During the Conference Championship weekend for 2014, Gallery Furniture, a Houston based furniture store offered up refunds to customers who a) correctly picked the winners of both the AFC and NFC championship games, and b) bought more than $5000 worth of furniture. As shown from the video below, the promotion worked either great, or horrible, depending on your point of view.
When companies run promotions like this which have the possibility to return a lot of money to people, they usually do some sort of statistical analysis to see what the odds of winning actually are. If they're not comfortable with that sort of risk, companies will frequently insure their promotions so they won't bear the full risk. The insurance company calculates the odds of success, bills the company making the promotion, then pays out the winnings if the contestant hits.
That leads us to two questions. The first is relatively easy to answer: What are the chances of each combination of winners in the Championship games? The second is more difficult: What will people be betting on?
The games themselves were very well matched. The Broncos and Seahawks were a combined 26-6 in the regular season, while the Patriots and the 49ers were "only" 24-8. Though their seeding didn't really reflect it, this was really a matchup of the two best teams in each conference. So, how did Gallery Furniture lose so much money?
Calculating the Probabilities of Winners in the Championship Games
The first calculation, and relatively speaking the easiest, is to figure out the probabilities of the winners of the two contests. The AFC Championship Game could have been won by either Denver or New England and the NFC Championship Game could have been won by either Seattle or San Francisco. The two games are said to be independent. That is, the outcome of one game has absolutely no effect on the other.
Initially, let's assume the teams (in either game) have a true 50/50 chance to win the game. We'll adjust our numbers afterwards. In order to figure out the probabilities of each combination of winners, we can use a decision tree because we only have 2 possibilities for 2 games. From there, we'll come to an easy shortcut to calculate the probabilities of independent events.
The first game to look at is New England at Denver. Again, each team will have a 50% chance of winning:
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| Probabilities of AFC Championship winners. Pretty simple... for now. |
Okay, simple enough. However, if we then add in the NFC Championship Game, both Seattle and San Francisco also have a 50/50 chance of winning, regardless of what happens with Denver and New England:
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| Probability of each possible outcome |
Since we have set the probabilities for both games to be a 50/50 proposition, it should be clear that all 4 possible outcomes are equal, at 25% a piece. This demonstrates the method of calculating the probabilities of independent events.
To calculate the probability of multiple independent events occurring, multiply their probabilities all together.
A Good Explanation?
These numbers don't explain anything at all though. If all of Gallery Furniture's customers picked evenly, we would expect roughly 75% of their customers to walk away with nothing (except some furniture) while 25% of customers walked away with free furniture. What actually happened? In the interview with KHOU, Gallery Furniture owner Jim "Mattress Mack" McIngvale said, "Six hundred thousand dollars of free furniture. Eighty percent of the customers were smart and picked the right teams." Wow, 80%? Was this by chance? Of course not. Football teams are not created equal. Some teams are better than others, so there's more than a 50/50 chance in each game.
Changing the Numbers
So, what are the correct probabilities for each game? It's hard to say, but one group that usually has some idea of who the favorites truly are, are a group that have collectively analyzed most games for minutiae, scoured scouting reports, and simulated matchups several hundred times over. Yes, I'm talking about Las Vegas bookies. One source had the Denver Broncos as 5.5 point favorites over the New England Patriots. That converts to a 65% chance of winning for the Broncos, using historical data.
Similarly, the Seahawks were 3 point favorites, making them a little less than 60% to win the game (though we'll simply use 60% for ease of calculations).
Given the two home teams, and #1 seeds were both favorites in this game, customers who didn't know anything about football could simply choose those two teams, believing they were the 2 best teams that day. Even if fans knew something about football, the home team has a decided advantage in the regular season, and the venues of Seattle and Denver were both tough places to play in for visiting teams (the 2 teams combined to go 14-2 at home in the regular season), making it possibly MORE likely to simply choose the #1 seeds.
How likely was it both #1 seeds would actually win the game? Adjusting our numbers and going back to the decision tree to calculate probabilities:
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| Modified probabilities of each possible outcome |
Picking Denver and Seattle to win would give a customer 39% chance to get free furniture, quite a bit more than picking the next best pair (Denver and San Francisco) and also quite a bit better than just randomly picking two teams if they were equal.
Conclusion
Ultimately, Mattress Mack is paying back all the customers to the tune of over $600,000. The "gamble" might not have paid off this time, but if there were a few plays going the other way, he might have kept those $600,000 dollars, and instead paid off the other 20% who picked different teams. And even then, those 20% didn't all pick the same 2 teams to win either.
Either way, his promotion has brought about a lot of publicity and earned himself a lot of goodwill. Mattress Mack will be going about this again for the Super Bowl. This time, he's offering refunds if Seattle wins. Since Seattle is an underdog in this game, it's a safer bet for him.
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