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Variable Ticket Pricing in Major League Baseball
Daniel A. Rascher
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407
Rascher is with the Sport Management Program, University of San Francisco, San Francisco, CA
94117. McEvoy is with the School of Kinesiology and Recreation, Illinois State University, Normal,
IL 61790. Nagel and Brown are with the Dept. of Sport and Entertainment Management, University of
South Carolina, Columbia, SC 29208.
Journal of Sport Management, 2007, 21, 407-437
© 2007 Human Kinetics, Inc.
Variable Ticket Pricing in Major
League Baseball
Daniel A. Rascher Chad D. McEvoy
University of San Francisco Illinois State University
Mark S. Nagel and Matthew T. Brown
University of South Carolina
Sport teams historically have been reluctant to change ticket prices during the
season. Recently, however, numerous sport organizations have implemented vari-
able ticket pricing in an effort to maximize revenues. In Major League Baseball
variable pricing results in ticket price increases or decreases depending on factors
such as quality of the opponent, day of the week, month of the year, and for special
events such as opening day, Memorial Day, and Independence Day. Using censored
regression and elasticity analysis, this article demonstrates that variable pricing
would have yielded approximately $590,000 per year in additional ticket revenue
for each major league team in 1996, ceteris paribus. Accounting for capacity
constraints, this amounts to only about a 2.8% increase above what occurs when
prices are not varied. For the 1996 season, the largest revenue gain would have
been the Cleveland Indians, who would have generated an extra $1.4 million in
revenue. The largest percentage revenue gain would have been the San Francisco
Giants. The Giants would have seen an estimated 6.7% increase in revenue had
they used optimal variable pricing.
Variable ticket pricing (VTP) has recently been a much-discussed topic in
the business of sport, especially as it relates to professional baseball, professional
hockey, and college football (King, 2003; Rovell, 2002a). VTP refers to changing
the price of a sporting-event ticket based on the expected demand for that event.
For example, Major League Baseball’s (MLB) Colorado Rockies had four different
price levels for the same seat throughout the season (Cameron, 2002). The different
price levels were based primarily on the time of the year (summer versus spring
or fall), day of the week (weekends versus weekdays), holidays (Memorial Day,
Independence Day, etc.), the quality of the Rockies’ opponent, or their opponents’
star players (e.g., Barry Bonds). The same seat in the outfield pavilion section of
Coors Field, the Rockies’ home stadium, ranged in price in 2004 from a high of
Economics and FinancE
408 Rascher et al.
$21 for what the Rockies labeled as “marquee” games to a low of $11 for what
were considered “value” games. MLB teams who used VTP in 2004 are detailed
in Table 1. Other sport organizations besides MLB franchises use VTP, as well.
Several National Hockey League (NHL) teams use VTP strategies, as do a number
of intercollegiate athletics programs (Rooney, 2003; Rovell, 2002a).
Some MLB teams have concluded that their 81 home games are not 81 units
of the same product, but rather, based on the aforementioned characteristics such
as the day of the week and quality of the opponent, are 81 unique products. As
such, the 81 unique products should each be priced according to their own char-
acteristics that make them more or less attractive to the potential consumer. MLB
attendance studies support this notion. For example, in a study including more
than 50 independent variables in explaining MLB game attendance, McDonald
and Rascher (2000) found variables such as day of the week, home and visiting
teams’ winning percentages, and weather, among many others, to be statistically
significant predictors of game attendance. Clearly, a variety of factors make some
games more appealing and others less appealing to consumers. It seems quite logical
to price tickets to these games at different levels, especially with teams constantly
searching for revenue sources to compete with their opponents for players (Howard
& Crompton, 2004; Zimbalist, 2003).
The varying quality of games throughout a season often creates a second-
ary market because demand for the most popular games might exceed available
supply. Independent ticket agents, or scalpers, broker tickets obtained from various
sources to fans unable or unwilling to purchase tickets from a team’s ticket office
or licensed ticket agency (Caple 2001; Reese, 2004). Ticket scalpers respond to
market demands (often in violation of city ordinances or state laws), but the team
initially selling the ticket does not realize any increased revenue during a scalper’s
transaction (“History of Ticket Scalping,” n.d.). For this reason, the Chicago Cubs
have recently permitted ticket holders to auction their Wrigley Field tickets on a
Table 1 2004 MLB Variable Ticket Pricing Programs
Team
Number
of
Levels Levels (price for typical outfield bleacher seats)
Arizona Diamondbacks 3 premier ($18), weekend ($15), weekday ($13)
Atlanta Braves 2 premium ($21), regular ($18)
Chicago Cubs 3 prime ($35), regular ($26), value ($15)
Chicago White Sox 2 weekend ($26), weekday ($22)
Colorado Rockies 4 marquee ($21), classic ($19), premium ($17), value ($11)
New York Mets 4 gold ($16), silver ($14), bronze ($12), value ($5)
San Francisco Giants 2 Friday–Sunday ($21), Monday–Thursday ($16)
Tampa Bay Devil Rays 3 prime ($20), regular ($17), value ($10)
Toronto Blue Jays 3 premium ($26), regular ($23), value ($15)
Note. Different seating configurations of each stadium make comparing like seats difficult; however,
this attempt was made to provide the reader with an idea of the range of price levels used by each team
for similar seats. Source: www.mlb.com.
Variable Ticket Pricing 409
Cubs affiliated Web site, with a fee being paid to the Cubs for this service (Rovell,
2002b; see also www.buycubstickets.com). It is believed that instituting a compre-
hensive VTP policy would diminish the influence of scalpers and permit greater
revenue to be generated by the team for games in high demand.
Many industries have previously embraced the variable pricing concept as a
method for increasing revenue and providing more efficient service to consum-
ers (Bruel, 2003; Rovell, 2002a). Airline flights are typically more expensive for
selected days of the week (Monday, Friday), times of the day (morning, late after-
noon), and days of the year (holidays) when travel demand is higher. The airlines
also use variable pricing to encourage passengers to book their flights early (typically
a purchase at least 10–14 days in advance results in a lower fare) or, in some cases,
at the last minute (“Travel Tips,” 2004). Hotel pricing characteristically reflects
expected demand, even though the actual physical product does not change, because
rooms for weekends or holidays are usually priced higher than for weekdays or
off-season visits. In fact, sometimes variable pricing even relates to major sporting
events like the Super Bowl. Many hotels substantially raise room rates during Super
Bowl week (Baade & Matheson, n.d.). Other industries such as transportation use
variable pricing; some toll roads now charge higher toll rates during peak times
and lower rates during off-peak times (“Group Commends,” 2001). The arts use
variable pricing; matinee movie pricing is one example (Riley, 2002).
Sports franchises are moving forward with VTP strategies before sufficient
research has been done to empirically evaluate its specific merits to the industry.
This article provides a straightforward assessment of optimal VTP. First, a review
of the literature reveals difficulties in estimating the nature of demand functions
in sports. Specifically, optimal pricing is partially determined by price elasticities
of demand, yet it is difficult to estimate ticket-price elasticities that are consistent
over time. Next, a theory of complementary demand is explained that will account
for nonticket products and services and the effect that ticket prices have on the
demand for these products and services. Then, using individual game data from
the 1996 MLB season, ticket prices and corresponding quantities are estimated
that would have maximized ticket revenue. These are compared with actual prices
and revenue to determine the yield from initiating a VTP policy. The final section
contains a discussion of the implications of the results. In summary, this article
shows that there are financial benefits to be gained from implementing VTP, details
how much can be gained from a general VTP policy, and provides strategies for
implementing VTP.
Review of Literature
Price Elasticity of Demand in Sports
Although the literature specifically investigating VTP in sport is limited, the litera-
ture on estimating demand functions and the corresponding elasticities for sporting
events is extensive. It is typical for these studies to estimate the price elasticity
of demand to see whether sports teams are setting price to maximize revenue (or
profit if it can be shown that variable costs are relatively negligible). In practice,
one could adjust season ticket prices and institute a VTP policy that increases
revenue based on the results of elasticity studies. One problem is that the results
410 Rascher et al.
are not consistent across studies. One explanation for this is that it is reasonable
for prices to be set in the elastic, inelastic, or unit elastic portion of demand under
various circumstances. For instance, profit maximization results in prices that are
in the elastic portion of demand if marginal costs are above zero. If marginal costs
are not above zero, then optimal prices are such that profit maximization equals
revenue maximization, which occurs at unit elasticity. If other revenue streams are
accounted for, such as concessions or parking, however, then optimal pricing can
be in the inelastic portion of demand. Thus, each of these three demand-elasticity
pricing strategies is justifiable. It is generally assumed in sports ticket pricing that
the marginal cost of selling an extra seat is so low that the elastic part of demand is
not optimal in terms of pricing. Any price from unit elasticity down into the inelastic
portion of demand is a likely finding, as shown in the literature.
Noll’s (1974) point estimates for elasticity for baseball were –0.49 for the
1970 and 1971 seasons. For the 1984 MLB season, Scully (1989) estimated point
elasticities of –0.63 and –0.76. Boyd and Boyd (1996) used Scully’s 1984 data
but added a measure of competition (recreational index for each city) and used
a recursive feedback loop that incorporated the effects of home-field advantage.
Namely, not only do more wins increase attendance, but enhanced attendance
increases the likelihood of winning because a greater home-field advantage is
created. In this study, point elasticities ranged from –0.58 to –1.20. Hence, Boyd
and Boyd discovered elasticities that were in the expected range, near or above
unit elasticity. It is important to note that economists have a habit of referring to
price elasticities as being positive even though they are actually negative. A price
elasticity of –1.5 is in the expected range for a profit-maximizing decision maker.
In fact, any price elasticity that is –1.0 or lower (meaning –1.5 or –2.0) is consistent
with profit maximization. A price elasticity of –2.0, however, will often be called a
higher elasticity than –0.8, referring to the absolute value of elasticity and ignoring
the sign (which is always negative).
Scully’s (1984), Noll’s (1974), and Boyd and Boyd’s (1996) estimates all had
large enough confidence intervals on the ticket-price coefficient to not exclude unit
elasticity as a possibility. In other words, none of those studies could reject the
hypothesis that teams set ticket prices to maximize revenue. A study by Whitney
(1988) that used more observations than those previously discussed, however, did
yield an estimate of price elasticity that fell within the inelastic portion of demand.
Furthermore, Marburger (1997) found price elasticities in the inelastic part of
demand using annual team-level data covering a 20-year period. The implications
of inelastic pricing will be explained in the Theoretical Foundations section.
Fort (2004) recently summarized the literature on spectator-sports demand
analysis and the difficulty in measuring price elasticities. He noted that simply
analyzing one revenue stream makes it appear that pricing is not profit maximizing
and that a more complete accounting of all revenue streams (e.g., tickets, conces-
sions, and local television) is consistent with profit-maximization pricing. Given
this discussion of price elasticities and profit maximization, the current study
incorporates models that attempt to include the relationship between ticket and
concession prices.
Variable Ticket Pricing 411
Ticket Pricing Issues
It has been difficult for researchers to show profit-maximizing ticket pricing by
sports teams. There are a number of reasons for this besides the inclusion of other
revenue streams. First, most pricing data is a simple average of prices that are
available for various seats for each team each season. Currently, Team Marketing
Report (TMR) collects pricing data that some researchers have used (e.g., Rishe &
Mondello, 2004; Rascher, 1999). Although it is likely an improvement over previ-
ously collected pricing data, it has lacked consistency across teams and over time.
Numerous discussions by the authors and TMR have revealed that TMR is able to
separate out the luxury-suite ticket prices. TMR has also separated out club-seating
prices for some, but not all, teams. Furthermore, this varies across seasons. TMR
relies on the teams to self-report. Because of the prominence of the TMR Fan Cost
Index, some teams potentially manipulate their reported prices to appear relatively
inexpensive. Moreover, the number of seats available at each price level does not
typically weight these prices. In addition, the number of seats sold is generally
known in aggregate, not separated by seat price. Second, Demmert (1973) noted
that there is a correlation between population and ticket price across many seasons
(likely based on the connection to income in which more highly populated areas
are associated with higher incomes, increasing demand and, therefore, prices). This
multicollinearity can cloud the interpretation of coefficients on price. Third, as
Salant (1992) pointed out, the long-term price of tickets might be optimal (adjust-
ing for risk), but in the short term a team might be over- or underpricing in order to
maintain consistency. This is a form of insurance in which the team bears the risk.
Fourth, similar to Fort’s (2004) findings, ticket prices might be kept relatively low
in order to increase the number of attendees at an event who are likely to spend
more money on parking, concessions, and merchandise and who will drive up
sponsorship revenue for the team, thus maximizing overall revenues, rather than
simply ticket revenues.
DeSerpa (1994) discussed the rationality of apparently low season-ticket
prices. Even though many games sell out in the National Basketball Association
and National Football League (focal sports in his study), it is rational for the seller
to price below the myopic short-term demand price in order to give a fan a reason to
purchase season tickets. In fact, DeSerpa discussed the possibility, but unlikeliness,
of charging different prices for each event based on its demand. He surmised that it
was administratively expensive and subject to potential negative fan reaction.
DeSerpa (1994) also noted that it is optimal to underprice season tickets if
fans will likely want to attend only some of the games and resell the tickets for
the remaining contests. The season ticket must be priced low enough for holders
to be able to at least recoup their initial investment after assuming the transaction
costs of resale (e.g., time, effort, search costs, and actual costs such as postage
and advertising). Lower priced season tickets also potentially created a home-
field advantage for teams. Each argument or concern DeSerpa proffered can be
addressed in a VTP system.
412 Rascher et al.
Marburger (1997) developed a model showing that pricing on the inelastic
portion of demand can be explained by accounting for nonticket purchases such as
concessions. Marburger noted that baseball teams set prices on the inelastic portion
of demand, but he did not investigate whether pricing was based on concessions
decisions, just that it occurs. Under multiple methods of measuring ticket price,
Coates and Harrison (2005) found that ticket demand is also quite price inelastic.
Variable Pricing Literature
Specific to variable pricing, Heilman and Wendling (1976) analyzed ticket-price
discounting by the Milwaukee Bucks of the National Basketball Association. The
Bucks discounted prices from $5 to $2 and from $3.50 to $2 for 15 games of the
1974–75 season. The fifteen 1973–74 games that corresponded to the 1974–75
discounted games averaged 9,307 fans and had only three sellouts. The discounted
1974–75 games averaged 10,396 fans and had nine sellouts. Certainly, several
factors (winter weather, player injuries, or even reversion to the mean) beyond the
discounted price could have contributed to the attendance increases. Other teams did
not duplicate the Bucks’ attempt to discount tickets, however. Although the increase
in attendance might appear minimal and result from other factors besides discount-
ing, when ancillary revenue sources (parking, concessions, and merchandise sales)
are added to the cost of a ticket, further investigation into VTP was warranted. The
Bucks, however, remained one of the few teams in American professional sport to
implement a form of VTP until 1999 (King, 2002a; Rovell, 2002b).
Although some research has been conducted regarding VTP, this limited body
of knowledge is not yet sufficient to provide evidence concerning the merits of
using VTP to set single-game ticket prices for sporting events. Despite this lack
of information, some teams have implemented variable pricing, but others have
remained skeptical (King, 2002a). This study investigates the financial gains of VTP
and provides some direction regarding how it should be implemented in MLB.
Theoretical Foundations
The demand for baseball games changes from game to game, partly because of
the varying quality and perception of quality of the home and visiting teams and
partly because of nonperformance factors such as day of the week or month. For a
given price, Table 2 (columns 2 and 3) shows that attendance varies greatly across
games. The average deviation from the mean is nearly 23%. For 11 of the Atlanta
Braves’ 81 home games, the deviation from the mean is over 30%, and the Braves
are not even in the top half of teams with high attendance variation.
In general, many organizations are trying to minimize the effect of team perfor-
mance, which is one of the key factors in the changing demand from game to game
(Brockinton, 2003; George, 2003). As shown in the literature, team performance
is one of the most significant demand factors that can be affected by an owner. For
example, Bruggink and Eaton (1996) and Rascher (1999) analyzed game-by-game
attendance and the importance of team performance. Using annual data, Alexan-
der (2001) showed that the variable with the highest statistical significance is the
number of games behind the leader, a measure of team performance. Teams are
building new stadiums, improving concessions and restaurants, and creating areas
413
Table 2 Summary of Effects of Variable Ticket Pricing (No Capacity or Nonticket-Revenue Adjustment)
1 2 3 4 5 6 7 8 9 10 11 12
Atlanta
35,793 5,832 16.3 13.06 8.1 467,458 471,825 4,367 37,864,102 38,217,807 353,706 0.9
Baltimore
45,475 1,930 4.2 13.14 2.1 597,539 597,909 371 48,400,634 48,430,660 30,026 0.1
Boston
28,687 3,847 13.4 15.43 6.7 442,643 445,436 2,794 35,854,064 36,080,352 226,288 0.6
California
22,476 4,899 21.8 8.44 10.9 189,697 193,539 3,842 15,365,441 15,676,653 311,212 2.0
Chicago (AL)
21,115 4,530 21.5 14.11 10.7 297,927 303,781 5,854 24,132,054 24,606,230 474,176 2.0
Chicago (NL)
28,606 6,854 24.0 13.12 12.0 375,309 382,932 7,622 30,400,069 31,017,468 617,399 2.0
Cincinnati
24,097 4,492 18.6 7.95 9.3 191,568 194,618 3,049 15,517,036 15,764,032 246,996 1.6
Cleveland
41,983 512 1.2 14.52 0.6 609,592 609,629 37 49,376,968 49,379,960 2,992 0.0
Colorado
48,037 80 0.2 10.61 0.1 509,675 509,679 4 41,283,673 41,284,030 357 0.0
Detroit
14,464 5,018 34.7 10.60 17.3 153,322 162,531 9,209 12,419,066 13,165,021 745,954 6.0
Florida
21,839 4,541 20.8 10.37 10.4 226,469 230,737 4,268 18,343,988 18,689,707 345,720 1.9
Houston
24,394 7,362 30.2 10.65 15.1 259,793 268,433 8,640 21,043,206 21,743,062 699,856 3.3
Kansas City
17,949 4,013 22.4 9.74 11.2 174,828 178,510 3,682 14,161,039 14,459,292 298,253 2.1
Los Angeles
39,364 7,038 17.9 9.94 8.9 391,274 395,669 4,394 31,693,231 32,049,165 355,934 1.1
Milwaukee
16,847 5,594 33.2 9.37 16.6 157,853 165,387 7,535 12,786,054 13,396,356 610,302 4.8
Minnesota
17,930 4,899 27.3 10.16 13.7 182,170 188,905 6,735 14,755,746 15,301,288 545,542 3.7
(continued)
414
1 2 3 4 5 6 7 8 9 10 11 12
Montreal
19,982 7,149 35.8 9.07 17.9 181,240 190,229 8,989 14,680,457 15,408,584 728,127 5.0
New York (AL)
28,371 8,999 31.7 14.58 15.9 413,655 428,965 15,310 33,506,040 34,746,176 1,240,136 3.7
New York (NL)
20,260 4,610 22.8 11.83 11.4 239,676 245,833 6,157 19,413,778 19,912,512 498,734 2.6
Oakland
14,339 5,183 36.1 11.34 18.1 162,607 171,942 9,335 13,171,166 13,927,263 756,097 5.7
Philadelphia
23,077 4,679 20.3 11.01 10.1 254,072 258,556 4,483 20,579,872 20,943,035 363,163 1.8
Pittsburgh
17,039 5,914 34.7 10.09 17.4 171,919 179,698 7,779 13,925,450 14,555,555 630,106 4.5
San Diego
27,258 10,474 38.4 9.88 19.2 269,311 284,010 14,698 21,814,230 23,004,773 1,190,543 5.5
San Francisco
17,548 6,898 39.3 10.61 19.7 186,182 198,697 12,515 15,080,772 16,094,448 1,013,676 6.7
Seattle
33,593 9,398 28.0 11.59 14.0 389,349 400,760 11,411 31,537,236 32,461,526 924,289 2.9
St. Louis
32,912 6,038 18.3 9.91 9.2 326,153 330,616 4,463 26,418,415 26,779,886 361,472 1.4
Texas
36,111 6,664 18.5 11.96 9.2 431,888 437,077 5,189 34,982,929 35,403,253 420,324 1.2
Toronto
31,600 2,718 8.6 13.93 4.3 440,190 441,845 1,655 35,655,410 35,789,472 134,063 0.4
Average
26,827 5,363 22.9 11.32 11.4 310,477 316,705 6,228 25,148,647 25,653,127 504,480 2.62
Note. The total change in ticket revenue accounting for variable ticket pricing across Major League Baseball is $14.1 million. 1= average attendance; 2 = average
absolute change; 3 = average deviation from the mean (%); 4 = average ticket price ($); 5 = average absolute change in price (%); 6 = average actual ticket revenue ($);
7 = average variation-pricing ticket revenue ($); 8 = average change in ticket revenue ($); 9 = total actual ticket revenue ($); 10 = total variation-pricing ticket revenue
($); 11 = total change in ticket revenue ($); 12 = change in revenue (%).
Table 2 (continued)
Variable Ticket Pricing 415
where kids and adults can enjoy themselves but not necessarily watch the game
(George, 2003). These improvements not only increase demand but also lessen the
importance that team performance uncertainty has on expected revenues.
At the same time, teams are beginning to use variable pricing in an attempt to
manage shifting demand from game to game, given that they are unable to com-
pletely remove the variation. The theory on which this analysis is based is simply
short-term revenue maximization with two goods that are complementary. Tickets
and concessions are complementary goods. The demand for tickets is higher if
concessions prices are lower because the overall cost of enjoying the game would
be lower (Marburger, 1997; Fort, 2004). Similarly, the demand for concessions is
higher if ticket prices are lower. The model consists of demand for tickets and a
separate aggregate demand for nonticket products and services (hereafter referred
to as concessions) that is affected by ticket price. This is where the complementarity
between the two demand functions occurs. The following three models describe
increasing degrees of complexity for the relationship between ticket demand and
concessions demand. As shown, VTP policies should account for the extent to
which there is complementarity between ticket demand and nonticket demand.
For Model 1, let
Q
1
= α
1
– β
1
P
1
(1.1)
be the demand for tickets, where Q
1
is quantity demanded, P
1
is ticket price, and
α
1
and β
1
are scalars describing the shape of the demand curve. In this model,
the demand for concessions, Q
2
, will be unaffected by ticket prices. The optimal
revenue maximizing ticket price is
P
1
1
1
2
*
=
α
β
. (1.2)
The price elasticity of demand (
η
PQ
) at
P
1
*
and
Q
1
*
, where
Q
1
1
2
1
*
= α
, is equal
to –1, a common result from microeconomic theory. Thus, in the model, price is
chosen where
η
PQ
= −1
. This model is applicable for teams that do not share in
concessions revenues or simply receive a fixed annual payment for concessions
rights from a vendor, perhaps having sold them up front to build a new stadium. In
general, much of the costs associated with operating a baseball team are fixed costs.
The marginal costs of selling an extra ticket are low; hence, revenue maximization
will be assumed in place of profit maximization. Relaxing this assumption adds a
marginal cost term to the analysis, but does not change the fundamental findings.
The marginal costs of MLB teams are unknown, and, therefore, the empirical
analysis does not incorporate it.
Model 2 is applicable for teams that receive all or a share of concessions
revenue. Let
Q
1
= α
1
– β
1
P
1
(2.1)
be ticket demand, as in Model 1. Furthermore, let Q
2
= Q
1
, meaning that each
person who purchases a ticket also buys some concessions. Moreover, the price of
concessions is exogenously determined by the concessionaire and will be noted
by
P
2
. Note that concessions do have a nonnegligible marginal cost that affects
total profitability. A more complete model would include marginal cost in the final
416 Rascher et al.
optimal ticket-price-setting equation. This would add unnecessary complexity,
however, and, more important, would make it more cumbersome to compare how
price is affected with Model 1. The resulting optimal revenue maximizing ticket
price is
P
P
1
1
1
2
2 2
*
= −
α
β
. (2.2)
As seen in Equation 2.2, the revenue-maximizing, or optimal, ticket price
is lower when accounting for the price of concessions (and any other nonticket
products or services such as merchandise and parking) than it would be if it were
set in a vacuum in which only ticket revenue is accounted for, as in Equation 1.2.
This is consistent with findings in the review of literature mentioned previously.
Specifically,
η
α
α β
PQ
P
P
=
−
+
<
( )
( )
1 2
1 1 2
1
, meaning that the elasticity for Model
2 is smaller in absolute value terms than for Model 1. The optimal ticket price is set
in the inelastic portion of demand. It is predictable that for low concessions prices
the impact of concessions revenue on ticket-price decision making is minimized. In
fact,
P
PQ2
0 1→ → −,η
, which is the optimal price elasticity when not accounting
for concessions revenues (Model 1).
Model 3 generalizes Models 1 and 2 by adding cross-price effects to ticket
demand and concessions demand, exhibiting the notion that the total price of attend-
ing a game is what matters to customers, not just ticket price. Therefore, let
Q P P
1 1 1 1 1 2
= − −α β γ
(3.1)
be ticket demand, where γ
1
is the incremental effect of concessions prices on ticket
demand. The demand for concessions will be shown by
Q P P
2 2 2 2 2 1
= − −α β γ
.
(3.2)
As noted in the equation, ticket price, P
1
, affects the demand for concessions
in a negative way. If ticket prices are raised, the demand for concessions declines
based on γ
2
, the marginal propensity to purchase concessions based on ticket price
changes. The optimal revenue-maximizing ticket price is
P
P
1
1
1
1 2 2
1
2 2
*
( )
= −
+α
β
γ γ
β
, (3.3)
with P
2
exogenous. Even though the concessionaire often sets concessions prices,
removing this assumption does not change the direction of the impact, only the
magnitude. Equation 3.3 shows that the ticket prices ought to be lower if fans care
about concessions prices. Specifically, higher γ
1
or γ
2
leads to lower optimal ticket
prices. The more sensitive customers are to the price of complementary goods and
services, the lower ticket prices should be in order to maximize profits. Thus, it is
important to account for cross-price effects when setting prices. Overall, the price
elasticity for Model 3 might be higher or lower than for Model 2, depending on
the relative magnitudes of β
1
, γ
1
, and γ
2
. Like Model 2, however, the absolute value
of the price elasticity for Model 3 is lower than for Model 1. In the analysis that
follows, variable pricing outcomes will be determined under two scenarios—one
without the cross effects (Model 1) and one with the cross effects (Model 3). Again,
Variable Ticket Pricing 417
Model 1 pertains to teams that either do not receive any concessions revenue or
receive a fixed payment in exchange for concessions rights. Model 3 applies to
teams that receive a share of concessions revenues.
To be clear, these models do not assume profit maximization, win maximiza-
tion, or something else; they only assume that a team’s objectives are consistent
throughout the season. For example, if a team is focused primarily on profits, it will
set ticket and concessions prices in order to maximize the sum of both revenues. In
a similar way, if a team is attempting to maximize wins, it will still want to price as
a profit maximizer because its relevant costs are not variable. Such a team would
likely spend more on players in order to improve winning than a profit-maximizing
team would. The team would still want to set prices in order to maximize revenues
from tickets and concessions, however, just as a profit-maximizing team would.
An exception to this argument is if a win-maximizing owner chose to price below
profit-maximizing levels in order to raise attendance (even though it is lowering
revenues) to increase the impact of home-field advantage, which would increase the
likelihood of winning more games and, therefore, satisfy his or her objectives.
The models also do not need to assume linear demand functions. Linear demand
is chosen for simplicity. As described in the next section, nonlinear demand changes
the magnitudes of the findings. Using linear demand generates more conserva-
tive findings—the gains from variable pricing are lower. The empirical analysis
operationalizes this by noting that regardless of an owner’s objectives (winning,
profits, or a combination of the two), it is assumed that prices are set to maximize
those objectives. For a particular game it might be that prices are too low or too
high given demand, but because one price is charged for the entire season, it is
objective maximizing on average.
One hypothesis stemming from these models is that adoption of VTP would
improve revenues for MLB teams. Another hypothesis is that for those teams who
are adjusting prices, the amount of adjustment is correct. For instance, the Cardi-
nals had only raised their prices for VTP games by $2 for 2002. In contrast, the
Rockies have had prices for particular seats that varied by as much as $6 (Rovell,
2002b). This analysis will provide a benchmark for how much teams should be
adjusting their prices.
It is important to note that there are public relations issues that play a role in
VTP. For example, the Nashville Predators have been thinking about incorporat-
ing VTP but fear a negative fan backlash at a time when they are trying to build
a loyal fan base (Cameron, 2002). A team might therefore opt to raise its prices
only nominally to see if there is a backlash in which fans react with an emotional
response that actually shifts demand (not slides along demand, as price changes
are expected to do). This analysis ignores any public relations issues.
Method
The first analysis tested Model 1 in which only ticket pricing is accounted for. The
methodology involved analyzing how demand for each game deviated from the
average demand for each team. For example, as shown in Figure 1, Point A is on the
average demand curve for the Atlanta Braves. It represents the actual average ticket
price ($13.06) and average attendance (35,793). The slope of the demand curve is
418 Rascher et al.
based on the assumption that the price elasticity equals –1.0 (This assumption can
be relaxed without loss of generality. For instance, it can be assumed that the team
prices on the inelastic portion of demand are at, say, –0.75.) Therefore, slope can
be determined from price, quantity, and elasticity.
Point B is the actual price (still $13.06) and attendance (48,961) for the Braves’
home opener. This is the demand for that game, given the price. Looking at actual
attendance reveals the demand. As described in Theoretical Foundations, ticket
prices, on average, were optimal for the Braves. It was assumed that each team was
doing its best at determining ticket prices and was setting them to account for the
average expected demand for the entire season. Therefore, the price elasticity was
set at –1.0 at Point A. At Point B the elasticity changed to –0.73, thus it is a subop-
timal price. Raising price to $15.46 (Point C) changed the elasticity back to –1.0
and lowered attendance to 42,371. Revenue was then calculated for this new price
and quantity and compared with the actual revenue from that game (measured by
multiplying the actual average price charged for that game with the actual quantity
of spectators for that game). These measurements were taken for each game of the
season for each team in order to be able to see how adjusted ticket prices affect
revenue. See the Appendix for a brief description of the calculations.
The previous example used linear demand. If a slightly curved demand func-
tion is used, the gains from variable pricing would be higher because the loss in
number of attendees is compensated by higher pricing as a result of the curvature
of the demand function. As shown in Figure 2, the simplified demand function,
Curved Increase, had an optimal price point at D, whereas the linear demand
function’s optimal price point was C. Table 3 provides the details of each of these
demand functions. Each demand function was shifted the same amount (as shown
by Point B). Figure 3 shows the associated revenue at each point. The curved
demand resulted in higher revenue ($18.52) from variable pricing (Point D) than
for the linear demand ($16.00 at Point C). Thus, an equal increase in the number of
attendees will lead to lower gains using linear demand instead of curved demand.
This is also true for a low-demand game. Point G is the optimal price for the linear-
demand function and Point F maximizes revenue for the curved demand. As shown
in Table 3, the curved-demand function resulted in higher revenues from VTP. This
was not surprising—for a given price, a curved-demand function will result in more
attendees (higher quantity) than a linear-demand function. A constant elasticity
of demand function (CED) has more curvature than the ones shown in Figure 2.
Revenue is constant regardless of price for CED. Prices can be set at any level
and yield the same revenue. CED is an unrealistic demand function for baseball.
An even more extreme demand function, a super-curved demand in which the
degree of curvature is greater than that for CED, is such that the revenue function
looks U shaped, not hill shaped, as in Figure 3. In that case, revenue-maximizing
prices are either very low or very high and unlikely to be consistent with reality
in baseball. An example of this type of demand function is P = 1/ln(Q). The use
of linear demand in the subsequent analysis is conservative in that the gains from
variable pricing are a lower bound of what would be the case if demand functions
for baseball are curved. This reason, along with simplicity and a lack of research
about the shape of baseball demand functions, was justification for using linear
demand in the following analysis. Parallel shifts of the demand function were
419
Figure 2 — Curved demand functions versus linear demand functions.
Figure 1 — Optimal variable pricing adjustment for Atlanta.
420
Table 3 Difference in Revenue Gain: Nonlinear Demand Versus Linear Demand
Model Demand function
Price
($) Quantity
Revenue
($)
Corresponding point
on graph
Gain in revenue
(new price vs. old price)
Linear P = 8 – 4Q 4.00 1.00 4.00 A N/A
Curved P = (Q – 3)
2
4.00 1.00 4.00 A N/A
Linear increase
P
= 16 – 4Q 8.00 2.00 16.00 C 33.33%
P
= 16 – 4Q at old price 4.00 3.00 12.00 B N/A
Curved increase
P
= (Q – 5)
2
11.11 1.67 18.52 D 54.32%
P
= (Q – 5)
2
at old price 4.00 3.00 12.00 B N/A
Linear decrease
P
= 6 – 4Q 3.00 0.75 2.25 G 12.50%
P
= 6 – 4Q at old price 4.00 0.50 2.00 E N/A
Curved decrease
P
= (Q – 2.5)
2
2.78 0.83 2.31 F 15.74%
P
= (Q – 2.5)
2
at old price 4.00 0.50 2.00 E N/A
Variable Ticket Pricing 421
also assumed because of simplicity and a lack of relevant research showing other
types of shifts. Unfortunately, attendance by seat location and specific price is not
publicly available. If it were, one could examine how much demand changes per
price point to get a sense of the nature of the shift in demand.
The subsequent analysis accounted for the possibility that stadium capacity
prevented the true demand from being revealed. In other words, sellouts typically
imply that there was excess demand beyond the capacity of the stadium. The
standard result would be to raise prices until the entire stadium is full and there
are no persons outside who are interested in attending the game at the new higher
ticket price. In order to determine how much to raise prices, the amount of excess
demand needed to be estimated. This was done using a censored regression, which
can forecast the true demand as though there were not a capacity constraint. It used
information from uncensored observations (those without a capacity constraint as
shown by not having sold out) to estimate what would have happened without the
constraint.
The censored regression used attendance as the dependent variable and vari-
ous demand factors listed in the second data set as the independent variables. The
result was an empirical model that can be used to forecast what attendance would
have been for the capacity-constrained games. The methodology was the same as
the first analysis, but used the new forecasted attendance when estimating optimal
prices and resulting revenue.
The final analysis included the focus of Model 3—how the prices of comple-
mentary goods (tickets and concessions) affect the demand and, hence, optimal price
for each other. This analysis created a single demand for the joint product of tickets
Figure 3 — Revenue functions of curved demand versus linear demand.
422 Rascher et al.
and concessions, with concessions prices exogenously determined. According to
Financial World, these nonticket revenues made up 35% of ticket plus nonticket
revenues for MLB teams during 1996 (Badenhausen & Nikolov, 1997). For every
dollar spent at a stadium by a patron, 35 cents were spent on concessions, mer-
chandise, and parking. Therefore, the nonticket price for each team was set at 54%
(54% = 35%/[1–35%]) of the ticket price because team-specific data on nonticket
revenue was unavailable. Given this new joint-demand function, optimal prices
were set for each game as in the two previous analyses. The censored regression
forecasts of attendance were used in this analysis. This analysis accounted for the
combined product of tickets and concessions, so, as a group, the demand elasticity
was –1.0. Given that the concessions price was fixed and positive, the new optimal
ticket price would be on the inelastic portion of demand. This was consistent with
the findings in the literature.
These three analyses determined the optimal variable ticket price for nearly
every game for the 1996 MLB season. The 1996 season was used because during
that year no MLB team used VTP. It should be noted that 1996 was the first full
season after the strike of 1994–95. It is possible that the findings here are not typi-
cal of a MLB season. An important factor in this analysis, however, is the shift
in demand from game to game. Attendance for the 1996 season has a standard
deviation that is only 5% greater than attendance for 2003. The use of more recent
data, which would include teams using VTP, raised validity concerns with the
attempt to predict additional revenue generated through the use of VTP. The use
of the 1996 data allows the analysis to be consistent across all teams. The analysis
showed what the ticket price should have been with the corresponding results if
every team had participated in optimal VTP. In order to achieve this, data for 2,193
of the 2,268 scheduled regular season games were used. The few games not used
in the analysis either lacked sufficient data, were double-headers, or were rainouts
that were never made up.
The data were broken into two sets. One set was used to forecast optimal
VTP. It included actual attendance, average ticket price, stadium capacity, and
average concessions expenditures. Attendance data came from www.sportsline.
com, ticket price data from Team Marketing Report, stadium capacity data from
www.ballparks.com, and concessions information from Financial World’s financial
report on baseball for the 1996 season (Badenhausen & Nikolov, 1997). Table 2
(columns 1 and 4) shows average attendance and average ticket price for each team
for the 1996 season.
The second set of data was used to make an adjustment to demand for games
that are censored by capacity constraints, namely games that are sold out or nearly
sold out. This adjusted demand was then used in the VTP analysis. This data set
contained actual attendance, the number of wins by the home team and visiting
team in the previous season, the population of the local Consolidated Metropolitan
Statistical Area (CMSA; term used by the U.S. Census Bureau), indicator variables
for opening day, a new stadium, a weekend game, and a game in April. The data
set came from www.sportsline.com, except population, which was obtained from
the U.S. Census Bureau. Table 4 contains summary statistics of the data.
Variable Ticket Pricing 423
Results
Based on the estimates from the test of Model 1, if the Atlanta Braves, for example,
had raised ticket prices for the opening game, actual attendance would have been
42,371, with actual ticket revenues increasing by $15,817, or 2.5% for that game.
An elasticity of –1.0 implies revenue maximization. The analysis, however, could
have begun with any elasticity as long as the resulting elasticity at Point C is the
same as that at Point A (see Figure 1). Therefore, this does not require revenue
maximization or profit maximization, only consistency in terms of the objectives
of the franchise throughout the season.
Continuing with the Braves example, Table 5 shows the results for every odd
home game. The findings show that there are fewer games that have excess demand
(although they have a higher average excess demand) than there are games that
have lower demand than average (Figure 4). In fact, in 30 out of the 81 Braves’
home games, demand exceeded the average, and the average optimal price increase
is estimated to be 11.0%, whereas the average decreased price is estimated to be
–6.5%. Also, as expected, the high-demand games generally are for an entire series.
Thus, one VTP strategy for the Braves would be to use variable pricing for series
that are in high demand and simply lower prices on the other games in general (as
a public relations move and to increase overall revenues).
The bottom row of Table 5 shows the average results for the entire Braves
season. The average per-game revenue increase for the season is $4,367, or 0.9%.
The results for each team are shown in Table 2. Columns 8 and 12 show the result
from Table 5 for the Braves. Over the course of the full season, the Braves could
have increased their ticket revenues by $353,706, or 0.9%.
Variable pricing would have yielded an average of approximately $504,000 per
year in additional revenue for each MLB team, ceteris paribus, or over $14 million
for the league as a whole. This amounts to only about a 2.6% increase above what
occurs when prices are not varied, as shown in Table 2. The amount of variation
Table 4 Summary Statistics of the Censored Regression Data
M SD Minimum Maximum
Game attendance 26,868 11,852 6,021 57,467
Home team’s previous season wins 81.92 10.02 56 100
Visiting team’s previous season wins 81.99 10.11 56 100
Opening day 0.008 0.090 0 1
Weekend game 0.477 0.499 0 1
New stadium 0.215 0.411 0 1
Population of CMSA 5,997,132 4,774,503 1,640,831 18,107,235
Games played during April 0.162 0.368 0 1
Note. CMSA = Consolidated Metropolitan Statistical Area, a measure of local population from the
U.S. Census Bureau.
424
Table 5 Summary of Atlanta Braves Game-by-Game Variable-Pricing Outcomes
1 2 3 4 5 6 7 8 9 10 11 12
1 48,961 13,168 36.8 42,377 13.06 15.46 18.4 639,431 655,247 15,817 2.5
3 30,271 –5,522 –15.4 33,032 13.06 12.05 –7.7 395,339 398,121 2,782 0.7
5 34,649 –1,144 –3.2 35,221 13.06 12.85 –1.6 452,516 452,635 119 0.0
7 26,635 –9,158 –25.6 31,214 13.06 11.39 –12.8 347,853 355,504 7,651 2.2
9 25,300 –10,493 –29.3 30,547 13.06 11.15 –14.7 330,418 340,462 10,044 3.0
11 31,893 –3,900 –10.9 33,843 13.06 12.35 –5.4 416,523 417,910 1,388 0.3
13 33,080 –2,713 –7.6 34,437 13.06 12.57 –3.8 432,025 432,696 671 0.2
15 37,697 1,904 5.3 36,745 13.06 13.41 2.7 492,323 492,653 331 0.1
17 35,471 –322 –0.9 35,632 13.06 13.00 –0.4 463,251 463,261 9 0.0
19 29,976 –5,817 –16.3 32,885 13.06 12.00 –8.1 391,487 394,573 3,087 0.8
21 28,583 –7,210 –20.1 32,188 13.06 11.74 –10.1 373,294 378,036 4,742 1.3
23 30,917 –4,876 –13.6 33,355 13.06 12.17 –6.8 403,776 405,945 2,169 0.5
25 49,553 13,760 38.4 42,673 13.06 15.57 19.2 647,162 664,433 17,271 2.7
27 29,984 –5,809 –16.2 32,889 13.06 12.00 –8.1 391,591 394,669 3,078 0.8
29 33,186 –2,607 –7.3 34,490 13.06 12.58 –3.6 433,409 434,029 620 0.1
31 32,199 –3,594 –10.0 33,996 13.06 12.40 –5.0 420,519 421,697 1,178 0.3
33 39,463 3,670 10.3 37,628 13.06 13.73 5.1 515,387 516,615 1,229 0.2
35 49,726 13,933 38.9 42,760 13.06 15.60 19.5 649,422 667,129 17,708 2.7
37 32,934 –2,859 –8.0 34,364 13.06 12.54 –4.0 430,118 430,864 746 0.2
39 34,823 –970 –2.7 35,308 13.06 12.88 –1.4 454,788 454,874 86 0.0
41 49,365 13,572 37.9 42,579 13.06 15.54 19.0 644,707 661,509 16,802 2.6
43 31,971 –3,822 –10.7 33,882 13.06 12.36 –5.3 417,541 418,874 1,333 0.3
425
45 33,186 –2,607 –7.3 34,490 13.06 12.58 –3.6 433,409 434,029 620 0.1
47 49,060 13,267 37.1 42,427 13.06 15.48 18.5 640,724 656,779 16,055 2.5
49 41,619 5,826 16.3 38,706 13.06 14.12 8.1 543,544 546,640 3,096 0.6
51 33,208 –2,585 –7.2 34,501 13.06 12.59 –3.6 433,696 434,306 610 0.1
53 36,953 1,160 3.2 36,373 13.06 13.27 1.6 482,606 482,729 123 0.0
55 32,708 –3,085 –8.6 34,251 13.06 12.50 –4.3 427,166 428,035 868 0.2
57 32,036 –3,757 –10.5 33,915 13.06 12.37 –5.2 418,390 419,678 1,288 0.3
59 32,401 –3,392 –9.5 34,097 13.06 12.44 –4.7 423,157 424,207 1,050 0.2
61 46,064 10,271 28.7 40,929 13.06 14.93 14.3 601,596 611,219 9,623 1.6
63 39,210 3,417 9.5 37,502 13.06 13.68 4.8 512,083 513,148 1,065 0.2
65 31,587 –4,206 –11.8 33,690 13.06 12.29 –5.9 412,526 414,140 1,614 0.4
67 29,213 –6,580 –18.4 32,503 13.06 11.86 –9.2 381,522 385,471 3,950 1.0
69 38,210 2,417 6.8 37,002 13.06 13.50 3.4 499,023 499,555 533 0.1
71 35,176 –617 –1.7 35,485 13.06 12.95 –0.9 459,399 459,433 35 0.0
73 47,130 11,337 31.7 41,462 13.06 15.13 15.8 615,518 627,242 11,724 1.9
75 32,109 –3,684 –10.3 33,951 13.06 12.39 –5.1 419,344 420,582 1,238 0.3
77 37,193 1,400 3.9 36,493 13.06 13.32 2.0 485,741 485,919 179 0.0
79 49,265 13,472 37.6 42,529 13.06 15.52 18.8 643,401 659,956 16,555 2.6
81 49,083 13,290 37.1 42,438 13.06 15.48 18.6 641,024 657,135 16,111 2.5
Average 35,793 5,832 16.3 35,793 13.06 13.06 8.1 467,458 471,825 4,367 0.9
Note. Odd-numbered games are shown to save space. The averages in the last row are averages of the absolute value of each number. 1 = game
number; 2 = attendance; 3 = difference from average; 4 = change from average (%); 5 = variable-pricing attendance; 6 = average ticket price for the
season ($); 7 = variable-pricing ticket price ($); 8 = price change (%); 9 = actual revenue; 10 = variable-pricing revenue; 11 = revenue increase; 12
= revenue increase (%).
426
Figure 4 — Atlanta Braves variable pricing.
Variable Ticket Pricing 427
in ticket prices is just over 11% on average. The fact that such a large price swing
only yields a revenue swing four times smaller is simply based on the large change
in attendance that occurs when prices are varied. This occurs with all downward
sloping demand curves and is not unique to baseball. For the 1996 season, the
largest revenue gain would have been for the New York Yankees, which would
have generated an extra $1.24 million in ticket revenue, or a 3.7% increase. The
largest percentage revenue gain would have been for the San Francisco Giants. The
Giants would have seen an estimated 6.7% increase in revenue, or $1.01 million,
if they had used optimal VTP. The smallest amount of impact would have been for
the Colorado Rockies, which averaged only plus or minus 80 patrons in absolute
deviation from the mean attendance per game throughout the 1996 season. In fact,
teams with the lowest average attendance benefit the most from variable pricing.
This is not surprising because those teams tend to have the highest variation in
attendance, allowing them to gain from dynamic pricing.
The Rockies would gain the least from VTP because they had many sellouts
in 1996. As described in the Method section, a censored regression is carried out
in order to forecast the true demand above the capacity constraint. Although there
are many more factors that affect game-by-game attendance than those used here,
this analysis used only those factors known before ticket-price setting occurred.
Thus, only factors known before the beginning of the season are used in order to
be consistent with what would be known by team management when setting prices.
The Wald chi-squared test of significance showed that the model was significant at
the .001% level, with a Wald statistic of 906.6. A potential problem is that the errors
for a series between two teams might not be independent. It is expected that across
different groups of games (a three-game series, for example) there is independence
of the errors but not necessarily in each group. This type of clustered correlation
leads to understating the standard errors. A robust estimator of the variance is used
to correct the standard errors. There is no evidence of multicollinearity among the
independent variables. As expected, there is evidence of omitted variables missing
from the regression. As explained, performance-specific factors that are only known
to price setters once the season has begun, such as the home pitcher’s earned-run
average at that point in the season, were omitted. The variance-inflation factor (VIF)
averaged 1.19 across the group of variables tested for multicollinearity, with the
largest VIF at 1.58. The Ramsey RESET test shows evidence of omitted variables
with an F-statistic of 29.67.
Table 6 shows the results of the censored regression. The signs of the coef-
ficients are as expected. Out of 2,193 games, only 109 were sold out. A sellout
is defined, for these purposes, as any game in which actual attendance is 99.0%
or higher of stadium capacity. The estimate of attendance for these 109 games is
based on the predicted values from the censored regression.
As shown in Table 7, 10 teams had adjustments to their attendance based on
the censored regression. The results are similar to that of Table 2, except column
13 shows the gain for those 10 teams in Table 7 if they account for the capacity
constraint when adjusting their prices for their VTP strategy. Overall, adjusting for
demand beyond stadium capacity raises the increased revenue from VTP policies
from $14.1 million to $16.5 million for the league as a whole.
The final analysis addressed Model 3 from the Theoretical Foundations sec-
tion by accounting for nonticket revenues such as concessions, merchandise, and
428
Table 6 Censored Regression Results to Create Forecasts for Capacity-Constrained Attendance
Dependent variable Game-by-
game
attendance
Number of observations 2,193
Number of uncensored
observations
2,084
Wald chi
2
906.60
Prob > chi
2
0.000
Log likelihood –21,989.20
Coefficient Standard error z P>|z|
95% Confidence Interval
Lower bound Upper bound
Constant term –28,220.88 5,587.69 –5.05 0.00 –40,513.80 –15,927.96
Home team’s last season wins 512.18 32.97 15.53 0.00 439.65 584.72
Visiting team’s last season wins 138.59 33.14 4.18 0.00 65.68 211.50
Opening day 14,522.00 3,024.93 4.80 0.00 7,867.16 21,176.84
Weekend game 6,182.30 357.90 17.27 0.00 5,394.92 6,969.68
New stadium 13,208.40 1,197.69 11.03 0.00 10,573.48 15,843.32
Population of CMSA 0.000053 0.0000090 5.84 0.00 0.000033 0.000073
Games played during April –3,045.52 745.38 –4.09 0.00 –4,685.36 –1,405.68
429
Table 7 Summary of Effects of Variable Ticket Pricing (With Capacity Adjustment, No Nonticket-Revenue
Adjustment)
1 2 3 4 5 6 7 8 9 10 11 12 13
Atlanta 35,793 5,878 16.4 13.06 8.2 467,458 472,549 5,091 37,864,102 38,276,489 412,387 1.1 58,682
Baltimore 45,475 2,098 4.6 13.14 2.3 597,539 600,204 2,665 48,400,634 48,616,492 215,859 0.4 185,832
Boston 28,687 3,952 13.8 15.43 6.9 442,643 447,216 4,574 35,854,064 36,224,534 370,470 1.0 144,182
California 22,476 4,899 21.8 8.44 10.9 189,697 193,539 3,842 15,365,441 15,676,653 311,212 2.0 0
Chicago (AL) 21,115 4,530 21.5 14.11 10.7 297,927 303,781 5,854 24,132,054 24,606,230 474,176 2.0 0
Chicago (NL) 28,606 7,044 24.6 13.12 12.3 375,309 385,912 10,603 30,400,069 31,258,882 858,813 2.8 241,414
Cincinnati 24,097 4,549 18.9 7.95 9.4 191,568 195,364 3,796 15,517,036 15,824,475 307,439 2.0 60,442
Cleveland 41,983 1,716 4.1 14.52 2.0 609,592 627,443 17,851 49,376,968 50,822,889 1,445,921 2.9 1,442,929
Colorado 48,037 144 0.3 10.61 0.1 509,675 510,365 690 41,283,673 41,339,542 55,869 0.1 55,512
Detroit 14,464 5,018 34.7 10.60 17.3 153,322 162,531 9,209 12,419,066 13,165,021 745,954 6.0 0
Florida 21,839 4,541 20.8 10.37 10.4 226,469 230,737 4,268 18,343,988 18,689,707 345,720 1.9 0
Houston 24,394 7,362 30.2 10.65 15.1 259,793 268,433 8,640 21,043,206 21,743,062 699,856 3.3 0
Kansas City 17,949 4,013 22.4 9.74 11.2 174,828 178,510 3,682 14,161,039 14,459,292 298,253 2.1 0
Los Angeles 39,364 7,038 17.9 9.94 8.9 391,274 395,669 4,394 31,693,231 32,049,165 355,934 1.1 0
Milwaukee 16,847 5,594 33.2 9.37 16.6 157,853 165,387 7,535 12,786,054 13,396,356 610,302 4.8 0
Minnesota 17,930 4,899 27.3 10.16 13.7 182,170 188,905 6,735 14,755,746 15,301,288 545,542 3.7 0
Montreal 19,982 7,155 35.8 9.07 17.9 181,240 190,326 9,086 14,680,457 15,416,441 735,984 5.0 7,857
New York (AL) 28,371 8,999 31.7 14.58 15.9 413,655 428,965 15,310 33,506,040 34,746,176 1,240,136 3.7 0
New York (NL) 20,260 4,610 22.8 11.83 11.4 239,676 245,833 6,157 19,413,778 19,912,512 498,734 2.6 0
Oakland 14,339 5,183 36.1 11.34 18.1 162,607 171,942 9,335 13,171,166 13,927,263 756,097 5.7 0
Philadelphia 23,077 4,679 20.3 11.01 10.1 254,072 258,556 4,483 20,579,872 20,943,035 363,163 1.8 0
(continued)
430 Rascher et al.
1 2 3 4 5 6 7 8 9 10 11 12 13
Pittsburgh 17,039 5,914 34.7 10.09 17.4 171,919 179,698 7,779 13,925,450 14,555,555 630,106 4.5 0
San Diego 27,258 10,532 38.6 9.88 19.3 269,311 284,842 15,531 21,814,230 23,072,216 1,257,986 5.8 67,444
San Francisco 17,548 6,898 39.3 10.61 19.7 186,182 198,697 12,515 15,080,772 16,094,448 1,013,676 6.7 0
Seattle 33,593 9,398 28.0 11.59 14.0 389,349 400,760 11,411 31,537,236 32,461,526 924,289 2.9 0
St. Louis 32,912 6,110 18.6 9.91 9.3 326,153 331,541 5,388 26,418,415 26,854,854 436,439 1.7 74,968
Texas 36,111 6,664 18.5 11.96 9.2 431,888 437,077 5,189 34,982,929 35,403,253 420,324 1.2 0
Toronto 31,600 2,718 8.6 13.93 4.3 440,190 441,845 1,655 35,655,410 35,789,472 134,063 0.4 0
Average 26,827 5,433 23.0 11.32 11.5 310,477 317,737 7,260 25,148,647 25,736,672 588,025 2.83 83,545
Note. VTP = Variable Ticket Pricing. 1 = average attendance; 2 = average absolute change; 3 = average deviation from the mean (%); 4 = average ticket price; 5 =
average absolute change in price ($); 6 = average actual ticket revenue ($); 7 = average variable-pricing ticket revenue ($); 8 = average change in ticket revenue ($);
9 = total actual ticket revenue ($); 10 = total variable-pricing ticket revenue ($); 11 = total change in ticket revenue ($); 12 = change in revenue (%); 13 = change in
revenue versus variable ticket pricing without capacity adjustment ($).
Table 7 continued
Variable Ticket Pricing 431
parking. Table 8 shows the results of allowing the team to vary ticket prices while
accounting for nonticket prices in order to maximize its objectives. Columns 9, 10,
and 11 in Table 8 illustrate that the average team would have gained $911,000 in
ticket and nonticket revenue by adopting a VTP policy while accounting for non-
ticket prices. The league overall would have gained $25.5 million. The Cleveland
Indians would have earned the most, over $2.2 million, from such a policy.
Discussion
This analysis has shown that MLB could have increased ticket revenues by approxi-
mately 2.8%, or $16.5 million, and total stadium revenues by about $25.5 million
for the 1996 season if teams used VTP. Total revenues in MLB are estimated to
have grown from $1.78 billion in 1996 to approximately $4.3 billion in 2003, or
250%. Similar changes in the effect of VTP strategies, as discovered in this study,
would yield nearly $40 million in ticket revenue and over $60 million in ticket plus
nonticket revenue for MLB. Therefore, it behooves team owners and the league
office to consider and implement VTP strategies, especially because teams and the
league are constantly searching for ways to increase revenues.
The San Francisco Giants would have seen an estimated 6.7% increase in ticket
revenue, or $1.01 million, if they had used optimal VTP in 1996. It is interesting
that the Giants had considered using VTP since the 1996 season because they had
noticed a huge variation in attendance patterns at Candlestick Park, the team’s
then-home facility (King, 2002a). In addition to weather issues (pleasant for day
games but frigid for night) in their facility, the Giants of the mid-1990s occasion-
ally fielded teams of lower quality. The results of this study would strongly sug-
gest that teams in similar facility or on-the-field talent situations maximize their
revenues through VTP.
The results of this study support the use of VTP both to increase and decrease
prices from average seasonal levels. The data showed fewer games with excess
demand than those with diminished demand. The selected games with excess
demand deviated, however, from the mean at a greater rate than those with decreased
demand. Currently, most MLB teams have focused their VTP strategies on the
revenue potential of increased prices from highly demanded games (King, 2002a).
It appears that some teams, however, have begun to realize the potential benefit of
attracting fans to less desirable contests by lowering prices (King, 2002b). The New
York Yankees sold $5 tickets in certain sections of Yankee Stadium on Mondays,
Tuesdays, and Thursdays in 2003 (King, 2003).
Lowering ticket prices for less desirable games would potentially create more
positive relationships between teams and local municipalities. MLB teams have
often been chastised for seeking subsidies for new revenue generating facilities
that are financially inaccessible to many taxpayers (Pappas, 2002; O’Keefe, 2004).
Given the number of games in a typical season for which demand is below the yearly
average (Figure 4), lowering prices creates an opportunity for teams to potentially
attract new or disenfranchised fans and presents local governments with a more
favorable reaction to their public-policy decisions supporting the local franchise.
Marketing less desirable games with lower ticket prices as “value” games, as the
Chicago Cubs, Colorado Rockies, New York Mets, Tampa Bay Devil Rays, and
Toronto Blue Jays did in 2004, allows teams to reach market segments perhaps
432 Rascher et al.
Table 8 Summary of Effects of Variable Ticket Pricing (With
Capacity Adjustment and Nonticket-Revenue Adjustment), Part 1
1 2 3 4 5 6 7 8
Atlanta 35,793 5,878 16.4 $13.07 7.18 467,458 475,184 732,451
Baltimore 45,475 2,098 4.6 $13.16 7.23 597,539 601,064 930,316
Boston 28,687 3,952 13.8 $15.46 8.49 442,643 449,290 693,186
California 22,476 4,899 21.8 $8.44 4.64 189,697 195,652 299,985
Chicago (AL) 21,115 4,530 21.5 $14.11 7.76 297,927 307,000 470,860
Chicago (NL) 28,606 7,044 24.6 $13.16 7.22 375,309 391,059 598,164
Cincinnati 24,097 4,549 18.9 $7.96 4.37 191,568 197,327 302,814
Cleveland 41,983 1,716 4.1 $14.73 7.99 609,592 632,454 972,537
Colorado 48,037 144 0.3 $10.62 5.84 509,675 510,557 791,065
Detroit 14,464 5,018 34.7 $10.60 5.83 153,322 167,596 251,923
Florida 21,839 4,541 20.8 $10.37 5.70 226,469 233,085 357,643
Houston 24,394 7,362 30.2 $10.65 5.86 259,793 273,185 416,071
Kansas City 17,949 4,013 22.4 $9.74 5.36 174,828 180,535 276,690
Los Angeles 39,364 7,038 17.9 $9.94 5.47 391,274 398,086 613,286
Milwaukee 16,847 5,594 33.2 $9.37 5.15 157,853 169,531 256,350
Minnesota 17,930 4,899 27.3 $10.16 5.59 182,170 192,609 292,802
Montreal 19,982 7,155 35.8 $9.07 4.99 181,240 195,308 295,006
New York (AL) 28,371 8,999 31.7 $14.58 8.02 413,655 437,386 664,896
New York (NL) 20,260 4,610 22.8 $11.83 6.51 239,676 249,220 381,042
Oakland 14,339 5,183 36.1 $11.34 6.24 162,607 177,076 266,509
Philadelphia 23,077 4,679 20.3 $11.01 6.06 254,072 261,022 400,762
Pittsburgh 17,039 5,914 34.7 $10.09 5.55 171,919 183,977 278,532
San Diego 27,258 10,532 38.6 $9.89 5.43 269,311 293,227 441,505
San Francisco 17,548 6,898 39.3 $10.61 5.84 186,182 205,580 307,980
Seattle 33,593 9,398 28.0 $11.59 6.37 389,349 407,036 621,177
St. Louis 32,912 6,110 18.6 $9.92 5.45 326,153 334,308 513,889
Texas 36,111 6,664 18.5 $11.96 6.58 431,888 439,931 677,470
Toronto 31,600 2,718 8.6 $13.93 7.66 440,190 442,756 684,860
Average 26,827 5,433 23.0 $11.33 6.23 310,477 321,466 492,492
Note. 1 = average attendance; 2 = average absolute change; 3 = average deviation from mean (%); 4
= average ticket price ($); 5 = nonticket price ($); 6 = average actual ticket revenue ($); 7 = average
variable-pricing ticket ($); 8 = average variable-pricing ticket and nonticket revenue ($).
otherwise unreachable because of pricing/income issues, in addition to the afore-
mentioned public-relations benefits.
Currently, teams might not want to implement multiple price points for each
game, as shown in Figure 4. As discussed by Levy, Dutta, Bergen, and Venable
(1997), menu costs affect the frequency and desire to change prices to reflect
changes in demand or supply. Menu costs are costs associated with physically
changing prices on products, having to look up prices to tell a customer the price
for a particular game, or, more generally, any costs associated with having more
than one price for a product or service. In addition, asymmetric information, search
costs, and simple confusion for customers regarding the price for different games
might cause franchises to have fewer prices for a particular seat throughout the
Variable Ticket Pricing 433
Table 8 Summary of Effects of Variable Ticket Pricing (With Capacity
Adjustment and Nonticket-Revenue Adjustment), Part 2
9 10 11 12 13 14 15
Atlanta 58,689,358 59,328,558 639,200 1.1 37,864,102 38,489,896 1.7
Baltimore 75,020,982 75,355,563 334,581 0.4 48,400,634 48,686,180 0.6
Boston 55,573,799 56,148,028 574,229 1.0 35,854,064 36,392,476 1.5
California 23,816,434 24,298,812 482,378 2.0 15,365,441 15,847,819 3.1
Chicago (AL) 37,404,684 38,139,656 734,972 2.0 24,132,054 24,867,027 3.0
Chicago (NL) 47,120,107 48,451,267 1,331,160 2.8 30,400,069 31,675,750 4.2
Cincinnati 24,051,406 24,527,936 476,530 2.0 15,517,036 15,983,459 3.0
Cleveland 76,534,300 78,775,478 2,241,177 2.9 49,376,968 51,228,769 3.8
Colorado 63,989,693 64,076,289 86,597 0.1 41,283,673 41,355,136 0.2
Detroit 19,249,553 20,405,782 1,156,229 6.0 12,419,066 13,575,296 9.3
Florida 28,433,181 28,969,046 535,865 1.9 18,343,988 18,879,853 2.9
Houston 32,616,970 33,701,747 1,084,777 3.3 21,043,206 22,127,983 5.2
Kansas City 21,949,610 22,411,903 462,293 2.1 14,161,039 14,623,331 3.3
Los Angeles 49,124,509 49,676,206 551,697 1.1 31,693,231 32,244,929 1.7
Milwaukee 19,818,383 20,764,351 945,968 4.8 12,786,054 13,732,021 7.4
Minnesota 22,871,407 23,716,997 845,590 3.7 14,755,746 15,601,336 5.7
Montreal 22,754,708 23,895,483 1,140,776 5.0 14,680,457 15,819,930 7.8
New York (AL) 51,934,362 53,856,573 1,922,211 3.7 33,506,040 35,428,250 5.7
New York (NL) 30,091,356 30,864,393 773,037 2.6 19,413,778 20,186,815 4.0
Oakland 20,415,308 21,587,258 1,171,950 5.7 13,171,166 14,343,116 8.9
Philadelphia 31,898,801 32,461,705 562,903 1.8 20,579,872 21,142,775 2.7
Pittsburgh 21,584,447 22,561,111 976,664 4.5 13,925,450 14,902,112 7.0
San Diego 33,812,057 35,761,936 1,949,879 5.8 21,814,230 23,751,402 8.9
San Francisco 23,375,197 24,946,394 1,571,197 6.7 15,080,772 16,651,969 10.4
Seattle 48,882,717 50,315,365 1,432,648 2.9 31,537,236 32,969,885 4.5
St. Louis 40,948,543 41,625,024 676,481 1.7 26,418,415 27,078,914 2.5
Texas 54,223,540 54,875,042 651,502 1.2 34,982,929 35,634,431 1.9
Toronto 55,265,885 55,473,682 207,797 0.4 35,655,410 35,863,207 0.6
Average 38,980,403 39,891,842 911,439 2.8 25,148,647 26,038,717 4.3
Note. 9 = total actual ticket and nonticket revenue ($); 10 = total variable-pricing ticket and nonticket revenue
($); 11 = total change in ticket and nonticket revenue ($); 12 = change in total revenue (%); 13 = total actual
ticket revenue ($); 14 = total variable-pricing ticket revenue ($); 15 = change in total ticket revenue (%).
season than variable pricing predicts. For this reason, many teams have only used
a minimal number of ticket-pricing tiers, usually two to four, in their VTP system
(Rovell, 2002b).
Confusion and the additional costs associated with changing ticket prices
might already be in the process of being eliminated. Kevin Fenton, Colorado
Rockies senior director of ticket operations, noted that once the initial confusion
regarding multiple price points for games is overcome, patrons realize that tickets
can be priced like other industries (Rovell, 2002b). In the near future, the nega-
tive fan reaction to changing ticket price will likely be alleviated if not eliminated
(Adams, 2003). Ticket offices are also now better equipped to handle menu costs
434 Rascher et al.
issues. Although ticket offices were not prepared to handle extensive VTP in the
1990s, recent technological advances have allowed most American professional
sport teams to implement new ticket policies such as bar-coded and print-at-home
tickets to prepare for extensive VTP in the future (Zoltak, 2002).
An initial VTP recommendation is that for every 10% increase in attendance
(or specifically, expected attendance) above the average, teams should raise ticket
prices by 5% and receive a gain of 1.2% in ticket revenue. The practical use of
variable pricing, however, would entail creating, at most, five different prices for
each seat in a stadium throughout the season, not a different price for each game.
High-demand games or series should be priced accordingly, but teams should not
forget the potential benefits of lowering prices for less desired games. The present
findings reinforce previous research identifying factors such as day of the week or
a rivalry game as affecting demand for MLB tickets.
Using the Atlanta Braves again as an example, the average attendance was
35,793. Based on the variable-pricing ticket prices from Table 5, the recommended
pricing schedule for 1996 would have been $12.00, $13.06, and $15.50. A descrip-
tive analysis of Braves attendance revealed three tiers of games that corresponded
with the three price points: games with attendance below 28,831 (greater than –1
standard deviation from the mean), games with an attendance of 28,832 to 42,755
(between 1 and –1 standard deviation from the mean), and games with an attendance
over 42,756 (greater than 1 standard deviation from the mean). A factor analysis
of games falling within each tier was then performed to finalize the recommended
pricing schedule.
For the Braves, a Tier 1 game (average price of $12.00) would have included
games from the second game of the season to May 14, played Sunday through
Thursday. Fifteen games would have therefore been classified as Tier 1. A Tier 3
game (average price of $15.50) would have included all games played on Saturday,
opening day, the July 4 game, the final home stand of the season, and games played
after May 14 against the Los Angeles Dodgers, a former division rival. Twenty-two
games would have fallen into this tier. The remaining 44 games would have been
classified as Tier 2, with an average ticket price of $13.06, which was the average
ticket price for the 1996 season.
The hypothesis that the few teams administering VTP are doing so properly
is consistent with the findings. In fact, the present analysis shows that optimal
VTP is managed by small changes in ticket prices. The Giants expected to gain
an additional $1 million from VTP in 2002 (Isidore, 2002; Rovell, 2002b). The
Giants VTP strategy in 2002 affected only 39 of their 81 home games (all weekend
dates). The present analysis shows a gain of about $1 million for the 1996 season
if optimal pricing were used by the Giants.
In 2002, the Atlanta Braves instituted a VTP strategy for 21 home games—Fri-
days in May through August and Saturdays throughout the whole season. During
these games ticket prices were increased by $3, or about 14%. Testing the same
policy for the 1996 data, the Atlanta Braves would have 22 home games with VTP
using a 9% increase in price. It is interesting that the Braves’ actual policy is more
aggressive than the data show for 1996. The St. Louis Cardinals raised prices in
2002 for summer games by $2, or 8%. The 1996 data show that an optimal VTP
strategy would raise prices by about 9%.
Variable Ticket Pricing 435
Directions for Future Research
There are many areas of inquiry for the future. An analysis of more recent data that
include teams using VTP is warranted. The practical application of VTP requires
one to be able to accurately forecast the relative attendance of future games. In
other words, in order to know which games should have higher prices and which
games should have lower prices, team management needs to know whether there is
consistency from one season to the next in terms of relative attendance. An interest-
ing behavioral issue is whether the implementation of VTP in earlier games affects
the demand for subsequent games.
One factor unaccounted for in this study is the marketing strategies used by
organizations in conjunction with VTP price levels. The projected revenue increases
identified in this study could potentially be increased substantially by incorporating
VTP pricing into teams’ marketing plans. Although many MLB teams assign each
game or product into VTP levels based on game or product characteristics, little
research has investigated how those games of varying characteristics are marketed
to different demographic segments of consumers.
In addition, research investigating education and public-relations activities
related to VTP should be conducted. Although fans might initially perceive variable
pricing as a gauging mechanism, for some fans VTP might allow some expensive
games to now become more affordable. Methods to assuage consumer fears and
to attract new consumers should be researched. In addition, implementation costs
of VTP programs such as menu costs and staff training should be examined and
accounted for in future economic examinations of VTP.
Finally, future research should investigate the practical application and public
reaction to future variable-pricing systems using technology to change prices by
the day, hour, or even minute. Few teams have implemented VTP at this point,
believing that widespread use of ticket pricing based completely on supply and
demand would not be met with agreement by some consumers (Cameron, 2002).
In particular, research should be conducted to identify methods of protecting or
enhancing value to season-ticket purchasers when a minute-by-minute VTP policy
is implemented.
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Appendix
In order to calculate the new price and quantity in which revenue is maximized
(
η = −1
) when the demand curve shifts, refer to Figure 1 at Point A and let
Q
A
= 35,793, P
A
= $13.06, and set
η
A A A A
A
P Q Q P= × = −( ) ( )∆ ∆ 1
.
At Point C, let
Q
C
= (Q
A
+ Q
B
)/2 = (35,793 + 48,961)/2 = 42,377,
P Q P Q
C A C A A
= × × − = − × × − =η ( ) , ( $ . , )1 42 377 13 06 35 793 $$ .15 46
.
The results for the new price and quantity rely on two attributes of linear
demand functions. First, the optimal quantity (Q
C
) is simply the average of the
old quantity (Q
A
) and the new actual quantity (Q
B
). Second, the new optimal price
uses the elasticity formula,
η
C C C A
A
P Q Q P= × = −( ) ( )∆ ∆ 1
, and solves for P
A
.
A key substitute is to note that (∆Q
A
/∆P
A
) = –P
A
/Q
A
, because the inverse of the
slope is constant for the old demand and new demand. Also, P
A
and Q
A
are given,
and
η
A
is set equal to –1. This can be seen in the previous elasticity formula,
η
A A A A
A
P Q Q P= × = −( ) ( )∆ ∆ 1
.
