Independent Events, Inference Errors and Super Bowl XLV

Papa John’s, the pizza chain, is betting big that the Super Bowl today will not go into overtime. They are offering a free pizza to everyone who registers if the game goes into overtime. 

If millions people register for this free offer, Papa John’s stands to lose big. The costs are not only the cost to make and deliver the pizza but also the lost sales because the franchises will be busy making these free pizzas instead of serving pizzas to paying customers.

If you watch the any of the TV sports anchor speak, you will hear them say,

In the history of Super Bowl, we never went into overtime.

Papa John’s could take comfort in those predictions. If their marketing manager who ran this campaign had reasoned that the likelihood of OT is close to 0 and hence their expected loss is $0, he cannot be more wrong.

The teams, their rosters, weather conditions, techniques, equipment, context, player conditions etc. are all completely different. The fact that past 44 consecutive events turned out one way does not tell you anything about how the 45th event will turn out.

Consider this simpler example. You pick 45 random people from a crowd and ask them all to pick a coin from their pocket and toss it. As you check the outcome, one after the other 44 of them got Heads. But the probability the 45th random person tossing her own coin will get heads is still half.

Other  similar statements we will hear from sportscasters  that you should give no second thought to:

“the team that led by 10 points or more at half-time always won”
“the team that scored first won 60% of the times”

If you are in mood for more math, here is a link to my article on Bayesian stats and independent events.

Regarding Papa John’s decision,  they could be doing this to get email addresses of customers, that is not a bad move as long as the goal is stated upfront and not after the fact. What we do not want to hear is, “yes we lost $10 million today but look at million emails we collected”

3 thoughts on “Independent Events, Inference Errors and Super Bowl XLV

  1. Typically on these type of promotions, a smart marketing manager will eliminate high cost of an unlikely event by transferring risk to an insurance company. If there is a 5% chance that the game will go into overtime, then the expected outcome is $500,000. Add maybe another $100,000 as a premium to the insurance company. So rather than bet between a $0 & $10 CPA, there is a definitive CPA of $0.60. By removing risk, you also align the entire organization around the program. Now if game goes into overtime, it becomes a money making opportunity: $10,000,000 in pizzas are paid by the insurance company. The hype around “losing” the bet and honoring your debts becomes a PR bonanza.

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