Determinants of dynamic pricing premiums in major league baseball.
Paul, Rodney J. ; Weinbach, Andrew P.
Determinants of Dynamic Pricing Premiums in Major League Baseball
Baseball teams, like many other firms, constantly attempt to adopt
the best technologies and strategies as it relates to policies of
pricing. Goals of being able to capture more consumer surplus by
invoking a variety of new pricing strategies are continuously attempted,
with successful strategies rising to the top and being adopted both
within and outside the industry. Baseball has evolved from single prices
for different seating sections within a stadium to variable pricing,
where factors such as opponent and day of the week led to price premiums
for certain games on the schedule. This strategy has now been replaced
in certain markets in Major League Baseball by dynamic pricing.
The strategy of dynamic pricing is likely best known in the airline
and hotel industries. Prices for the same exact room or seat on a flight
differ based upon a variety of factors and fluctuate during the relevant
timing window (until the flight leaves or the night in question for the
hotel stay is reached). An increase in demand for a particular flight or
stays in a certain city will result in higher prices than were seen
previously. Excess supply of seats or rooms is cleared within the market
by a decrease in price. Prices are not known with certainty until the
customer attempts to book a given flight or stay. People sitting next to
each other on the plane or in adjacent rooms at a hotel may pay vastly
different prices based upon when they booked their flight or room.
The San Francisco Giants began the dynamic pricing revolution in
Major League Baseball. By allowing prices to fluctuate across games and
section seating, the fans of baseball were exposed to a new form of
buying tickets from a team. Fans, of course, were not completely
unfamiliar with this practice, as the secondary market for baseball (and
events in general) has seemingly always been thriving. Whether through
ticket scalpers outside of the stadium, ticket brokers, online entities
such as Stubhub, or auction-markets such as EBAY, most fans have some
form of familiarity with prices for tickets being based on current
market conditions, rather than prices set at the start of the season.
As with any new venture from a business, there was a certain level
of risk that consumers would rebel and turn away from the product with a
change from the traditional form of pricing. Russ Stanley, Managing Vice
President of Ticket Sales and Service of the San Francisco Giants, noted
in an interview with Forbes Magazine (Rishe, 2012), "The Giants
organization was initially concerned that fans might not understand the
concept. They are familiar with this type of pricing in the airline and
hotel industry, but this was a big leap for a sports team to implement
the idea into the box office. As it turned out, our concerns were
unfounded. Sports ticketing has such a vibrant secondary market that I
think fans had a better understanding of market value pricing then we
realized" (para. 20).
The dynamic pricing strategy of the Giants turned out to be quite
successful and, as with any other successful strategy, other firms
(teams in this case) were quick to follow. In the 2011 season, three
additional teams adopted a dynamic pricing model: the St. Louis
Cardinals, Chicago White Sox, and Houston Astros. The sentiments
discussed by the Giants were similar to those of members of the St.
Louis Cardinals organization. Joe Strohm, Vice President of Ticket Sales
of the Cardinals, stated in his interview with Forbes, "The biggest
challenge was communicating the new pricing structure to our fans and
overcoming the concern of season ticket holders that we would be
undercutting their price" (para. 21).
Overcoming the fears of their customers also occurred during the
adoption of variable pricing. When the San Diego Padres began charging
higher prices for interleague games against the New York Yankees, fan
and media reaction were quite hostile. Anger was directed at the team
officials, even though these premiums were relatively small compared to
prices for Yankees games charged by scalpers or ticket brokers. The
Padres persevered through the complaints and their "variable"
pricing schemed worked to the effect of increased profitability.
Predictably, other teams, both across baseball and other sports, copied
this winning strategy and variable pricing became the norm in short
order. Although variable pricing helped the bottom line of baseball
teams, there were still pricing efficiencies to be gained through
alternative strategies such as dynamic pricing.
Looking back at previous pricing strategies used in Major League
Baseball, Stanley stated in his interview with Forbes (Rishe, 2012),
"We had been utilizing variable pricing for years and were finding
that even that was not precise enough. A Friday against the Dodgers was
still different than a Sunday game against the Dodgers. All games are
not created equal. We have seen an increase of 7% in the back to back
years we implemented dynamic pricing" (para. 23). Although media
and fan attention often focuses on the premier games with the highest
prices, it must also be noted that this strategy works across different
ticket price levels. Stanley continued, "We have also been able to
sell more tickets to lesser games because we can follow what the market
will bear and accurately price tickets" (para. 23).
The sincerest form of flattery in terms of dynamic pricing
strategies is other teams adopting it for their teams. Qcue, the company
that represents many of the dynamically-priced baseball tickets, entered
agreements with the New York Mets and Seattle Mariners to sell tickets
under dynamic pricing for the 2012 season. Overall, half of Major League
Baseball teams are using some form of dynamic ticket pricing (for all
seats, certain sections, certain games, etc.) in the 2012 baseball
season.
Although dynamic pricing in Major League Baseball is a relatively
recent development, some economic literature does exist around dynamic
pricing in other industries. Elmaghraby and Keskinocak (2003) provide a
background of the literature on dynamic pricing, distinguishing between
posted-price or price-discovery market research. Building on earlier
work by Bremaud (1980), Gallego and van Ryzin (1994) model the
continuous-pricing problem based on intensity control theory, deriving
optimality conditions that demonstrate for a given point in time, the
optimal price is lower as inventory increases, and the optimal price is
higher the greater the duration remaining in which to sell.
Beat and Fuchs (2004) outlined a model for airline pricing whereby
the dynamic program starts by selling seats at a predetermined offer
price, with an ability to automatically adjust price over time based on
the number of remaining seats and the level of observed demand. Escobari
(2009) analyzed the offered rates for non-stop flights from Miami to
Boston in the fall of 2005, and found fares were significantly higher
for planes with a higher percentage of seats sold, significantly lower
for flights on Tuesday, relative to Thursday, and lower rates for
flights further into the future.
This research investigates the determinants of closing prices for
different ticket levels, by section, for the four teams which used
dynamic pricing during the 2011 Major League Baseball season. The
closing prices formed in this dynamic setting are different from prices
set in variable pricing schemes, where prices for tickets are set a
priori. In dynamic pricing, the closing price in the market changes with
consumer demand and prices will substantially deviate from game-to-game.
Our data consists of the closing price for the tickets across sections
for these four teams, but we do not have the corresponding quantities
associated with these sales by section by team. Related research has
used both prices and quantities formed in a dynamic ticket pricing
setting with data from outside sellers of baseball tickets through EBAY
and Stubhub (Sweeting, 2012). In these settings, which involve selling
tickets by individuals rather than the team itself, Sweeting (2012)
found that the dynamic pricing setting allowed for an increased the
seller's expected payoff by 16%.
Drayer, Rascher, and McEvoy (2012) also examined secondary market
ticket prices and quantity sold with data provided from a secondary
market firm. The authors were able to obtain average sold ticket price
and the number of tickets sold for games from the National Football
League. They show that prices respond to consumer demand in the
secondary market and that resellers of tickets are able to capture
$260,000 worth of consumer surplus in this setting.
Rascher, McEvoy, Nagel, and Brown (2007) examined variable pricing
in Major League Baseball, where teams set different prices for different
games based upon opponent, weekday, month, and special events. These
prices are set at the beginning of the season. The authors found that
the use of variable pricing would have increased revenues by 2.8%, with
the Cleveland Indians and San Francisco Giants (who would later be the
first adopter of dynamic pricing) having the largest increases in
revenues.
Our paper focuses on identifying the determinants of the closing
prices formed for these teams in the dynamic pricing sections. The key
difference between our data and data used in dynamic pricing studies of
Stubhub and EBAY is that the ticket prices we compiled are directly
offered by the teams themselves, rather than by individual resellers.
The difference between our data and studies of variable pricing is that
the prices we compiled changed over the course of the season while teams
that use variable pricing set individual game prices at the start of the
season (and they do not fluctuate over time).
Another key difference of this paper compared to the papers
mentioned above is that we only have closing price for each ticket
section for each team for the four teams who used dynamic pricing.
Without the corresponding quantities sold, which would only be available
directly from the teams or from a company that runs the dynamic pricing
for the teams, studies of the elasticity of demand or revenue are not
currently feasible. We hope this data will be made available to study in
the future. That said, however, this data set (which is difficult to
compile but publicly available on the team websites) offers insight into
the premiums or discounts that a wide variety of independent variable
can have on ticket price (in this setting) and allows a comparison to
variable pricing (set at the start of the season) or a single fixed
price model for each seat in the stadium.
Using common independent variables used in attendance studies of
baseball, we investigate sport-specific and baseball-specific factors
(1) which likely influence prices in these markets with a particular
focus on the magnitude of the premiums or discounts which exist for
these attributes.
The second section describes the empirical model, focusing on
explaining the independent variables included in the regression model to
explain dynamic ticket prices for the four teams studied. Section three
presents and analyzes the regression results. The final section
concludes the paper and offers thoughts about the future of dynamic
pricing in sports.
Regression Model
The four teams which used dynamic ticket pricing during the 2011
season were the San Francisco Giants, (2) St. Louis Cardinals, Chicago
White Sox, and Houston Astros. Data was gathered each day from the team
websites, capturing the closing price for each section of the stadium
incorporating the dynamic pricing model for the game played on that day.
It is assumed that the closing prices reflect information and that the
teams (and companies involved such as Qcue) have the incentive to set
and move prices to attempt to maximize revenues and profits for the
teams. The four teams offered an interesting cross-section of teams as
the Giants were the defending 2010 World Series champions, the Cardinals
became the eventual 2011 World Series Champions, the White Sox were a
considerable disappointment compared to preseason expectations, and the
Astros were the worst team in Major League Baseball.
Before describing the regression model, it is useful to present the
summary statistics for the variables used. The information provided by
the summary statistics offers a benchmark for comparison and analysis of
the regression model results that will follow. Table 1 summarizes the
non-binary independent variables in the regression model for each of the
four teams that used dynamic pricing of tickets in the 2011 season. The
mean, median, and standard deviation of attendance, win percentage (over
the course of the season), wind speed, and temperature are shown.
There is sizable variation across each of the categories for the
four teams. St. Louis used dynamic pricing for premium tickets (high
average price), while Chicago and Houston had an average price less than
fifty dollars. The Giants and Cardinals had much higher levels for win
percentage than Chicago or Houston, who had the worst record in Major
League Baseball during the 2011 season. The wind speed and temperature
in Houston is distorted by the fact that many games were played with the
roof closed, leading to zero wind speed and a fixed temperature of 73
degrees. One other interesting sideline is the lower level of standard
deviation in the data for wind speed and temperature in San Francisco,
compared to a wider variation of results for these variables in Chicago
and St. Louis.
Table 2 provides summary statistics for each level of variable
ticket pricing available for the four teams who used this pricing
system. The mean, median, and standard deviation of the closing price of
these sections of the stadium across the season are presented.
As is easily seen in the tables, there is a wide range of ticket
option prices available across the teams in the sample. San Francisco
had 18 sections that used dynamic pricing, St. Louis used 12 different
sections, Chicago had nine, while Houston only used four. There appears
to be substantial variation both within-section, across sections, and
across teams to perform statistical analysis of what drives these price
differences.
The last grouping of summary statistics is presented in Table 3.
This table presents frequencies for the dummy variables used as
independent variables in the regression analysis. These categories
include days of the week, month of the season, key opponents, starting
pitcher, divisional and interleague games, and weather type. Some
promotions are common across the teams studied, while others differ
substantially. The weather variables also differed considerably across
teams, which is evident below.
Similar to the other summary statistics tables, the frequency table
above illustrates considerable differences in some key variables, such
as weather, promotions, key opponents, and number of starts for
different pitchers. Other factors are predictable, due to the way the
schedule is created, with similar frequencies of games played across
months and days of the week.
In using the variables described in the summary statistics above,
the dependent variable in our model is ticket price. The ticket price
reported is the closing price reported by the teams on their website for
each section of the stadium that used dynamic pricing. The regression
model is performed for each team and is run as a fixed-effects model
with each ticket section included in the regression. The full fixed
effects of the individual sections offering dynamic ticket pricing in
the stadium are available from the authors.
From the summary statistics, it is clear there are similarities and
differences in the way teams used dynamic pricing in the 2011 season in
terms of number of sections of dynamic pricing in the stadium and
differences in terms of the quality (higher or lower prices) of seats.
There were also substantial differences in the prices in these sections,
by team, as noted in the summary statistics above. Due to the
considerable differences across cites, we ran the regressions
individually for each team and will present the results side-by-side for
comparison purposes to note the similarities and differences in results.
The regression model was also run with the natural log of ticket price
as the dependent variable, with similar results. Results shown in the
tables in this section are presented in levels.
Independent variables chosen to be included in the model are based
on a wide array of studies of baseball attendance. Many published
articles exist studying the topic of the factors which drive baseball
attendance.
The rationale for the inclusion of our independent variables is
given in the description of the regression model below.
The regression model is as follows
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The independent variables included in the model represent various
factors which have been shown to influence fan decisions when studying
attendance. Most of these are general to sports and entertainment, but
some are baseball-specific. The independent variables start with dummy
variables for the day of the week and the month of the year during the
baseball season. The omitted day of the week is Wednesday and the
omitted month of the baseball season is June. Given the opportunity cost
of time, we would expect that weekend days would be much more popular
than weekdays, likely resulting in higher prices due to increased demand
for weekend games. For the months of the baseball season, due to weather
concerns early season games (except the pageantry of opening day) are
likely to be less popular than the summer months. Later summer months
are likely to be more popular for well-performing teams due to the
possibility of a playoff push. For teams without a realistic hope for
the playoffs, later months may see a decrease in interest and prices for
tickets as the season progresses.
To account for quality of the team, the win percentage of the team
is included in the regression model. The win percentage is calculated as
a running average throughout the season with the win percentage going
into the current game used as the relevant data point for each
observation of the dependent variable. Assuming that fans prefer good
teams to poor teams, win percentage should have a positive and
significant effect on fan demand and, therefore, ticket prices in a
dynamic pricing setting.
The opponent is likely a very important determinant of individual
game attendance and ticket prices. Baseball teams play an unbalanced
schedule across the league with more divisional games played than games
within the National or American league. A limited number of interleague
games are also played. The interleague games are played against natural
local interleague rivals and other teams on a rotating basis. Previous
research on interleague play has found some success of interleague play,
in particular with specific matchups and popular teams such as the New
York Yankees. For our model, we included specific dummy variables for
regional rivals and the generally accepted most popular teams in the
league (New York Yankees, Boston Red Sox, Chicago Cubs, and Philadelphia
Phillies), in addition to a dummy variables encompassing all other
division and interleague games. Ex-ante, we would expect the most
popular teams to be easily reflected at the gate with higher prices for
these teams using dynamic ticket pricing strategies.
Promotions offered during each home game were available for these
teams through their website and were included in the regression model as
a class of independent variables. The promotions were broken into
recognizable categories which capture many different promotional
activities or merchandise offered during these games. If fans enjoy the
promotions and are willing to pay more to see or get the promotional
event or merchandise, ticket prices could be markedly higher for these
games. The promotional categories we decided to use consist of
merchandise, fireworks, events, kids' group night, family nights,
autographs, Six Flags tickets, dogs to the park, fan appreciation night,
and ethnic nights.
Another category of independent variables we included in the model
was for the home starting pitcher. Fans of baseball teams may prefer to
see some starting pitchers compared to others. These popular starters
could be based on historical longevity or on recent performance.
Starting pitchers are announced in advance and are available on team
websites, newspapers, television, etc. Therefore, it is quite likely
that many fans know in advance who the starting pitcher will be and may
base their consumption decision on seeing a particular pitcher. For each
of the four teams that used dynamic pricing, we included a dummy
variable for any pitcher who started nine or more games in the 2011
season.
The final category of independent variables included in the model
was weather effects. This data was taken from the box score of each home
game played. We included data on the temperature, wind speed, and
weather classification category noted in the box score. It is assumed
that nicer weather will increase demand for baseball games. Some of
these effects are likely included in the months of the season, (3) but
given the availability of data on these variables, we decided to
investigate the extent that which weather influences fan behavior in
these four cities using dynamic pricing. The correlation matrix for the
independent variables in the regression model for each of the four teams
is included in the appendices (one per team).
Regression Results
To allow for comparison across teams and categories the regression
results are presented over four tables. The reported results all stem
from the same regression, but are presented in four groups. Table 4
examines the results by day of the week, months of the season, and team
performance (win percentage). Table 5 presents the results for the
independent variables related to the opponent (team, divisional
opponent, and interleague opponent dummy variables). Table 6 examines
the promotional dummy categories and Table 7 shows the starting pitcher
results. Descriptions of the results for each individual section follow
each table.
The regression is run using Ordinary Least Squares (OLS). Due to
initial findings of heteroskedasticity and autocorrelation in the
original regression results, Newey-West Heteroskedasticity and
Autocorrelationconsistent (HAC) standard errors and covariances were
used. Those results are presented in the tables below. Coefficients and
t-statistics (in parentheses) are presented. *-notation denotes
statistical significance at the 10% (*), 5% (**), and 1% (***) level.
Although there are some key differences, the regression results as
they relate to the day of the week, month of the season, and team
performance are similar across the four teams which used dynamic pricing
during the 2011 season. For the days of the week, Wednesday was the
omitted category. Not surprisingly, weekend games were more popular with
baseball fans in these cities, which resulted in higher prices for these
games. Friday commanded a premium of anywhere from $5.17 (Chicago) to
$11.32 (St. Louis) over the prices on Wednesday. (4) Saturday games saw
even higher prices, ranging from a minimum increase of $4.95 (Chicago)
to $19.83 (St. Louis) compared to Wednesday. All of the results for
Friday and Saturday were statistically significant at the 1% level.
Sunday games were not quite as popular, but positive and significant
increases in price were seen in San Francisco ($11.07) and Chicago
($4.65).
Early and mid-week games were not found to be as dramatically
different from the omitted day category, Wednesday, as the weekend
games. Mondays were generally the least popular games in the dynamic
pricing sections for these teams as negative and statistically
significant results were found for St. Louis and Chicago. Tuesdays were
found to have negative and significant effects in San Francisco and St.
Louis, but a positive and significant effect in Houston. Some of these
individual results likely represent city- or fan-specific demands on
time, other entertainment options, etc. for mid-week games.
The months of the season highlighted some of the key differences
between being in playoff contention versus being virtually and then
mathematically eliminated from Playoff contention. The St. Louis
Cardinals, who eventually went on to win the 2011 World Series, and the
San Francisco Giants (the 2010 World Series champions), stayed in
playoff contention (or qualified for the playoffs in the case of the
Cardinals) throughout the season. This led to an increase in prices
(compared to the omitted monthly dummy of June) in July and August for
St. Louis (a premium of $18 and $13, respectively, compared to June) and
in August for San Francisco ($11 premium).
Perhaps somewhat surprisingly, San Francisco, who ultimately did
not make the playoffs in 2011, saw a positive and significant increase
in September, while St. Louis, who did make the playoffs, saw a
negative, but insignificant, effect on ticket price. It appears that
fans in St. Louis may have lost faith in the ability of the team to make
the playoffs in the closing weeks, which was likely justified
statistically by the low-probability combination of events that
eventually led to a playoff berth. On the other hand, the Chicago White
Sox, who delivered a sub-par season compared to expectations, saw
decreases in prices later in the season. Houston, who was rather poor
for the entire season, saw only slight fluctuations during the months of
the baseball season.
Team performance, in terms of the win percentage of the team
(calculated as a running average going into that team's game), was
shown to have a positive and significant effect on ticket prices in San
Francisco, St. Louis, and Chicago. In all three cases, the impact of win
percentage was found to be statistically significant at the 1% level.
Although changes in win percentage may be generally small as the season
progresses, St. Louis fans seemed to be most sensitive to winning (a
coefficient of over 260 on win percentage), while San Francisco (61.64)
and Chicago (19.05) did appear to take winning into account when
deciding to purchase tickets for these teams. Houston, who did not have
a good season and only had four sections using dynamic pricing, showed
win percentage as a positive, but insignificant, determinant of ticket
prices.
The specifics of popular opponents (including traditional rivals),
interleague play, and divisional play yielded some astounding results in
terms of willingness to pay for baseball games by fans in these dynamic
pricing cities. Each team has some specific foes that attracted
considerable attention from local fans, driving prices for these games
to, in some cases, extremely high levels. The San Francisco Giants fans
responded favorably to some key opponents. Legendary rivals, the Los
Angeles Dodgers, commanded a large premium ($20.83) for their games.
Recent National League powerhouse, the Philadelphia Phillies, saw an
increase in Giants tickets by nearly $22 for their games, while the
Chicago Cubs (with many followers across the country) drove prices up by
over $6. Other interleague games for the giants were shown to increase
prices by nearly $5 (significant at the 1% level), but other divisional
opponents (San Diego Padres, Colorado Rockies, Arizona
Diamondbacks) did not command a premium, but actually sold at a $2
discount compared to other games. In addition, the local rivalry with
the Oakland A's in interleague play, was shown to not have a
significant impact on ticket prices.
In St. Louis, local and popular rivals also had a large positive
and significant effect on ticket prices for the Cardinals. The
Cardinals' biggest historical rivals, the Chicago Cubs, led to a
$22 increase in price for the Cubs games in St. Louis (statistically
significant at the 1% level). In addition, the defending (at the time)
National League champions, the Philadelphia Phillies, also saw an
increase in price at Cardinals games when they visited town with an
increase of over $11, significant at the 1% level. The key interleague
rival for the Cardinals, the Kansas City Royals, also showed a sizeable
increase in price for their games, with a $12 premium on their contests.
Other interleague games were also shown to have a positive and
significant increase in ticket prices for these games.
The Chicago White Sox fans also showed a considerable reaction to
the visiting team. For their cross-city interleague games against the
Cubs, prices increased by $50.30 per ticket per game. This was, by far,
the largest increase by an opponent in our four-team sample. The White
Sox, as an American League franchise, had the pleasure of hosting the
two most popular teams across the league, the New York Yankees and the
Boston Red Sox. Yankees games saw an increase of $20.77 and the Red Sox
saw an increase of $18.15 per game. All of these results were found to
be statistically significant at the 1% level. Interleague games saw a
small, but significant increase in price for White Sox games, but
divisional opponents were not found to be a significant determinant of
ticket pricing for these games.
The Houston Astros, who had the poorest season of the teams using
this pricing model, had fans react to the opponent for their home games.
The Astros hosted the Boston Red Sox in interleague play, which led to
an increase of over $20 per ticket for these games (significant at the
1% level). Interstate interleague rival, the Texas Rangers, also saw a
significant increase in ticket prices ($9.48) for these interleague
games. The other interleague opponents also led to an increase of over
$9 per ticket for these games (also significant at the 1% level).
National League teams did not fare as well for the Astros, although the
Philadelphia Phillies games saw an increase of nearly $4 a ticket
($3.90). Chicago Cubs' games did not lead to a statistically
significant effect on ticket prices for the Astros and other divisional
opponents actually led to a statistically significant decrease in ticket
prices for these games (-$3.44).
Overall, the opponent was very important in determining prices in
dynamic pricing models for these four baseball teams. Teams such as the
Yankees, Red Sox, and Phillies led to dramatic increases in ticket
prices. Local rivals such as the Cubs for the White Sox and the
Cardinals, also saw major increases in ticket prices for these popular
games. The size of these increases easily surpasses teams charging
higher prices for these games under variable ticket pricing strategies.
Most promotions were popular in many of these cities, as
promotional nights led to an increase in ticket prices under dynamic
pricing models. In San Francisco, firework nights led to an increase in
ticket prices of well over $20 per ticket ($22.87). Merchandise
giveaways ($8.66) and kids' groups (Junior Giants) ($16.56) were
also popular nights for the fans. Other promotional events also saw an
increase of $5.92 at Giants games. All of the Giants' ticket price
increases related to game-day promotions were found to be statistically
significant at the 1% level.
In St. Louis, opening day led to a $45 increase in prices,
significant at the 1% level. Kids' nights, passes to Six-Flags
amusement park, dogs-to-the-park nights, and merchandise giveaways also
showed positive and significant increases in ticket prices. Somewhat
surprisingly, however, some promotions led to a decrease in ticket
prices. Whether this is due to the promotion itself, something else
about its timing, or the way it was marketed is not known, but fireworks
nights and family nights each showed a statistically significant
decrease in ticket prices for these promotional nights at the stadiums.
In Chicago, most of the promotional nights were found to have a
positive and significant increase in ticket prices for White Sox games.
Most increases in Chicago were relatively small (i.e., $2.93 for
kids' group nights, $5.21 for dogs-to-the-park night, $1.44 for
merchandise giveaways, $1.57 for fireworks, $3.79 for events), except
for opening day, which commanded a premium of over $37 per ticket
(significant at the 1% level).
Fans in Houston did not appear to respond to many of the promotions
for Astros' games. Fireworks displays were shown on every Friday
night following a home game. Therefore, fireworks cannot be separated
from the Friday weekday dummy variable seen in the previous table.
Fireworks may have a significant impact on attendance in Houston, but
due to having fireworks every Friday, its impact cannot be separated
from the day-of-the-week dummy. The only promotional variable shown to
have a significant effect on prices under their dynamic pricing scheme
was family nights. Family nights commanded a $7.54 premium on these
nights and were found to be statistically significant at the 5% level.
Starting pitchers were shown to have a relatively small impact on
ticket prices in the four cities that used dynamic pricing in the 2011
season. The city where the starting pitcher seemed to have the largest
impact on fan interest (and, hence, ticket prices), with positive and
significant increases for some of their key starting pitchers, was San
Francisco. Matt Cain had the biggest effect, with an increase in ticket
prices of $4.94 for his starts (significant at the 1% level). National
League 2010 Cy Young winner Tim Lincecum (who did not have as dominant a
season in 2011) saw an increase in ticket prices of $1.13 for his starts
(not statistically significant). Madison Bumgarner also showed a slight
increase in ticket prices for his starts ($2.34-significant at the 1%
level). Otherwise, the only positive and significant increase in ticket
prices seen due to the starting pitcher was in Chicago with Jake Peavy
($3.28--significant at the 1% level). St. Louis had some starting
pitchers who actually had negative impacts on ticket prices, while none
of the starting staff in Houston led to any noticeable effects on ticket
prices.
The temperature only had a significant effect on price in one city,
San Francisco, where it had a positive and significant effect. Wind was
shown to have a negative and significant effect across all four cities
in the sample. Fans did not appear to enjoy windy days when determining
which baseball games to attend.
Effects of the weather classifications noted in the box scores had
mixed effects across teams. Sunny days were shown to have a positive and
significant effect in San Francisco and St. Louis. Overcast days were
shown to increase ticket prices in San Francisco, while cloudy days were
shown to have a negative and significant effect. Rain caused an obvious
decrease in fan interest and prices in St. Louis, while days classified
as clear had a positive and significant effect on ticket price in
Houston (when the roof was open on game day).
Conclusions
The innovation of dynamic pricing in Major League Baseball was
initiated by the San Francisco Giants. Using the general method which
had been utilized in the past to price airline flights and hotel rooms,
the Giants initiated a system of charging different prices for different
games in different seating sections with considerable success. With this
in mind, other teams were soon to copy the model of the Giants,
beginning their own form of dynamic pricing in their cities. For the
2011 season, the season with the data available for this study, three
teams (in addition to the Giants) also used dynamic pricing, the St.
Louis Cardinals, Chicago White Sox, and Houston Astros. In addition to
the unique availability of this data for study, the teams offering these
dynamic ticket prices differed greatly in terms of success as the St.
Louis Cardinals eventually won the World Series, while the Astros
finished with the worst record in baseball.
Given the availability of price data for these four teams, but the
lack of corresponding quantity data by section, a study of elasticity of
demand or revenue estimation is not possible at this point. With this in
mind, this paper focused on the sign and magnitude of various
independent variables as they relate to closing prices of ticket prices
by section for these baseball teams. Using a variety of independent
variables which have been shown in the past to influence overall
attendance, we analyzed the impact of these factors on dynamic ticket
prices. These factors include the day of the week, month of the baseball
season, team success (win percentage), opponent, promotions, and
starting pitcher.
Although many of the results will likely confirm what many
researchers of baseball already know, the magnitude of some variables in
terms of their overall effect on premiums on price were likely
surprising. In terms of the days of the week, weekends were the most
popular with fans. Saturdays were shown to have the biggest increase in
price with premiums of $5 (Astros) to $20 (Cardinals). Win percentage
was shown to have a positive and significant effect on ticket prices for
three of the four teams in the sample, with the last-place Astros as the
only exception.
The quality of the opponent, which was already well known as a
significant determinant of attendance and was a key element of variable
pricing strategies, played a major role in the determination of price
premiums for these four dynamic-pricing teams. The most astounding
result was found with the Chicago White Sox when the cross-town National
League rival Chicago Cubs was the opponent. These interleague games
resulted in a price premium of $50 per ticket, on the average, across
the different seating sections. Similar results were seen with key
rivals of the St. Louis Cardinals (Chicago Cubs) and San Francisco
Giants (Los Angeles Dodgers) with premiums of $20 per ticket common
across sections at these stadiums. In addition, the most popular teams
in Major League Baseball, the New York Yankees and Boston Red Sox,
commanded nearly $20 or more in premiums when they visited the Chicago
White Sox and Houston Astros during the 2011 season. These premiums far
exceed additional costs charged by teams in a variety of variable
pricing schemes.
Promotions were also shown to have some positive and significant
effects on ticket prices, although they considerably differed across
teams. More research will need to be performed to analyze the extent of
the premiums seen in these cities. Starting pitchers also showed some
positive and significant results, but significant premiums were mainly
seen in San Francisco, who boasts lauded starters in Matt Cain and Tim
Lincecum. The premiums for these pitchers, however, did not exceed $6 on
the average, rather small compared to premiums seen for other factors.
Overall, dynamic pricing of baseball tickets appears to be a
success with fans illustrating their willingness to pay for weekends,
key opponents, winning teams, some promotions, and key starting
pitchers. With the success of dynamic pricing in San Francisco and,
presumably, in the other three cities in the 2011 sample, more teams are
introducing dynamic (or demand-based) pricing for the 2012 season. As
more detailed data becomes available, the dynamic pricing models of
these teams are likely to become a popular avenue for study for sports
economists. Studies of the elasticity of demand, revenue, temporal
analysis, and more detailed examination of the determinants of price
differences across sections and teams will likely follow and we are
likely to learn much more about the preferences of baseball and other
sports fans in the near future. In the meantime, we offer some insight
into the determinants of premiums on ticket prices for the four teams
who were early adopters of dynamic pricing strategies and show that the
willingness to pay of baseball fans far exceeds many of the ticket
premiums charged in the common previous pricing strategy of variable
pricing.
References
Beckman, E., Cali, W., Esrock, R., & Lemke, R. (2012).
Explaining game-to-game ticket sales for Major League Baseball over
time. Journal of Sports Economics, 13(5), 536-553.
Bremaud, P. (1980). Point processes and queues, martingale
dynamics. New York, NY: Springer-Verlag.
Burger, B., & Fuchs, M. (2004). Dynamic pricing--A future
airline business model. Journal of Revenue and Pricing Management, 4(1),
39-53.
Drayer, J., Rascher, D., & McEvoy, C. (2012). An examination of
underlying consumer demand and sport pricing using secondary market
data. Sport Management Review, 15, 448-460.
Elmaghraby, W., & Keskinocak, P. (2003). Dynamic pricing in the
presence of inventory considerations: Research overview, current
practices, and future directions. Management Science, 49, 1287-1309.
Escobari, D. (2009). Systematic peak-load pricing, congestion
premia and demand diverting: Empirical evidence. Economics Letters, 103,
59-61.
Gallego, G., & van Ryzin, G. (1994). Optimal dynamic pricing of
inventories with stochastic demand over finite horizon. Management
Science, 40, 999-1020.
Rascher, D., McEvoy, C., Nagel, M., and Brown, M. (2007). Variable
ticket pricing in Major League Baseball. Journal of Sport Management,
21, 407437.
Rishe, P. (2012, January 6). Dynamic pricing: The future of ticket
pricing in sports. Forbes Magazine. Retrieved from
http://www.forbes.com/sites/
prishe/2012/01/06/dynamic-pricing-the-future-of-ticket-pricing-insports/
Endnotes
(1) There are many studies of the determinants of demand for
baseball game. A recent study, which includes an overview of this
literature in addition to adding their own findings, can be found in
Beckman, Cali, Esrock, and Lemke (2012) in the Journal of Sports
Economics.
(2) The first two games of the 2011 San Francisco Giants did not
have price information on their website, therefore these two dates are
excluded from our sample. In addition, this is why there is not a value
for the opening day promotional dummy variable for the San Francisco
Giants. All other home dates for the Giants and the other three teams
are included in the sample.
(3) Running the regression without the weather variables revealed
the same statistically significant variables for the monthly dummies.
Therefore, although the ultimate impact on weather is likely split
between the monthly dummies and the weather category dummies (in
addition to temperature and win speed), we believe all of these
variables offer some insight into the willingness to pay of the baseball
fan and are included in the regression model.
(4) The average Wednesday price in the dynamic pricing sections,
for comparison purposes, in the four cities were as follows: San
Francisco ($56.16) St. Louis ($101.23), Chicago ($48.17), Houston
($33.85).
Rodney J. Paul, PhD, is a professor in the Falk College of Sport
and Human Dynamics at Syracuse University. His research interests
include the economics and finance of sport, efficient markets, and
behavioral economics/finance.
Andrew P. Weinbach, PhD, is an associate professor in the
Department of Accounting, Finance and Economics at Coastal Carolina
University. His research interests include measuring and forecasting
consumer actions and interest in individual live sporting events and
sports betting markets.
Table 1
Summary Statistics--Non-Binary Variables
Variable Average Win Wind Temperature
Price Percentage Speed
(Dynamic)
San Francisco Giants
Mean $62.33 0.5463 12.19 61.84
Median $50.00 0.5517 12 61
Std. Dev. $41.88 0.0218 3.52 4.63
St. Louis Cardinals
Mean $109.63 0.5408 8.26 76.35
Median $99.00 0.5340 7 77
Std. Dev. $42.88 0.0189 5.01 13.50
Chicago White Sox
Mean $46.77 0.4809 11.18 68.77
Median $45.00 0.4873 10 72
Std. Dev. $20.86 0.0475 4.63 14.04
Houston Astros
Mean $41.81 0.3417 2.5062 74.51
Median $40.00 0.3457 0 73
Std. Dev. $9.60 0.0336 5.44 3.80
Table 2
Individual Ticket Section Prices Summary Statistics
San Fran. Giants
Section Center Field Left Low Left High Left Field
Bleachers Bleachers Bleachers Bleachers
Mean $23.29 $43.19 $37.73 $22.37
Median $20.00 $38.00 $34.00 $20.00
Std. Dev. $8.78 $16.11 $13.47 $13.45
Section Left Field View Box Arcade Coors Light
View Box Silver
Bullpen
Mean $30.56 $44.81 $47.77 $62.99
Median $30.00 $43.00 $47.00 $62.00
Std. Dev. $9.33 $12.44 $12.43 $12.57
Section Left Field Outfield Infield Left Club
Club Club Club
Mean $62.46 $90.68 $104.40 $139.69
Median $59.00 $88.00 $100.00 $136.00
Std. Dev. $19.97 $23.55 $21.59 $25.58
St. Louis Cardinals
Section Homers Left Coke Coke Score-
Landing Field Rooftop board Patio
Landing Deck
Mean $80.72 $80.91 $98.84 $92.88
Median $75.00 $75.00 $94.00 $93.00
Std. Dev. $15.42 $14.72 $20.19 $25.36
Section BOA Club Legends Champions
Club Club
Mean $113.82 $103.23 $136.67
Median $111.00 $102.00 $136.00
Std. Dev. $21.32 $29.50 $28.66
Chicago White Sox
Section Club Box Lower Box Premium Lower
Club Reserve
Mean $59.61 $48.45 $69.61 $43.93
Median $60.00 $47.00 $65.00 $43.00
Std. Dev. $16.09 $15.30 $14.42 $14.61
Section Premium Premium
Lower Box Upper Box
Mean $69.78 $34.00
Median $65.00 $32.00
Std. Dev. $14.48 $12.19
Houston Astros
Section Field Field
Box--Low Box--High
Mean $25.62 $41.30
Median $27.00 $39.00
Std. Dev. $14.89 $9.47
Giants
Section Outfield Infield Right Field
Reserved Reserved Reserved
Mean $27.50 $40.45 $31.96
Median $26.00 $41.00 $30.00
Std. Dev. $11.78 $14.31 $11.80
Section Left Field Lower Box Premium
Lower Box Box
Mean $54.41 $74.32 $83.22
Median $51.00 $71.00 $79.00
Std. Dev. $19.18 $24.44 $22.50
Section Premium
Mean $162.45
Median $155.00
Std. Dev. $25.07
Section PowerAde U.S. Musial
Bridge Cellular Bridge
MVP Deck
Mean $96.13 $92.50 $93.43
Median $93.00 $92.00 $92.00
Std. Dev. $22.23 $21.07 $20.07
Section Redbird Commissioner's
Roost Box
Owners
Suite
Mean $184.85 $216.75
Median $190.00 $215.00
Std. Dev. $23.67 $14.70
Section Bleachers Upper Box Upper
Reserve
Mean $42.65 $30.72 $22.14
Median $42.00 $29.00 $18.00
Std. Dev. $13.96 $10.42 $9.22
Section
Mean
Median
Std. Dev.
Section Club II--Low Club II--High
Mean $27.84 $42.33
Median $30.00 $41.00
Std. Dev. $15.90 $9.76
Table 3
Frequency Table for Dummy Independent Variables
Variable San Francisco Giants St. Louis Cardinals
Sunday 13 13
Monday 9 8
Tuesday 13 11
Wednesday 13 13
Thursday 7 11
Friday 12 12
Saturday 12 13
April 7 11
May 12 13
June 16 14
July 13 14
August 19 13
September 12 15
Division Games 27 31
Interleague Games 6 3
Los Angeles 9 0
Oakland 3 0
Chicago Cubs 3 9
Philadelphia 4 5
Kansas City 0 3
New York Yankees 0 0
Boston 0 0
Texas 0 0
Pitcher 1 15 (Cain) 17 (Carpenter)
Pitcher 2 17 (Lincecum) 16 (Westbrook)
Pitcher 3 15 (Bumgarner) 15 (Garcia)
Pitcher 4 16 (Vogelsong) 14 (Lohse)
Pitcher 5 9 (McClelland)
Pitcher 6
Opening Day 0 1
Merchandise 23 23
Fireworks 1 3
Event 6 0
Kids' Day 4 2
Family 0 1
Autograph 0 5
Six Flags 0 3
Dogs to Park 0 1
Fan Appreciation 0 1
Ethnic Night 0 0
Clear 28 13
Sunny 9 7
Cloudy 10 16
Drizzle 0 0
Overcast 5 7
Rain 1 1
Partly Cloudy 26 37
Closed Roof 0 0
Variable Chicago White Sox Houston Astros
Sunday 13 13
Monday 11 10
Tuesday 12 13
Wednesday 12 13
Thursday 7 6
Friday 13 13
Saturday 13 13
April 12 15
May 11 13
June 16 16
July 13 9
August 16 15
September 13 13
Division Games 36 33
Interleague Games 6 3
Los Angeles 0 0
Oakland 0 0
Chicago Cubs 3 6
Philadelphia 0 3
Kansas City 0 0
New York Yankees 4 0
Boston 3 3
Texas 0 3
Pitcher 1 15 (Buehrle) 15 (Myers)
Pitcher 2 14 (Floyd) 17 (Norris)
Pitcher 3 14 (Danks) 13 (Rodriguez)
Pitcher 4 13 (Humber) 15 (Happ)
Pitcher 5 9 (Jackson)
Pitcher 6 10 (Peavy)
Opening Day 1 1
Merchandise 20 19
Fireworks 17 13
Event 7 0
Kids' Day 7 0
Family 0 14
Autograph 0 0
Six Flags 0 0
Dogs to Park 1 2
Fan Appreciation 0 0
Ethnic Night 3 0
Clear 13 8
Sunny 7 3
Cloudy 16 3
Drizzle 0 0
Overcast 7 0
Rain 1 0
Partly Cloudy 37 2
Closed Roof 0 65
Table 4
Dynamic Ticket Pricing Regression Results--Days, Months,
Win Percentage
Variable San Francisco Giants St. Louis Cardinals
Intercept -65.5151 *** -63.7675 *
(-4.8523) (-1.6484)
Sunday 11.0723 *** -3.9617
(8.8808) (-1.2082)
Monday -0.6758 -12.8446 ***
(-0.8312) (-4.6428)
Tuesday -3.8818 *** -9.3283 ***
(-6.1637) (3.6432)
Thursday -0.9494 2.6707
(-1.1419) (1.1841)
Friday 8.1232 *** 11.3203 ***
(8.7749) (3.8618)
Saturday 19.8350 *** 18.5786 ***
(11.5241) (5.8912)
April 7.9728 *** 3.3073
(4.8891) (0.5567)
May 8.1444 *** 9.0582 ***
(4.0482) (2.9408)
July 2.5195 18.2682 ***
(1.5011) (4.9259)
August 11.1673 *** 13.3838 ***
(7.1484) (3.7580)
September 14.3532 *** -0.6274
(8.3855) (-0.1675)
Win Percentage 61.6419 *** 261.7356 ***
(3.6253) (3.9268)
Variable Chicago White Sox Houston Astros
Intercept 7.2807 ** 35.8156 ***
(2.1676) (2.9054)
Sunday 4.5652 *** 2.4460
(6.4321) (0.6590)
Monday -12.1462 *** 1.6612
(-11.8713) (1.5017)
Tuesday 0.6834 3.5597 ***
(1.2917) (3.0011)
Thursday 0.7978 2.2848
(1.2282) (1.1728)
Friday 5.1734 *** 9.3858 ***
(5.9733) (6.3825)
Saturday 4.9453 *** 16.4641 ***
(7.1293) (9.9541)
April -6.5195 *** 0.4515
(-9.8890) (0.3416)
May -1.3631 * -1.6716 *
(-1.7191) (-1.7672)
July -2.5338 *** 0.5921
(-3.2273) (0.4893)
August -2.5877 *** 2.2424
(-3.4195) (1.4397)
September -2.2593 *** -6.3084 ***
(-4.0384) (-4.7583)
Win Percentage 19.0468 *** 1.0501
(4.4734) (0.0724)
Table 5
Regression Results--Division Play, Interleague Play,
Specific Opponents
Variable San rancisco Giants St. Louis Cardinals
New York Yankees
Boston Red Sox
Texas Rangers
Philadelphia 21.7298 *** 11.3568 ***
Phillies (7.0745) (3.7290)
Chicago Cubs 6.5567 *** 22.0758 ***
(5.6561) (8.1416)
Los Angeles 20.8306 ***
Dodgers (14.567)
Oakland A's 2.3968
(1.0543)
Kansas City 11.9132 ***
Royals (2.8643)
Division-Other -2.2089 ** -3.0047 *
(-2.4789) (-1.7839)
Interleague-Other 2.1355 9.4945 *
(1.4316) (1.6623)
Variable San Chicago White Sox Houston Astros
New York Yankees 20.7792 ***
(21.7060)
Boston Red Sox 18.1516 *** 20.8807 ***
(15.5804) (12.4406)
Texas Rangers 9.4859 ***
(7.6900)
Philadelphia 4.0367 **
Phillies (2.3746)
Chicago Cubs 50.2957 *** -1.7875
(13.6814) (-1.0534)
Los Angeles
Dodgers
Oakland A's
Kansas City
Royals
Division-Other 0.1626 -3.4422 ***
(0.2711) (-3.8217)
Interleague-Other 1.7143 ** 9.0849 ***
(2.0895) (10.1181)
Table 6
Regression Results--Promotions
Variable San Francisco Giants St. Louis Cardinals
Opening Day 45.0869 ***
(7.4752)
Merchandise 8.6574 *** 5.5405 **
(7.2516) (2.5620)
Fireworks 22.8656 *** -3.3435 *
(12.2741) (-1.6971)
Events 5.9168 ***
(4.5795)
Kids' Group 16.5585 *** 12.9539 **
(11.7058) (2.4867)
Family Night -18.3501 *
(-2.0401)
Autographs 0.4752
(0.1565)
Six Flags Ticket 9.3337 ***
(2.6890)
Dogs to Park 11.0500 *
(1.7395)
Fan Appreciation -7.5647
(-1.4163)
Ethnic Night
Variable San Chicago White Sox Houston Astros
Opening Day 37.5492 *** -2.1077
(11.9624) (-0.7999)
Merchandise 1.4383 *** 0.2430
(2.7045) (0.2954)
Fireworks 1.5685 *
(1.7148)
Events 3.7937 ***
(4.3001)
Kids' Group 2.9380 ***
(3.3838)
Family Night 7.5451 **
(2.5441)
Autographs
Six Flags Ticket
Dogs to Park 5.8064 *** -0.8416
(4.1084) (-0.6566)
Fan Appreciation
Ethnic Night 0.8446
(-0.9230)
Table 7
Regression Results--Starting Pitchers
Variable San Francisco Giants St. Louis Cardinals
Pitcher 1 Cain Westbrook
4.9366 *** -0.2252
(5.6921) (-0.1297)
Pitcher 2 Lincecum McClelland
1.1272 -4.1959 *
(1.3149) (-1.8822)
Pitcher 3 Bumgartner Lohse
2.3419 *** -3.1495 *
(2.8941) (-1.6819)
Pitcher 4 Vogelsong Carpenter
0.9367 -2.5742
(1.1044) (-1.2381)
Pitcher 5 Garcia
-6.3493 ***
(-3.5645)
Pitcher 6
Variable Chicago White Sox Houston Astros
Pitcher 1 Peavy Myers
3.2752 *** 0.5942
(4.1726) (0.8092)
Pitcher 2 Floyd Rodriguez
-0.2843 0.8983
(-0.3805) (1.2051)
Pitcher 3 Danks Happ
-0.2119 0.2951
(-0.2249) (0.4756)
Pitcher 4 Jackson Norris
0.0547 0.1845
(0.0520) (0.2198)
Pitcher 5 Buehrle
-1.3768
(-1.5517)
Pitcher 6 Humber
-0.7751
(-0.8831)
Table 8
Regression Results--Weather Effects
Variable San Francisco Giants St. Louis Cardinals
Temperature 0.6001 *** -0.0694
(6.8742) (-0.7507)
Wind -0.4296 *** -0.3952 **
(-4.1261) (-2.2014)
Closed Roof
Clear -0.0628 0.7297
(-0.1116) (0.4032)
Sunny 5.9438 *** 5.6075 *
(6.4007) (1.9331)
Cloudy -3.0490 *** 0.2723
(-2.9665) (0.1721)
Drizzle
Overcast 3.5563 ** -4.0393
(2.2573) (-1.6315)
Rain -0.5590 -6.6889 *
(-0.2501) (-1.7664)
R-squared 0.9510 0.8863
Adj. R-squared 0.9495 0.8808
F-statistic 642.6702 161.3576
Variable Chicago White Sox Houston Astros
Temperature 0.0343 -0.0117
(1.6185) (-0.0819)
Wind -0.1264 ** -0.1757 *
(-2.4943) (-1.8665)
Closed Roof -0.6699
(-0.3627)
Clear 1.2485 3.2619 **
(1.5419) (2.2659)
Sunny -0.2015 2.7148
(-0.3890) (1.4098)
Cloudy 2.6414 *** 1.3343
(4.5630) (0.5148)
Drizzle -0.8692
(-0.9005)
Overcast -0.0794
(-0.1197)
Rain
R-squared 0.9493 0.8992
Adj. R-squared 0.9465 0.8779
F-statistic 340.1356 42.3529
