Rethinking Dynamic Pricing for High-Demand Sporting Events.

To maximize revenue for sellout games, ticket prices should be lowered over time — not raised.

Dynamic pricing of tickets has become an increasingly common practice in the sports industry. Teams are attempting to optimize revenue by modifying prices as supply and demand circumstances change. Dynamic pricing has occurred for many years in other industries where perishable goods are sold (e.g., airline tickets, hotel rooms) and its increased use in sports reflects the steadily increasing sophistication of business practices in our industry.

However, there are some situations in sports where dynamic pricing is misapplied. This note seeks to illustrate the misapplication of dynamic pricing in one specific situation: when tickets for highly-anticipated, must-see events are first released for sale.

What usually happens when highly-anticipated tickets first go on sale.

At some point, most teams will be involved in games that are are so highly anticipated that everyone in the ticket buying market expects they will sell out. College football games against traditional rivals and highly ranked teams are examples of these kinds of events. So are Taylor Swift concerts and other events that sell out very quickly, sometimes in a matter of minutes.

Highly anticipated events are characterized by exuberant demand for tickets when they are first released for sale. If a seller is employing dynamic pricing, the usual instinct is to raise prices as a reaction to the volume of early sales — i.e., a price increase is justified by strong demand and a decreasing amount of supply. However, an under-appreciated and problematic aspect of managing an initial on sale in this fashion is that a significant amount of would-be revenue has already been forfeited.

The problem is that many of the early buyers would have willingly paid a higher price than they did. Figure 1 illustrates how some customers who purchased at the initial price (P1) would have also paid the higher price (P2) in the first place— and some would have been willing to pay an even higher price than that. In economic terms, this is called consumer surplus — it’s the amount of revenue that buyers were willing to pay but the seller failed to capture because the asset was mispriced.

For example: Let’s say your favorite baseball team has made the playoffs for the first time in more than 20 years (go Jays go!). The team has 50,000 playoff tickets remaining for a scheduled public sale beginning on Monday morning at 9am. The initial price for these tickets is $100, but they will be subject to dynamic pricing. A few minutes before 9am on Monday morning many fans are on their computers with open browsers ready to pounce on the tickets when they are first released. In the opening 15 minutes of the sale, the team sells 25,000 tickets, or half of the available supply. In response, the team raises the price to $125 and then sells the remaining tickets over the rest of the day. The tickets are very popular and being listed on the secondary market for over $200.

The problem, of course, is that many of the early buyers (i.e., the ones who were most enthusiastically awaiting the tickets) would likely have paid more than $100 had the team asked for it. Given that secondary prices are so high, and that the second tranche of 25,000 primary tickets easily sold for $125, we can reasonably suggest that the first 25,000 would have sold for at least $125 as well. This means the team lost around $625,000 to consumer surplus by setting the starting price too low in the first place.

Maximize revenue by decreasing prices over time.

From a theoretical standpoint, the only way to maximize revenue at the initial release of tickets for a highly anticipated event is to start the price as high as possible and decrease it steadily over time.

This strategy assures that all buyers are given a chance to purchase tickets at the maximum price that they are each willing to pay. And, since there is a universal expectation that tickets for these hot events will eventually sell out, customers who really want to attend the game are more likely to opt in at their own maximum tolerable price.

The simplified demand curve in Figure 2 illustrates how, in theory, at least some number of buyers would choose to purchase their tickets at the very high starting price. And as the price decreases to P2, P3, and so on, the number of willing buyers increases until no primary market quantity is remaining.

How to maximize revenue for a highly anticipated public on sale.

Below is an approach for maximizing revenue during a highly anticipated public on sale.

• Set the starting price much higher than you expect most people would pay. If brokers are already listing inventory on secondary markets, you can refer to these listings to gain an understanding of an appropriately high starting price.
• Attempt to keep prices competitive with the secondary market. The total supply of tickets in the market includes tickets for sale on secondary channels as well, so primary prices must be competitive with secondary listings. Secondary market prices also tend to start high and decline over time as the event approaches, so keeping primary and secondary prices in lockstep is very manageable.
• Publish the schedule of price declines to buyers in advance. In other words, tell buyers in advance how much tickets will cost and when prices will change. Advanced disclosure increases the perceived transparency of this pricing system. It gives buyers confidence about how ticket prices will change over time and mitigates complaints about the fairness of the system, because buyers understand they can opt in at whatever price they are comfortable paying (i.e., as long as tickets remain).
• Do not disclose the remaining quantity of tickets. This opaqueness forces buyers to make a choice about the maximum price they are willing to pay without being influenced by knowledge of the specific quantity of tickets that are remaining. The only information about supply that shapes their decision-making is a belief that it will indeed reach zero at some point, due to the robust popularity of the event.

This kind of dynamic pricing system theoretically eliminates consumer surplus. It allows everyone to pay an amount that approaches the maximum that they are willing to pay.

Importantly, this approach also assumes that your most important customers — e.g., season ticket holders, donors, and sponsors — already have tickets and don’t need to participate in this market. Thus, for college football there would only be a limited supply of tickets available for this kind of sale and the vast majority of buyers would be either occasional fans or visiting fans.

“Predictable Dynamic Pricing”

At Stanford, we’ve implemented the aforementioned theoretical approach and successfully sold single game football tickets according to a pricing system that we call “Predictable Dynamic Pricing” (PDP).

PDP is a method where ticket prices start very high and are lowered to pre-announced (i.e., “predictable”) prices at pre-announced intervals over a period of a few weeks, or until primary supply is gone. If tickets remain after the initial schedule of price declines, the remaining quantity is sold according to conventional dynamic pricing methods so the price can be increased or decreased depending on market conditions.

We do not subject our season ticket holders to PDP (they are able to buy earlier at a fixed price), and we find that a good number of PDP buyers are visiting fans. More information about PDP can be found in this presentation that we gave at the MIT Sloan Sports Analytics Conference in March of 2015.

We’ve generated significant incremental revenue using PDP. For example, our home game against USC in 2014 sold out on the morning of the game (theoretical perfection!) and set a single game revenue record.

Caveats

The idea that revenue is maximized by decreasing prices over time is very counterintuitive, especially in a sales culture where we’ve traditionally encouraged customers to “buy early and save”. Accordingly, there is usually a significant amount of confusion about PDP and it is helpful to consider the following conceptual points and caveats while evaluating its merits.

• In sports ticket sales, primary market supply does not represent the actual supply in the entire market. Basic economics would of course suggest that, for a given level of demand, prices should be raised as supply decreases. This is obviously true, but the presence of the secondary market in sports ticketing means that judgements of supply must also consider tickets that are available for purchase on secondary channels. This greatly complicates what appears to be a simple supply and demand optimization exercise, because the primary seller doesn’t have full knowledge or control of the total supply available to buyers.
• People are willing to pay different prices for the same asset. In other words, the same ticket is worth different amounts of money to different people, depending on their individual level of demand for the ticket and their individual perceptions of scarcity. For example, a customer who needs to find six seats together is willing to pay more — and thus buy earlier — than a single ticket buyer. Someone coming to a game from out of town is willing to pay more and buy earlier to ensure their tickets are secured ahead of time. Visiting fans may perceive that tickets will sell out faster than they actually will, and are thus willing to pay more and buy earlier to ensure they get seats. Other fans highly value the location of their seats and are willing to pay more and buy early to ensure they sit in their preferred location. And so on.
• When given the option to buy now or wait for a lower price, people who are not price sensitive sometimes prefer the convenience of buying immediately. Some buyers are simply not willing to deal with the inconvenience and psychological work of waiting for the price to drop, and prefer to get the transaction over with. For a highly anticipated event that they really want to attend, some buyers are willing to pay for the convenience of buying immediately. Any behavioral economist will tell you that buyers are not perfectly rational.

Conclusion

This note explained how dynamic pricing is often misapplied for highly anticipated ticket releases. Most often, prices start too low and are then raised in reaction to strong early demand. Revenue is unfortunately lost because of the consumer surplus that occurred before prices were raised.

An alternative and counterintuitive approach that maximizes revenue for highly anticipated events involves starting prices high and reducing them over time, according to a pre-announced schedule. Such an approach significantly reduces consumer surplus and maximizes revenue for the seller because it encourages customers to buy at the highest price they are willing to pay.

As long as the most important customers have already been accommodated, teams should implement strategies like Stanford’s “Predictable Dynamic Pricing” for selling limited public inventory to highly anticipated games.