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Marketing Optimization Modeling. Theme Park Case Study. Overview and Disclaimer. The following is a real case study from a regional theme park. Data, labels and brand names have been masked to preserve confidentiality. Situation.

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Marketing Optimization Modeling

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marketing optimization modeling

Marketing Optimization Modeling

Theme Park Case Study


Overview and Disclaimer

  • The following is a real case study from a regional theme park. Data, labels and brand names have been masked to preserve confidentiality.
  • The client is a small regional theme park. It’s core marketing budget is modest, about $2.5M and is spread across outdoor, radio and print advertising. Apart from this, there is a special TV advertising effort in November and December to promote the park’s special Holiday Lights program. In the past year, overall attendance has been flat. Theme parks are very seasonal businesses and are significantly impacted by short-term weather patterns. For the past year, the management of the theme park has been concerned about the impact of rising fuel prices. Their main interest is to be able to understand how to leverage their modest marketing budget for re-igniting attendance growth at the park.
  • Model Architecture
  • Decomposition of Attendance Drivers
  • Marketing Variance Analysis
  • Seasonal and Days-of-Week Effects
  • Sensitivity Analyses
    • Media
    • Gate Price
    • Fuel Prices
    • Weather
  • Impact of Promotional Events
  • Marketing Efficiencies: Revenue per Expenditure
  • Marketing Spending Optimization
  • Media Schedule Optimization
  • Attendance Simulation and Forecast
  • Model Validation

Model Architecture

Outdoor, Print, Radio, Magazines


Maximum Daily Temperature

Weather Temperature



By Day

Sunshine, Precipitation



Promotional Events

Special “Themed” Events and Programs

Weekly average pump price

Auto Fuel Prices

Daily park attendance as affected by media, promotional events, pricing, weather, holidays, and fuel prices.


Month and Day of Week

Gate Price

Attendance paid price

Holiday Lights TV

Annual special holiday event TV adv., Nov 24-Jan 4

decomposition of theme park annual attendance
Decomposition of Theme Park Annual Attendance

For the past year, total media, including Holiday Lights, drove 13.8 percent of total attendance at the park. “Themed” Promotional Events were responsible for driving 2.8 percent of total attendance. The largest contributor was print media, followed by Holiday Lights TV

marketing variance analysis drivers of annual attendance trends oct 06
Marketing Variance Analysis: Drivers of Annual Attendance Trends Oct ‘06

Total park attendance for the year was basically flat at -0.6 percent. Improved performance from Events and Promotions and Print media were the largest positive contributors for the year. Cooler weather, a 25% increase in fuel prices and a -91% reduction in radio advertising were the key negative contributors year-over year.

monthly seasonal effects
Monthly Seasonal Effects

Park attendance is highly seasonal, with peaks occurring in Spring (April) and an uptick in the early Fall (October)

theme park day of the week effect
Theme Park “Day of the Week” Effect

There is a recurring pattern of attendance for days-of-the-week. Attendance peaks on Thursdays due to regular 25% admissions price discounts.

theme park media sensitivities
Theme Park Media Sensitivities

On a dollar-for-dollar basis, radio and print are the most responsive media forms, with magazine and outdoor being considerably less responsive.

Daily Attendance

Monthly Spending $000

gate admissions price and average daily attendance
Gate Admissions Price and Average Daily Attendance

Raising the gate admissions price from $10.00 to $10.50 cost the park about -3.7% in daily attendance

Daily Attendance

Admissions Price

impact of auto fuel prices on theme park daily attendance
Impact of Auto Fuel Prices on Theme Park Daily Attendance

Rising auto fuel prices impact attendance at the park and pose a future risk to increasing attendance. This effect is of slightly greater importance than that of gate prices.

Daily Attendance

Average Pump Price for Regular Self-Serve

temperature weather impact on daily attendance
Temperature & Weather Impact on Daily Attendance

Short-term weather conditions of temperature and precipitation have a profound impact on daily attendance at the Theme Park.

Daily Attendance

Maximum Daily Temperature

impact of special events and holidays on theme park daily attendance
Impact of Special Events and Holidays on Theme Park Daily Attendance

Special park theme events have played an increasingly important role in driving incremental attendance at the park. Easter and Holiday Lights events were of particular importance. Over the past year, average attendance gains from these events more than doubled.

Incremental Daily Attendance

theme park media revenue per dollar of ad investment
Theme Park Media Revenue per Dollar of Ad Investment

Because our models were built from individual media vehicles used, we are able to isolate the effects of each media vehicle. In the past year, 35 percent of the media vehicles generated greater than $1 break-even revenue. This compares unfavorably to the past year, when 65% of the media vehicles generated greater than $1 per dollar investment. Cutting radio advertising in the current year eliminated one of the most efficient and effective media vehicles.


incremental impact on attendance from a 100 increase in media spending
Incremental Impact on Attendance from a $100 increase in Media Spending

Radio and print media stand out as generating the most incremental attendance per dollar investment.

theme park current and optimal marketing investments
Theme Park Current and Optimal Marketing Investments

When comparing the investment in the four media, we see that OOH and Magazines generate proportionately less attendance than their share of spending, while Holiday Lights, Radio and Print media generate more. Thus our optimized solution calls for more spending for Holiday Lights, print and radio and less for the other media. At constant total spending, this shift to a more efficient media mix is estimated to generate +13 percent higher total attendance.

theme park total attendance and returns per media investment
Theme Park Total Attendance and Returns per Media Investment

Presently, the park’s marketing generated about $1.56 in revenue per dollar of marketing investment. This above “break-even” productivity can still be maintained up to +20% of current spending levels. Still, the dilemma is that this $1.56 impact was a -22% decline from the prior year and strongly supports an effort to improve and optimize spending efficiencies going forward.

Revenue per $1 media investment

Annual Attendance

Prior Year

Current Year

optimizing the media schedule
Optimizing the Media Schedule
  • The next two charts compare current versus an optimized schedule. The optimized schedule places each media, as per the overall mix optimization, in the weeks such that its overall impact on attendance will be maximized.
  • This schedule calls for increases in print, radio and Holiday Lights advertising, and reductions in magazine and outdoor media.
  • The overall effect of this schedule optimization is to place more “weeks-of-execution” for media in a more continuous fashion. Doing so, per the plan outlined, is expected to increase attendance +1.5% with the current and constant dollars.
current media schedule
Current Media Schedule

The current media plan does not begin until April, is heavy on outdoor advertising and

has about a 10 week hiatus in the Fall.

optimized media schedule
Optimized Media Schedule

The optimized plan calls for more spending on print, radio and Holiday Lights advertising.

Overall, compared to the current plan, each media is placed into more total weeks and

advertising begins three weeks earlier than the current plan.

theme park projecting results of optimal media spending

Optimal Spending Strategy estimated to result in about a +9.3 percent gain in daily attendance

Theme Park: Projecting Results of Optimal Media Spending

To address the stagnant attendance trends for the park, our solution calls for an optimized

spending plan as outlined below. This includes the benefits from optimizing media schedul-

ing. The opportunity points towards a+9.3 percent growth in attendance without the require-

ment of spending incremental marketing funds.

Change in Daily Attendance

conclusions and recommendations
Conclusions and Recommendations
  • The results of this modeling exercise has enabled us to crystallize some key insights regarding key drivers of the Theme Park business.
    • We learned that the Theme Park’s attendance trends have been flat to stagnant over the past year. While cooler weather, rising fuel and admissions prices were major negative factors, total marketing efforts barely covered these short-falls.
    • We know that temperature and weather has a significant impact on short-term daily attendance and we succeeded in quantifying those effects.
    • We uncovered and quantified a new challenge to the park’s efforts to grow attendance, rising fuel prices. Continued increases in fuel prices are likely to pose a major challenge and risk to growing the park’s attendance.
    • We accurately quantified the regular and recurring seasonal and days-of-the-week effects on park attendance.
    • We learned that the +5% increase in admissions price at the park cost -3.7 percent in foregone attendance.
  • Over the past year, the park’s marketing efforts, while generating greater than break-even revenues of $1.56 per dollar spent, fell short in terms of driving substantial growth in park attendance.
    • With the impact of pricing factored in, the net effect of all media and marketing efforts generated only a +0.3 percent year-over-year impact.
    • That there was a -22% decline in the efficiency of media in terms of revenue per expenditure. A major reason for this decline in efficiency is due to the large reduction in radio advertising.
  • Going forward, our modeling has uncovered a key opportunity for the Theme Park to re-ignite attendance growth and improve overall marketing efficiencies.
    • Our optimized solution calls for a shift in marketing spending by the park
      • Increase investments in print, radio and Holiday Lights TV advertising
      • Reduce spending on outdoor and magazine ads
      • Improve media scheduling by maximizing weeks of activity and minimizing ad hiatus’.
    • In addition, the park should continue and expand past successful efforts through special themed events and promotions
    • By optimizing spending going forward the park can reverse stagnant attendance trends and grow overall attendance by +9.3 percent, all without the requirement of increasing total marketing budgets.
model validation
Model Validation
  • The insights presented here are only as good as the models produced. To assure the highest level of integrity from this analysis, the following is a summary of our validation efforts. This validation effort is designed to demonstrate the “predictive ability” of these models. In order to demonstrate and validate this validity, we withheld 15% of the data observations completely from the models. We then compared how well our models predict actual performance across these unknown data points. The results of this exercise are shown on the following chart. In all cases, our holdout forecasts showed high predictive capabilities and were well within tolerances so we can conclude that these models are all robust and highly predictive.
actual v model fit
Actual v. Model Fit

R2 =96.2%, Holdout R2= 87.9%, MAPE=+/-8.7%


Michael Wolfe, President

Bottom-Line Analytics LLC