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Data-Driven Sports Ticket Pricing for Multiple Sales
Channels with Heterogeneous Customers
Hayri A. Arslan
Department of Economics, Queen’s University, arslan.alper@econ.queensu.ca
Robert F. Easley
Mendoza College of Business, University of Notre Dame, reasley@nd.edu
Ruxian Wang
Johns Hopkins Carey Business School, ruxian.wang@jhu.edu
¨
Ov¨un¸c Yılmaz
Leeds School of Business, University of Colorado Boulder, ovunc.yilmaz@colorado.edu
Problem Definition: We develop a framework to study purchase behavior from distinct segments of het-
erogeneous customers, and to optimize prices for different policies in a sports ticket market with multiple
sales channels. Academic/Practical Relevance: Sports teams face challenges maintaining or increasing
ticket sales levels. With the growth of analytics, they aim to implement data-driven pricing techniques to
improve gate revenues; however they do not have state-of-the-art demand estimation and price optimization
tools that take into account the range of valuation across different seat sections and opponent match-ups.
Methodology: Partnering with a college football team, we develop a data-driven pricing tool which: (1)
segments customers in two sales channels using transaction-level data and anonymous customer profiles; (2)
explores the decision-making process of different customers within these segments using the Multinomial
Logit and Mixed-Multinomial Logit frameworks; and (3) decides optimal or near-optimal prices subject to
some business constraints enforced by the team management. In addition, our method takes the sequential
arrivals of customers and the capacity constraints of seat categories into account. Results: Our estimation
results show that customers differ significantly in their sensitivities to price and distance to the field within
each segment, in addition to the differences across segments. We also observe that customers become less
likely to choose a seat category as its remaining inventory falls below a certain point. Managerial Impli-
cations: By analyzing different policies, we show that price optimization could increase revenue by as much
as 7.6%. In addition, better categorization of games and further refinement of seat category differentiation
and related pricing may help further boost this figure up to 11.9%.
Key words : Pricing; Discrete Choice Models; Analytics; College Football; Events/Sports Tickets
History : July 22, 2020
1
Electronic copy available at: https://ssrn.com/abstract=3447206
2Arslan et al.: Data-Driven Sports Ticket Pricing
1. Introduction
The North American sports market has already reached 70 billion U.S. dollars in annual revenues,
and continues to grow rapidly. Although gate revenues and media rights, both worth approximately
19 billion U.S. dollars annually, remain the two major revenue sources, sports organizations and
teams have been struggling to keep ticket sales and game attendance at the same level, as the
competition from game broadcasts increases (PwC 2018). With the growth of analytics, teams aim
to implement data-driven pricing techniques to improve gate revenues. Since each seat for each
game offers a unique value, teams have started to use advanced techniques such as (i) tiered pricing,
also known as “scaling the house,” where teams offer different categories of seats at different prices;
(ii) variable pricing, where teams charge different prices across games; and (iii) dynamic pricing,
where teams set single-game ticket prices dynamically in real time. However, choosing which of
these options to implement, and then making optimal pricing decisions, is often a challenging task
due to the complex dynamics in the sports ticket market (Courty 2015, Xu et al. 2019).
Of the three methods, dynamic pricing has been found to be the most sensitive to season length
and number of games played. Because of the high single-game ticket inventory and lengthy regular
seasons, dynamic pricing has been widely used in some professional sports leagues such as Major
League Baseball, the National Basketball Association, and the National Hockey League (PwC
2014). A recent study by Xu et al. (2019) develops a framework to estimate a demand model for
single-game tickets for a Major League Baseball team, and reports that optimal dynamic pricing
can bring up to 17.2% revenue improvement in this channel. On the other hand, teams in the
National Football League or college football have been hesitant to use dynamic pricing techniques
because of the smaller number of home games (Fisher 2014).1These teams often have strong
demand for season tickets, and their single-game tickets can sell out even before the season starts.
In this setting, dynamic pricing is of little use, reserved for just the few thousand tickets that
teams keep in order to make their games accessible to fans (Mathews 2019), or that are returned
from the opponent team (Green Bay Packers 2014). Thus, football teams have been working with
tiered and variable pricing policies, under which they charge different prices across different seat
categories and games, respectively.
In this applied research project, we partnered with a college football team,2which followed the
trends in the industry and added variable pricing to their existing tiered pricing policies in the 2017
season. Our goal is to develop a framework that estimates the demand of season tickets and single-
game tickets, and optimizes prices by taking into account the multiple sales channels, i.e., season
tickets and single-game tickets, that are sold sequentially and aim to target different customer
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 3
Figure 1 Architecture of the Pricing Tool.
Estimation
module
Optimization
module
groups. The methodology developed in this paper is three-fold: (i) we analyze the historical data
to understand the customer behavior, (ii) we output the optimal prices that capture the market
dynamics for college football tickets, and (iii) we develop a pricing tool that is flexible to capture
various heterogeneities among customers and provide useful guidance for different management
preferences.
The architecture of the pricing tool is illustrated in Figure 1. It consists of a segmentation
step and two major modules: estimation and optimization. As is the case within both college and
professional football, within each channel, there are multiple customer segments which differ in
their sensitivities to prices, seat locations, etc. The tool first segments customers by analyzing
the individual transaction data that includes anonymous customer profiles. After this step, the
estimation module explores the decision-making process of different customer segments within these
two sales channels. We assume that the choice process is governed by a multinomial logit (MNL)
model for each segment in the season ticket channel (similar to the discrete mixed MNL framework
used in Li et al. 2019), and a mixed multinomial logit (MMNL) model for each customer segment
in the single-game ticket channel (see, e.g., Train 2009). Using the output of the estimation module,
the optimization module computes the optimal prices, subject to the business constraints enforced
by the team management. This module allows changing seat category availability due to sequential
customer arrivals, provides a near-optimal approximation for this real-world problem, and allows
us to derive managerial insights through counterfactual analyses.
Electronic copy available at: https://ssrn.com/abstract=3447206
4Arslan et al.: Data-Driven Sports Ticket Pricing
1.1. Related Literature
Our paper is closely related to several streams of literature on price discrimination, event revenue
management, choice-based price optimization, and the effects of sales and remaining inventory
information on customer choices.
Second-degree price discrimination. The economics literature points to revenue management as
an example of price discrimination. Tiered and variable pricing strategies discussed in this paper
are particular examples of two common types of second-degree price discrimination, quality dis-
crimination and peak-load pricing (see Varian 1989, Crew et al. 1995 for a review). The benefit of
these strategies in the entertainment domain has been investigated in multiple empirical studies.
Leslie (2004) develops a structural model for the data set from a Broadway play, and shows that
selling different theater seats at different prices brings revenue improvements around 5%. Courty
and Pagliero (2012) find a similar figure for the benefit of tiered pricing using data from the North
American concert industry. Rascher et al. (2007) show that Major League Baseball could have
increased ticket revenues by approximately 3% by utilizing variable pricing. In a recent paper,
Arslan et al. (2019) show a similar increase in primary market sales, and explain this through
the interplay between primary and resale markets, using a quasi-experimental data set from the
National Football League.
Event revenue management. The entertainment industry has many characteristics (e.g., limited
capacity, advanced ticket sales, etc.) that seem well-suited to revenue management (Talluri and
van Ryzin 2004). In the operations management literature, there is a growing interest in event
pricing. Based on a survey conducted by a professional baseball franchise in Japan, Veeraraghavan
and Vaidyanathan (2012) develop a measure of seat value based on the location of the seat and
customer characteristics. Tereya˘go˘glu et al. (2017b) study the individual level purchase data from
a symphony orchestra and show that price commitment to a decreasing monotone discount policy
can improve revenues significantly. Xu et al. (2019) focus on single-game tickets for a Major League
Baseball franchise and estimate a comprehensive demand model to implement dynamic pricing
policies for single-game tickets. Maclean and Odegaard (2020) study the optimal dynamic capac-
ity allocation for multiple-seat purchases in order to deal with sparse unsold single tickets. In a
modeling paper, Cui et al. (2014) discuss the impact of scalpers for the primary ticket market and
identify the scenarios where a resale market may be beneficial. Alley et al. (2019) develop a price
optimization model for selling tickets on a secondary market, incorporating the price sensitivities
at the individual ticket level.
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 5
Price optimization under choice models. In this paper, we employ the multinomial logit (MNL)
model and one of its variations, the mixed MNL or MMNL (see, e.g., Train 2009) to model purchase
behavior, because the customers in the single-game ticket channel make a series of decisions for
different seats and games in the stadium. We then optimize prices based on our estimation results, so
we reference the literature which studies pricing under the MNL model and its variations. Aydın and
Porteus (2008) investigate the optimal inventory levels and prices for a multi-product assortment
in a newsvendor setting and discuss the case with MNL demand. Federgruen and Yang (2009)
investigate price competition under the MNL model and its generalization with yield uncertainty.
Li and Huh (2011) focus on nested logit (NL) models where customers make a decision among
subfamily groups before making a choice at the product level. They show that the profit function
is concave with respect to market shares and the markup is constant across all products. Gallego
and Wang (2014) relax the identical price-sensitivity assumption and focus on the pricing problem
with product-differentiated price sensitivities, and simplify the multi-product pricing problem to
a single-dimension optimization by showing the adjusted markups are product-invariant. Li et al.
(2015) and Huh and Li (2015) extend the previous work with a multi-stage NL model. Wang (2018)
incorporates a reference price into the MNL model and investigates its effects on decision making.
Li et al. (2019) investigate optimal pricing under discrete MMNL demand, and show that the
equal-markup property fails to hold due to heterogeneity in price sensitivities for customers from
different segments.
Customers’ use of information on sales and remaining inventory. In our setting, customers use a
seat selection platform which shows remaining seat inventory, thus allowing them to deduce the sales
which occurred before their arrival. The literature discusses a number of ways in which sales and
inventory information affect customer decisions. Du et al. (2016) study a pricing problem under an
MNL choice model in which the utility of purchasing each good depends on the total consumption
level for that product, known as the network effect. Wang and Wang (2017) illustrate several
fundamental properties of a similar model and show that the revenue-ordered assortment, plus an
additional item, could be optimal for the assortment optimization problem. Using randomized field
experiments in Amazon, Cui et al. (2018) show the existence of a herding effect, where a decrease
in product availability attracts more future sales. Glaeser et al. (2019) study the spatiotemporal
location problem of a Buy-Online-Pick-Up-In-Store grocery retailer which uses delivery trucks
instead of offline stores, and show evidence of a synergistic effect, i.e., an increase in sales of each
pickup location with an increase in the number of available pickup locations, for neighborhoods
which started with limited number of pickup locations. Cachon et al. (2018) use an automotive
Electronic copy available at: https://ssrn.com/abstract=3447206
6Arslan et al.: Data-Driven Sports Ticket Pricing
dealership data set, and demonstrate the scarcity effect, wherein adding inventory decreases sales
if variety is held constant. Finally, Tereya˘go˘glu et al. (2017a) analyze a data set on a symphony
orchestra and explore whether customers’ seating area choice is influenced by their past observations
of prices and occupancy levels, known as reference effects.
1.2. Our Contributions and Managerial Insights
Although the existing literature shows the positive impact of tiered and variable pricing strategies,
there is a gap between theoretical results and empirical findings, because the former lacks data and
often makes strong assumptions while the latter analyzes outcomes based on sub-optimal pricing
strategies. This paper intends to bridge this gap between theory and practice by (i) developing a
data-driven price optimization tool, and (ii) demonstrating that price optimization amplifies the
revenue improvement enabled by these strategies.
Methodological Contributions. There also remain opportunities to develop significant extensions
to current methodologies. First, even if the customer segmentation performs well, the heterogeneity
in customer tastes within the same segment cannot be ignored, e.g., a customer may be more (or
less) price-sensitive than another customer in the same segment. Second, unlike other sports fans,
those buying single-game football tickets often have to make their decisions for multiple games at
the same time before the season starts, which implies potential correlation between these purchase
decisions. Third, due to the sequential nature of their arrivals, customers see different seat options.
We contribute to the operations management literature in this regard by developing a framework
that incorporates customer heterogeneity within each segment,3as well as correlations in observed
factors within multiple decisions of the same customer, and the effects of availability, or remaining
seat inventory. This model also does not exhibit the independence of irrelevant alternatives (IIA)
property, which often leads to restrictive substitution patterns as observed under the standard
logit models, and therefore it allows more flexible substitution patterns with correlations among
the utilities for different alternatives.
Our pricing module embeds sophisticated optimization algorithms into sports and event ticket
price management and is unique in the sense that: (i) it considers multiple sales channels (e.g.,
season tickets and single-game tickets) for the seats; (ii) there are capacity constraints for each seat
category for each game; and (iii) it dynamically updates the choice sets and choice probabilities
based on changing availability due to sequential arrivals.
Finally, although the academic literature suggests that high sales or low inventory levels affect
future demand in a positive direction for a specific product, we find compelling empirical evidence
for the opposite in our study on a data set of college football tickets. As the seat availability in
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 7
a section falls below a certain point, fans are less likely to choose seats in that seat category. We
call this the periphery effect: The value of seats in a section is fairly consistent in and around the
center of the region, but in the periphery the value increases or decreases depending on whether it
borders higher or lower priced sections.
Managerial Insights. Our paper provides several key managerial insights for the sports industry.
First, we show that customers within each segment differ significantly in their sensitivities to price
and distance to the field (in addition to the differences across segments) and ignoring this in
estimation and optimization may result in sub-optimal ticket pricing decisions. Second, we find that
customers value seats not only based on the angle of view with respect to the field, but also relative
to the sun and the videoboard, which may have crucial implications for the pricing management
of sports tickets.
Our analysis shows that the current implementation of variable pricing brought in an additional
4.9% revenue over the previous tiered-only pricing policy. Moreover, price optimization can provide
a bigger revenue boost, up to 7.6% over the current implementation. There are even more oppor-
tunities: The team can change the number of games in the game categories (the team introduced
three game categories, each having two home games with the same price for a given tier or seat
category) for an extra 3.6% revenue gain, or can use an asymmetric pricing scheme (e.g., that
differentiates otherwise symmetric end-zone seats based on views of the videoboard) for a further
4.0% revenue improvement.
2. Setting and Data
In this research, we partner with a College Football Division I team with annual revenue greater
than 100 million U.S. dollars. This figure places the team in the top 10 of the National Collegiate
Athletic Association in football revenues (U.S. Department of Education 2018). The team has a
stadium with capacity of around 80,000 seats, and has been using a combination of tiered pricing
and variable pricing since 2017. The pricing decisions were made based on the athletic department’s
informed suggestions, but without using any sophisticated model-based or data-driven decision-
making methods.
2.1. Sales Channels
College football teams play five to seven home games in each regular season from late August to
early December. Teams sell tickets mainly through two channels: Season tickets and single-game
tickets. The season ticket sales take place early in the year, beginning right after the end of the
previous season. After the season ticket market closes in late April, single-game tickets are offered
Electronic copy available at: https://ssrn.com/abstract=3447206
8Arslan et al.: Data-Driven Sports Ticket Pricing
Figure 2 Timeline of the Ticket Sales Process.
Applications for season
and single-game tickets
Team’s pricing decision
Season ticket sales
(simultaneous)
Single-game ticket sales
(sequential)
through a pre-sale to certain individuals (e.g., donors, alumni). At the end of the pre-sale, just
before the regular season starts, any remaining seats become available to the general public. See
Figure 2 for the timeline of the ticket sales process, which typically happens to most top college
football teams.
Season tickets. A season ticket grants the holder access to all home games during the season.
Different than other sports, football season ticket prices are usually equal to (or very close to) the
sum of single-game ticket prices in the same tier, due to the small number of home games. Other
than the advantage of securing a preferred seat, there are additional benefits of being a season
ticket holder, including complimentary parking, complimentary tickets to some other college sports
games, and priority access to away-game ticket sales.
Although big donors (i.e., people contributing to the university above a certain threshold) and
faculty/staff can have direct access to season tickets, the general public is required to make an
annual donation to obtain these tickets. Long wait-lists for season tickets have been common in
College Football, and customers often have to make significant contributions (more than ticket
prices for our case) to be able to purchase season tickets.4Most of the season ticket sales are renewals
from the previous season and all new season ticket members have to complete an application before
the announcement of the prices. Therefore, the team can easily estimate the market size for this
channel before making the pricing decisions.
Single-game tickets. A single-game ticket grants the holder access to a specific game. When these
tickets are sold to the public, it is common that brokers purchase tickets for popular games early, to
resell them later in a resale market for profit. Therefore, most football teams have started to offer
pre-sales to fans who are somehow connected to the team.5Our partner team is one of the pioneers
of this idea and provides early access to big donors, alumni, and students’ parents. Each customer
has to make an application for this pre-sale at the end of the previous season and some customers
may also need to pay a small entry fee. The team assigns a selection time to customers and may
limit the number of tickets or the list of games to be chosen, based on the size of contributions
or seniority.6The ticket selection times vary up to 3 months apart (i.e., late April to early July),
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 9
Table 1 Stadium Capacity and Relative Ticket Prices.
Price Point SeatCat Capacity Price-C Price-B Price-A
Preferred 20,21 3.37% 166.67 208.33 250.00
Lower Prime 8,9 8.27% 120.83 133.33 208.33
Upper Prime 18,19 4.89% 104.17 125.00 187.50
Lower Side 6,7 11.66% 91.67 112.50 170.83
Upper Side 16,17 9.35% 79.17 100.00 154.17
Lower Corner 3,4,5 19.00% 75.00 91.67 141.67
Upper Corner 12,13,14,15 10.16% 62.50 79.17 133.33
Lower End 1,2 17.07% 58.33 70.83 108.33
Upper End 10,11 16.25% 37.50 54.17 79.17
Note. For confidentiality reasons, the capacities are given in percentages and
prices are scaled such that Upper Side price for a B game is $100. There are only
three lower corner seat categories, because one is allocated to students.
so customers who have an earlier selection time are at a major advantage in choosing where they
want to sit in the stadium, and the games for which they want to purchase tickets for. After the
pre-sale period is over, unsold seats are offered to the general public, although historically, the
team observes only a few games per year that have a small number of tickets remaining available
for public sales.
2.2. Data Sources
The team provided us with access to four important data sources for the 2018 season:
•The customer database stores the necessary information for each unique identification number
to decide the season-ticket eligibility, pre-sale selection time, etc.
•The stadium database offers an interactive map of the stadium inventory with capacities. There
are nine price points in the stadium (preferred seating, lower and upper 50-yard, lower and
upper side, lower and upper corner, lower and upper end zone) with more than 70 sections.
To reduce the computational burden of analyzing more than 70 seat sections in the stadium,
we create 21 seat categories with the help of the ticket management team. All the sections in
a seat category are priced identically, and face the same direction. For example, seat sections
in the lower end zones are split into North and South lower end zone categories. The second
and third columns of Table 1 list the seat categories in each price point and their relative
capacities. The team reserves the right to give away some seats for their own purposes, e.g.,
student groups, the band, away teams, special guests, athletic recruiting, contractors, etc.
Therefore, some areas in the stadium are not available for sale, and the team provided us
detailed information on such allocations.
•The price database provides the season and single-game ticket prices for each price point.
In the 2018 season, the team introduced three game categories, each having two games. For
anonymity, we use names A1, A2, B1, B2, C 1, and C2 for these games where Agames are the
Electronic copy available at: https://ssrn.com/abstract=3447206
10 Arslan et al.: Data-Driven Sports Ticket Pricing
Table 2 Customer Segmentation.
Channel Segment Information Restriction
Season tickets 1 Big donors, no annual gift Preferred or lower prime zone
2 Public, annual gift None
3 Employees, no annual gift End zone, max. of 2 tickets
Single-game tickets 4 Donors, no entry fee None
5 Alumni, entry fee None
6 Parents, no entry fee Three selected games only
Table 3 Summary Statistics for Segments.
Season ticket channel
Segment 1 (N=343) Segment 2 (N=3878) Segment 3 (N=2149)
Mean SD Min Max Mean SD Min Max Mean SD Min Max
Price 1146.8 180.1 833.3 1250.0 601.1 165.3 333.3 1250.0 442.2 41.8 333.3 458.3
Quantity 4.45 1.73 1 8 2.60 1.22 1 8 1.99 0.10 1 2
Single-game ticket channel
Segment 4 (N=6977) Segment 5 (N=9681) Segment 6 (N=1456)
Mean SD Min Max Mean SD Min Max Mean SD Min Max
Games 2.62 1.60 1 6 1.96 1.29 1 6 1.28 0.45 1 2
Price 119.2 38.6 37.5 250.0 95.6 32.3 37.5 208.3 76.3 20.8 37.5 133.3
Quantity 3.75 1.86 1 12 2.66 1.02 1 8 3.31 0.92 1 4
Note. Prices are scaled as discussed under Table 1. A few observations (e.g., high number of tickets due to a small
number of special deals.) are excluded. For price and quantity for the single-game ticket channel segments (i.e.,
Segment 4-6), the average of transaction-level data is provided.
most popular and therefore the most expensive. The last three columns of Table 1 provide the
relative single-game ticket prices for each price point across game categories.
•The transaction database stores the information on each transaction in both channels, includ-
ing a unique identification number for each customer, number of seats purchased, seat location,
price paid per ticket, and opponent team for single-game tickets.
2.3. Segmentation
It is likely that the customers who purchased tickets in different channels are heterogeneous in
terms of their preferences. Several categorization schemes for single-game ticket channels have
been already mentioned in the literature. Cui et al. (2014) split customers into two groups in
their modelling framework, die-hard fans who plan well in advance and busy professionals who
purchase tickets at the last minute. Based on their estimation results, Xu et al. (2019) suggest
a segmentation of loyal fans (less price- and performance-sensitive), fair-weather fans (less price-
but more performance-sensitive, season-ticket targets (more price- but less performance-sensitive),
and value seekers (price- and performance-sensitive).
In our setting, the majority of purchases (i.e., season ticket sales and pre-sale) take place before
the start of the season, and customers are assigned to selection times for tickets, therefore team
performance and arrival time are not useful for customer segmentation. On the other hand, the
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 11
customer base is heterogeneous in terms of their tastes. For example, big donors may be price
insensitive and may just want to have the best experience for the games they go to. By contrast, a
die-hard fan may only care about supporting her team in the stadium. Therefore, we use the priority
program data available to us, which provides detailed information such as donations, connection
to school (e.g., alumni), length of the connection, etc. We identify six segments (three within each
channel) under the guidance of the team management. Table 2 provides detailed information on
the characteristics of customers and the restrictions that apply for each segment. Table 3 provides
the summary statistics for each segment. One can observe that there are significant differences
between different segments, but also within the same segment. Therefore, in this paper we aim to
develop a framework that not only takes the differences between these segments into account, but
also uses customer heterogeneity within segments in our pricing tool.
3. Choice Modeling
In this section, we study customers’ ticket purchase decisions in two different sales channels. The
first channel is season ticket sales, where each customer iin customer segment kwith quantity
allocation qichooses a seat category jwhich grants her access for all home games. The second
channel is the single-game ticket sales, where each customer tof segment kchooses a seat category
j(or no-purchase, j= 0) for a home game g.7
3.1. Season Ticket Sales: the Multinomial Logit (MNL) Model
First, we discuss the purchase behavior for season ticket sales. The season ticket price for seat
category jis denoted by rS
j. The customer’s problem, given she completed an application and
decided to purchase season tickets already, is to choose a seat category that maximizes her overall
utility, denoted by US
ij , among all seat categories J. This utility may be different than the sum
of utilities from individual games, that is PG
g=1 Ug
ij , because a season ticket can be evaluated as a
package with additional benefits discussed earlier. Therefore, a customer ibelonging to segment k
gains the following utility from purchasing a season ticket from seat category j
US
ij =Xjβk+Ziδjk +rS
jγk+ijk ,(1)
where βkis the parameter vector of seat category attributes Xjfor a seat category j,δjk is
the parameter vector that captures differences in seat category valuations according to customer
attributes Zi,γkis the price sensitivity parameter for a given segment k, and ijk is the customer
i’s idiosyncratic utility term for the seat category j.
Since the sales of season tickets take place early in the year when all seat categories are open for
sale, the team did not historically have any issues with selection feasibility in this channel, even for
Electronic copy available at: https://ssrn.com/abstract=3447206
12 Arslan et al.: Data-Driven Sports Ticket Pricing
the most popular seat categories. Therefore, a customer i’s utility-maximizing seat category choice
for season tickets is
j∗= arg max
jUS
ij .(2)
Under this linear utility structure, we can estimate the parameters of the utility function for
each segment. Assume the idiosyncratic utility terms (i.e., ijk ’s) are i.i.d. Gumbel (or extreme
value type 1) random variables as shown in Train (2009) under the MNL framework. Then, the
probability for customer iof segment kchoosing the seat category jfor a season ticket is
Pijk (θk) = exp(Xjβk+Ziδjk +rS
jγk)
PJ
j0=1 exp(Xj0βk+Ziδj0k+rS
j0γk),
where θk:= (βk, δjk , γk) represents the parameters to be estimated for each segment. We can write
the log-likelihood function for the observations in the data set as follows:
LL(θk) =
N
X
i=1
J
X
j=1
yij log(Pij (θk)),(3)
where yij = 1 if customer ichooses the seat category j;yij = 0 otherwise. We adopt the clas-
sical Maximum Likelihood Estimation (MLE) procedure and estimate the model parameters by
maximizing the log-likelihood function LL(θk) to derive ˆ
θk, i.e.,
ˆ
θk= arg max
θ∈ΘLL(θk).(4)
3.2. Single-Game Tickets Sales: the Mixed Multinomial Logit (MMNL) Model
A customer’s utility of purchasing a single-game ticket for game galso depends on the game
characteristics (e.g., opponent characteristics, date and time of the game, etc.) in addition to the
relevant attributes for season tickets. Assuming that a single-game ticket price for seat category j
for a game gis denoted by rg
j, a customer tbelonging to segment kgains the following utility from
purchasing a single-game ticket from seat category jfor game g
Ug
tj =Xj˜
βk+Zt˜
δjk +αg
k+rg
j˜γk+g
tjk ,(5)
where ˜
βkis the parameter vector of seat category attributes Xjfor a seat category j,8˜
δjk is
the parameter vector that captures differences in seat category valuations according to customer
attributes Zt,αg
kis the parameter vector of game-fixed effects, ˜γkis the price sensitivity parameter
for a given segment k, and g
tjk is the customer t’s idiosyncratic utility term for the seat category j
at game g. Game-fixed effects allow us to capture the effect of owning the right to watch the game
live from the stadium. Note that the no-purchase alternative, denoted by j= 0, is also a possible
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 13
option for customers in this channel. Without loss of generality, we assume that the deterministic
part of its utility is normalized to 0.
Estimating the parameters of the utility function under the standard MNL framework is straight-
forward, but the model has several limitations: First, this strategy does not allow random taste
variation between individuals (e.g., different price sensitivities). Second, its substitution pattern is
restricted by the independence of irrelevant alternatives (IIA) property, and thus cannot accom-
modate different substitution patterns across seat category options. Third, the vector of the unob-
servable parts of a customer’s utility, tjk =1
tjk ,...,G
tjk , can be correlated for all Ggames,
because a customer may have similar valuations for the same seats over different games. In order to
overcome these limitations, we adopt the mixed multinomial logit (MMNL) that can approximate
any discrete choice model under the random utility maximization framework as closely as desired;
see McFadden and Train (2000) for details. We follow the MMNL framework in Train (2009) and
rewrite the customer t’s utility from purchasing a single-game ticket from seat category jfor game
gas
Ug
tj =Xj˜
βkt +Zt˜
δjkt +αg
kt +rg
j˜γkt +g
tjk ,(6)
where ˜
βkt,˜
δjkt ,αg
kt, and ˜γkt are now individual-specific (i.e., varying over customers, but being con-
stant for each customer) preference parameters which allow random taste variation and correlation
in observed factors over a customer’s multiple decisions. Unlike the MNL model, the MMNL model
is not restricted by the IIA property, and therefore it allows more flexible substitution patterns
among alternatives.
In order to provide advantages to the fans who contribute more to their athletic programs, most
top football programs assign fan-specific selection times for single-game ticket purchases using
well-defined priority programs.9Selection time assignment creates a controlled sequence of arrivals
to the sales system, so customers see different options, due to the limited capacity of seat categories
(see Figure 3 for an example user interface for seat selection). In this setting, a standard choice
model would not capture the difference in available seat category options depending on purchase
time.
Therefore, we need to incorporate the feasible choice sets for a customer tfor game gat the
time of the purchase. In particular, the utility-maximizing seat category choice of customer tfor
the game gis given by
j∗
g= arg max
j∈Fg
t
Ug
tj ,(7)
where Fg
tis the set of feasible seat categories for the game gat the time of customer t’s decision.
Electronic copy available at: https://ssrn.com/abstract=3447206
14 Arslan et al.: Data-Driven Sports Ticket Pricing
Figure 3 Available seats at a customer’s selection time.
Note. Left panel shows the initial screen when a customer can see the available (in green) seat categories. If she
clicks on one of them, she will be able to see the right panel with available (in green) seats.
Now consider a vector of seat categories, where each element represents a choice for a different
game, ψ= [j1, j2,...,jG]. Denote ϕkt = ( ˜
βkt,˜
δjkt ,˜αjkt ,˜γk t) as the parameters to be estimated for each
segment. Note that the ϕkt varies over customers in each segment with a density f(ϕ). Conditional
on ϕkt and feasible seat categories Fg
t, the probability that the customer tchooses a specific vector
ψis
Ltψ(ϕk t) =
G
Y
g=1
exp(Xjg˜
βkt +Zt˜
δjgkt +αg
kt +pk
jg˜γkt )
1 + Pj0∈Fg
texp(Xj0
g˜
βkt +Zt˜
δj0
gkt +αg
kt +pk
j0
g˜γkt ),(8)
since the error term g
tjk ’s are independent across games. The unconditional choice probability is
the integral of this product over all values ϕas follows:
Ptψ =ZLtψ(ϕ)f(ϕ)dϕ, (9)
where f(ϕ) is specified to be a Normal density function with mean µϕand covariance Wϕ. Note that
this is another difference from the model by Li et al. (2019), which uses a fixed set of parameters
for each segment.
The estimation follows the same principle as shown in Equations (3) and (4). Due to the high
dimensionality of the integration, we adopt the Maximum Simulated Likelihood Estimation pro-
cedure, as its efficiency has been well recognized (see, e.g., McFadden and Train 2000).
4. Estimation
4.1. Model Estimation and Results
Based on the empirical models described in §3 and the variables in Table 4, we use the mlogit
package in R to estimate the choice models for each segment within each channel. Table 5 summa-
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 15
Table 4 List of Variables.
Category Name Description
Seat category
attributes Distance Distance to the field (0=field, 1=lower bowl, 2=upper
bowl)
Direction Direction relative to the field (West is the base
category)
Customer
attributes Segment Segment a customer belongs to (see §2.3 for details)
ST Quantity Number of season tickets a customer purchased, can be
limited by the team for certain segments
SGT Quantity
Number of single-game tickets a customer purchased
for a specific game, can be limited by the team for
certain segments
Price ST Price Price of a season ticket for a seat category
SGT Price Price of a single-game ticket for a seat category and
game
Game effects* A1,A2,B1,B2,C1,C2 Indicator for the game to be purchased
Availability* 400 SeatsLeft A dummy variable if less than 400 available seats
remain in a seat category for a game
200 SeatsLeft A dummy variable if less than 200 available seats
remain in a seat category for a game
100 SeatsLeft A dummy variable if less than 100 available seats
remain in a seat category for a game
Note. ∗denotes the variable categories that only apply to single-game ticket channel models.
Table 5 Parameter Estimates for Season Ticket Segments.
Segment 1 Segment 2 Segment 3
Coef. SE Coef. SE Coef. SE
ST Price 0.2077∗∗∗ (0.0663) -0.6645∗∗∗ (0.0464) 1.4086∗∗ (0.5301)
Distance - -1.2552∗∗∗ (0.1131) -
Direction XXX
Quantity XXX
N 343 3878 2149
LL -404 -10576 -2251
Note. Since Segment 1 and Segment 3 can only select from two specific price points
in the stadium, ST Price and Distance are perfectly correlated for these segments, and
coefficients for them cannot be identified simultaneously.
rizes the parameter estimates under the MNL model for the segments in the season-ticket channel,
while Table 6 presents the parameter estimates under the MMNL model for the segments in the
single-game ticket channel. Note that we have a variance-covariance matrix estimated for price and
distance variables, in addition to the estimates of their coefficients for these segments. We now
discuss the estimation results and the potential implications on the ticket pricing management.
Price sensitivities. We have several important observations regarding the price sensitivities.
First, the estimated price coefficients for Segments 1 and 3 are positive. Segment 1 is for big donors
who have direct access to season tickets in the two most expensive categories without paying any
additional contribution (e.g., annual gifts for season tickets). Segment 3 is for the faculty and staff,
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16 Arslan et al.: Data-Driven Sports Ticket Pricing
Table 6 Parameter Estimates for Single-Game Ticket Segments.
Segment 4 Segment 5 Segment 6
Coef. SE Coef. SE Coef. SE
SGT Price -1.2810∗∗∗ 0.0641 -2.5510∗∗∗ 0.0790 -4.1024∗∗∗ 0.5206
Distance -0.4546∗∗∗ 0.0514 -0.3003∗∗∗ 0.0649 -1.0605∗∗ 0.3470
var(SGT Price) 2.5407∗∗∗ 0.1155 2.0558∗∗∗ 0.0933 8.4892∗∗∗ 1.7361
var(Distance) 1.8380∗∗∗ 0.0753 1.4191∗∗∗ 0.0558 2.6356∗∗∗ 0.5470
cov(SGT Price,Distance) 2.0845∗∗∗ 0.0901 1.6950∗∗∗ 0.0703 4.7301∗∗∗ 0.9626
Direction X X X
Quantity X X X
Seat Availability X X X
Game Effects X X X
Seat Category Feasibility X X X
N 6977 9679 1456
LL -62689 -73747 -6790.7
Note. The variance-covariance matrix for SGT P rice and Distance coefficients is specified to be a Nor-
mal density function. Direction- and game-fixed can be found in Figure 4. Seat availability coefficients are
provided in Table 7.
who do not pay any contribution to access season tickets in these two cheapest categories. Since
these two segments can only select from two specific price points in the stadium, the ST Price and
Distance variables are perfectly correlated for these segments, and the coefficients for them can-
not be identified simultaneously. Therefore, the positive sign of the price sensitivities here implies
only that these customers are interested in the best alternatives available to them at the given
prices.10 This indicates opportunities for revenue improvement regardless of the small number of
these customers.
Second, the customers in the single-game ticket channel significantly differ in their price sensitiv-
ities not only across different segments, but also within the same segment. For example, the price
coefficient estimate for Segment 4 is -1.2810 (p < 0.001), but the results show a variance of 2.5407
(p < 0.001), which suggests that the price sensitivity is heterogeneous within the same segment.
The high variances (relative to the means) are consistent with our practical observations that some
customers (e.g., the die hard fans) are not sensitive to price in the sports market.
Direction effects. The team currently uses identical prices for seat categories located in symmetric
locations lying in different directions (e.g., North and South end zones). Using direction-fixed effects
allows us to understand the customers’ preference for directional orientation to the field. Figure 4a
demonstrates the direction-fixed effects by segment.
Our results show that customers in each segment prefer West to East, and North to South. This
is consistent with common-sense expectations: Sitting West prevents facing the setting sun and
also helps to be closer to the home team’s sideline. Sitting North provides a direct view of the
videoboard that is located above the South end of the stadium.
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Arslan et al.: Data-Driven Sports Ticket Pricing 17
Figure 4 Direction- and Game-Fixed Effects.
A1
A1
A1*
A2
A2
A2*
B1
B1
B1*
B2 B2
B2
C1
C1
C1
C2 C2 C2
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
Segment 4 Segment 5 Segment 6
Game Fixed Effects
E
E
E
E
E
S*
S
S
S
S
N*
N
N
N
N
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Segment 1 Segment 2 Segment 4 Segment 5 Segment 6
Direction Fixed Effects
Note. (a) The reference direction is West. North and South seats are not available for Segment 1, therefore only East
fixed effect is presented. East and West are not available for Segment 3, therefore it is not presented in the figure.
For this segment, North fixed effect (reference direction is South) is 0.3087, parallel to other segments.
(b) A1, A2, and B1 games are not available for Segment 6.
Game effects. As mentioned in §2.2, the team introduced three game categories, each having two
games (A1, A2, B1, B 2, C1, and C2). Figure 4b provides the game-fixed effects by segment.11 Our
estimation results reveal an interesting phenomenon: Although customers value the games in the
same order as the teams’ assignment of value buckets, the A1 game was valued much higher than
the A2 game. We believe that this is due to two major factors: The A1 game was also the first
home game of the season, whereas the A2 game took place late in the season and there is more
uncertainty about the conditions as weather worsens and as the season progresses. These results
suggest that game categorization should have been implemented very carefully. We will discuss a
pricing policy with a better game categorization in §6.3.
Availability effects. Another interesting observation is related to the effects of remaining inven-
tory in a seat category. Table 7 provides the coefficient estimates for seat-availability variables.
Our analysis shows that customers become less likely to choose a seat category as the remaining
inventory decreases beyond a certain point. This result contradicts the network, herding, synergis-
tic, scarcity, and reference effects discussed in §1.1. One potential reason is the heterogeneity of
the seats in a given seat category which are nonetheless priced the same. Since the better seats
within a seat category are chosen first, the remaining inventory often includes inferior seats. For
example, a customer choosing between lower and upper end zone may be inclined to buy a ticket
in the upper end zone when only high-numbered row seats in the lower bowl remain available. We
refer to this as the periphery effect.
Another explanation may be the unavailability of consecutive seats for the fans who want to
go a the game together and therefore are particularly interested in a large number of tickets.
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18 Arslan et al.: Data-Driven Sports Ticket Pricing
Table 7 Estimates for Seat Availability Coefficients.
Segment 4 Segment 5 Segment 6
Coef. SE Coef. SE Coef. SE
400 SeatsLeft -2.6683∗∗∗ 0.0869 -1.7431∗∗∗ 0.0801 0.4853 0.3693
200 SeatsLeft -2.4276∗∗∗ 0.0571 -2.5102∗∗∗ 0.0519 -0.8995∗∗∗ 0.2011
100 SeatsLeft -2.4608∗∗∗ 0.0360 -1.5814∗∗∗ 0.0318 -0.5606∗∗∗ 0.1080
Note. The effects presented in the table are inclusive (e.g., 400 SeatsLeft=1 if
200 SeatsLeft=1 ).
Table 8 Estimates for Quantity and Availability Interaction.
Segment 4 Segment 5 Segment 6
Coef. SE Coef. SE Coef. SE
SGT Quantity ×100 SeatsLeft -0.6597∗∗∗ 0.0455 -1.1684∗∗∗ 0.0536 -0.1450 0.2667
In order to test this hypothesis, we rerun our single-game ticket channel model with an interac-
tion term between the quantity purchased (SGT Quantity) and our most limited availability term
(100 SeatsLeft). The associated coefficient estimates for this interaction term are given in Table 8.
Our results show that as the purchased ticket quantity for the customers in Segment 4 or Segment
5 increases, they become less likely to choose a seat category with only a small number of available
seats (e.g., less than 100 seats). This finding may be attributable to customers’ desire to find a
large number of seats together, which is consistent with our practical observations. As shown in
Table 3, Segment 6 can buy up to 4 tickets, therefore it is expected to have an insignificant estimate
for this segment.
4.2. Validation of MMNLseg
f
As mentioned in §3.2, our single-game ticket demand model, denoted by MMNLseg
f, takes into
account a variety of heterogeneity such as (i) different segments, (ii) correlation between an indi-
vidual’s decisions for different games, (iii) feasible choice sets, and (iv) the remaining inventory.
We now present the empirical results on the model fitting and prediction accuracy relative to the
traditional models.
Model fitting. In order to demonstrate the improvement in the model fitting, we compare
MMNLseg
fwith the discrete-mixed MNL model discussed in Li et al. (2019), denoted by MNLseg,
where a traditional MNL is used for each segment. Table 9 summarizes the results of our com-
parative study for each segment. Larger McFadden’s R2’s for each segment suggest that MMNLseg
f
offers a better model fit. Moreover, we observe that the MMNLseg
fperforms the best in terms of
AIC and BIC model selection criteria, indicated by smaller figures.
Prediction accuracy. In order to quantify the improvement in the performance of prediction, we
first compare MMNLseg
fwith (i) traditional MNL where segmentation is not used, and (ii) MNLseg
discussed earlier through a twofold cross-validation for each segment. Since each customer makes
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Arslan et al.: Data-Driven Sports Ticket Pricing 19
Table 9 Model Fit Comparison.
Segment 4 Segment 5 Segment 6
MNLseg MMNLseg
fMNLseg MMNLseg
fMNLseg MMNLseg
f
LL -74443 -62689 -81938 -73747 -6879 -6790
R239.98% 49.48% 51.63% 56.46% 46.06% 46.76%
AIC 149012 125456 163940 147569 13817 13653
BIC 149298 125793 164227 147910 14002 13882
Table 10 Cross-Validation Results.
Segment 4 Segment 5 Segment 6
MNL MNLseg MMNLseg
fMNL MNLseg MMNLseg
fMNL MNLseg MMNLseg
f
MAE 1.34% 1.03% 0.98% 1.15% 0.53% 0.47% 2.16% 0.73% 0.60%
(26.66%) (4.35%) (59.43%) (12.08%) (72.19%) (18.17%)
SMAPE 56.92% 56.89% 51.52% 69.56% 35.77% 36.27% 86.47% 49.21% 45.84%
(9.48%) (9.43%) (47.85%) (-1.39%) (46.98%) (6.83%)
MAPE0.5 2.31% 1.85% 1.75% 2.02% 1.01% 0.89% 3.47% 1.38% 1.13%
(24.03%) (5.46%) (55.81%) (12.05%) (67.60%) (18.23%)
MAPEL38.01% 44.23% 38.59% 31.95% 21.69% 17.56% 63.11% 19.74% 16.05%
(-1.54%) (12.75%) (45.04%) (19.04%) (74.57%) (18.71%)
Note. Improvements versus benchmarks are given in the parentheses under each benchmark.
purchasing decisions for six games, our customers in each segment are randomly partitioned into
two subsamples of roughly equal size: The first subsample is used to train the model (i.e., estimate
parameters for different models) and the second subsample is retained as the validation data to
test the model (i.e., compare the prediction accuracy of different models).
In the validation data, we particularly focus on the difference between predicted and observed
choice probabilities. We use four metrics to compare the three aforementioned models: the MAE
(Mean Absolute Error), SMAPE (Symmetric Mean Absolute Percentage Error, Makridakis 1993),
MAPE0.5 (an adjusted Mean Absolute Percentage Error where 0.5 is added into the denominator
in the percentage error calculations to deal with undefined instances; see, e.g., Jagabathula et al.
2019), and MAPEL(an adjusted Mean Absolute Percentage Error where only original choice prob-
abilities greater than 5% are considered after the exclusion of the no-purchase probability). Table
10 summarizes the cross-validation results for these models. Note that our results illustrate the
significant importance of segmentation (i.e., MNLseg performs much better than MNL). Moreover,
the MMNLseg
fperforms exceptionally well compared to the benchmarks in terms of the prediction
accuracy in the validation data.
This first analysis considers the overall choice probabilities. We next focus on game-by-game
choice probabilities and compare MMNLseg
fand MNLseg. We use the same four metrics here. The top
panel of Table 11 reports the average of these game-by-game calculated metrics and improvement
for Segment 5. In addition, we calculate the APE (Absolute Percentage Error) for the no-purchase
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20 Arslan et al.: Data-Driven Sports Ticket Pricing
Table 11 Detailed Comparison for Segment 5.
MNLseg MMNLseg
fImprovement
MAE 0.94% 0.75% 20.45%
SMAPE 74.14% 59.39% 19.89%
MAPE0.5 1.77% 1.41% 20.53%
MAPEL36.60% 33.82% 7.61%
APEno-purchase 0.68% 0.51% 24.26%
APErevenue 18.48% 15.58% 15.68%
Note. The figures in this table are based on the average of
game-by-game metrics.
probabilities and revenues, and present these in the bottom panel of Table 11. Our results show that
MMNLseg
foutperforms other models not only in aggregate, but also at the game-level performance.
We provide detailed game-level metrics in Table 13 in Appendix A.
4.3. Customer Ticket Quantity Decision
In our setting regarding the ticket sales by the team, fans have to submit an application for a
specific number of tickets and the team may limit the number of tickets that a fan can buy, so the
quantity is not an endogenous choice, which is different from the consumer-goods. Nevertheless,
the quantity is treated as a customer attribute captured in Zifor season ticket and Ztfor single-
game ticket models. This variable enables us to estimate the effects of the fans’ ticket quantity on
seat selection, as well as on the decision on whether or not go to a game in the single-game ticket
market). For example, we find that fans who request a large number of tickets in Segment 4 (big
donors) are more likely to choose the most expensive seat categories while fans with larger demands
in Segment 6 (parents) are more likely to choose the cheaper seat categories. Although these results
are not directly connected to the price sensitivities, they show that more price-sensitive fans (e.g.,
Segment 6 compared to Segment 4) are even more interested in cheaper seat categories as they
request more tickets. See Figure 7a in Appendix B for the coefficients estimates for ticket quantity.
Although ticket quantity is not an endogenous decision variable for a customer in our current
setting for college football tickets, there may be other scenarios where it is appropriate to treat the
purchase quantity as a decision variable for customers. In the marketing literature, there is prior
art that discusses how to jointly estimate both brand choice and quantity decisions. Krishnamurthi
and Raj (1988) develop a framework to estimate an MNL (for choice) and OLS (for quantity)
jointly. Chiang (1991) further incorporates the no-purchase option and a budget constraint into this
model. Chintagunta (1993) replaces the OLS with an estimation strategy that uses indirect utility
functions through Roy’s identity and accounts for the unobserved heterogeneity. Although sports
tickets are not regular consumer goods, ticket quantities can also be incorporated into customer
choices. For example, Major League Baseball teams play 81 home games each season and most of
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Arslan et al.: Data-Driven Sports Ticket Pricing 21
the tickets are sold directly to the public, unlike the college football tickets where pre-applications
are required. In a recent study, Xu et al. (2019) study the dynamic pricing strategy of an MLB
team and use a negative binomial model for the number of purchased tickets, and the estimation
is independent of customers’ arrivals and seat choices.
Interestingly as shown in Figure 7b in Appendix B, fans often buy an even number of tickets for
sport events. In these settings, we believe that the OLS and Negative Binomial models used in the
previous literature may not work well. Therefore, we suggest a multinomial choice model where
the maximum number of tickets may be limited by the sports organization. One can add customer
characteristics, game characteristics, some aggregate-level price variables, etc. as predictors in this
model. Due to potential censoring issues, it may be a good strategy to include an indicator for
the maximum number of tickets. In such models, a joint estimation would be possible, following a
structure similar to those in the aforementioned marketing papers.
5. Price Optimization
As mentioned in §2.1, college football teams often estimate the market size fairly well for each game
based on the application process for season tickets and pre-sale of single-game tickets. Therefore,
our estimation module primarily focuses on the seat selection decision for both channels, and also
on whether to purchase a ticket (or not) in the single-game ticket channel, two important factors
to be considered in the optimization module.
In this section, we first provide details of our setting and then formulate the optimization
problem. Due to the complexity of the optimization problem, we propose an expectation-based
optimization algorithm, because its efficiency and performance have been well documented in the
literature (see, e.g., Jasin and Kumar 2012).
5.1. Model Setting
We consider the ticket price optimization problem for a sports team that plays Ghome games for
a regular season. Its stadium is divided into Jseat categories; each seat category jhas a starting
capacity Cjg for game g12, a season ticket price rj, and a single game price rjg , where g∈ {1,2, .., G}
and j∈ {1,2, .., J }. For notational convenience, let Cbe a J×Gmatrix with starting capacities
at each seat category jfor game g.
There are Ncustomers in the season ticket channel, arriving simultaneously. Each customer
iin this channel requests qitickets in the season ticket application. In addition, let Pij denote
the choice probability of customer ifor a given seat category j, determined by the segment the
customer belongs to. For ease of exposition, let Qibe a G×Gdiagonal matrix of identical ticket
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22 Arslan et al.: Data-Driven Sports Ticket Pricing
quantities for each customer ifor each game, and Pibe a J×Gmatrix of seat category choice
probabilities Pij with identical columns.
There are Tcustomers in the single-game ticket channel, arriving sequentially based on the
selection time assigned by the team. The selection time is indexed backwards, e.g., t=Tis the
first customer in the arrival sequence. Each customer tin this channel requests the ticket quantity
of qtg for each game if she chooses to go. The reason for game-specific ticket quantities is that
some games have quantity restrictions imposed by the team due to high demand.13 Ptg(j) denotes
the probability of a customer tchoosing seat category jfor game g, which also depends on the
segment that the customer belongs to. Each customer in the single-game ticket channel makes total
of Gchoices, i.e., one choice per game. When we include the no-purchase option, there are in total
(J+ 1)Gpossible options that a customer can choose. Again, for notational brevity, let:
•Qtbe a G×Gdiagonal matrix of ticket quantities for customer tfor each game;
•ψ= [j1, j2,...,jG]∈Ψ be the length Gvector of seat categories chosen by customer tfor each
game;
•Ltψ be the probability of each possible vector ψ, which can be written as QG
g=1 Ptg(ψ);
•Eψbe a J×Gmatrix which maps ψ, i.e., has all zeros except for a single 1 value for the seat
category jchosen for game g.
5.2. Formulation of the Optimization Problem
Given the starting inventory C, the price optimization problem for multiple games with heteroge-
neous customers in different channels can be formulated as follows:
V(C) = max
rs,RN
X
i=1
J
X
j=1
Pij qirj+VT(C0),(10)
where C0denotes the inventory of all seat categories in each game that remains after the season
ticket sales. The first term PN
i=1 PJ
j=1 Pij qirjaccounts for the total revenue from season ticket
customers, who arrive early and usually do not encounter any sold-out seat categories, so the
deterministic approximation is suitable in this price optimization. We use a dynamic program
to compute the total revenue from all single-game ticket customers for all games, so we round
the expected remaining inventories to integers for computational simplicity, i.e., C0=round{C−
PiQi}.
In particular, the second term VT(C0) computes the total revenue of single game customers who
arrive sequentially after season ticket customers, and may experience sold-out seat categories upon
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Arslan et al.: Data-Driven Sports Ticket Pricing 23
arrival. We use the following dynamic program to approximate the total expected revenue from
the remaining seats for all categories in all the home games:
Vt(X) =
G
X
g=1
J
X
j=1
Ptg(j)qtg rj g +X
ψ
Ltψ(X)Vt−1(X−EψQt),(11)
where the first term PG
g=1 PJ
j=1 Ptg(j)qtg rj g accounts for the expected revenue from the single-
game customer t, and the second term PψLtψ(X)Vt−1(X−EψQt) accounts for the expected
revenue for the remaining inventory available to all customers who will arrive in period t−1
or later. The choice probability Ltψ(X) changes based on the segment the customer belongs to,
but also reflects availability effects, therefore it is inventory-dependent. The boundary conditions
are Vt(X) = −∞ for any xjg <0 and V0(X) = 0 for any X≥0. This dynamic program (11) is
computationally intensive given the state space and path of choice probabilities,14 therefore we
further employ an expectation-based approximation and replace the second term with Vt−1(E[X−
EψQt]).
Since the optimization problem does not exhibit the desired structure, e.g., the convexity, we
develop an optimization algorithm which uses the Nelder and Mead (1965) method to search for
the optimal prices that maximize the expected revenue function subject to some constraints, which
is implemented in the constrOptim package in R. A sketch of this algorithm can be found in
Appendix C. The Nelder-Mead method is known to be relatively slow, but it performs remarkably
well for this particular data set. Moreover, our extensive simulation study on the accuracy of the
expectation-based algorithm shows that the algorithm always returns a near optimal solution in
a timely manner: The difference between the expected revenues calculated by the algorithm and
by the simulation study is consistently less than 0.4%. The detailed discussion on the simulation
study is relegated to §6.5.
6. Insights based on the Optimization Results
In this section, we use the proposed price optimization tool to calculate the expected revenues for
several scenarios, and thus quantify the impact of: (i) adding variable pricing over tiered pricing; (ii)
optimizing prices for the current implementation; (iii) adjusting the number of games in the game
categories; and (iv) using an asymmetric pricing strategy. In our analyses, we treat the expected
revenue at the current prices (using a combination of variable and tiered pricing, denoted as TV)
as the benchmark in the comparison. Due to confidentiality reasons, we will report the percentage
changes in the expected revenues instead of the actual revenue figures.15
Electronic copy available at: https://ssrn.com/abstract=3447206
24 Arslan et al.: Data-Driven Sports Ticket Pricing
6.1. Benefits of Variable Pricing
The team has used tiered pricing for several years before the implementation of variable pricing.
In order to show the benefits of variable pricing, we first calculate the expected revenue of tiered
pricing (denoted as Tiered). For a reasonable comparison with the variable pricing, we use the
average of single-game ticket prices for each seat category as the fixed prices. Our counterfactual
analyses show that the implementation of variable pricing with tiered pricing (TV) could add as
much as 4.93% to the total revenue for the team. Given the differences in the game-fixed effects
presented in §4.1, we and the team management conclude that variable pricing had significant
revenue implications for the team.
6.2. Benefit of Price Optimization
The team made pricing decisions for the 2018 season without employing any data-driven decision-
making methods. Using our price optimization tool, we first compute the optimal prices for a policy
(denoted as TV∗
2-2-2) that combines the variable and tiered pricing with two games in each game
category, and then calculate the expected revenue of this policy.
While computing the optimal prices for a given scenario, we enforce the following constraints
based on the inputs of the team management:
•Season ticket prices cannot increase by more than 10%.
•Season ticket price must be equal to the sum of single-game ticket prices for a given seat (i.e.,
abundle pricing constraint).
•Prices decrease as the distance to the field increases (e.g., lower to upper bowl).
•Prices decrease as the angle of view worsens (e.g., side to corner).
Our counterfactual-based analyses show that the optimized prices could increase the revenues
by as much as 7.62%, which further verifies the crucial importance of price optimization to the
team. In order to understand the sources of this revenue increase, Figure 5 provides a detailed
look at the optimization results, which reveal several important managerial insights for the team
management:
Season tickets. In each category other than the corner seat categories, the optimization algorithm
suggests a price increase of roughly 10% for season tickets. As a result, the revenue for this channel
could increase as much as 7.32%.16 This shows that current season tickets are underpriced, because
their market values are significantly higher.
Single-game tickets. For games A1 and A2, the pricing module suggests an adjustment in prices
that is nearly equivalent to creating a two-tiered pricing policy where preferred, prime, and side
seat categories are priced higher than corner and end seat categories. For games B1 and B2, the
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 25
Figure 5 Game-Level Price and Revenue Changes for TV∗
2-2-2 policy.
-2.5%
3.9%
2.5%
14.3%
24.5%
-4.4%
1.5%
12.9%
18.1%
7.6%
26.1%
31.4%
9.0%
1.9%
-6.1%
8.3%
1.3%
-3.3%
31.8%
2.5%
-2.4%
2.8%
-8.0%
-9.4%
8.3%
14.9%
12.1%
20
70
120
170
220
270
320
123456789123456789123456789
A B C
Price ($)
Game / Seat Category
0%
5%
10%
15%
20%
25%
A1 A2 B1 B2 C1 C2
Rev. Change (%)
Game
Note. A, B, C represent the three game categories. Seat categories are numbered 1 to 9 for each game category in
descending order of prices. Prices are scaled as discussed under Table 1. For each stacked bar, the bottom (dark)
portion shows the actual ticket prices. The top (light) portion shows the change offered by the price optimization
tool. Suggested price drops are shown by dotted squares. The percentage changes are provided for each bar. The inset
provides the percentage game-level revenue changes.
algorithm re-balances the prices and results in revenue improvements of more than 10% for each
game (see the inset in Figure 5). For games C1 and C2, the algorithm suggests a significant increase
(i.e., 32%) in the price of the most expensive seat category and makes several adjustments in other
prices. As with the season ticket prices, we observe that lower corner seat category was overpriced.
In order to quantify the improvement of simultaneously optimizing season and single-game prices,
we also analyze: (i) a policy that optimizes the single-game ticket prices while the season ticket
prices remain unchanged, and (ii) another policy that optimizes the single-game ticket prices with-
out consideration of the season ticket sales, but still allows price changes for the season tickets
through the bundle pricing constraint. These policies improve the total revenues by 1.46% and
7.13% respectively, which further indicates the advantages of our approach.
6.3. Improvement Through Better Game Categorization
The team management used a structure of three game categories, each having two games, to
simplify the single-game ticket selection process. Although they were not originally interested in
changing the number of game categories, our earlier analysis in §4.1 showed that the A1 game was
preferred to the A2 game, which was expected due to the time of the games and the quality of these
two opponents. Based on our discussions with the team management and following the estimated
game-fixed effects, we compute the optimal prices for a policy (denoted as TV∗
1-2-3) when there is
only a single game (i.e., A1) in the top game category, and calculate the expected revenue of this
policy.17
Electronic copy available at: https://ssrn.com/abstract=3447206
26 Arslan et al.: Data-Driven Sports Ticket Pricing
Figure 6 Game-Level Price and Revenue Changes for TV∗
1-2-3 policy.
0%
5%
10%
15%
20%
25%
A1 A2 B1 B2 C1 C2
Rev. Change (%)
Game
-4.9% 1.3%
4.6%
23.5%
27.2% 48.2% 46.1%
32.2%
53.3%
11.9%
37.5% 40.7%
28.7% 44.2%
4.8% 14.5% 27.1%
11.2%
34.2%
21.3%
17.9%
16.9%
2.4%
-6.8%
8.1% 13.8%
18.9%
20
60
100
140
180
220
260
300
123456789123456789123456789
A B C
Price ($)
Game / Seat Category
Note. A, B, C represent the three game categories. Seat categories are numbered 1 to 9 for each game category in
descending order of prices. Prices are scaled as discussed under Table 1. For each stacked bar, the bottom (dark)
portion shows the actual ticket prices. The top (light) portion shows the change offered by the price optimization tool.
The percentage changes are provided for each bar. The inset provides the percentage game-level revenue changes.
Our counterfactual-based analysis shows that changing the game categorization may bring
another 3.59% over the price optimization (i.e., 11.48% revenue increase over the revenue generated
by the original prices used by the team). Figure 6 provides a detailed look at the optimization
results, and reveals the following important managerial insights for team:
Season tickets. Similar to the TV∗
2-2-2, our price optimization algorithm suggests a nearly 10%
increase for the season tickets except for the corner seat categories. The revenue increase in this
channel is only 7.06%, suggesting that the main driver of the significant revenue improvement is
the single-game ticket channel.
Single-game tickets. The price optimization module suggests a price increase for each category
with two exceptions: preferred seat category for A game and lower corner seat category for C games.
This makes practical sense and would be straightforward to implement, because we basically moved
a top category game to the second, and a second category game to the bottom category. For the
A1 game, the optimization algorithm suggests significant price increases (i.e., 20% to 55%) in side
to end seat categories to exploit the high demand for this game. This strategy leads to a revenue
increase nearly 25% (see the inset in Figure 6). For the B1 game, the derived optimal prices are also
significantly higher than the original prices, since now it is in the same bucket with a better game
(i.e., A2), resulting in a revenue increase in low-20% range (see the inset in Figure 6). For games
C1 and C2, although the prices are slightly increased due to the inclusion of game B2 into the
bucket, the optimization algorithm suggests closing the gap between cheap seat categories while
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 27
keeping these accessible for everyone. We note that A2 and B2 games moved down to a lower game
category in this pricing policy. Due to this change, the optimal prices translate into a price decrease
for these games (with an exception of the two most expensive seat categories for the B2 game). For
these two games, the revenue increase is much more limited compared to other games, since the
increase in sales volume barely balances the revenue loss due to the price reduction (see the inset
in Figure 6). Overall, this game categorization re-balances the single-game ticket prices and indeed
improves revenues. Partially inspired by this study, the team ticket management implemented a
policy that is consistent with this price optimization scheme by introducing a similar strategy for
the 2019 season which included only one game in the top game category.
6.4. Improvement Through Asymmetric Pricing
The team currently prices seat categories across from each other identically (e.g., North and South
end zone). However, as mentioned in §4.2, customers value seat categories in the West and North
over the East and South due to factors such as the sun and the videoboard. Therefore, we investigate
a policy (denoted as TV∗
1-2-3(asym)), where the team uses the game categorization with a single
game in the top category and is able to price-differentiate between symmetric seat categories. In
order to make a fair comparison with previous policies, we add a constraint such that the season
ticket average of symmetric seat categories cannot be increased by more than 10%.
Our counterfactual-based analysis shows that this asymmetric pricing may bring 4.00% addi-
tional revenue over the price optimization (i.e., 11.93% revenue increase over the revenue generated
by the original prices used by the team). The optimal prices show that more preferred directions
may be priced at up to a $12 premium for single-game tickets and up to $55 for season tickets.
6.5. Simulation Study
Recall that the optimization algorithm uses an expectation-based approximation where the remain-
ing inventory after a customer’s arrival is calculated as an expectation. On the other hand, realis-
tically, a customer purchases tickets only from a specific seat category, based on individual-specific
and inventory-dependent choice probabilities. Therefore, only inventory for a specific seat category
is affected by a customer’s single-game ticket purchase. In order to evaluate performance of our
optimization algorithm and check the robustness of the improvement figures discussed in previous
subsections, we conduct a simulation study where we replicate the real-world ticket purchasing
process. In these simulations, we reproduce the customers’ arrivals and choices, and dynamically
update the remaining inventories, which generates different trajectories due to the nature of random
choice models.
Electronic copy available at: https://ssrn.com/abstract=3447206
28 Arslan et al.: Data-Driven Sports Ticket Pricing
Table 12 Expected Total Revenues under Different Scenarios.
Pricing Policy Categorization Season Tickets SG Tickets E[∆Ra]E[Ra]−E[RSim
a]
E[RSim
a]E[∆RSim
a]
TV 2-2-2 Current prices Current prices N/A -0.31% N/A
Tiered None Old prices Old prices -4.70% -0.28% -4.73%
TV∗
2-2-2 2-2-2 Up to ↑10% Bundle pricing 7.62% -0.35% 7.67%
TV∗
1-2-3 1-2-3 Up to ↑10% Bundle pricing 11.48% -0.17% 11.33%
TV∗
1-2-3(asym) 1-2-3 Up to ↑10% Bundle pricing 11.93% -0.18% 11.78%
The expected revenues of different policies and their performance compared to benchmark policy
(TV) were calculated by the optimization algorithm (see Table 12 for a summary), denoted E[Ra]
and E[∆Ra] respectively where arepresents a specific policy. We perform 200 simulation runs for
each policy using given prices (i.e., original prices for TV and Tiered, and optimal prices for other
policies), each operating as a facsimile of real-world process, and calculate the expected real-life
revenues E[RSim
a].
In the last two columns of Table 12, we report two important metrics. First, we provide the
percentage difference between E[Ra] and E[RSim
a], and show that our expectation-based approxi-
mation performs exceptionally well. The error in expected revenue calculation is consistently less
than 0.4%. Second, we calculate the performance of each policy against the benchmark policy
(TV) using the E[RSim
a] figures. The percentage change in expected revenues, denoted E[∆RSim
a],
is remarkably close to the numbers E[Ra], which further establishes the robustness of our price
optimization framework.
6.6. Comparison of Optimizations based on MMNLseg
fand MNLseg
In §4.2, we show that the MMNLseg
fmodel exhibits a better model fitting and a more accurate
prediction than the MNLseg. In order to quantify the missed revenue opportunity due to the model
mis-specification in the optimization, we first compute the optimal prices using the parameters
derived from the MNLseg model, then calculate the revenue given by these prices with the assump-
tion that customers make decisions based on MMNLseg model parameters. Our analysis shows that
this would have reduced revenues by 1.93% (1.85% based on simulations) relative to the revenue
achieved by using the MMNLseg
fmodel parameters as presented in §6.2.
7. Concluding Remarks
In this applied research, we have developed a data-driven pricing tool to improve the ticket rev-
enues of a college football team that sells tickets in multiple channels. Because of the potential
heterogeneity of customers within each channel, our tool starts with a segmentation based on the
detailed data on ticket purchase transactions and anonymous customer profiles. Next, the estima-
tion module helps us understand how customers in each segment make their purchase decisions.
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 29
Although this module uses a traditional MNL model for segments in the season ticket channel, it
employs a mixed MNL model for segments in the single-game ticket channel, due to the potential
correlation between the multiple decisions customers make in the single-game ticket channel. We
further modify the model to capture the potential impact of remaining seat availability on cus-
tomer decision-making. Our extensive empirical studies show that the newly proposed modeling
framework performs significantly better than the models extant in the revenue management and
pricing literature. Using the output of the estimation module, the optimization module computes
the optimal prices for different policies under given sets of business constraints. Because the result-
ing revenue maximization problem is intractable due to the magnitude of the state space, we adopt
an expectation-based approximation, whose efficiency and effectiveness have been further verified
by an extensive simulation study.
There are several key takeaways from our study on the event ticket pricing management. First,
we provide evidence that customers differ significantly in their sensitivities to prices, seat locations,
etc., and therefore aggregate-level demand models should be replaced by more sophisticated models
when rich data is available. With the development in analytics tools, tracking customers is currently
much easier than in the past, therefore teams can benefit from focusing on demand models that
use market segmentation, and allow the correlation between customers for different games. Second,
we show that teams can significantly improve their variable and tiered pricing strategies. Equipped
with the newly developed pricing tool, the team management could increase revenue substantially.
However, there are further opportunities to improve ticket pricing management. At this moment,
most professional or college football teams use simple conventions such as putting an equal num-
ber of games into different game categories, or setting the same prices for directionally opposite
seat categories. Our empirical results show that customers value games differently and consider
different factors in their choice process such as the sun’s direction or the videoboard location. Our
optimization results suggest that teams can turn these managerial insights into significant revenue
gains with careful categorization of the games and the use of asymmetric pricing.
Finally, we share an observation that may have important implications for the ticket manage-
ment: Customers are less likely to choose a seat category as its remaining inventory falls below
a certain point, and this negative preference is concentrated in seats bordering other tiers. This
periphery effect may also be strengthened as a large number of tickets are purchased. Meanwhile,
we are also aware of some analytics tools offering the flexibility of only selling the “cheapest avail-
able” or “best available” seats without displaying the seat map, or an option not to let customers
purchase seats if the purchase results in a single empty seat. We believe that these tools may be
Electronic copy available at: https://ssrn.com/abstract=3447206
30 Arslan et al.: Data-Driven Sports Ticket Pricing
beneficial, although the impact of these policies on customers’ decision-making has not been thor-
oughly examined. Nevertheless, it is possible to incorporate these new features into our data-driven
estimation and optimization tool, and therefore more sophisticated analytics tools for event ticket
management can be expected in the near future.
Notes
1Football teams have 5 to 8 home games per season, compared to 81 in Major League Baseball.
2Throughout the text, we refer to our partner as the team.
3Note that the discrete MMNL model assumes homogeneity ex ante within a segment.
4See https://bit.ly/2XfcfKF for an example from Alabama Crimson Tide Football.
5See https://bit.ly/2RMUBwS for an example from Seattle Seahawks.
6See https://bit.ly/2YuDJ0e for an example from University of Michigan’s priority program.
7Due to the significant differences between two channels, we use two different notations (i, t) for customers.
8Seat category attributes, such as the number of seats left, may change from a customer to another. For the models
including such attributes, the notation Xjcould be replaced with Xtj .
9See https://bit.ly/2YuDJ0e for the priority points program of University of Michigan.
10Note that season ticket customers are committed to purchase a ticket and only choose a seat category, as explained
in §3.1.
11In order to make the coefficients for game-fixed effects easy to interpret, we normalized their sum to 0.
12As mentioned in §2.2, the team allocates some of the seats to students, band, away team, etc. and these numbers
may slightly change game to game, resulting in different starting capacities for seat categories.
13For example, a family of four who wants to go to each game together may be restricted to get only two tickets for
some popular games of the season. There are also some segments that simply do not have access to tickets in these
popular games, as explained in §2.3.
14There are (226)Tpossible paths of choice probabilities.
15Note that top College Football teams have ticket revenues above $30 million U.S. dollars per year, according to
USA Today’s NCAA Finances Database (see https://sports.usatoday.com/ncaa/finances/).
16The suggested changes for upper and lower corner are +5.00% and -6.13% respectively.
17We place games A2 and B1 into the second category and the rest to the bottom category, C.
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Arslan et al.: Data-Driven Sports Ticket Pricing 1
Online Supplement
Data-Driven Sports Ticket Pricing for Multiple Sales
Channels with Heterogeneous Customers
In the Online Appendix, we provide additional material for the paper titled “Data-Driven Sports
Ticket Pricing for Multiple Sales Channels with Heterogeneous Customers.”
Appendix A. Game-Level Performance Comparison of MNLseg and
MMNLseg
f
The four metrics (MAE, SMAPE, MAPE0.5, and MAPEL) for each game are calculated using
the difference between predicted and observed choice probabilities for seat categories (including
the no-purchase option). The game-level results confirm that MMNLseg
foutperforms MNLseg in
all metrics. Please note that SMAPE and MAPELare quite sensitive to undefined instances or
outliers, therefore it is not surprising to observe some games where MMNLseg
fis not the better one
for these two metrics.
Table 13 Game-Level Cross-Validation Results for Segment 5.
MAE SMAPE MAPE0.5 MAPEL
Game MNLseg MMNLseg
fMNLseg MMNLseg
fMNLseg MMNLseg
fMNLseg MMNLseg
f
A1 1.44% 1.38% 75.16% 66.82% 2.62% 2.54% 25.02% 29.97%
(4.02%) (11.10%) (2.80%) (-19.79%)
A2 0.98% 0.86% 72.73% 64.06% 1.85% 1.62% 56.21% 36.32%
(11.91%) (11.91%) (12.65%) (35.38%)
B1 1.29% 0.77% 94.41% 58.82% 2.40% 1.42% 41.25% 24.62%
(40.02%) (37.69%) (40.69%) (40.33%)
B2 0.81% 0.39% 77.58% 36.33% 1.52% 0.73% 27.57% 21.18%
(52.09%) (53.17%) (52.20%) (23.17%)
C1 0.70% 0.64% 67.15% 63.92% 1.35% 1.21% 30.43% 46.48%
(9.58%) (4.82%) (10.33%) (-52.75%)
C2 0.46% 0.47% 57.79% 66.42% 0.88% 0.92% 39.14% 44.34%
(-3.91%) (-14.92%) (-4.17%) (-13.29%)
Mean 0.94% 0.75% 74.14% 59.39% 1.77% 1.41% 36.60% 33.82%
Note. Improvements versus benchmark are given in the parentheses.
Electronic copy available at: https://ssrn.com/abstract=3447206
2Arslan et al.: Data-Driven Sports Ticket Pricing
Appendix B. Ticket Quantity Figures
Figure 7 Cross-Segment Analysis for Customer Ticket Quantities.
0%
25%
50%
75%
100%
1 2 3 4 5 6 7 8
Ticket Quantity
S1 S2 S3 S4 S5 S6 Mean
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8 9
Quantity Coefficients
Seat Category
S4 S6
Note. (a) The reference is “not going to the game”. Seat categories are numbered 1 to 9 in descending order of price.
Seat category 1 (Preferred) was not available for Segment 6, and therefore only the coefficient estimate for Segment
4 is presented.
(b) The yellow line shows the percentages for all transactions.
Appendix C. Price Optimization Algorithm with Expectation-Based
Approximation
Step 0 Initialization.
a. Take starting capacities at each category for each game from stadium database.
b. Take individual preference parameters from the estimation module based on the segment
the customer belongs to.
c. Randomly generate price and distance sensitivities of customers in the single-game ticket
channel by using the mean vector and covariance matrix of the joint distribution.
d. Fix all individual preference parameters.
Step 1 Set a price vector including season and single-game ticket prices for each seat category.
Step 2 For each segment in the season ticket channel, predict the sales for the given price vector.
Repeat the following for each customer:
a. Retrieve the quantity and available seat category information for the customer from the
customer database.
b. Calculate choice probabilities for the customer and given price vector.
c. Calculate expected sales for each customer multiplying choice probabilities with the quan-
tity.
Electronic copy available at: https://ssrn.com/abstract=3447206
Arslan et al.: Data-Driven Sports Ticket Pricing 3
d. Update the sales for each seat category by adding the expected sales.
Step 3 For each seat category and game, calculate the expected remaining inventories by subtracting
the expected sales from the starting capacities. Round down the number to nearest integer.
Step 4 For each segment in the single-game ticket channel, predict the sales for each game for the
given price vector. Repeat the following for each customer for each game:
a. Take the quantity and available game information for the customer from the customer
database.
b. Check whether there exists a sold-out seat category. Remove sold-out seat categories from
the choice set of the customer.
c. Calculate choice probabilities for the customer, for the remaining inventory and given
price vector.
d. Calculate expected sales for each customer multiplying choice probabilities with the quan-
tity.
e. Update the sales for each seat category by adding the expected sales.
Step 5 Calculate the total expected revenue by multiplying the price vector and expected total sales
in both channels.
Step 6 Search for the price vector which maximizes the revenues subject to some business constraints.
Electronic copy available at: https://ssrn.com/abstract=3447206