# Puck Pricing : Dynamic Hockey Ticket Price Optimization

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3 THEORY Pricing strategies often require a holistic approach due to the varying business constraints as well as the multitude of methods in deriving an optimal price. For the purposes of this paper, a three phase approach was developed to model dynamic resale ticket pricing. Exploratory Data Analysis Elasticity Models Figure 1. Model Approach Illustration Price Optimization EXPLORATORY DATA ANALYSIS The first phase analyzed the correlations between the input factors and average price/demand. The purpose of this phase was two-fold: To understand the dynamic nature of resale ticket prices To explore the factors that influence resale ticket prices so that they can be controlled for in the price elasticity models ELASTICITY MODELS The second phase determined how sensitive fans are to hockey ticket prices. Elasticity measures the estimated quantity change due to the estimated price change as follows: Elasticity = % Change Quantity % Change Price In order to approximate elasticity, a Hierarchical Bayesian model was built at the opponent level. Hierarchical Bayesian models were chosen due to the low sample size available for each game. Since the sample size is low, Bayesian models will shrink the estimates towards the overall average, thus producing more reliable estimates. These models followed the following equation form: Ln(Quantity) = Elasticity Ln(Price) + μ 1 Var 1 + μ 2 Var μ n Var n Where: Var i = Input variables as mentioned in Table 1 such as Number of tweets u i = Coefficient for Var i n = Number of statistically significant predictive input variables In order to produce reasonable estimates, positive elasticity estimates were truncated to zero. This was supported by research done by Emory Sports Marketing Analytics that suggests the Midwest team for which the data was pulled is among a set of hockey teams that are relatively insensitive to price. Accordingly, the price elasticity would be closer to zero and demand would remain relatively constant regardless of price. PRICE OPTIMIZATION After modeling elasticity, time based input variables such as prior date ticket price were incorporated into a price optimization algorithm. Table 2 outlines the non-linear program used in this problem. Copyright 2015 Deloitte Development LLC. All rights reserved. 3

4 Maximize Daily Games Revenue = New Price i New Quantity i i=1 (1) Subject To: Games (Elasticity i % Price Change i ) Old Quantity i + Old Quantity i i=1 Games New Quantity i = 0 Abs(% Price Change i ) 10% i=1 Games New Quantity i Remaining Tickets i i=1 Table 2. Price Optimization Formulation (2) (3) (4) Where: Old Price i = Yesterdays seat geek price for Game i Old Quantity i = Yesterdays seat geek quantity sold for Game i New Price i = New optimized price for Game i New Quantity i = New estimated quantity sold for Game i Remaining Tickets i = Remaining supply of tickets (listing count) for Game i Elasticity i = Elasticity for Game i (based on the opponent) % Price Change i = % price change for Game i = New Price i Old Price i Old Price i In the above formulation, the new price is a free variable whose value is determined through the optimization. Equation (1) is the objective function which attempts to maximize revenue defined as the new price multiplied by the estimated quantity sold based on the new price. Equations (2) through (4) are constraint functions: Equation (2) estimates the new quantity based on the classic elasticity equation relating % price change to % quantity change Equation (3) ensures that the total price change in any given ticket cannot be farther than 10% from the original price. This constraint tempers any drastic changes to produce reasonable prices Equation (4) constrains the estimated quantity to be less or equal to the available resale ticket supply RESULTS EDA and Elasticity Results A thorough EDA identified the top factors that affected price/quantity for each opponent. As shown in Figure 2, the overall trends over time ( Days Until Game ) suggested that the sales quantity decreased while the average price increased slightly approaching game day. Copyright 2015 Deloitte Development LLC. All rights reserved. 4

5 Figure 2. Average Resale Ticket Price vs. Quantity Sold Over Days Until Game Along with the overall time trends, the EDA showed strong relationships in each of the variable categories. The following graphs show the top variables shown to have a relationship with price and quantity. Franchise Value Time of Game Number of Tweets Month of Day in Ticket Sales Copyright 2015 Deloitte Development LLC. All rights reserved. 5

6 Week of Day in Ticket Sales Playoff Division Figure 3. EDA Results As shown in Figure 3, the covariate data was found to have strong linear and non-linear relationships to price and quantity sold. However, many of these relationships served as proxies for the opponent. Thus, when the price elasticity was modeled at the opponent level these relationships were washed out and captured by the random intercept. Figure 4 shows the fixed variables that were significant in the elasticity models (log of price was used as a random variable): Solutions for Fixed Effects Variables Parameter Estimate Std. Error DF T Value P Value Intercept <.0001 Franchise Value Time of Game Night Indicator Time of Game Early Afternoon Indicator Number of Tweets Month of Day in Ticket Sales <.0001 Week of Day in Ticket Sales <.0001 Days Until Game Playoff West Division Indicator Playoff East Division Indicator <.0001 Playoff Final Indicator Figure 4. Significant Price Elasticity Factors Price Optimization Results The opponent elasticity was then used in an optimization algorithm to derive an optimal price per game. The average price change was \$10.17 for daily incremental expected revenue of \$109K for tickets in the secondary market. Figure 5 displays the optimization results by division opponents. Copyright 2015 Deloitte Development LLC. All rights reserved. 6

7 Volume (Qty Sold) Figure 5. Optimization Results by Division Opponents The optimization results show that although the quantity decreased due to an increase in price, the price increase is large enough to still generate positive incremental revenue. This suggests that the previous prices were priced below the optimal revenue point. It is also interesting to note that the majority of the optimal prices were bounded by the ±10% constraint on maximum price changes. This suggests that most prices were not only priced below the optimal revenue point but that they were drastically under this point. In order to better analyze how far below the optimal point the current sales were, an efficient frontier was developed. Optimizations were run to determine the optimal revenue at varying volumes and plotted to determine the shape of the frontier. Figure 6 displays this graph which clearly shows that the current baseline sales are priced well below an optimal point. 27,000 26,500 26,000 Efficient Frontier Runs Baseline Sales Optimal Sales 25,500 25,000 24,500 24,000 \$2.50M \$2.60M \$2.70M Revenue Figure 6: Efficient Frontier Copyright 2015 Deloitte Development LLC. All rights reserved. 7

8 CONCLUSION This paper highlighted the key drivers of dynamic ticket prices for a hockey team and discussed the methodology to optimize prices using elasticity. It was found that the largest drivers of dynamic ticket prices were days until game, time of game, daily home team tweet count, opponent previous season playoff status, opponent franchise value and the current month/week. After using these factors to determine the price elasticity, an optimization was performed to arrive at an optimal resale ticket price. Many of the optimal prices were bounded by the constraint that tempered price changes to ±10% of the original price. The model suggested that with an average price change of \$10.17, the secondary ticket market could generate \$109K of incremental revenue. This finding of price increase was supported by the fact that the secondary tickets were priced below the optimal resale price point. It should be noted that the expected revenue is based on a single day s worth of incremental revenue in the resale market at the time of this analysis. Future considerations can be made to simulate the benefits over time as game day approaches. Furthermore, since the data was collected at a stadium level, section level insights were impossible to discern. In reality, certain sections may have different price sensitivities and/or be closer to the optimal revenue point resulting in marginal incremental revenue. To implement the use of dynamic pricing, hockey teams may also choose to begin by using a tiered system instead of dynamically pricing each individual ticket. Tickets would have 1 of 3 possible prices, depending on the tier of the game. For example, Saturday night rivalry games would have a value of High, and front row tickets might cost \$200 for all High games. On the other hand, Wednesday afternoon games would have a value of Medium, and front row tickets might cost \$100 for all Medium games. Using a tiered system could provide fans with increased transparency into dynamic pricing methods. While hockey teams may use dynamic pricing as a way to increase revenue, special consideration should also be given to the possibility of not varying ticket prices at the cost of alienating their core fan base. Ultimately, analytics has the potential to play an integral role in hockey but, as with any business, should be applied in the overall context of sound business objectives. Copyright 2015 Deloitte Development LLC. All rights reserved. 8

9 REFERENCES Business Insider. CHART: English Soccer Lags Way Behind Top American Sports In Revenue. Retrieved November 30, Emory Sports Marketing Analytics NHL Fan Quality Analysis. Retrieved January 12, 2015 from ESPN. NHL Standings Retrieved November 30, 2014 from Fan Page List. NHL Teams on Facebook. October Retrieved November 30, 2014 from Fan Page List. NHL Teams on Twitter, March Retrieved November 30, 2014 from Forbes. NHL Team Values, The Business of Hockey. Retrieved November 30, 2014 from NHL.com NHL Awards. Stanley Cup Champions and Finalists. Retrieved November 30, 2014 from SeatGeek. Red Wings Listing Count and Average Price for the season. Retrieved December 20, 2014 from SeatGeek. NHL Dynamic Pricing: A Handful of Teams Trying It this Season. Retrieved January 12, 2015 from Team Marketing Report. NHL Fan Cost Index. October Retrieved November 30, 2014 from Temple University. The importance of sports analytics, both in the game and off the field. Retrieved January 12, 2015 from Topsy. Daily Twitter Posts Counts #redwings. Retrieved December 20, 2014 from USA Today NHL Top 25 Player Salaries. Retrieved November 30, 2014 from Yahoo Sports. Are hockey fans, scalpers ready for 'dynamic' ticket prices? Retrieved January 12, 2015 from Copyright 2015 Deloitte Development LLC. All rights reserved. 9

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