Posts Tagged 'probability'

Wanna bet that Hillary will be the next President?


There is a movement afoot to allow Las Vegas casinos to take bets on Presidential elections.  Betting on who will be the next President has the potential to increase the interest level in the election and perhaps voter turnout as a consequence. Of course, it will also bring more revenue to Nevada casinos. Detractors of the idea cite the typical arguments against gambling of any kind. I suppose campaign insiders could engineer a campaign emergency to sabotage their candidate and collect winning bets they have made on the other side.

One aspect that hasn’t been discussed is whether betting on elections would make for better predictions than current polling methods.

Election polling is simple at its core. Pollsters find a representative sample of likely voters and ask a basic question:  if the election were held today, whom would you vote for?  While the question itself is basic, polls often disagree on the answers. Differences in the polls tend to stem from how the sample was drawn, how “likely voters” are classified, and context (issue questions that may have preceding the voting question). On the whole, the major polling organizations do a good job with election polls, and, especially if you group all the polls together, they make excellent predictions. But, the pollsters are not always right. If we had left it up to the major polling organizations to select our Presidents, our children would be learning about the policies of President Alf Landon and President Thomas Dewey. (Of course if we trusted the polls and not the actual election, we also would be teaching about President Al Gore, but that is another story.)

A few election cycles back a few firms tried a new approach. Rather than ask “whom would you vote for?” the new approach asked “regardless of whom you may favor or vote for, who do you think will win the election?” This was seen as an attempt to get over the difficulty of predicting turnout. It was sort of a way to crowd source an election poll. The approach worked well, but has been tried too infrequently to make a definitive judgment. While election polls are great experiments in that we can judge their success or failure by a real-world result, they aren’t so good in that the sample size of national elections is small.

An interesting approach to the last few election cycles was taken by Intrade. Intrade was a “prediction market” — an exchange that traded shares for future events that had a “yes/no” type outcome, for instance, “will Barack Obama win the election?” The share price for this would be between $0 and $1. Once the election is over, a share of Obama would close at $1 if he won, and $0 if he lost. Since there was an active market in this trading, you could make real bets with real money on the election depending on where you stood. For instance, if an Obama share was trading at 72 cents, this could be interpreted as saying the market feels he has a 72% chance of winning. If you felt Obama had a greater than 72% chance of winning you’d buy his “stock.” When the election was over, you’d either lose 72 cents if he lost the election or make 28 cents if he won. What was interesting about the approach was watching how the stock price would move as the campaign season progressed.

After the conventions or debates, Obama’s share price would change. At any moment, the share price reflected the probability of victory. A good speech would move his price (and probability of winning) up a few points. Intrade was an excellent predictor and took into account the uncertainty inherent in predictions in an understandable way. The share prices of the candidates clearly showed their probability of winning in real time.

Allowing Vegas style betting on Presidential elections would be similarly interesting. But would it be accurate?

Vegas bookmakers establish initial odds on an event, and these odds (or a point spread in the case of football) evolve depending on how the betting comes in. Many people don’t realize that the oddsmakers are not actually concerned about the probability of who might win the football game. Instead, they set and adjust odds/point spreads to attract an even amount of money bet on both sides of the game, as that is how the casino maximizes its profits. So, the spread might not reflect the probability of winning, especially for teams with large, rabid fan bases, who may irrationally wager on their team (providing a buying opportunity on the other side for the rest of us). How do they do? In a perfect world (from the casino’s point-of-view), 50% of the underdogs would win and 50% of the favorites would win. In 2013, 512 regular season NFL games were played. The favorites won 248 times (48.9%). This is not significantly different than 50% in a statistical sense, so it appears that the sports books do a pretty good job.

It would not surprise me if allowing Vegas casinos to take election bets would result in a better prediction than the polls. Money tends to flow rationally and in response to new information, and it likely behaves more rationally than individual respondents in a poll. The polls won’t go out of business, as the polls have an excellent ability of understanding who voter for whom and why, and these results drive campaign decisions and cable TV news content. Of course the best approach to predicting who the next President will be is probably to just ask Nate Silver. 🙂

Why Do Market Researchers Play the Lottery?

Lottery Balls

The current Mega Millions jackpot is $550 million and climbing. It seems that whenever the lottery jackpot grows this large, it replaces the weather as the small talk conversation topic most meetings and calls start with. “Did you play it yet?” “What will you do if you win?”

I work around a lot of astute market researchers. These are individuals who have advanced statistical training and often advanced degrees. They are the type of people who should be able to see that from an odds-of-winning standpoint, playing the lottery makes no rational sense. Yet, if anything, they seem more likely to play than other people I hang around.


This is because these folks know that when the jackpot reaches a certain level, your expected return can actually exceed your expected investment. The odds of winning the Mega Millions jackpot are 1 in 258,890,850. This means that you have a 0.0000004% chance of winning. Double that if you buy two tickets!

Here are a few things that are more likely to happen to you than winning the jackpot:  getting hit by lightning, bit by a shark, or getting a hole in one. Or, likely all three at the same time.

Because there are lesser prizes other than the jackpot, your odds of having a winning ticket of some sort are actually a little better than 1 in 15. But, many of these prizes just allow you to get your $2 back, and what fun is that?

With odds of winning the jackpot being about 1 in 259 million and the tickets costing $2, if you consider the jackpot only, the lottery will have an actual expected return greater than $2 whenever the jackpot reaches $518 million or more. If you consider the money paid out with lesser prizes, your $2 investment can be expected to yield more than $2 whenever the jackpot reaches $363 million or more.

So, does it make rational sense to play the Mega Millions if the jackpot is >$363 million? Not so fast! There are other factors involved. First, the government will take their share in taxes. How much depends on how you take the payments and where you live. In June 2013, a person Florida claimed the $590 million Power Ball jackpot. Her lump sum payment was $371 million. This is before taxes. After taxes, that will likely be a third less.  Her $590 million jackpot quickly became $247 million. With this math, you keep roughly 42% of the jackpot, so perhaps it is time to discuss the concept of deceptive marketing with the State governments.

Using this 42% discount, the break-even for the $2 investment then becomes $864 million. Which is a figure larger than any previous jackpot, so in practice there has never been a lottery that pays off on average.

Also, you can’t assume you’ll be to sole winner, which tends not to be the case with large jackpots. So many people play these large jackpot lotteries that the odds of having unique numbers declines. Of course, you can do something to help your odds of being the sole winner if you do win. I’d suggest picking number combinations that are as likely as any others to come up victorious, but that most people can’t see ever winning. I pick numbers like 5, 10, 15, 20, 25, and 30. Or, 20, 21, 22, 23, 24 and 25. Want to have fun with the non-statistically inclined? Tell them that the numbers 1, 2, 3, 4, 5, and 6 are just as good as any others to choose.

So, why do market researchers play the lottery? Of course it makes no rational sense to play the lottery, but you do get value beyond the potential of winning. For $2, you get to dream about what you would do with the money if you won. That alone is probably $2 worth of value. Or perhaps you derive some value from providing additional tax revenue to your state government. The money is largely used for education after all!

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