8 First Outfield Lower 0.180 0.169 0.167 0.167 0.112

9 First Infield Upper 0.170 0.163 0.157 0.156 0.165 0.162

10 First Outfield Upper 0.160 0.147 0.154 0.145 0.119

11 Field Infield Lower 0.141 0.149 0.151 0.155 0.151 0.126

12 Grass Outfield Upper 0.148 0.144 0.172 0.148


argue for the continued availability of upper deck seatsfor customers.

Backnet Seats: Backnet seats are often considered tobe the best seats in the stadium. However, it is unclearhow the franchise should price them across consumersegments.

Our analysis implies that the franchise can offer agebased discounts as summarized in Table 10. For con-sumers in the age group 10–19, the recommendedsegment-specific prices are 13% lower than the currentsingle ticket Backnet prices, whereas for the age group30–39, the recommended prices are 9.7% lower thancurrent prices (see Table 10). In effect, according to oursegment-specific pricing scheme, high-school/collegestudents (in age group 10–19) should receive roughly a5% discount for single-ticket Backnet prices, comparedwith the age group 30–39. The franchise can achieve theservice-level objective of a5 15% by suitably discountingthe backnet seat prices, as indicated in Table 10.

Grass Seats: Grass seats located further in the out-field are similar to upper deck seats. Customersperceive significantly higher value at grass seats. Incontrast to upper deck seats, this higher value isdriven by a mean shift in its distribution. Conductinga segment-specific pricing analysis similar to that car-ried out for the Backnet seats, we find that we canincrease the grass seat ticket prices and still keep theprobability of low SVI within 15%.

3. Segment-Specific Prices Based on Frequency of Visits:We find that repeated visits to the ballpark reduce theprobability that a customer would report extreme SVI.For example, we find that a customer visiting the ball-park for the eighth time has an 8% lower probabilityof reporting SVI 5 high as compared with a first-timevisitor (Table 3 shows that the probability of reportingSVI 5 high reduces by 1% for every additional visit).Looking at the results of the Generalized ThresholdModel in greater detail, we infer that a likely expla-nation for the reduced tendency of the more frequentcustomers to report extreme SVIs is that they usestricter thresholds ðd̂211 � d̂111 ¼ b̂111 � b̂211 ¼ 0:141Þ.

13 Inother words, for the same experience and realizationof net value, the more frequent customers are lesslikely to be ‘‘surprised’’ and are therefore less likely torespond with extreme reactions.

While the difference in reporting thresholds seemsto be the most likely explanation for the observeddistribution of SVIs, one cannot rule out the possibil-ity that the distribution of net values might beheteroskedastic with respect to frequency of visits.In fact, the results of the heteroskedastic model wouldsuggest that the distribution of realized values for themore frequent customers does have a lower varianceðĝ11 ¼ �0:057Þ as well as a lower mean ðb̂11 ¼ �0:081Þ.This would support the notion that baseball games are

experience goods with residual uncertainty thatdecrease with repeated visits to the ballpark.

Based on the segment-specific pricing analysis, wecan recommend price discounts for each seat locationbased on frequency of visits. These prices aresummarized in Table 11. First, we find that the rec-ommended price discounts increase with increasingfrequency of visits. Second, we observe that the rec-ommended ticket prices can be higher or lowercompared with the current prices. For example, atthe Third Base, the recommended prices are 5–12%higher, whereas at the Backnet, they are 9–10% lowerthan the current prices. This leads to a subtler thirdinsight, that the price discounts offered to a seasonregular (relative to a first-timer) can be as high as 6%(for the Third Base) and as low as 2% (for the Backnet).

6. Conclusions and Future DirectionIn this paper, we first developed SVI, a measure of netvalue perceived by a consumer after attending anevent. Then, we established the relationship betweenthe SVIs reported by consumers and their seat loca-tions. Finally, we provide directions that would helpthe firm achieve a ‘‘desired level of seat value’’ bysuitably increasing or decreasing ticket prices in eachsegment. The key steps of our approach and method-ology can be summarized as follows:

1. Capture on some ordinal scale the net value per-ceived by consumers, using a survey instrument.

2. Design a SVI measure.3. Investigate how the SVI is influenced by con-

sumer characteristics, seat location attributes,and event-related factors, using a series of Ordi-nal Logit Models. Deviation from proportional-odds (verified using Brant test) suggests thepresence of heterogeneity in the model, whichcan be incorporated in two ways: (i) The Gener-alized Threshold Model, which assumes thatconsumers use different thresholds, and (ii) TheHeteroskedastic Model, which assumes that thevariance of the idiosyncratic value term differsacross covariates.

4. Estimate current service-levels as the probabilityof a given customer seated at a particular locationreporting SVI 5 low. Then, optimize the prices toachieve the aforementioned probability thresholdacceptable to the firm (as derived in Lemma 1).

We illustrated the application of our methodologyby applying it to two survey data sets collected by aprofessional league baseball franchise in Japan. Ourfindings provide a characterization of seat value per-ceived by consumers in a stadium based on theirage, location of the seat, and the number of visits.We showed that a careful study of the interactions


between SVI and the explanatory variables, specificallyaccounting for systematic heterogeneity in responsethresholds and distributions of seat value across cus-tomer segments, reveals some relatively unexpecteddependencies (asymmetries, etc.). Detailed analysis re-veals that the seat location plays a crucial role in howseat values are distributed, which enables us to con-sider pricing based on individual segments.

The insights on seat value that we derive in thispaper provide the crucial initial steps in planning howseats should be sold, and how to price tickets basedon segment-specific and consumer-specific informa-tion for different sections of the stadium/theater.

Limitations: Finally, our paper is not without limi-tations, typical for a paper exploring empirical RMaspects. The first limitation is that our pricing recom-mendations ignore the effects of substitution. Pricingchanges might modify the valuations and choices thatconsumers make. Hence, it is important for the fran-chise to keep this limitation in mind and furtherestimate the changes in demand or customers’ futurevaluations. This could be achieved by perturbingprices and observing the resulting demand and re-evaluating customers’ responses.

The second limitation is that consumer responses toprice changes might change the optimal assortment ofdifferent ticket categories both in prices and capacityoffered at that price. The assortment decision can bestudied with additional data on how customersarrived at their revealed preferences. Analyzing Ca-pacitated Multinomial Logit assortment problems is achallenging stream of research. For example, seeRusmevichientong et al. (2010), and references there-in. Owing to paucity of data on how consumers chosetheir seats, we did not model the optimal assortmentdecision in this paper.

A third limitation is around the design of the sur-vey. Most customers in the survey reported SVI 5 2.Although this may be a natural response of consum-ers in our context, we cannot rule out the possibilitythat respondents avoided using extreme response cat-egories (referred to as central tendency bias). Futurework can focus on improved survey design and bettermeasurement of consumer responses in order tocounter these biases.

Furthermore, Neelamegham and Jain (1999) arguethat modeling customers’ expectations (through emo-tional stimulation and latent product interest) beforethe choice is made and modeling post-choice evalu-ations (determined by consumers’ post-consumptionexperience) are both important in modeling the con-sumption of experience goods. Thus our findings onpost-consumption perceived value, combined withthe decision models of customers’ revealed prefer-ences, would allow firms to explore the impact ofsubsequent decisions in greater detail.

Finally, SVI is clearly influenced by the actual pricepaid by consumers. However, we were unable to in-corporate seat prices directly into our model andstudy its effects in detail, as our data set lacked gran-ular prices at the consumer level. This presents anopportunity for future work, where more granularprice data could be gathered to simultaneously studythe impact of price and seat location on consumervaluations.

Nevertheless, we hope that our analysis of differingseat values provides sports franchises and theater es-tablishments with the first steps in analyzingcustomer perceptions of different seats, and factoringthose perceptions while making their pricing deci-sions. In a variety of sporting events/performances,the attending customers value their experience differ-ently based on their seat locations. Although someseats might appear similar, they might provide differ-ent valuations for long-time patrons who have a well-developed sense about which seats have better value.Exploring such nonobvious differences in the valueperceived by customers located in different seats pro-vides sports and theater establishments with anopportunity to improve their customer base throughmore efficient pricing, or better selling mechanisms.

AcknowledgmentsThe authors would like to thank the NPB franchise and YutaNamiki for the data. We thank Eric Bradlow, Gerard Cachon,Michael Lapre, Serguei Netessine, Devin Pope, Scott Rosner,Rob Shumsky, Ken Shropshire, a senior editor, two anony-mous reviewers, and the participants at the WSBI seminar,2008 Behavioral Operations Conference at Alberta, Canada,the 2008 INFORMS Revenue Management and PricingConference at Montreal, Canada, and the 2009 MSOM Con-ference at Boston, MA for their thoughts and comments. Weacknowledge financial support from the Wharton SportsBusiness Initiative and the Fishman-Davidson Center forService and Operations Management.

Notes

1Although there are differences between aisle seats andmiddle seats, most seats in the same travel class (business oreconomy) are perceived to provide comparable valuationsfor consumers. Of late, these seat value differences based onseat location are gaining attention. See www.seatguru.com.

2This notion is analogous to ‘‘fill-rate’’ measures employedin retail settings. While focusing on a desired fill-rate mightbe sub-optimal for short-run profit maximization, it im-proves availability, leading to long-run benefits. Quantityadjustments are more difficult in stadiums/theaters, butprice adjustments to ‘‘satisfice’’ value can be made.

3We treat age as a continuous variable in our model inorder to preserve the order information contained. We testedan alternate specification treating age as categorical, butrejected it in favor of the continuous specification based on


the AIC values of the two models. In addition, we also con-sidered an alternate continuous specification for age, whereeach age group is represented by its midpoint. We find thatour results remain largely unchanged.

4Note that the actual price paid may have an effect onconsumer valuations and the ex-post survey scores re-ported. While our approach can incorporate price into theregression, our data set lacks granular price data at theconsumer level. Therefore, we do not explicitly considerprice in our model. Instead,

Date post:	24-Jan-2021
Category:	Documents
Upload:	others
View:	0 times
Download:	0 times

PRODUCTION AND OPERATIONS MANAGEMENT POMS · 2019. 12. 12. · Measuring Seat Value in Stadiums and...

Documents